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An experimental investigation of dual-polarized atmospheric propagation at 73 GHz Peters, John Basil 1982

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AN EXPERIMENTAL INVESTIGATION OF DUAL-POLARIZED ATMOSPHERIC PROPAGATION AT 73 GHz by JOHN BASIL PETERS B . A . S c . , The University of B r i t i s h Columbia, 1977 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n THE FACULTY OF GRADUATE STUDIES (Department of E l e c t r i c a l Engineering) We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA February 1982 © John Basil Peters I n p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r a n a d v a n c e d d e g r e e a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e a n d s t u d y . I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may b e g r a n t e d b y t h e h e a d o f my d e p a r t m e n t o r b y h i s o r h e r r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l n o t b e a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . D e p a r t m e n t o f ^<-<sc- S u e  The U n i v e r s i t y o f B r i t i s h C o l u m b i a 1956 Main M a l l V a n c o u v e r , C a n a d a V6T 1Y3 D a t e Ct^JL ~i , i 9 8 2 -D E - 6 (3/81) ABSTRACT This thesis describes the design, construction and results of an accurate, 73 GHz, dual-polarized atmospheric propagation experiment conducted over a 1.8 km total length radar path. The millimetre-wave equipment consisted of a switched-polarization transmitter and a two-channel receiving system which included a phase-compensated crosspolar cancellation network and a novel, high-performance microstrip IF/LO diplexer. Meteorological instru-mentation consisted of an improved electrostatic disdrometer, a raingauge network with high temporal and spatial resolution and a three-vector anemo-meter. A comprehensive experimental model was developed to predict the system crosspolar discrimination (XPD) response during a wide variety of conditions. This model was used to analyze, for what i s believed to be the f i r s t time, the effects of: orthomode transducer port mismatches, the frequency response and error sensitivity of crosspolar cancellation systems and the range of possible cancelled system XPD responses during rain. This model also led to the development of a phase compensation technique used to improve the s t a b i l i t y of the crosspolar cancellation network. The application of the experimental model resulted in far more accurate determinations of path XPD than would have been otherwise possible. The cancelled XPD results showed a reasonable correlation to horizontal wind velocities and agreed with model predictions for effective i i mean canting angles ranging between 0 and 6°. The frequent observation of negative differential attenuations and erratic uncancelled XPDs led to the conclusion that drops along the path often did not have consistent shapes and canting angles. This i s believed to be due to extremely variable wind condi-tions. Copolar attenuations considerably lower and higher than expected from the standard predictions were observed. The higher attenuations are satis-factorily explained as resulting from vertical wind conditions and are correlated to the predictions from a proposed model which includes the effects of constant vertical wind velocities. i i i TABLE OF CONTENTS Page Abstract » i i Table of Contents iv List of Figures . xv List of Tables. xxix 1. Introduction 1 1.1 Spectrum Demand 2 1.2 Millimetre Applications 4 1.3 Advantages and Disadvantages of Millimetre Frequencies . . . 8 1.4 Millimetre Semiconductors and Integrated Circuits 9 1.5 Orthogonal Polarization Frequency Reuse 10 1.6 Propagation Theory and Experiment. . . 12 1.7 Previous Dual-Polarized Propagation Experiments. . . . . . . 15 1.8 Previous Single-Polarized Propagation Experiments 20 1.9 Thesis Objectives 23 2. Millimetre-Wave Experimental System « . 26 2.1 Comparison of Dual-Polarization Measurement Methods. . . . . 26 2.2 Transmitting System 29 2.2.1 Klystron and Supply 29 2.2.2 Reference Signal and Calibrated Attenuator 33 2.2.3 Feedline and Pressurization 34 iv 2.2.4 P o l a r i z a t i o n Switching. . . . . 2.2.4.1 Comparison of P o l a r i z a t i o n Switching Methods . . . . . . . . . . . 2.2.4.2 P o l a r i z a t i o n Switch S p e c i f i c a t i o n s and Testing 2.2.4.3 P o l a r i z a t i o n Switch Subsystem . . . . 2.2.5 Signal Levels i n the Transmitting System. . . . Receiving System 2.3.1 Receiver. . 2.3.1.1 Receiver S p e c i f i c a t i o n s . . . . . . . 2.3.2 D i g i t a l Amplitude Measurement Units 2.3.3 Two-Channel Front End 2.3.3.1 Basic Mixer Considerations 2.3.3.2 Front-End C i r c u i t Description . . . . 2.3.3.3 Harmonic Mixers 2.3.3.4 Mixer S p e c i f i c a t i o n s 2.3.3.5 IF/LO Diplexer. 2.3.3.6 Local O s c i l l a t o r Frequency M u l t i p l i e r 2.3.3.7 Frequency M u l t i p l i e r S p e c i f i c a t i o n s and Testing 2.3.3.8 Local O s c i l l a t o r Power Ampli f i e r . . . 2.3.3.9 LO Frequency M u l t i p l i e r C i r c u i t Configurations v Page 2.3.3.10 Mixer Bias Circuits . 84 2.3.3.11 D i g i t a l l y Programmable IF Attenuator, 84 2.3.3.12 IF Preamplifier 86 2.3.4 Frequency Counter . 89 2.3.5 Receiving System Performance 90 2.3.5.1 Calculated Sensit ivi ty 90 2.3.5.2 Measured Receiving System Sensit ivi ty . . . 93 2.3.5.3 Receiving System Small-Signal Performance . 96 2.3.5.4 Receiving System Isolation and Frequency Response 98 2.3.5.5 Front-end Alignment . 98 2.4 Propagation Path 101 2.5 Antennas and Orthomode Transducers 101 2.5.1 Crosspolar Cancellation Network . . . . . . . . . . . 110 2.5.1.1 XPD Improvement Methods 114 2.5.1.2 XPD Improvement in this Experiment. . . . . 120 2.5.1.3 RF vs . IF Cancellation 120 2.5.1.4 Crosspolar Cancellation C i r c u i t Description 122 2.5.2 Antenna Mounting and Rain Shields 124 2.5.3 Antenna Alignment 127 Page 2.9 Data Acquisition System. . . . . . . . . . 134 3. Meteorological Instrumentation. . . . . . . . . . . . . 136 3.1 Raingauge Network 136 3.1.1 Path-Rainrate Measurement 136 3.1.2 Rain Gauge Types. . . . . . . . . . . . 138 3.1.3 Rain Gauges . . . . . . . . . . 141 3.1.4 Raingauge Locations 144 3.2 Raindrop Size Measurement. 147 3.3 Raindrop Size Transducer Methods . . . . . . . . . 147 3.3.1 Optical Methods . . . . . . . . . . . . . 148 3.3.1.1 Optical Scanning Methods. . . . . 148 3.3.1.2 Optical Array Methods 150 3.3.1.3 Laser S c i n t i l l a t i o n Correlation 151 3.3.1.4 Optical Scattering and Extinction Methods 152 3.3.2 Electromechanical Methods 152 3.3.2.1 Moving Coi l i n Magnetic Field Method. 153 3.3.2.2 Piezoelectric Method 153 3.3.2.3 Other Electromechanical Disdrometers. . . . 154 3.3.2.4 Factors Affecting the Accuracy of Electromechanical Methods . 155 3.3.3 Electrostatic Methods 155 3.3.4 Comparison of Methods 157 v i i Page 3.4 Disdroraeter Transducer 159 3.5 Disdrometer E l e c t r o n i c s 168 3.6 Disdroraeter System Test Results 173 3.7 Disdrometer C a l i b r a t i o n 177 3.8 Anemometer * • 183 3.9 Temperature Measurement. . 186 4. T h e o r e t i c a l l y Predicted Propagation Parameters 187 4.1 Meteorological Inputs 188 4.1.1 Rainrate • • 189 4.1.2 Drop Size D i s t r i b u t i o n s 190 4.1.3 Drop Shape. 193 4.1.4 Canting Angle . . . . . 194 4.1.5 Rain Temperature 198 4.1.6 S p a t i a l Uniformity 199 4.2 Scattering Amplitudes 199 4.3 Calculated Propagation Parameters 200 4.3.1 P r i n c i p a l Plane Attenuations and Phase S h i f t s . . . . 201 4.3.2 Propagation Parameters f o r Canted Raindrops 205 4.4 E f f e c t s of V e r t i c a l Wind on Copolar Attenuation 216 4.5 Backscatter C a l c u l a t i o n » 220 5. Dual-Polarized Experimental Model . . 5.1 Previous Work v i i i 225 227 Page 5.2 Simplifications, Approximations and Assumptions. . . . . . « 227 5.3 Notation and Units 229 5.4 System Descriptive Equations «• 235 5.5 Analysis Without the Crosspolar Cancellation Network . . . . 237 5.5.1 Contribution of Antenna XPD's to Clear Weather Crosspolar Signal Level 238 5.5.2 Effect of Reflected Signals on the Clear Weather Crosspolar Signal Level . . . . . . . . 243 5.5.2.1 Basic OMT Operation . 244 5.5.2.2 Calculated Results and Comparisons to Experimental Data. 248 5.5.2.3 System XPD Improvement Using Mismatches . . 257 5.6 Crosspolar Cancellation Network Operation i n Clear Weather. 258 5.6.1 Sensitivity to Amplitude and Phase Errors 259 5.6.2 Cancelled System Frequency Response . . . 259 5.6.3 Cancelled System Temperature D r i f t . , . . . 269 5.6.4 Phase Compensation of the Crosspolar Cancellation Network 270 5.7 Model Predicted System XPD Performance 273 5.7.1 Effects of Polarization Insensitive Attenuation or Phase S h i f t . . . . . . . . . 274 5.7.2 E f f e c t s of Antenna XPD Angle 275 i x Page 5.7.3 Effects of Different ia l Attenuation and Phase Shift . . . . . . . 278 5.7.4 Effects of Antenna XPD Magnitudes 282 6. Experimental Results. . . . < . 285 6.1 Preliminary Discussion 285 6.1.1 Disdrometer Data. . . . . . . . . . . . . . . . . . . 286 6.1.2 Receiving System Noise Levels 291 6.1.3 Different ia l Attenuation Calculations . . . 291 6.2 Experimental Results for 81.11.30.10 292 6.2.1 Attenuation Data for 81.11.30.10. . 301 6.2.1.1 Attenuation During T j , 0.20-0.23 h 306 6.2.1.2 Attenuation During T 2 , 0.23-0.26 h . . . . . 306 6.2.1.3 Attenuation During T 3 , 0.27-0.29 h 311 6.2.1.4 Attenuation During T 4 , 0.31-0.34 h . . . . . 314 6.2.1.5 Attenuation During T 5 , 0.72-0.74 h 317 6.2.1.6 Attenuation During T g , 0.74-0.78 h . . . . . 320 6.2.1.7 Attenuation During T ? , 0.78-0.84 h 320 6.2.1.8 Attenuation During T 8 > 0.87-0.89 h . . . . . 320 6.2.1.9 Attenuation During T g , 0.89-0.93 h . . . . . 327 6.2.2 XPD and Different ia l Attenuation Data for 81.11.30.10 . 327 6.2.2.1 XPD and Different ia l Attenuation During T 1 Q , 0.62-0.72 h 334 x Page 6.2.2.2 XPD and Different ia l Attenuation During T n , 0.72-0.78 h . . « . 6.2.2.3 XPD and Different ia l Attenuation During T^^j 0»78"~0«85 ti» » • • • > • • » • • • > • * • 6.2.2.4 XPD and Different ia l Attenuation During T^ >^ 0o88~0»93 • • > • • • • • • • • • * • • 6.2.2.5 XPD and Different ia l Attenuation During T j , 0.93—0.99 h . . . . » » » » . » » . « • 6.3 Experimental Results for 81.11.30.18 . 6.3.1 Attenuation Data for 81.11.30.18. . . . . . . . . . 6.3.2 XPD and Different ia l Attenuation Data for 81.11.30.18 6.4 Experimental Results for 81.11.30.19 . . . . 6.4.1 Attenuation Data for 81.11.30.19 6.4.2 XPD and D i f f e r e n t i a l Attenuation Data for 81.11.30.19 xi 339 339 342 342 345 357 357 367 377 6.4.1.1 Attenuation During Tl» 0.24-•0.28 ll • • • • • 377 6.4.1.2 Attenuation During T 2 , 0.28-•0.33 tl • • * • • 382 6.4.1.3 Attenuation During T3> 0.33--0.43 h. • • • • 385 6.4.1.4 Attenuation During T V 0.47--0.53 \l m • • * • 385 6.4.1.5 Attenuation During T5> 0.53--0.55 l l # • • * • • 385 6.4.1.6 Attenuation During T 6 ' 0.55--0.59 l l • • • • • 392 6.4.1.7 Attenuation During 0.59--0.71 l l • • • • • 395 6.4.1.8 Attenuation During T8« 0.71- -0.83 h. • • • • 395 395 Page 6.4.2.1 XPD and Different ia l Attenuation During T 8, 0.71-0.83 h o . . . 405 6.4.2.2 XPD and Different ia l Attenuation During T g, 0.83-0.99 h . 407 6.5 Experimental Results for 81.11.30.21 410 6.5.1 Attenuation Data for 81.11.30.21 417 6.5.1.1 Attenuation During T p 0.50-0.80 h. . . . . 417 6.5.1.2 Attenuation During T 2 > 0.80-0.89 h. . . . . 421 6.5.1.3 Attenuation During T 3, 0.89-0.99 h. . . „ . 421 6.5.2 XPD and Different ia l Attenuation Data for 81.11.30.21 426 6.5.2.1 XPD and Different ia l Attenuation During T 4, 0.65-0.80 h , . . 426 6.5.2.2 XPD and Different ia l Attenuation During T 5, 0.80-0.99 h . . . 433 6.6 Experimental Results for 81.11.30.22 436 6.6.1 Attenuation Data for 81.11.30.22 436 6.6.1.1 Attenuation During 444 6.6.1.2 Attenuation During 0.13-0.26 ti • • • • • 444 6.6.1.3 Attenuation During T 3 ' 0.26-0.31 ti • • • • • 452 6.6.1.4 Attenuation During 0.31-0.37 ti • • • • • 452 6.6.1.5 Attenuation During 0.37-0.45 ti • * • • • 452 6.6.1.6 Attenuation During 0.45-0.54 ti • • • • • 457 6.6.1.7 Attenuation During T 7 , 0.54-0.63 ti • • • • • 457 x i i Page 6.6.1.8 Attenuation During T g, 0.63-0.66 h. . „ . . 464 6.6.1.9 Attenuation During T g, 0.66-0.73 h. . . . . 464 6.6.2 XPD and D i f f e r e n t i a l Attenuation Data for 81.11.30.22 464 6.7 Experimental Results f o r 80.05.22.10 . . . . . . . . . . . . 6.7.1 Attenuation Data f or 80.05.22.10 471 6.7.1.1 Attenuation During T x, 0.20-0.25 h. . . . . 477 6.7.1.2 Attenuation During T 2, 0.25-0.31 h 482 6.7.1.3 Attenuation During T 3, 0.31-0.35 h 482 6.7.1.4 Attenuation During T^, 0.42-0.47 h. . . . . 485 6.7.1.5 Attenuation During T 5, 0.48-0.61 h 485 6.7.1.6 Attenuation During T 6, 0.61-0.75 h 485 6.7.2 XPD and D i f f e r e n t i a l Attenuation Results f o r 80.05.22.10 490 6.7.2.1 XPD and D i f f e r e n t i a l Attenuation During T j - T 3 , 0.20-0.25 h 497 6.7.2.2 XPD During T 2, 0.25-0.31 h and T 3, 0.31-0.35 h 497 6.7.2.3 XPD and D i f f e r e n t i a l Attenuation During T 6, 0.61-0.75 h 497 6.8 Experimental Results f o r 81.06.18.15 . 504 6.8.1 Attenuation Data f o r 81.06.18.15 510 6.8.2 XPD and D i f f e r e n t i a l Attenuation Data f o r 81.06.18.15 . . . . . . . . 510 6.9 Experimental Results f o r 81.11.14.07 523 x i i i Page 6.9.1 Attenuation Data f o r 81.11.14.07 530 6.9.1.1 Attenuation During 0.56-0.65 h. . . 530 6.9.1.2 Attenuation During T ?, 0.65-0.77 h. . . . . 535 6.9.1.3 Attenuation During T 3, 0.77-0.84 h 539 6.9.2 XPD and D i f f e r e n t i a l Attenuation Data for 81.11.14.07 539 6.9.2.1 XPD and D i f f e r e n t i a l Attenuation During T j , 0.56-0.65 h 548 6.9.2.2 XPD and D i f f e r e n t i a l Attenuation During T 3, 0.77-0.84 h 548 7. Conclusions 553 7.1 Millimetre-Wave Equipment. 554 7.2 Meteorological Instrumentation 555 7.3 Experimental Model 555 7.4 Experimental Results 556 7.4.1 XPD Results 556 7.4.2 Conclusions Regarding Drop Shape and Canting Angle. . 556 7.4.3 E f f e c t s of V e r t i c a l Wind V e l o c i t i e s on CPA. 557 7.4.4 Future Work 559 560 8. References x i v LIST OF FIGURES Page F i g . 1.1. Geosynchronous s a t e l l i t e in orbit and planned . . . . 3 F i g . 1.2. Atmospheric attenuation due to molecular absorption . 5 F i g . 2.1. Basic millimetre-wave experimental system 27 F i g . 2.2. Transmitting system block diagram 30 F i g . 2.3. Klystron power supply c i r c u i t 32 F i g . 2.A. Polarization switching methods 36 F i g . 2.5. Polarization switch subsystem schematic . AO F i g . 2.6. Polarization switch subsystem photograph. . . . . . . Al F i g . 2.7. Polarization switch control unit schematic A3 F i g . 2.8. Receiving system block diagram A6 F i g . 2.9. Receiver block diagram A 8 F i g . 2.10. Complete front-end block diagram 5A F i g . 2.11. Detailed block diagram of one channel . . . . . . . . 55 F i g . 2;12. IF/LO diplexers, LO amplifiers and frequency multipliers . . . . . . . . . . . . . . . . 56 58 . i v t F i ? . 2.1 A. Complete front-end • F i g . 2.13. Front-end without IF preamplifiers and attenuators. . . . 59 F i g . 2.15. IF injection and matching c i r c u i t . 63 F i g . 2.16. IF injection and matching c i r c u i t performance . . . . 66 F i g . 2.17. 3.5 GHz microstrip bandpass f i l t e r . . . . . . . . . . 70 F i g . 2.18. IF injection and matching c i r c u i t photograph 72 F i g . 2.19. 3.5 GHz bandpass f i l t e r photograph 72 F i g . 2.20. 3.5 GHz bandpass f i l t e r performance 73 xv Page F i g . 2.21. Frequency multiplier frequency response . . . . . . . 78 F i g . 2.22. Frequency multiplier conversion l o s s . . 79 F i g . 2.23. LO frequency multiplier chain c i rcui t configurations. 82 F i g . 2.24. Mixer bias c i rcui t schematic 85 F i g . 2.25. Receiver: s ignal , IF, LO and noise i n the frequency domain. 91 F i g . 2.26. Spectrum analyzer display of 1st IF s ignal . . . . . . . 95 F i g . 2.27. Receiving system small signal performance on the bench. 97 F i g . 2.28. Receiving system frequency response . . . . 99 F i g . 2.29. Effect of LO level on conversion loss 100 F i g . 2.30. Effect of mixer bias current on front-end performance 102 F i g . 2.31. Propagation path details 103 F i g . 2.32. Propagation path photograph . . 105 F i g . 2.33. Antenna crosspolar isolat ion performance. . . . . . . 106 F i g . 2.34. Orthomode transducer test configuration . 108 F i g . 2.35. Orthomode transducer test results with matched terminations 109 F i g . 2.36. Orthomode transducer test results with one port mismatched . . . . . . . . . . . I l l F i g , 2.37. Orthomode transducer test with the receiving system front-end. 112 F i g . 2.38. Test results for F i g . 2.37. . 113 F i g . 2.39. Crosspolar cancellation network 125 F i g . 2.40. Transmitting antenna photograph . . . 126 F i g . 2.41. System XPD for different antenna alignments . . . . . 128 F i g . 2.42. Reflector photograph 126 x v i Page F i g . 3.1. Rain c e l l examples. 137 F i g . 3.2. Attenuation spread f o r d i f f e r e n t raingauge spacing and i n t e g r a t i o n times 139 F i g . 3.3. P r e c i p i t a t i o n gauge e f f i c i e n c y as a function of ho r i z o n t a l windspread 142 F i g . 3.4. P r o b a b i l i t y of exceeding a s p e c i f i e d r a i n r a t e i n Vancouver. 143 F i g . 3.5. Raingauge with cover removed 145 F i g . 3.6. Disdrometer transducer g r i d 160 F i g . 3.7. Disdrometer transducer dimensions 165 F i g . 3.8. Disdrometer transducer with cover removed 166 F i g . 3.9. Complete disdrometer transducer 167 F i g . 3.10. Disdrometer system block diagram 169 F i g . 3.11. Transducer preamplifier 170 F i g . 3.12. Peak detector 172 F i g . 3.13. Peak pulse amplitude vs g r i d voltage f o r d i f f e r e n t drop diameters 174 F i g . 3.14. Peak pulse amplitude vs. R^ n 175 F i g . 3.15. Pulse period vs. R i n . 176 F i g . 3.16. Apparatus for creating small drops. . . . . 178 F i g . 3.17. Disdrometer c a l i b r a t i o n f o r drops at terminal v e l o c i t y 179 F i g . 3.18. Square root of pulse amplitude vs drop diameter 180 F i g . 3.19. E f f e c t of drop v e l o c i t y on pulse amplitude. . . . . . 181 F i g . 3.20. Anemometer photograph 184 F i g . 3.21. Anemometer pro p e l l e r angular response 185 x v i i .Pa9e. Fig. 4.1. Canting angle as a function of size and height. . . . 195 Fig. 4.2. Magnitude of principal plane attenuation vs. rainrate. 203 Fig. 4.3. Angle of principal plane attenuations vs. rainrate. . 204 Fig. 4.4. Geometry for canted drop calculations . . . . . . . . 206 Fig. 4.5. Differential attenuation vs. rainrate and canting angle . . . . . . . . . . 210 Fig. 4.6. Differential phase shift vs. rainrate and canting angle 211 Fig. 4.7. Magnitude of T 2 1 vs. rainrate 212 Fig. 4.8. Angle of T 2 1 vs. rainrate 213 Fig. 4.9. XPD vs. rainrate for horizontal polarization. . . . . 214 Fig. 4.10. XPD vs. CPA for horizontal polarization . . . . . . . 215 Fig. 4.11. Horizontal CPA vs. rainrate for different vertical wind velocities. 219 Fig. 5.1. Experimental system signal flow diagram 226 Fig. 5.2. Contribution of antenna XPDs to clear weather crosspolar signal at the front-end input 241 Fig. 5.3. Orthomode transducer construction and operation . . . 245 Fig. 5.4. OMT model options . . . . . . . . . 247 Fig. 5.5. Mismatched transmit OMT signal flow diagram 249 Fig. 5.6. Effect of a mismatch at the crosspolar rectangular OMT port on the effective transmit OMT complex XPD. . 251 Fig. .5.7. Crosspolar signal level at plane D-D for XPDTX=XPDRx=37dB and one mismatch with return loss = lOdB 253 Fig. 5.8. Crosspolar signal level at plane D-D for XPDTX= XPDRX=37dE and A 6 x p D = 150° 254 x v i i i Page F i g . 5.9. Effect of crosspolar cancellation network ^ amplitude errors. . . . . . F i g . 5.10. Effect of crosspolar cancellation network phase errors 261 F i g . 5.11. Clear weather cancelled system XPD vs . frequency. . . 267 F i g . 5.12. Effect of phase compensation on cancelled system XPD. 271 F i g . 5.13. Effects of d i f f e r e n t i a l attenuation on system XPD for no path depolarization 276 F i g . 5.14. Effects of d i f f e r e n t i a l attenuation on system XPD for path XPD = 40 dB<0° 277 F i g . 6.1.1 Disdrometer-raingauge #1 comparison, Nov. 14, 1981, 8:41-8:52 288 F i g . 6.1.2 Disdrometer-raingauge #1 comparison, Nov. 15, 1981, 15:29-15:40 . . 289 F i g . 6.1.3 Disdrometer-raingauge #1 comparison, Nov. 30, 1981, 10:59-11:12 290 F i g . 6.2.1 Rainrates for 81.11.30.10 293 F i g . 6.2.2(a) Horizontal wind veloci ty , 10 s avg. for 81.11.30.10 294 F i g . 6.2.2(b) Horizontal wind veloci ty , 30 s avg. for 81.11.30.10 295 296 F i g . 6.2.3(a) Vert ical wind veloci ty , 30 s avg. and NB(0.5)/ND(1.0) for 81.11.30.10 . F i g . 6.2.3(b) Vertical wind velocity , 60 s avg. for 81.11.30.10 297 F i g . 6.2.4(a) Signal levels for horizontal polarization transmitted, 10 s avg. for 81.11.30.10 . 298 F i g . 6.2.4(b) Signal levels for horizontal polarization transmitted, 30 s avg. for 81.11.30.10. . 299 F i g . 6.2.5 Signal levels for v e r t i c a l polarization transmitted, 2 s avg. for 81.11.30.10 . xv ix . . . Page F i g . 6.2.6 CPA during T1 . 307 Fi g . 6.2.7 Drop di s t r i b u t i o n s for 308 F i g . 6.2.8 CPA during T 2 309 Fi g . 6.2.9 Drop d i s t r i b u t i o n for T 2 . 310 F i g . 6.2.10 CPA during T 3 . . . . 312 Fi g . 6.2.11 Drop d i s t r i b u t i o n s for T 3 313 Fi g . 6.2.12 CPA during 315 F i g . 6.2.13 Drop di s t r i b u t i o n s f o r 316 F i g . 6.2.14 CPA during T 5 318 F i g . 6.2.15 Drop di s t r i b u t i o n s for T 5 319 F i g . 6.2.16 CPA during T 6 . . . . . . . . . ' 321 F i g . 6.2.17 Drop di s t r i b u t i o n s for Tfi 322 F i g . 6.2.18 CPA during T ? 323 F i g . 6.2.19 Drop di s t r i b u t i o n s for T y . 324 F i g . 6.2.20 CPA during Tg 325 F i g . 6.2.21 Drop d i s t r i b u t i o n s for Tg 326 F i g . 6.2.22 CPA during T g . . . 328 F i g . 6.2.23 Drop di s t r i b u t i o n s for T g . 329 F i g . 6.2.24 XPD for horizontal transmitted p o l a r i z a t i o n , 30 s avg. for 81.11.30.10 . 330 F i g . 6.2.25(a) XPD for v e r t i c a l transmitted p o l a r i z a t i o n 2 s avg. for 81.11.30.10 331 Fig . 6.2.25(b) XPD for v e r t i c a l transmitted p o l a r i z a t i o n 30 s avg. for 81.11.30.10 332 Fi g . 6.2.26 D i f f e r e n t i a l attenuation for 81.11.30.10. 335 Fi g . 6.2.27 XPDH during T 1 0 338 xx Page Fig. 6.2.28 XPDR during T n 340 Fig. 6.2.29 XPDR during T 1 2 . 341 Fig. 6.2.30 XPDH during T 1 3 . . . 343 Fig. 6.2.31 XPDH during Tj . . . 344 Fig. 6.3.1 Rainrates for 81.11.30.18 346 Fig. 6.3.2 Wind direction for 81.11.30.18 347 Fig. 3.3.3(a) Horizontal wind velocity, 2 s avg. for 81.11.30.18 348 Fig. 6.3.3(b) Horizontal wind velocity, 10 s avg. for 81.11.30.18 349 Fig. 6.3.3(c) Horizontal wind velocity, 99 s avg. for 81.11.30.18 350 Fig. 6.3.4(a) Vertical wind velocity, 10 s avg. for 81.11.30.18 . . . . . 351 Fig. 6.3.4(b) Vertical wind velocity, 30 s avg. for 81.11.30.18 352 Fig. 6.3.5 Drop distributions for Tj, 0.0-0.04 h 353 Fig. 6.3.6 Drop distributions for T , 0.23-0.27 h 354 Fig. 6.3.7 Drop distributions for 0.35-0.39 h 355 Fig. 6.3.8 Drop distributions for T. , 0.83-0.87 h : . . 356 Fig. 6.3.9 Signal levels for horizontal polarization transmitted, 10 s avg. for 81.11.30.18. 358 Fig. 6.3.10 Signal levels for vertical polarization transmitted, 10 s avg. for 81.11.30.18 359 Fig. 6.3.11 CPA during T5, 0.32-0.40 h 360 Fig. 6.3.12 CPA during T 2, 0.40-0.45 h 361 xxi Page Fig. 6.3.13 CPA during T y, 0.48-0.54 362 Fig. 6.3..14(a) XPD for horizontal transmitted polarization, 10 s avg. for 81.11.30.18 363 Fig. 6.3.14(b) XPD for horizontal transmitted polarization, 99 s avg. for 81.1.1.30.18 364 Fig. 6.3.15(a) XPD for vertical transmitted polarization, 10 s avg. for 81.11.30.19 365 Fig. 6.3.15(b) XPD for vertical transmitted polarization, 99 s avg. 81.11.30.18 . 366 Fig. 6.3.16 Differential attenuation for 81.11.30.18. . . . . . . 368 Fig. 6.4.1 Rainrates for 81.11.30.19 369 Fig. 6.4.2(a) Horizontal wind velocity, 10 s avg. for 81.11.30.19 370 Fig. 6.4.2(b) Horizontal wind velocity, 30 s avg. for 81.11.30.19 371 Fig. 6.4.3(a) Vertical wind velocity, 10 s avg. for 81.11.30.19 . 372 Fig. 6.4.3(b) Vertical wind velocity, 30 s avg. and ND(0.5)/ND(1.0) for 81.11.30.19 373 Fig. 6.4.3(c) Vertical wind velocity, 60 s avg. for 81.11.30.19 374 Fig. 6.4.4 Signal levels for horizontal polarization transmitted, 10 s avg. for 81.11.30.19. 375 Fig. 6.4.5 Signal levels for vertical polarization transmitted, 10 s avg. for 81.11.30.19. . . . . . . . 376 Fig. 6.4.6 CPA during T1 380 Fig. 6.4.7 Drop distributions for T ^ . . . . ".' 381 Fig. 6.4.8 CPA during T £ 383 Fig. 6.4.9 Drop distributions forng 384 Fig. 6.4.10 CPA during T 3 386 xxi i Page F i g . 6.4.11 Drop distributions for T 3 . . . . „ . 387 F i g . 6.4.12 CPA during 388 F i g . 6.4.13 Drop distributions for . 389 F i g . 6.4.14 CPA during T 5 . . . . . . . 390 F i g . 6.4.15 Drop distributions for T R . . 391 F i g . 6.4.16 CPA during T 6 . . . . . . . . . . . . 393 F i g . 6.4.17 Drop distributions for T 6 394 F i g . 6.4.18 CPA during T y 396 F i g . 6.4.19 Drop distributions for T ? 397 F i g . 6.4.20 CPA during T g 398. F i g . 6.4.21 Drop distributions for Tg 399 F i g . 6.4.22(a) XPD for horizontal transmitted polar izat ion, 10 s avg. for 81.11.30.19 . 400 F i g . 6.4.22(b) XPD for horizontal transmitted polarizat ion, 30 s avg. for 81.11.30.19 . 401 F i g . 6.4.23(a) XPD for ver t i ca l transmitted polarizat ion, 10 s avg. for 81.11.30.19 402 F i g . 6.4.23(b) XPD for ver t i ca l transmitted polarizat ion, 30 s avg. for 81.11.30.19 . 403 F i g . 6.4.24 Different ia l attenuation for 81.11.30.19 404 F i g . 6.4.25 XPDH during Tg, 0.71-0.83 h 408 F i g . 6.4.26 XPDR during T g , 0.83-0.91 h 409 F i g . 6.5.1 Rainrates for 81.11.30.21 411 F i g . 6.5.2 Horizontal wind veloci ty , 10 s avg. for 81.11.30.21 412 F i g . 6.5.3(a) Vert ical wind veloci ty , 30 s avg. for 81.11.30.21 413 x x i i i Page F i g . 6 . 5 . 3(b) V e r t i c a l wind v e l o c i t y , 60 s avg. f o r 8 1 . 1 1 . 3 0 . 2 1 414 F i g . 6 . 5 . 4 S i g n a l l e v e l s f o r ho r i z o n t a l transmitted p o l a r i z a t i o n , 10 s avg. for 81 .11.30 .21 . 415 F i g . 6 . 5 . 5 S i g n a l l e v e l s f o r v e r t i c a l transmitted p o l a r i z a t i o n , 10 s avg. f o r 8 1 . 1 1 . 3 0 . 2 1 . 416 F i g . 6 . 5 . 6 CPA during . . . 419 F i g . 6 . 5 . 7 Drop d i s t r i b u t i o n s f o r T1 420 F i g . 6 . 5 . 8 CPA during T 2 422 F i g . 6 . 5 . 9 Drop d i s t r i b u t i o n s f o r T 2 423 F i g . 6 . 5 . 1 0 CPA during T 3 424 F i g . 6 . 5 . 1 1 Drop d i s t r i b u t i o n s f o r T 3 425 F i g . 6 . 5 . 1 2 XPD f o r h o r i z o n t a l transmitted p o l a r i z a t i o n , 10 s avg. for 8 1 . 1 1 . 3 0 . 2 1 . 427 F i g . 6 . 5 . 1 3 XPD f o r v e r t i c a l transmitted p o l a r i z a t i o n , 10 s avg. for 8 1 . 1 1 . 3 0 . 2 1 428 F i g . 6 . 5 . 1 4 D i f f e r e n t i a l attenuation f o r 8 1 . 1 1 . 3 0 . 2 1 430 F i g . 6 . 5 . 1 5 XPD H during 431 F i g . 6 . 5 . 1 6 XPD V during T^. . . . 432 F i g . 6 . 5 . 1 7 XPD H during T 5 435 F i g . 6 . 5 . 1 8 XPD H during T g 435 F i g . 6 . 6 . 1 Rainrates f o r 8 1 . 1 1 . 3 0 . 2 2 437 F i g . 6 . 6 . 2 Wind d i r e c t i o n 10 s avg. for 8 1 . 1 1 . 3 0 . 2 2 438 F i g . 6 . 6 . 3 H o r i z o n t a l wind v e l o c i t y , 10 s avg. and N D ( 0 . 5 ) / N D ( 1 . 0 ) r a t i o for 8 1 . 1 1 . 3 0 . 2 2 . 439 F i g . 6 . 6 . 4(a) V e r t i c a l wind v e l o c i t y , 30 s avg. f o r 8 1 . 1 1 . 3 0 . 2 2 440 xxiv Page F i g . 6.6.4(b) Vert ical wind veloci ty , 60 s avg. for 81.11.30.22 . 441 F i g . 6.6.5 Signal levels for horizontal transmitted polarization, 10 s avg. for 81.11.30.22 442 F i g . 6.6.6 Signal levels for ver t i ca l transmitted polarization, 10 s avg. for 81.11.30.22 . . . . . . . 443 F i g . 6.6.7 CPA during T j 448 F i g . 6.6.8 Drop distributions for Tl 449 F i g . 6.6.9 CPA during T 2 450 F i g . 6.6.10 Drop distributions for T 2 . . . 451 F i g . 6.6.11 CPA during T a . , . 453 F i g . 6.6.12 Drop distributions for T 3 454 F i g . 6.6.13 CPA during 455 F i g . 6.6.14 Drop distributions for T^ 456 F i g . 6.6.15 CPA during T 5 458 F i g . 6.6.16 Drop distributions for T 5 . . . 459 F i g . 6.6.17 CPA during T 6 460 F i g . 6.6.18 Drop distributions for T & . . . . 461 F i g . 6.6.19 CPA during T ? 462 F i g . 6.6.20 Drop distributions for T ? 463 F i g . 6.6.21 CPA during T 8 465 F i g . 6.6.22 Drop distributions for T g . . . 466 F i g . 6.6.23 CPA during T g 467 F i g . 6.6.24 Drop distributions for T g 468 F i g . 6.6.25 XPD for ver t i ca l transmitted polar izat ion , 10 s avg. for 81.11.30.22 . . 469 F i g . 6.6.26 Different ia l attenuation for 81.11.30.22 470 xxv Page F i g . 6 . 7 . 1 R a i n r a t e s f o r 8 0 . 0 5 . 2 2 . 1 0 472 F i g . 6 . 7 . 2 ( a ) Wind d i r e c t i o n , 2 s a v g . f o r 8 0 . 0 5 . 2 2 . 1 0 473 F i g . 6 . 7 . 2 ( b ) Wind d i r e c t i o n 10 s a v g . f o r 8 0 . 0 5 . 2 2 . 1 0 . . . . . . . 474 F i g . 6 . 7 . 3 H o r i z o n t a l wind v e l o c i t y , 10 s a v g . f o r 8 0 . 0 5 . 2 2 . 1 0 475 F i g . 6 . 7 . 4 V e r t i c a l wind v e l o c i t y , 10 s a v g . f o r 8 0 . 0 5 . 2 2 . 1 0 476 F i g . 6 . 7 . 5 S i g n a l l e v e l s f o r h o r i z o n t a l t r a n s m i t t e d p o l a r i z a t i o n , 10 s a v g . f o r 8 0 . 0 5 . 2 2 . 1 0 478 F i g . 6 . 7 . 6 S i g n a l l e v e l s f o r v e r t i c a l t r a n s m i t t e d p o l a r i z a t i o n , 10 s a v g . f o r 8 0 . 0 5 . 2 2 . 1 0 479 F i g . 6 . 7 . 7 CPA d u r i n g T j 483 F i g . 6 . 7 . 8 CPA d u r i n g T 2 484 F i g . 6 . 7 . 9 CPA d u r i n g T 3 486 F i g . 6 . 7 . 1 0 CPA d u r i n g T 4 487 F i g . 6 . 7 . 1 1 CPA d u r i n g T 5 488 F i g . 6 . 7 . 1 2 CPA d u r i n g Tg 489 F i g . 6 . 7 . 1 3 XPD f o r v e r t i c a l t r a n s m i t t e d p o l a r i z a t i o n , 10 s a v g . f o r 8 0 . 0 5 . 2 2 . 1 0 492 F i g . 6 . 7 . 1 4 XPD f o r h o r i z o n t a l t r a n s m i t t e d p o l a r i z a t i o n , 10 s a v g . f o r 8 0 . 0 5 . 2 2 . 1 0 493 F i g . 6 . 7 . 1 5 D i f f e r e n t i a l a t t e n u a t i o n f o r 8 0 . 0 5 . 2 2 . 1 0 494 F i g . 6 . 7 . 1 6 XPD V f o r T ^ T g 498 F i g . 6 . 7 . 1 7 XPD R f o r T x - T 3 499 F i g . 6 . 7 . 1 8 XPD V f o r T 2 500 F i g . 6.7.19 XPD V f o r T 3 . . . 501 F i g . 6 . 7 . 2 0 XPD y f o r T & . 502 x x v i Page F i g . 6.7.21 XPD R f o r T £ 503 F i g . 6.8.1 Rainrates f o r 81.06.18.15 . . . . . . 505 F i g . 6.8.2 Wind d i r e c t i o n , 10 s avg. f o r 81.06.18.15 506 F i g . 6.8.3 Horizontal wind v e l o c i t y , 10 s avg. f o r 81.06.18.15 507 F i g . 6.8.4(a) V e r t i c a l wind v e l o c i t y , 10 s avg. for 81.06.18.15 508 F i g . 6.8.4(b) V e r t i c a l wind v e l o c i t y , 30 s avg. f o r 81.06.18.15 509 F i g . 6.8.5(a) Signal l e v e l s f o r h o r i z o n t a l p o l a r i z a t i o n transmitted 10 s avg. f o r 81.06.18.15 511 F i g . 6.8.5(b) Signal l e v e l s f o r h o r i z o n t a l p o l a r i z a t i o n transmitted, 30 s avg. f o r 81.06.18.15 512 F i g . 6.8.6 Signal l e v e l s f o r v e r t i c a l p o l a r i z a t i o n , 10 s avg. for 81.06.18.15 . . . 513 F i g . 6.8.7 CPA during 81.06.18.15 514 F i g . 6.8.8(a) XPD f o r h o r i z o n t a l transmitted p o l a r i z a t i o n , 10 s avg. for 81.06.18.15 . ., 515 F i g . 6.8.8(b) XPD f o r ho r i z o n t a l transmitted p o l a r i z a t i o n 30 s avg. f o r 81.06.18.15 516 F i g . 6.8.9 XPD R during 518 F i g . 6.8.10 XPD f o r v e r t i c a l transmitted p o l a r i z a t i o n 10 s avg. f o r 81.06.18.15 520 F i g . 6.8.11 XPD V during T 1 521 F i g . 6.8.12 D i f f e r e n t i a l attenuation during 81.06.18.15 . . . . . 522 F i g . 6.9.1 Rainrates f o r 81.11.14.07 . . . . . . . . . 524 F i g . 6.9.2 Wind d i r e c t i o n f o r 81.11.14.07. . 525 F i g . 6.9.3 Horizontal wind v e l o c i t y , 10 s avg. for 81.11.14.07 . 526 xxv i i F i g . 6.9.A Vert ical wind veloci ty , 30 s avg. for 81.11.14.07 . • • F i g . 6.9.5(a) Signal levels for horizontal polarization transmitted, 10 s avg. for 81.11.14.07. . . . . . F i g . 6.9.5(b) Signal levels for horizontal polarization transmitted, 30 s avg. for 81.11.14.07. . . F i g . 6.9.6 Signal levels for v e r t i c a l polarization transmitted, 10 s avg. for 81.11.14.07. . . . F i g . 6.9.7 CPA during T x . . F i g . 6.9.8 CPA during T 2 . F i g . 6.9.9 CPA during T 2(a) . . . F i g . 6.9.10 CPA during T 2(b) . . , F i g . 6.9.11 CPA during T 3 . . . F i g . 6.9.12 CPA during T 3 (a) , F i g . 6.9.13(a) XPD for horizontal transmitted polarizat ion, 10 s avg. for 81.11.14.07 . . . . F i g . 6.9.13(b) XPD for horizontal transmitted polarizat ion, 30 s avg. for 81.11.14.07 F i g . 6.9.14 XPD for ver t i ca l transmitted polar izat ion, 10 s avg. for 81.11.14.07 . . . F i g . 6.9.15 Dif ferent ia l attenuation for 81.11.14.07. . F i g . 6.9.16 XPDH for T j . . . . . . . F i g . 6.9.17 XPDV for 71 F i g . 6.9.18 XPDR for T 3 F i g . 6.9.19 XPDV for T 3 x x v i i i Table 1 Table 2.1 Table 2.2 Table 2.3 Table 2.4 Table 2.5 Table 2.6 Table 4.1 Table 4.2 Table 5.1 Table 5.2 Table 5.3 Table 6.2.1 Table 6.2.2 .Table 6.4.1 Table 6.4.2 Table 6.5.1 Table 6.5.2 Table 6.6.1 Table 6.7.1 LIST OF TABLES Page Summary of WARC-79 allocations above 40 GHz . . . . . . 6 DBB-614-LE2 electromechanical DPST waveguide switch waveguide switch specifications . . . . . . 39 Transmitting system signal levels 44 -Scientific Atlanta model 1751 receiver specifications . 50 TRG 922-V harmonic mixer specifications 60 A . I . Grayzel OX-3.5 frequency multiplier specifications 77 TRG V822 antenna specifications at 73.5 GHz 105 Forward scattering amplitudes at 74 GHz 200 Drop terminal veloci t ies i n s t i l l a i r . . . . . . . . . 217 Effects of d i f f e r e n t i a l attenuation and phase shif t on cancelled and uncancelled systems. . . . . . . 279 Range of possible system XPDs for different antenna XPD angles 281 Range of possible system XPDs for different antenna XPD magnitudes 283 Summary of attenuation data for 81.11.30.10 302 Summary of XPD and d i f f e r e n t i a l attenuation data for 81.11.30.10 336 Summary of attenuation data for 81.11.30.19 . . . . . . . 378 Summary of XPD and d i f f e r e n t i a l attenuation data for 81.11.30.19 - 406 Summary of attenuation data for 81.11.30.21 . . . . . . 418 Summary of XPD and differential-attenuation data for 81.11.30.21 429 Summary of attenuation data for 81,11.30.22 445 Summary of attenuation data for 80.05.22.10 480 xxix Table 6.7.2 Summary of XPD and d i f f e r e n t i a l data for 80.05.22.10 Table 6.9.1 Summary of attenuation data for 81.11.14. Table 6.9.2 Summary of XPD and d i f f e r e n t i a l attenuati data for 81.11.14.07 XXX ACKNOWLEDGEMENTS I would l i k e foremost, to acknowledge the cont r i b u t i o n , encouragement and moral support of Dr. M.M.Z. Kharadly whose wealth of knowledge about p r a c t i c a l and t h e o r e t i c a l microwave techniques and c r i t i c a l i n s i g h t helped make th i s project s u c c e s s f u l . I am also very g r a t e f u l to Dr. Peter Watson, of the Un i v e r s i t y of Bradford, U.K. f o r providing the forward s c a t t e r i n g amplitudes on which the c a l c u l a t i o n s i n Chapter 4 are based. Mr. Jack Stuber, formerly of the E l e c t r i c a l Engineering machine shop, made several contributions to t h i s work, incl u d i n g the construction of: the antenna and r e f l e c t o r mounts and s h i e l d s , raingauges, disdrometer and numerous waveguide s e c t i o n s . Mr. James Johnston, who was a technician i n our lab was also very h e l p f u l i n : the f i n a l disdrometer c a l i b r a t i o n , microcomputer software and preparation of t h i s report. I would also l i k e to s p e c i a l l y thank G a i l Schmidt for typing t h i s r e p o r t . Mr. Tony Leugner, of the E l e c t r i c a l Engineering Department was extremely h e l p f u l by s e r v i c i n g the data a c q u i s i t i o n minicomputer system and by constructing the disdrometer preamplifier and mixer bias c i r c u i t s . Many members of the departmental technical s t a f f , i n c l u d i n g : A l MacKenzie, Chris S h e f f i e l d , Derek Daines, Dave Fletcher, and Wally Walters, provided invaluable assistance at one time or another during the course of th i s work. xxxi Assistance i n the development of the f i r s t version of the disdrometer was provided by: Mike Koombes, Vince Loney and William Wong. The software f o r data handling and presentation was developed by: Ian Vogelesang, Brian Thompson, Peter Chun, Lisbeth Seeley, E r i c MInch, Andrew Milne, Ramon Valerda, Ho Jun Lee and Len Smart. The Postgraduate Scholarship I received from the Natural Sciences and Engineering Research Council i s also g r e a t f u l l y acknowledged. Funds f o r t h i s project were provided by the Communications Research Center, Ottawa, under the following DSS contracts: OSU77-00056, 0SU77-000261, 0SU78-00012, 0SU79-00009, 0SU80-00129, 0SU81-00057, and by the Natural Science and Engineering Research Council under grant A-3344. xxxii 1 1. INTRODUCTION Increasing u t i l i z a t i o n of the microwave spectrum has created an active interest in the application of the millimetre-wave bands [1.1]-[1.12] and orthogonal polarization frequency reuse [1.6]/ [1.13]-[1.15]. Many new systems employing atmospheric propagation of the higher microwave and m i l l i -metre frequencies are now being developed. The main uses planned for these higher frequencies are wideband terrestrial and sa t e l l i t e communication links, (both analog and digital) and a variety of radar applications. M i l l i -metre-wave systems are also rapidly becoming practical because of advances in higher frequency solid-state components and integrated circuit technologies. To be able to effectively apply the millimetre frequencies and the techniques of polarization frequency reuse, accurate information about the effects of atmospheric propagation, especially during rain, must be available to system designers. The mathematical methods for predicting the important atmospheric propagation parameters during rain are f a i r l y well developed and l i t t e controversy persists about the basic theory. However, the usefulness of these mathematical models is limited because very l i t t l e is known about some of the meteorological parameters necessary for accurate predictive calculations. There have also been a significant number of reported experimental measurements which do not appear to agree with the basic theoretical predictions based on simultaneous meteorological observations. In most instances, this i s probably due to inaccurate or incomplete meteorological instrumentation or inadequacies in the meteorological or 2 experimental models. These factors create a definite need for accurate millimetre-wave and dual-polarized propagation data with comprehensive raeterological observations to verify the basic theory and to learn more about the meteorological conditions important to these areas of atmospheric propagation. 1.1 Spectrum Demand Increasing demand for ter res t r ia l microwave systems and the phenomenal growth i n s a t e l l i t e communications has s ignif icant ly reduced the a v a i l a b i l i t y of licensable channels i n the lower microwave spectrum. In Canada, the recent rate of growth of licenced assignments has been 10-20% per year i n this frequency range [1.16]. The main areas of increasing application are multi-channel entertainment video, high-speed business data and telephony. Spectrum congestion problems have been compounded by the rapid increase i n s a t e l l i t e communications systems, which i n the past, have shared frequency bands with t e r r e s t r i a l services. As more s a t e l l i t e systems are planned for urban areas, frequency coordination with te r res t r ia l services has become increasingly d i f f i c u l t [1.17], [1.18], Frequency coordination problems w i l l spread to higher frequencies and become even more severe for lower frequencies, due to the large number of new s a t e l l i t e systems planned for the next few years, as shown i n F i g . 1.1 [1.19]. Since i t is unusual for channel allocations to be relinquished once they have been assigned, the radio spectrum i s , i n some ways, similar to a nonrenewable resource. In response to the need for more licensable spectrum, the 1979 World Administrative Radio Conference (WARC-79) s ignif icant ly revised the 18-40 GHz (2) \ 11-17 GHz-(1) BELOW 6 GHz (14) BELOW 6 GHz (23) 18 -40 GHz (8) 11 -17 GHz (8) 7 -9 GHz (13) BELOW 6 GHz (50) 18-40 GHz] (6) |ll-17 GHz I (39) t 7-9 GHz (4) BELOW 6 GHz (54) 1965-69 1970-74 1975-79 INTERVAL 1980-84 1.1. Geosynchronous s a t e l l i t e s i n o r b i t and planned, 4 International Table of Frequency Allocations above 40 GHz. These new allocations are considered to "reflect a high level of interest and activity in this portion of the spectrum" and were "created with the objective of stimulating development of this spectrum resource" [1.20]. The millimetre-wave spectrum, referred to here as 30-300 GHz (i.e. the EHF band) can be roughly characterized by bands defined by regions of high clear-weather attenuation caused by molecular-resonance absorption. Fig. 1.2, shows the atmospheric attenuation bands caused by oxygen and water vapour [1.21]. Table 1(a) from [1.20], gives the frequency limits and band designations for the absorption bands and windows in the frequency range 40-275 GHz. A summary of the WARC-79 allocations, from [1.20] i s shown in Table 1(b) to 1(e). Complete spectrum allocations resulting from WARC-79 are included i n [1.22]. 1.2 Millimetre Applications Even though a l l types of services are allocated in the frequency range above 40 GHz, the specific characteristics of these frequencies make certain applications more advantageous than others. Applications employing atmospheric propagation where millimetre-wave systems have some benefit over microwave or optical systems include: - short haul point-to-point or local distribution t e r r e s t r i a l links [1.23], [1.26], [1.29], [1.30], [1.31], [1.36]. - small, lightweight, portable communication systems [1.5], [1.24], [1.30], [1.31] , [1.32] , [1.33]. 5 10 20 50 100 200 350 Frequency (GHz) F i g . 1.2. Atmospheric attenuation due to molecular absorption. TABLE 1(a) SUMMARY OF ALLOCATIONS ABOVE 40 GHz Total Width of Spectrum Allocated 235 GHz Number of Services 21 Bands Allocated Exclusively 0 Average Spectrum/Band: <100 GHz 2 . 5 GHz >100 GHz 5 . 8 GHz Average Services/Band 3 . 5  TABLE 1(b) ATMOSPHERIC WINDOW AND ABSORPTION BAND LIMITS Window Absorption Band Limits (GHz) W l 3 9 . 5 - 5 1 . 4 A l 5 1 . 4 - 6 6 w 2 6 6 - 1 0 5 A 2 1 0 5 - 1 3 4 W 3 1 3 4 - 1 7 0 A 3 1 7 0 - 1 9 0 — " I , 1 9 0 - 2 7 5 7 TABLE 1(c) ALLOCATIONS TO SATELLITE SERVICES Service w l A l w 2 A 2 W 3 A 3 w 4 Total Total Bandwdith, GHz Amateur-Satellite 1 2 2 2 7 2 1 . 7 Fixed 4 5 3 5 17 6 9 . 5 Inter 2 2 4 8 4 4 . 0 Mobile 3 4 1 2 10 5 2 . 5 Broadcasting 1 1 2 4 Radionavigation 1 2 1 2 6 4 4 . 5 TABLE 1(d) ALLOCATIONS TO SCIENTIFIC SERVICES Service W l A l w 2 A 2 W 3 A 3 w 4 Total Total Bandwidth, GHz Earth Exploration- 1 5 2 2 2 2 4 18 6 9 . 8 Satellite Radio Astronomy 1 1 1 1 1 2 7 49 Space Research 1 5 2 2 2 2 4 18 6 9 . 8 Z z J Z . — — • — -TABLE 1(e) ALLOCATIONS TO TERRESTRIAL SERVICES .Service W l A l w 2 A 2 W 3 A 3 w „ Total Total Bandwidth, GHz Amateur 1 2 2 2 7 2 1 . 7 Fixed 6 3 7 2 4 4 6 32 1 2 4 . 7 Mobile 8 3 9 2 5 4 7 38 169 Broadcasting 1 1 2 4 Radiolocation 1 3 1 2 3 10 53 Radionavi gation 1 2 1 2 6 4 4 . 5 1 8 - a wide variety of high resolution radar applications [1.23], [1.24], [1.26], [1.28]. - secure communication links operating i n absorption bands (especially at 60 GHz) [1.5], [1.23], [1.24], [1.26], [1.32], [1.33]. - very wideband d i g i t a l l inks [1.25], [1.31], [1.35]. - multichannel video systems [1.30]. - s a t e l l i t e communication systems [1.2], [1.4], [1.23], [1.24], [1.26], [1.27]. and - radiometer, remote sensing and imaging systems, [1.23], [1.24], [1.25], [1.26], [1.27], [1.28], [1.34]. 1.3 Advantages and Disadvantages of Millimetre Frequencies The major factors which make millimetre frequencies advantageous in these applications arise from the short wavelength, large operating bandwidths and a v a i l a b i l i t y of spectrum. Shorter wavelengths result in physically smaller components, higher antenna gains and lower antenna beamwidths (for a specified antenna aperture). Narrow antenna beamwidths are desirable because they ease frequency coordination problems, reduce multipath fading, lower the probability of unauthorized reception or jamming, and yield higher resolutions i n radar and radiometer systems. Bandwidths of several gigahertz are more easily obtainable in millimetre systems because they represent a smaller percentage of the operating frequency. The a v a i l a b i l i t y of spectrum in the millimetre range w i l l mean that more systems, with high-er bandwidths,, can be licensed in any geographical area. Another 9 advantage of millimetre-wave systems in high resolution radar applications Is their a b i l i t y to penetrate fog, smoke and dust [1.23], [1.24]. In communication systems requiring a high degree of security, the absorption bands in the millimetre range, especially at 60 GHz, are an advantage because they can further reduce the probability of unauthorized reception. [1.23], [1.32], [1.33]. The disadvantages of millimetre-wave systems are higher copolar -attenuation (CPA) due to rain and molecular absorption and lower component perforraance/cost ra t ios . Attenuation due to rain and other hydrometeors increases with frequency up to approximately 100 GHz. This factor w i l l ultimately l imit the r e l i a b i l i t y of millimetre systems employing atmospheric propagation. Millimetre components are currently more expensive than microwave components of comparable performance because higher mechanical precision is required, semiconductors are more d i f f i c u l t to fabricate and production volumes are low. Even though nothing can be done about higher rain attenuation, great advances are being made in millimetre components. 1.4 Millimetre Semiconductors and Integrated Circuits In the past few years, developments In millimetre semiconductors have led to dramatic improvements i n device performance. For the past few years, the power output levels of solid-state millimetre sources has been increasing at the rate of 3 dB per year 11.37], It is now possible to obtain 17 W peak at 94 GHz in low-duty-cycle pulses from a single IMPATT diode [1.38] and 63 W peak at 92 GHz from combined IMPATTS [1.39], Recently, a 61 GHz IMPATT amplifier with 50 dB gain and a 2.5 W power output was demonstrated [1.40]. 10 At the TRG division of Alpha Industries, signficant advances have been made i n the millimetre application of beam lead diodes. This technology has improved the performance of mixers at frequencies up to 140 GHz and allows mass production techniques to be used to reduce costs [1.41], [1.42]. These beam lead diodes were used i n a suspended s t r ipl ine mixer which yielded a total double sideband receiver noise figure of 5.8 dB at 110 GHz [1.33]. Recent advances in millimetre frequency integrated c i r c u i t technologies also promise to reduce the cost of components. Several types of transmission l ine structures have been demonstrated to be advantageous for millimetre-wave IC fabricat ion. These include: - d i e l e c t r i c waveguide [1.43 ], [1.44 ], [1.46 ] . - image waveguide [1.45], [1.46]. - f i n l ine [1.47], [1.48]. - microstrip l ine [1.49 ], [1.50 ], [1.51 ] . - suspended s t r ip l ine [1.41], [1.42], [1.52]. and - E-plane waveguide [1.53]. These techniques w i l l y ie ld large reductions in component costs when volumes can j u s t i f y the use of modern integrated c i rcui t production methods [1.38]. 1.5 Orthogonal Polarization Frequency Reuse Orthogonal polarization frequency reuse can double spectrum u t i l i z a t i o n and result i n significant system cost reductions. During normal clear-weather conditions i t is possible to transmit two orthogonal (l inear or 11 c i r c u l a r ) p o l a r i z a t i o n s through one pair of antennas with i n s i g n i f i c a n t atmospheric coupling between p o l a r i z a t i o n s . This can allow separate communications channels to occupy the same frequency or can be used to a l l e v i a t e frequency coordination problems i n congested areas. P o l a r i z a t i o n frequency reuse can o f f e r tremendous cost advantages i n both t e r r e s t r i a l and s a t e l l i t e system because both p o l a r i z a t i o n s can share a common antenna system. In t e r r e s t r i a l systems, topographical conditions often necessitate the use of large towers to support antennas. These towers can often cost more than the systems' e l e c t r o n i c components. By using a common antenna f o r two p o l a r i z a t i o n s , the t o t a l cost of purchasing, shipping, i n s t a l l i n g and maintaining the antenna and tower can be gr e a t l y reduced. In s a t e l l i t e systems, these economic advantages are even greater because antennas are a la r g e r portion of t o t a l system costs and because mounting a d d i t i o n a l antennas on the actual s a t e l l i t e would be extremely expensive. Unfortunately, some atmospheric conditions can cause coupling between po l a r i z a t i o n s and a reduction i n the path crosspolar d i s c r i m i n a t i o n (XPD) and therefore system r e l i a b i l i t y . A reduction i n path XPD can occur as si g n a l s propagate through r a i n (or other hydrometeors) or during multipath propagation. Multipath XPD reduction i s very important i n the lower microwave region but because t h i s report i s concerned only with m i l l i m e t r e propagation, multipath XPD w i l l not be discussed i n d e t a i l . Rain can cause a reduction i n XPD because raindrops are not sp h e r i c a l and i n the presence of v e r t i c a l wind gradients can have a preferred axis o r i e n t a t i o n , or canting angle. Depolarization occurs because the two p o l a r i z a t i o n s experience a 12 d i f f e r e n t i a l attenuation and d i f f e r e n t i a l phase s h i f t propagating through the a n i s o t r o p i c r a i n medium. 1.6 Propagation Theory and Experiment To be able to design economical systems with predictable r e l i a b i l i t y using millimetre-waves or p o l a r i z a t i o n frequency reuse, accurate knowledge of atmospheric propagation phenomena i s required. At the present time, s u f f i c i e n t , r e l i a b l e information i s not a v a i l a b l e on propagation at higher frequencies and i n d i f f e r e n t geographical regions. The advancement of p r a c t i c a l atmospheric propagation knowledge requires a combination of t h e o r e t i c a l and experimental i n v e s t i g a t i o n s . The basic mathematical methods f o r p r e d i c t i n g atmospheric propagation through r a i n are f a i r l y well developed. In the case of the c a l c u l a t i o n of r a i n attenuation f o r a set of assumed r a i n conditions, the e a r l i e r u n c e r t a i n t i e s and controversies appear to have been resolved i n the past few years. T h e o r e t i c a l methods f o r p r e d i c t i n g d u a l - p o l a r i z a t i o n propagation parameters during r a i n are le s s mature but there appears to be agreement on the basic techniques. Several in v e s t i g a t o r s are continuing to r e f i n e the c a l c u l a t i o n of XPD, mainly by including more comprehensive meteorological models. The main inadequacy i n the t h e o r e t i c a l p r e d i c t i o n of atmospheric propagation during r a i n i s a lack of knowledge about the meteorological inputs to the c a l c u l a t i o n s . To c a l c u l a t e r a i n attenuation, the number and s i z e s of raindrops at a l l points within the propagation path must be known. This i s extremely d i f f i c u l t to predict because very l i m i t e d actual drop s i z e 13 data are a v a i l a b l e and i t i s known that the drop siz e d i s t r i b u t i o n depends on r a i n r a t e - which also has large temporal, s p a t i a l and geographical v a r i a t i o n s - the type of rainstorm, v e r t i c a l wind v e l o c i t i e s , p o s i t i o n within a r a i n c e l l and other meteorological conditions. For d u a l - p o l a r i z a t i o n propagation c a l c u l a t i o n s , i n addi t i o n to the previous information, i t i s necessary to know the drop shape and canting angle s t a t i s t i c s . Because of the extreme d i f f i c u l t y of accurately measuring these parameters i n natural r a i n , almost no information about canting angles presently e x i s t s . Radio system designers i n Canada are very fortunate to have a re c e n t l y published, d e t a i l e d study of r a i n r a t e s t a t i s t i c s across Canada [1.54]. S i m i l a r data, with less geographical r e s o l u t i o n , have also recently been published by Crane, showing ra i n r a t e regions f o r a l l areas of the earth [1.55], [1.56]. While these data bases g r e a t l y Improve the accuracy of system r e l i a b i l i t y p r e d i c t i o n s , much more data are needed to be able to make accurate m i l l i m e t r e or d u a l - p o l a r i z a t i o n propagation p r e d i c t i o n s . For mi l l i m e t r e propagation p r e d i c t i o n s , drop s i z e information i s important because the c a l c u l a t i o n s are very much more s e n s i t i v e to drop d i s t r i b u t i o n than i n the microwave range due to the la r g e r drop size-to-wavelength r a t i o . For accurate XPD pre d i c t i o n s , the canting angle s t a t i s t i c s are e s s e n t i a l . The d i f f i c u l t y of measuring these parameters means that system designers w i l l not be able to accurately predict millimetre or dual-polarized propagation parameters, i n a given geographical l o c a t i o n , by using a v a i l a b l e meteor-o l o g i c a l s t a t i s t i c s and propagation c a l c u l a t i o n s . Because i t i s not f e a s i b l e to measure a l l the required meteorological parameters accurately, there i s 14 considerable Interest in attempting to determine effective rain conditions by comparing simultaneous propagation and measurable rain conditions. Experimental data on atmospheric propagation with simultaneous meterological observations are needed to: validate the theoretical methods, provide practical and direct ly applicable propagation data and to gain knowledge of the effective meteorological parameters required for propagation predictions during natural r a i n . Many investigators have mentioned the need for experimental data for comparison to theoretical calculations, including: Neves and Watson [1.57], Zavody and Harden ]1.59], Llewellyn Jones [1.60], Bulter [1.61], Evans, Uzunoglu and Holt [1.62], Dintelmann and Rucher [1.13] and Ippolito [1.19]. Data obtained on propagation i n one frequency range and location can be useful i n a variety of applications. If adequate meteorological information is included with the propagation data, i t is possible to improve predictions i n other geographical areas i f s imilar , comparable meterological s ta t i s t i cs are available. Propagation information obtained on ter res t r ia l l inks can also be useful i n predicting l ink performance on s a t e l l i t e paths [1.8], [1.64], [1.65]. Specific propagation results can also be useful at other frequencies by the use of frequency scaling [1.55], [1.66]. The need for accurate experimental data is especially great above about 40 GHz because very limited data have been published [1.9], [1.58], [1.59], [1.60], [1.63]. Experimental work is also important i n the millimetre range because the larger drop size-to-wavelength ratio and freedom from multipath give most importance to different propagation problems than those which are f a i r l y well understood i n the microwave region. In addition, 15 there have been a number of cases where data from experiments, especially dual-polarized or millimetre frequency Investigations, did not agree with theoretical calculations, probably because of inadequate meterological observations [1.61], [1.62], [1.64], [1.67]-[1.73]. More, specific examples of this lack of agreement are included i n the next two sections which survey previous propagation experiments. 1.7 Previous Dual-Polarized Propagation Experiments The experiments reviewed i n this section are described here by the general term dual-polarized because they use two polarizations to study the anisotropic nature of atmospheric propagation during r a i n . This short survey of higher frequency, dual-polarized experiments is included to outline the different experimental techniques, survey the experimental system perform-ances, and review the results obtained. At frequencies below about 18 GHz, there have been several excellent investigations of dual-polarized propaga-t ion . These studies are not mentioned here for the sake of brevity and because the important meterological conditions and propagation effects are, to some extent, different in the microwave and millimetre wave frequency ranges. There have also been several comprehensive dual-polarized sa te l l i te propagation experiments at frequencies up to 30 GHz which are not dicussed here. DeLange, Dietrich and Hogg have reported a 60 GHz dual-polarized experiment on a 1.03 km. l ink at Bel l Labs, Holmdel, New Jersey [1.74]. A switched transmitted polarization and a switched polarization single-channel receiver were used. Approximate isolations of 30 dB and 34 dB were achieved. 16 F i g . 4 in this reference shows a sharp, deep nul l in one polarization discrimination characteristic of the operating system. (These nulls are believed to be similar to those described i n Section 2.5 of this report.) In the discussion of the experimental results , the authors describe the results for one storm behaving "the way one might expect from simple theory: i . e . d i f f e r e n t i a l attenuation always positive (fade i n horizontal polarization was greater than in v e r t i c a l ) . The crosstalk [XPD] variations were pretty much the same for both polarizations, with the ratio [XPD] becoming poorer during the deeper fade". However, a different storm "did not produce results expected from the simple theory. For a considerable portion of the time, the d i f f e r e n t i a l attenuation was negative, indicating that the attenuation of the ver t ica l component was greater than that of the horizontal component. The fact that the crosstalk ratio i n both channels ( F i g . 9) improved s l i g h t l y i n this case may be explained by referring to (Fig . 4) [the system isolation] which shows the clear weather operating point near +0.5 degree; a negative rotation (caused by the rain) of the ver t i ca l component from this value would reduce the cross-coupled energy and thereby improve the r a t i o " . This report concludes that the 60 GHz d i f f e r e n t i a l attenuation " i s seldom greater than 2 dB and the average d i f f e r e n t i a l i s only 1.25 dB, even for fades greater than 30 dB". Hogg and Chu [1.75] have presented data from this experiment i n the form of a graph relating horizontal CPA to XPD. These results show a lower value of XPD than expected. This is attributed to the low clear-weather, crosspolar-discrimination level of their measuring system. No attempt was 17 made to separate this clear weather XPD level from the atmospheric measure-ments. Thomas [1.76] has compared some of the 60 GHz XPD data from this experiment to his calculated values. The effect of the f i n i t e experimental system isola t ion on the measured data seems to have been considered as a simple scalar addition. Using this technique, good agreement with calculated values was obtained for the two data points compared. Neves and Watson have described a dual-polarized 36.5 GHz experimental investigation conducted over a 13.6 km l ink near the University of Bradford, U.K. [1.77]. In this study, the CW transmitted signal was polarized at 4 5 ° . Separate antennas continously monitored the ver t ica l and horizontal compo-nents of the received s ignal . This experimental method was chosen to f a c i l i -tate accurate measurements of d i f f e r e n t i a l attenuation, d i f f e r e n t i a l phase shif t and 45° crosspolarization. With this set up, the received signals w i l l have similar levels and high S.N.R. thus improving the accuracy of dif feren-t i a l measurements. This polarization w i l l also y ie ld the highest levels of depolarized signals , but w i l l result in a low sensi t ivi ty to canting angle measurements. Also included i n this reference are ear l ier results for XPD over the same path for ver t ical transmitted polarization. The rain instrumentation for this experiment consisted of a rapid response rain gauge and disdrometer at the receiving s i t e . This data, along with wind information was used to construct a "synthetic storm model" to describe the meterological conditions along the path. The authors conclude that their crosspolarization, d i f f e r e n t i a l phase and d i f f e r e n t i a l attenuation measurements were in good agreement with a 18 theoretical rain model with 3° to 4° canting angle, 20° mean modulus and 20° to 25° standard deviation. They also report a greater number of larger drops i n medium-heavy r a i n f a l l than given by the Laws-Parson drop size d i s t r i b u t i o n . Seraplak conducted an experiment to measure 30.9 GHz polarization rotation over a 2.6 km path at Bel l Labs, Holmdel, New Jersey [1.78]. In this experiment, the transmitted wave was oriented v e r t i c a l l y and the receiver polarization was rapidly switched between plus and minus 45° with respect to v e r t i c a l . The sum and difference powers for both received signals was used to calculate the polarization rotation. The XPD was then calculated using: XPD (dB) = 20 l o g 1 Q (tan a) (1.1) where a i s the measured polarization rotation. Results from this experiment showed that the minimum value of XPD was about 10 dB lower than Its average value over a wide range of copolar attenuations. Semplak also showed a dependence of polarization rotation on cross-path wind veloci ty . An ear l ier experiment by Semplak, also at 30.9 GHz, but over a 1.89 km path in the same location, used a similar experimental system to measure d i f f e r e n t i a l attenuation [1.79]. In this case, the transmitted wave was polarized at 45° and the receiver was switched between ver t i ca l and horizontal polarizations. The average relationship between the observed copolar and d i f f e r e n t i a l attenuations agreed well with the theoretical predictions. Rainrate does not appear to have been measured in either of these two experiments. 19 Turner described a dual polarization experiment at 22 GHz conducted over a 4 km l ink i n Suffolk, England [1.80]. Two different modulation frequencies were used, but i t was also necessary to switch the transmitted polarization to prevent interaction between channels within the IF ampli-f i e r s . Isolations of 29 dB and 30 dB were achieved. Variations i n cross-polar signal levels observed during high wind veloci t ies were attributed to Inadequate antenna mount s t a b i l i t y . Thirteen rainstorms were observed with copolar attenuations up to 8 dB and rainrates i n excess of 15 mm/hr and on "no occasion [was] significant crosspolarization due to rain observed". However, on occasions when multipath was observed on other links i n the area, "considerable variation i n crosspolar signal was seen". Slow variations in crosspolar signal levels were also reported during apparently stable condi-tions with some indication that these effects were related to sunrise and sunset. Suggestions as to the cause of this effect included: moisture on radomes, multipath and variations in refractive index. Shimba and Morita conducted a crosspolarization measurement experiment on 2.9 km and 4.3 km paths in Japan [1.81]. A single, 19 GHz, horizontally polarized signal was transmitted and both received polarizations were moni-tored. The receiving system crosspolar discrimination was approximately 35 dB. It i s interesting to note that the data presented i n this paper shows two periods during rainstorms where the measured XPD increased by appoxi-mately 10 dB. This effect was not commented on by the authors. Morita, Hosoya and Akeyama [1.82] reported another 19 GHz dual-polarization experiment at a second location i n Japan over a 4 km path. In this experiment two different transmitted frequencies (19.3 and 19.4 GHz) and 20 switched frequency receivers were employed. This method resulted i n very high system isolations of 46 and 56 dB. The results for this location showed lower values of depolarization than for the similar experiment [1.81] des-cribed previously. Data presented i n this paper also shows values of XPD more than 10 dB higher than clear weather values. The authors conclude that "the correlation between rain attenuation and depolarization was not necessarily high" . In a later paper describing both of the previous experiments, Shimba, Morita and Akeyama [1.83] conclude that there was a high correlation between attenuation and XPD for the combined data from both experiments. The large scatter of XPD data points at low attenuations, including values higher than the clear weather i so la t ion , were thought to result from raindrop adherence to the radomes. No explanation as to why the wet radomes would cause this effect was offered. This paper also concludes that the copolar attenuation was about 30% greater than predicted. 1.8 Previous Single-Polarized Propagation Experiments This section includes a short review of single-polarization millimetre propagation experiments designed to measure rain attenuation. Most of the experiments surveyed are the higher frequency investigations with good meteorological instrumentation. Sander reported a millimetre wave attenuation investigation using v e r t i c a l l y polarized waves at 52, 90.8 and 150 GHz simultaneously [1.84]. The experiment was conducted over a 1008 m total length radar path using a corner reflector at the Massachusetts Institute of Technology. Raingauges 21 and Lammers type electrostatic disdrometers were used at three locations along the path. The disdrometers used i n the experiment had a 25 cm2 sampling area and six size classes. The author mentions that the instrument was subsequently redesigned to have a 100 cm2 sample area and sixteen categories, but no details or results from the improved instrument were included i n this reference. The results from this experiment show a wide scatter i n the attenuation vs rainrate plots . Sander concludes that "Mainly because of the imperfections of the meteorological equipment used, but also because of the inhomogeneity of ra in , only the s t a t i s t i c a l averages of our results ver ify the theoretical assumptions." Humpleman and Watson conducted a 60 GHz attenuation experiment on a 680 m v e r t i c a l l y polarized l ink at the University of Bradford, England [1.85]. Fast-response raingauges were located at each end of the path. An electrostatic disdrometer, developed by Sander [1.84], with a sampling time of 1 min. was used to measure the dropsize dis t r ibut ion. Synthetic storm models using the 700 mb or 850 mb pressure level effective wind veloci t ies from radiosonde information were used to calculate path rainrates from the raingauge and disdrometer data. The calculated path rainrate gave a dramatic improvement in the correlation with measured attenuation for individual storms compared to using either of the rainrates measured at the ends of the path. Disdrometer evidence is presented which indicates that the variations i n the attenuation-calculated path rainrate relation are due to dropsize distr ibutions . The attenuation calculated using the disdrometer data also shows much better agreement with the observed attenuation than the calculations using 22 the Laws and Parsons dis t r ibut ion. In certain periods of heavy r a i n , attenuations were measured which were considerably lower than predicted for the Laws and Parsons dropsize distr ibutions. An example is also included which shows a transistion from larger to smaller drops as a storm traverses the path. Keizer, Snieder and de Haan have reported a 94 GHz, v e r t i c a l l y polar-ized attenuation experiment over a 935 m path near The Hague, Netherlands [1.86], [1.87]. Path rainrate was measured with the raingauges spaced about 500 m apart. An electromechanical disdrometer with a 50 cm2 sample area and 83 second sample period was used to monitor the drop size dis t r ibut ion . Horizontal windspeed, wind direct ion, pressure and humidity were also recor-ded. The agreement between the measured attenuation and the attenuation calculated from the disdrometer data was considered to be "very s a t i s -factory." For low rainrates the measured attenuations were, in most cases, s l i g h t l y higher than calculated. This was attributed to an increase i n water vapour concentration of 1-2 g/m 3 resulting in a predicted 0.1 to 0.2 dB/km increase i n attenuation. Llewellyn Jones and Zavody conducted a 110 GHz attenuation experiment over a 2.65 km path i n the Windsor-Slough area, England [1.88], [1.89], [1.90]. No meteorological data appears to have been recorded i n this experiment. In this investigation, the objective was to record data for a one year period and determine l ink r e l i a b i l i t y s ta t is t ics for this location. Zavody and Harden have simultaneously measured ver t ica l attenuation at 36 GHz and 110 GHz on a 220 m path in Slough, England [1.59]. Four rapid response raingauges, spaced about 40 ia apart were used to measure the path 23 rainrate. An electromechanical disdrometer with a 50 cm2 sample area and 30 second sample period was also used. At 36 GHz, good agreement between measured attenuation and predicted attenuation for spheroidal drops was obtained. The 110 GHz results show a much larger scatter i n the attenuation vs. rainrate plots . The authors state that a "significant number of the measured values l i e outside the l imit ing curves for this range." An example i s also Included i n this paper showing a reduction in drop sizes as a storm travels across the path. During another event, drops were much smaller than predicted by Laws and Parsons. In this storm no drops larger than 2.1 mm diameter were observed in rainrates over 15 mm/hr. 1.9 Thesis Objectives The principal objective of this work is to develop an experimental system to study dual-polarized atmospheric propagation near 73 GHz. This investigation is part of an ongoing research program into millimetre-wave propagation which is being supported by the Communications Research Centre, Department of Communications, Ottawa. As an earl ier part of this research program, a preliminary study of single-polarization 74 GHz copolar attenuation was conducted over the same path at the University of Br i t ish Columbia [2.1]. During this investigation, attenuation and rainrate data were recorded for rainrates up to 10 mm/hr. The data were compared with the theory of Ryde and Ryde. Some of the equipment developed for this previous study was retained for this project, including: most of the data acquisition computer interface and software, parts of the raingauge network and the basic ref lec tor . 24 More s p e c i f i c a l l y , the f i r s t objective of t h i s work i s to record simultaneous meteorological and dual-polarized 73 GHz propagation data which are as accurate and as complete as p o s s i b l e . These propagation data include copolar attenuation and crosspolar d i s c r i m i n a t i o n for v e r t i c a l and h o r i z o n t a l p o l a r i z a t i o n s . The second objective i s to construct and test a model capable of describing the XPD response of the experimental system. The f i n a l o b j e c t i v e i s to attempt to i n t e r p r e t some of the propagation observations i n terms of various meteorological parameters i n c l u d i n g : h o r i z o n t a l and v e r t i c a l wind v e l o c i t i e s , dropsize d i s t r i b u t i o n and type of rainstorm. The achievement of these objectives required the design and construction of a dual-polarized millimetre-wave transmitter, receiver and antenna system and meteorological instrumentation f o r measuring r a i n and wind parameters. A dual-polarized millimetre wave l i n k was established over a path on the U n i v e r s i t y of B r i t i s h Columbia campus. D i f f e r e n t dual-polarized experimental methods were compared to determine which was most s u i t a b l e f o r t h i s i n v e s t i g a t i o n . After a basic method had been chosen, applicable 73 GHz transmitting and r e c e i v i n g antenna systems were designed and constructed with the maximum possible performance compatible with the budget a v a i l a b l e . Comprehensive t e s t i n g of components, subassemblies and the e n t i r e system was c a r r i e d out to characterize, as thoroughly as po s s i b l e , the millimetre-wave systems and thus reduce the uncertainty i n the data a r i s i n g from the nonideal behaviour of the experimental system. The previous sections I l l u s t r a t e d the importance of accurate, comprehensive meteorological instrumentation i n t h i s type of i n v e s t i g a t i o n . To measure path r a i n r a t e , a network of raingauges with high temporal and 25 s p a t i a l r e s o l u t i o n was i n s t a l l e d along the propagation path. A f t e r a study of measurement methods, an accurate instrument to measure raindrops s i z e s , r e f e r r e d to here as a disdrometer, was developed. An anemometer was included to measure three components of the wind v e l o c i t y vector. An experimental model was developed to separate, as f a r as possib l e , the e f f e c t s of the experimental system from the dual-polarized atmospheric propagation measurements. This model s i g n i f i c a n t l y improves the accuracy of the comparisons between the observed and t h e o r e t i c a l l y predicted crosspolar d i s c r i m i n a t i o n (XPD). The t h e o r e t i c a l c a l c u l a t i o n s used the well e s t a b l i s h e d , basic mathematical techniques and meteorological observations to predict the atmospheric propagation conditions. The model incorporates actual measurements made of the experimental system dual-polarized performance, and reduces the uncertainty i n the r e s u l t s due to the nonideal behaviour of the system components. The experiment was designed to ensure the millimetre wave propagation data was as accurate and complete as possible within the a v a i l a b l e time and budget. These data should be useful to improve the basic understanding of the e f f e c t s of the millimetre components and atmosphere ( e s p e c i a l l y during rain) on millimetre-wave systems employing atmospheric propagation. These r e s u l t s should also be h e l p f u l i n the v e r i f i c a t i o n of the basic t h e o r e t i c a l p r e d i c t i o n methods. In summary, th i s experiment should add to what i s already known about dual-polarized and mill i m e t r e wave systems and improve the accuracy of the predicted performances of a v a r i e t y of systems employing atmospheric propagation. 26 2. MILLIMETRE-WAVE EXPERIMENTAL SYSTEM The dual-polarized millimetre-wave system used for investigating atmospheric propagation characteristics at 73.5 GHz used switched-polarization sampling and basically consisted of a CW transmitter, radar path and two channel receiver. A radar path was chosen because of the operational advantages of locating the transmitter and receiver i n the same laboratory. Identical parabolic antennas with dual-polarity feeds were used for transmitting and receiving. Dual-polarization propagation measurements were made by periodical ly switching the transmitted signal between v e r t i c a l and horizontal polarizations. The two-channel receiver continually monitored both linear polarizations. This resulted in each received channel representing a time multiplexed sample of one copolar and one crosspolar signal l e v e l . The basic system is shown in F i g . 2.1. 2.1 Comparison of Dual-Polarization Measurement Methods The basic measurement methods which can be used to study linear dual-polarization propagation employ either a two-frequency dual-polarized trans-mitted signal or a switched-polarization transmitted s i g n a l . In the dual-frequency method, either two s l ight ly different frequencies - which are close enough to be considered as propagating identical ly - or two different modulation frequencies on a common carrier frequency are transmitted with perpendicular polarizations. In the receiving subsystem, frequency selective c i rcui ts in both polarization channels separate the frequencies corresponding to each or ig inal ly transmitted polarization. This method yields four TRANSMITTING SOURCE 27 POLARIZATION CONTROL DEMULTIPLEXING SIGNAL VERTICAL COPOLAR SIGNAL VERTICAL CROSSPOLAR SIGNAL HORIZONTAL COPOLAR SIGNAL HORIZONTAL CROSSPOLAR SIGNAL REFLECTOR VERTICAL TRANSMITTED POLARIZATION HORIZONTAL TRANSMITTED POLARIZATION -*. TIME F i g . 2.1. Basic millimetre-wave experimental system. 28 simultaneous signals each corresponding to one element of the dual-p o l a r i z a t i o n transmission matrix. In the switched-polarization method, the transmitted s i g n a l i s sequentially switched between v e r t i c a l and h o r i z o n t a l p o l a r i z a t i o n and a two-channel receiver continually monitors both received p o l a r i z a t i o n s . The switching rate i s designed to be higher than the temporal r e s o l u t i o n of the meteorological measuring equipment. With t h i s system, the received signals must be demultiplexed to determine the four transmission matrix elements. The switched p o l a r i z a t i o n scheme was chosen f o r t h i s experiment because of i t s implementation advantages. The dual-frequency schemes require e i t h e r two separate transmitting s i g n a l sources, or h i g h - l e v e l modulation c i r c u i t s . If the two-source method i s used, e i t h e r the sources have to be phase-locked to each other or the receiver must include two phase-locked l o c a l o s c i l l a t o r s , one f o r each transmitting source. If a s i n g l e source with high l e v e l modulators i s used, two frequency s e l e c t i v e c i r c u i t s f o r each received channel are needed. It i s very d i f f i c u l t to r e a l i z e frequency s e l e c t i v e c i r c u i t s and a m p l i f i e r s with the high i s o l a t i o n and dynamic range required f o r t h i s type of experiment. Because complex f i l t e r s are not f e a s i b l e at m i l l i m e t r e frequencies, f i l t e r i n g would have to be done at an intermediate frequency (IF) or baseband. F i l t e r i n g at IF i s possible but so p h i s t i c a t e d f i l t e r s must be employed to achieve the necessary s i g n a l i s o l a t i o n . Baseband f i l t e r s are easier to b u i l d but the large dynamic range of the s i g n a l s puts t i g h t constraints on the e n t i r e receiving system l i n e a r i t y , ( n o n l i n e a r i t i e s before the baseband f i l t e r s would produce intermodulation d i s t o r t i o n which would 29 reduce the i s o l a t i o n between channels and degrade the system accuracy). Dual-frequency schemes also require four s i g n a l l e v e l measuring subsystems to f i l t e r , average, detect and d i g i t i z e the received amplitudes. The switched p o l a r i z a t i o n method requires a p o l a r i z a t i o n switching c i r c u i t but uses only a si n g l e transmitting source and one l o c a l o s c i l l a t o r . In t h i s case, only two received s i g n a l l e v e l measuring subsystems are necessary. The advantages of reduced complexity and cost made the switched p o l a r i z a t i o n method f a r more des i r a b l e i n t h i s experiment. 2.2 Transmitting System The transmitting system block diagram i s shown i n F i g . 2 . 2 . The system consists of a kl y s t r o n o s c i l l a t o r , k l y s t r o n power supply, i s o l a t o r s , frequency reference coupler, power l e v e l monitor, c a l i b r a t e d attenuator, f e e d l i n e , p r e s s u r i z a t i o n system and p o l a r i z a t i o n switch. 2.2 .1 Klystron and Supply The transmitting s i g n a l i s generated by a Varian model 2101B r e f l e x k l y s t r o n o s c i l l a t o r . The k l y s t r o n power supply c i r c u i t s , cooling system and load i s o l a t o r were designed to minimize i n c i d e n t a l frequency modulation and transients i n the tube output. This i s important to ensure that the system s e n s i t i v i t y Is not impaired and that the r e l i a b i l i t y of the phase lock system i s not reduced. The k l y s t r o n i s extremely susceptible to frequency modulation of i t s output by induced voltages on i t s power leads, stray magnetic f i e l d s or changes i n load impedance. For example, the modulation s e n s i t i v i t y of the 0 KLYSTRON POWER SUPPLY FREQUENCY REFERENCE X TO RECEIVING I p SYSTEM 1 t PRESSURATION POWER METER TO DATA AOUISITION SYSTEM CALIBRATED ATTENUATOR © > ** U/P—9ft WR-28 FEEDLINE AND WR-I5/WR-28 ADAPTERS POLARIZATION SWITCH ISOLATORS TO ANTENNA ORTHOMODE TRANSDUCER F i g . 2.2. Transmitting system block diagram. o 31 tube r e f l e c t o r voltage i s approximately 3 MHz/V. Incidental power l i n e frequency modulation on the klystron output w i l l reduce the received s i g n a l -to-noise l e v e l because the 60 Hz modulation sidebands w i l l be rejected by the 30 Hz bandwidth of the receiver second IF f i l t e r s (see Section 2.3.2). Klystron frequency purity and s t a b i l i t y also affect the r e l i a b i l i t y of the receiver phase lock c i r c u i t s (see Section 2.3.1). If the receiver loses phase lock, reacquisition must be done manually. Because the experiment i s often operated unattended, loss of phase lock can result i n long periods of l o s t data. Loss of lock occurs when the change i n the klystron frequency exceeds the receiver phase locked loop hold-in range or tracking rate. This usually occurs on a transient condition caused by a power l i n e transient, thermal transient or "micro-arc" within the klystron tube. Micro-arcs unavoidably occur within tubes of this type because the extremely small c a v i t i e s required for millimetre frequencies result i n high f i e l d potentials between tube elements. I f frequency modulation i s also present on the klystron s i g n a l , the receiver's available lock range and a b i l i t y to track transient frequency changes i s reduced because the phase locked loop must also track the periodic frequency modulation. The klystron power supply c i r c u i t i s shown i n F i g . 2.3. The Weinschel Z815C klystron supply was chosen because i t has a heavily f i l t e r e d dc filament supply. Low r i p p l e on klystron filament supplies i s necessary to prevent d i r e c t 60 Hz modulation v i a the tube cathode. A transient suppression network i s included between the supply and klystron to l i m i t currents during periods of micro-arcing. This c i r c u i t w i l l reduce the transient frequency excursion and help prevent in t e r n a l p i t t i n g of the tube REF 1 CATH WEINSCHEL 7 815 C KLYSTRON FILI+) POWER SUPPLY FILH BEAM WHITE ARC SUPPRESSION NETWORK IK 2W •A/VvV— -1 lu l _ _ . _ l Voltages: Reflector 1 Beam Filament 640 V 2500 V 6.3 V VRE 2101 B F i g . 2.3. Klystron power supply c i r c u i t , 33 elements during arcing. If the tube elements become pitted i t w i l l be more susceptible to arcing because of the higher f i e l d gradients around the discontinuities in the damaged area. With the voltages shown i n F i g . 2.3 the measured klystron output was 470 mW. The klystron is mounted on a large aluminum heat sink (Varian model VAE-2000C/2) which is cooled by a 100 cfm blower. The blower is mounted approximately one metre from the klystron and the a i r flow is directed to the tube via a section of 10 cm diameter f lex ible plast ic tubing. This was necessary to prevent modulation of the klystron output by induced 60 Hz currents and f ie lds from the blower motor. An isolator is included after the klystron because i t was observed that even with the isolat ion provided by the feedline loss and with a measured feedline VSWR of less than 1.2:1, the klystron frequency shifted approximately 200 kHz when the polarization was switched. This was due to frequency pull ing as a result of small changes in the load impedance presented to the klystron in the different polarization switch states. This step change in frequency occasionally caused the receiver phase-lock system to lose lock. With the isolator i n the c i r c u i t no frequency pull ing could be measured. 2.2.2 Reference Signals and Calibrated Attenuator The power level and operating frequency of the klystron were continually recorded to ascertain that these quantities did not d r i f t during data acquisi t ion. The frequency reference signal i s derived from a 20 dB direct ional coupler and is used to phase lock the receiving system to the 34 transmitted s ignal . Frequency monitoring of the klystron i s accomplished Indirectly by recording the receiver local osci l la tor frequency, a multiple of which was phase locked to the klystron frequency. This i s explained in detai l i n Section 2.3.4. The level reference signal was sampled through another 20 dB coupler and measured by a Hughes model 44894H temperature compensated thermistor mount connected to an HP-432A power meter. The output signal from the power meter is connected to one of the analog Inputs of the data acquisition system. A calibrated rotary vane attenuator i s permanently mounted i n the path of the transmitting signal to f a c i l i t a t e checks of receiver l i n e a r i t y and noise l e v e l . 2.2.3 Feedline and Pressurization A waveguide feedline is used to carry the klystron signal from the laboratory up one floor to the roof where the polarization switch was loca-ted. The polarization switch was mounted adjacent to the transmitting antenna to avoid having to run two feedlines to the transmitting antenna. WR-28 waveguide was used for the feedline because the theoretical and meas-ured attenuation of this oversize waveguide was lower than for the WR-15 waveguide used elsewhere in this experiment [2.1], [2.2], [2.3]. The meas-ured attenuation of the 6.5 meter WR-28 feedline and WR-15/WR-28 adapters at 73.5 GHz was 9.5 dB, approximately 1.5 dB higher than specified in [2.1]. This discrepancy is l i k e l y due to increased corrosion on the inter ior wave-guide walls . The frequency response of the oversize feedline was measured to be better than ± 0 . 5 dB over a 400 MHz band centered at 73.5 GHz. 35 The feedline was l i g h t l y pressurized to prevent an accumulation of condensation. Dry a i r was connected to the waveguide through a directional coupler instal led so that the incident wave was coupled to the internal coupler termination, as shown i n F i g . 2.2. 2.2.4 Polarization Switching 2.2.4.1 Comparison of Polarization Switching Methods Accurate measurement of crosspolarization propagation parameters in this frequency range requires very high polarization isolat ion and measuring system s e n s i t i v i t y . The polarization switch isolat ion and insertion loss direc t ly degrade total system isolat ion and s e n s i t i v i t y . Switching methods were evaluated by trading-off switch isolat ion and insertion loss against cost and delivery time. Three basic switching schemes were compared: Faraday rotation, waveguide junction with absorptive single-pole single-throw (SPST) switches and single pole double-throw (SPDT) switches. These methods are shown schematically in F i g . 2.4. Faraday rotation in a section of cy l indr ica l waveguide provides the most direct method of polarization switching. Linear polarization rotation is controlled by varying the dc current through a c o i l which changes the magnetization of the ferr i te element in the waveguide. A device of this type i s the TRG-V145. Unfortunately, this type of polarization switch is not applicable to this experiment because i t has only 20 dB crosspolarization i s o l a t i o n . Additional isolat ion cannot be obtained by cascading because each section would result i n a further ninety degree polarization rotation. 36 RECTANGULAR TO CIRCULAR WAVEGUIDE ADAPTER FARADAY ROTATION POLARIZATION SWITCH (a) Faraday r o t a t i o n (b) Junction with absorptive SPST switches (c) DPDT switch F i g . 2.4. P o l a r i z a t i o n swiching methods. 37 The other two basic methods, shown in F i g . 2.4(b) and 2.4(c), u t i l i z e an orthomode transducer. An orthomode transducer is a passive reciprocal waveguide junction with one circular and two rectangular waveguide ports. A signal with arbitrary polarization entering the circular waveguide w i l l be resolved into two orthogonal polarization components which w i l l leave the junction through the rectangular ports. Because the junction is rec iprocal , i f signals are applied to the rectangular ports they w i l l leave the junction v i a the circular port but with orthogonal linear polarizations. Standard orthomode transducers i n this frequency range w i l l have losses below 1 dB and isolations of 30-35 dB. Both of these schemes achieve polarization switching by sequentially applying the transmitting signal to either the ver t i ca l or horizontal port on the orthomode transducer. SPST switches are used in the method shown i n F i g . 2.4(b) because, in this frequency range, these switches are much easier to implement than SPDT switches. When using SPST switches the transmitting signal i s divided i n a waveguide spl i t ter (either a "T" junction or a 3 dB hybrid) resulting in only half the available signal being applied to the antenna. The switches must be absorptive to avoid reflections at one port of the waveguide junction when the switch is in the off state. PIN diode switches with isolators and Faraday rotation attenuators were considered for the absorptive SPST switches. Isolators are required with the diode switches because they are unmatched in the off state. A typical PIN diode switch is the Hughes 47974VA-1000. This single diode switch has a 2.5 dB insertion loss and only 15 dB i s o l a t i o n . Cascading three similar switch sections would provide adequate isolations but would also 38 yie ld an unacceptably high insertion l o s s . Faraday attenuators achieve on-off attenuation by rotation of the waveguide polarization either p a r a l l e l , or perpendicular to, a resist ive attenator card. A device of this type, the TRG-V120 has a 10 ys switching time, 1.4 dB insertion loss and 40 dB i s o l a t i o n . The only available type of SPDT switch i n this frequency range is an electromechanical waveguide switch. These switches use a solenoid to physically connect an input waveguide port to either of two output waveguide ports. Several manufacturers supply switches of this type. The Systron-Donner DBB-614-LE2 SPDT waveguide switch is specified at 50 dB isolat ion and 0.7 dB insertion l o s s . The most suitable schemes for polarization switching i n this experiment used either the Faraday rotation attenuators and waveguide s p l i t t e r or the SPDT electromechanical waveguide switch. Insertion loss i n the f i r s t method would be at least 4.4 dB compared to only 0.7 dB for the SPDT switch. The isolat ion of the Faraday attenuators was also only 40 dB compared to 50 dB for the second method. A f i n i t e lifespan resulting from mechanical wear appeared to be the only disadvantage of the electromechanical switch. The SPDT electromechanical waveguide switch was chosen for this experiment because of i t s superior specifications, considerably lower cost and shorter quoted delivery time. 2.2.4.2 Polarization Switch Specifications and Testing A summary of the e l e c t r i c a l specifications of the Systron-Donner model DBB-614-LE2 waveguide switch used in this experiment are given i n Table 2.1. 39 TABLE 2.1 DBB-614-LE2 Electromechanical DPST Waveguide Switch Specifications. Insertion loss 0.7 dB VSWR 1.15 Isolation 50 dB min Switching time 30 ms Operating lifespan 100 000 cycles min. 250 000 cycles typ. Solenoid power 28 VDC @ 50 W Measurements were made on the waveguide switch at 73.5 GHz to ver i fy i t s specif icat ions . The measured Insertion loss of the switch was below 0.7 dB in either state. Isolation between output ports was measured to be between 75 and 80 dB. 2.2.4.3 Polarization Switch Subsystem The waveguide switch, integral power supply, and switching c i r c u i t were assembled in a waterproof steel enclosure and mounted adjacent to the transmitting antenna. The schematic diagram of the polarization switch subsystem i s shown i n F i g . 2.5. A photograph showing the internal layout and construction is included as F i g . 2.6. Referring to F i g . 2.5, the purpose of the power transistor switch is to reduce the current which must be remotely switched to control the switch solenoid. A non-resetable electromechanical counter is included to record the number of switching cycles for the purpose of monitoring switch condition and l i f e t i m e . The switch assembly is controlled by a control unit located near the data acquisition electronics. The schematic of the control unit is shown in 120 v AC 0UT0OOH BULKHEAD CONTROL . SIGNAL >-INPUT (FROM CONTROL UNIT) HAMMOND HPFS 2B 020 POWER SUPPLY 2 8 v © 2.0 A ELECTRO-MECHANICAL COUNTER 6 v COIL -w-- 2N3 OUTPUTS TO TRANSMITTING ANTENNA ORTHOMODE TRANSDUCER. INPUT FROM FEEDLINE POLARIZATION SWITCH STATUS ITO IF ATTENUATORS IN FRONT END) COAXIAL CONNECTORS ARE TYPE-N BULKHEAD JACKS SEALED ENCLOSURE F i g . 2.5. P o l a r i z a t i o n switch subsystem schematic. 4 1 Fig. 2.6. Polarization switch subsystem photograph. 42 F i g . 2.7. The control unit has the provision for automatic, manual and remote switching. Automatic switching times derived from the 60 Hz l i n e frequency are front panel switching selectable for periods of 1 s, 2 s, 5 s, 10 s, 15 s, 20 s, 30 s, 1 rain. 1 min. and 4 min. An LED is provided to give a visual indication of the switch status in any mode. A status signal is supplied for input to the data acquisition system so the status of the polarization switch can be recorded and subsequently used as a data demultiplexing s i g n a l . Isolators are instal led between the outputs of the polarization switch and the inputs to the transmitting antenna. These are necessary because the waveguide switch presents a short c i r c u i t to the output port which is not connected to the input port. Without the isolator , a reactive immittance would be presented to the unused port on the transmitting antenna orthomode transducer. This was found to seriously degrade the polarization provided by the orthomode transducer. I n i t i a l measurements made without the Isolators indicated that the total system polarization isolat ion was extremely frequency sensitive and was degraded by as much as 5 to 15 dB, depending on the angle of the reflect ion coefficient presented to the orthomode transducers. This effect is discussed further i n Sections 2.5 and 5.5.2. 2.2.5 Signal Levels in the Transmitting System The measured signal levels at certain points throughout the transmitting system are given i n Table 2.2. The reference points are identif ied by letters A-H on the transmitting system block diagram, F i g . 2.2. F i g . 2.7. P o l a r i z a t i o n switch c o n t r o l u n i t schematic. TABLE 2.2 Transmitting System Signal Levels LOCATION Klystr o n Output Af t e r Klystron I s o l a t o r Input to Feedline Input to P o l a r i z a t i o n Switch Horizontal Output of P o l a r i z a t i o n Switch V e r t i c a l Output of P o l a r i z a t i o n Switch Input to Horizontal Ant. Port Input to V e r t i c a l Ant. Port From Table 2.2 i t should be noted that the s i g n a l transmitted with h o r i z o n t a l p o l a r i z a t i o n i s 2 dB higher than f o r v e r t i c a l p o l a r i z a t i o n . This i s due to the d i f f e r e n c e i n lengths and number of bends of the waveguide needed to connect the waveguide switch and antenna po r t s . This d i f f e r e n c e was corrected f o r during data a n a l y s i s . The s i g n a l loss from the k l y s t r o n to the antenna ports i s approximately 18 dB and 20 dB f o r h o r i z o n t a l and v e r t i a l transmitted p o l a r i z a t i o n s , r e s p e c t i v e l y . This i s mainly due to unavoidable component i n s e r t i o n l o s s , f e e d - l i n e loss and the t y p i c a l 2 dB/m i n s e r t i o n l o s s of s t r a i g h t WR-15 waveguide. Up to 8 dB could be gained i f the k l y s t r o n and REF F i g . 2.2 r o u t (dBm) A B C D 26.7 25.3 23.0 13.5 10.1 8.4 8.5 H 6.5 45 power supply were mounted on the roof In proximity to the transmitting antenna. This was not done because of the d i f f i c u l t i e s of providing adequate shelter for these components. 2.3 Receiving System The basic components of the two-channel dual-conversion receiving system are the millimetre-wave front-end, phase locked receiver and d i g i t a l signal l e v e l measurement uni t s . A block diagram i s shown i n F i g . 2.8. Down-conversion of the 73.5 GHz signal to the f i r s t IF frequency i s accomplished i n the millimetre-wave front-end. To reduce signal l o s s , the front-end i s mounted adjacent to the receiving antenna. The receiver generates the fundamental phase-locked l o c a l o s c i l l a t o r signal and l i n e a r l y converts the f i r s t IF signal to the second IF frequency. Local o s c i l l a t o r signals and f i r s t IF signals are carried between each channel of the front end and receiver on a common coaxial cable. The second IF signal output from the receiver i s processed and converted to a d i g i t a l value by the d i g i t a l amplitude measurement uni t s . This d i g i t a l , data i s then interfaced to the data acqu i s i t i o n system. 2.3.1 Receiver The receiver used i n this experiment i s a S c i e n t i f i c Atlanta model 1751 which was available i n the E l e c t r i c a l Engineering Department. This receiver Is not i d e a l l y suited for the millimetre frequency range because of i t s low l o c a l o s c i l l a t o r and IF frequencies. However, these disadvantages FROM RECEIVING ANTENNA ORTHOMODE TRANSDUCER MM WAVE PI VERTICAL | INPUT I MM WAVE HORIZONTAL INPUT DUAL CHANNEL FRONT ENO DUAL CHANNEL RECEIVER DIGITAL AMPLITUDE DISPLAY UNIT VERTICAL SIGNAL DIGITAL DATA SECOND IF SIGNALS , TO DATA > AOUISITION SYSTEM DIGITAL AMPLITUDE DISPLAY UNIT HORIZONTAL SIGNAL ' DIGITAL DATA Fig. 2.8. Receiving system block diagram. 4> 47 were not serious enough to j u s t i f y the purchase or construction of a l t e r n a t i v e equipment. F i g . 2.9 i s a s i m p l i f i e d block diagram of the model 1751 receiver adapted from the receiver manual. The diagram i s included to help e x p l a i n the aspects of the receiver operation relevant to the front-end design and system operation. The receiver was designed with a very small e f f e c t i v e predetection bandwidth i n order to improve s e n s i t i v i t y . For t h i s reason the l o c a l o s c i l l a t o r has to be phase locked to the transmitted s i g n a l to c o r r e c t f o r frequency d r i f t i n both the l o c a l o s c i l l a t o r and transmitted s i g n a l . The millimetre-wave reference s i g n a l i s a sample of the k l y s t r o n output as described i n Section 2.2.2. This 73 GHz s i g n a l i s the RF input to the automatic phase co n t r o l (APC) channel external mixer. The f i r s t l o c a l o s c i l l a t o r i s a 2-4 GHz backward wave o s c i l l a t o r (BWO) which supplies an LO s i g n a l to the APC harmonic mixer and external two channel-front end. The phase of the IF s i g n a l from the APC channel i s compared to the 45 MHz reference o s c i l l a t o r to generate the error s i g n a l applied to the BWO. By t h i s method the f i r s t IF i n both s i g n a l channels i s maintained exactly at the frequency of the 45 MHz reference o s c i l l a t o r . To acquire phase lock, the receiver LO must be manually tuned to within a few k i l o h e r t z of the locked frequency. This lack of automatic search and a c q u i s i t i o n means that i f the receiver loses lock due to a transient frequency change or loss of power, no data w i l l be recorded u n t i l the receiver i s manually relocked. To help reduce data loss due to t h i s and FIRST IF AMPLIFIERS SECOND IF AMPLIFIERS F i g . 2.9. Receiver block diagram. oo 49 other r e s e t t a b l e e l e c t r o n i c f a i l u r e s d u r i n g unattended o p e r a t i o n , an a larm system i s connected to the te lephone l i n e s . A f t e r a m p l i f i c a t i o n i n the 45 MHz f i r s t IF a m p l i f i e r , the s i g n a l i s conver ted by the i n t e r n a l second mixer and c r y s t a l - c o n t r o l l e d second LO to the 1 kHz second IF f requency . A f t e r f u r t h e r a m p l i f i c a t i o n In the second IF a m p l i f e r , the 1 kHz s i g n a l i s a p p l i e d to an i n t e r n a l ana log ampl i tude meter ing system and r e c e i v e r output j a c k s . The 1 kHz second IF output i s the i n p u t to the d i g i t a l ampl i tude measuring u n i t s . Th is r e c e i v e r was designed to be used w i t h harmonic mixers s i m i l a r to the S c i e n t i f i c A t l a n t a model 13 s e r i e s . These mixers have a waveguide RF i n p u t po r t and a s i n g l e c o a x i a l connec t ion to the mixer d iode to supp ly the LO s i g n a l and remove the IF s i g n a l . Th is s i n g l e c o a x i a l connec t ion to the mixer reduces the c o a x i a l cab le requirements and i s a d e f i n i t e advantage when the mixers are l o c a t e d some d i s t a n c e from the r e c e i v e r . 2 . 3 . 1 . 1 R e c e i v e r S p e c i f i c a t i o n s A summary of the r e l e v a n t s p e c i f i c a t i o n s of the S c i e n t i f i c A t l a n t a model 1751 r e c e i v e r are g i v e n i n Table 2 . 3 . 50 TABLE 2.3 Sc ient i f i c Atlanta Model 1751 Receiver Specifications Local osc i l la tor frequency 2 - 4 GHz Local osc i l la tor power output 16 dBm Firs t IF frequency 45 MHz Second IF frequency 1 kHz Dynamic range* 60 dB Linearity* ±0 .25 dB for 60 dB 45 MHz IF signal range greater than -110 dBm. * With Sc ient i f i c Atlanta Model 13 series mixers. No specifications are given for the receiver IF bandwidths. The f i r s t IF stages have a measured 3 dB bandwidth of approximately 7 MHz and therefore do not reduce the predetection bandwidth of the receiver . When used alone, the receiver effective predetection bandwidth is essentially limited by the 1 kHz second IF frequency. However, when the receiver i s used i n conjunction with i t s companion d i g i t a l amplitude measurement uni ts , second IF f i l t e r s in these units determine the overall receiver predetection bandwidth. 2.3.2 Digi ta l Amplitude Measurement Units The Scient i f ic Atlanta model 1832 d i g i t a l amplitude measurement units amplify, f i l t e r , detect, average and d i g i t i z e the second IF signals from the receiver. Active f i l t e r s in this unit l imit the entire receiver predetection bandwidth to 30 Hz. For this experiment the signal averaging time was 51 selected to be 1 second. The amplitude of the signal is converted to a d i g i t a l number with 0.1 dB resolution and ± 0.1 dB accuracy. This d i g i t a l data is interfaced to the data acquisition system in binary coded decimal (BCD) format, 2.3.3 Two-Channel Front-End 2.3.3.1 Basic Mixer Considerations Measurement of dual polarization propagation phenomena near 73 GHz required a more sophisticated front-end than could be supplied by the receiver manufacturer. Single polarization measurements at this frequency over the same radar path with larger antennas and using the Scient i f ic Atlanta model 13A-50 mixers yielded a fade margin which was reported as 40 dB [2.1]. This was considered as being the indicated signal level above the indicated noise l e v e l . Due to a reduction in receiver l inear i ty at low signal levels the useful measurement range may have been closer to 35 dB for that system. For this dual-polarization propagation experiment, economic constraints dictated the use of smaller diameter antennas. The clear weather crosspolar signal level was also estimated to be about 40 dB below the copolar signal level using these antennas. For these reasons considerably more front-end sensi t iv i ty was required to provide an acceptable dual-polarization measurement range. Sc ient i f i c Atlanta had produced a superior V-band mixer called the model 17-50-45. This mixer had a diode frequency t r i p l e r to increase the LO frequency and hence reduce mixer conversion loss . Early attempts to use this mixer ware not successful because of inadequate receiver L0 output [2.1). 52 This mixer was modified to incorporate a loca l osci l la tor power amplif ier . The modified model 17-50-45 mixer has a 7-8 dB increase i n sensi t iv i ty over the model 13A-50. Modifications and test results of this mixer are documented i n [2.4]. Preliminary dual-polarization measurements with this mixer showed that i t s sensi t iv i ty was not adequate. For these reasons the decision was made to design a completely new two-channel front-end. The front-end c i rcui t configuration evolved from design constraints imposed by cost and the available receiver. In the frequency range of interest , low noise signal amplification requires prohibit ively expensive maser or parametric amplifiers . For this reason the incoming RF signal from the antenna is direct ly converted down to the 45 MHz IF frequency. The f e a s i b i l i t y of employing fundamental mixers i n the front-end was investigated because conversion losses of under 10 dB are achievable. Three possible schemes for generating the fundamental local osc i l la tor were considered: - a free running klystron LO and t r i p l e conversion receiving system. This method would use a free running klystron to downconvert the incoming signal to an IF in the low GHz range. After amplification, this IF signal would be mixed with the receiver phase-locked LO to produce a second IF signal compatible with the receiver. (With this scheme the receiver phase locked loop would have to track frequency changes i n both klystrons, resulting i n lower lock r e l i a b i l i t y . ) - a klystron LO phase locked to a harmonic of the receiver BWO. - a millimetre LO generated by frequency multiplication of the receiver BWO. 53 Unfortunately none of these a l t e r n a t i v e s came close to being possible within the budgetary constraints of t h i s p r o j e c t . As a result, the two-channel front-end was designed around harmonic mixers. 2.3.3.2 Front-End C i r c u i t Description The two-channel 73.5 GHz receiver front-end was designed to be as s e n s i t i v e as economically p o s s i b l e , provide i d e n t i c a l s i g n a l t r a n s f e r c h a r a c t e r i s t i c s on each channel, have high channel-to-channel i s o l a t i o n and operate i n conjunction with the S c i e n t i f i c Atlanta 1751 r e c e i v e r . -Each of the i d e n t i c a l front-end channels consists b a s i c a l l y of a harmonic mixer, i s o l a t o r , mixer bias c i r c u i t , l o c a l o s c i l l a t o r chain, IF preamplifier, IF d i p l e x e r and d i g i t a l l y programmable IF attenuator. A block diagram of the complete two-channel front-end i s shown In F i g . 2.10. A more d e t a i l e d drawing of one channel which shows part numbers, port impedances and s i g n a l l e v e l s Is shown i n F i g . 2.11. A l o c a l o s c i l l a t o r a m p l i f i e r and frequency t r i p l e r i s incorporated to reduce the mixing harmonic-number and hence conversion l o s s . An IF diplexer i n t e r f a c e s the IF and LO signals to t h e i r common co a x i a l cable. To improve s e n s i t i v i t y , a low-noise IF preamplifier i s included. The mixer bias current required for optimum mixer performance i s supplied by the mixer bias c i r c u i t s . The e n t i r e two-channel front-end and power supply i s enclosed i n a waterproof housing and i s mounted i n close proximity to the r e c e i v i n g antenna to minimize the RF s i g n a l attenuation. A photograph of the IF/LO d i p l e x e r s , LO a m p l i f i e r s and frequency m u l t i p l i e r s i s shown i n F i g . 2.12. A photograph of the two-channel nxi poor LF. INJECTION AND MATCHINO 5.3 GHZ BANDPASS FILTER 2-4 OHZ POWER AMPLIFIER MULTIPLIER DIGITALLY PROGRAMMABLE I.F. ATTENUATOR «TTCtlU»TOl CONTROL >4-< 45 MHZ IF. PREAMPLIFIER k«-L 0 . F i MIXER I RX2 PORT k<—>H IF. INJECTION A NO MATCHING 1.3 OHZ BANDPASS FILTER 2-4 GHZ POWER AMPLIFIER XJ MULTIPLIER ISOLATOR nil DIGITALLY PROGRAMMABLE I.F. ATTENUATOR I.F. PREAMPLIFIER « « M >f-«-MONITOR 117 VAC POWER SUPPLY LO _ MIXER 2*^ 1 J 1 ISOLATOR r t MIXER I COAXIAL CONNECTORS ARE TVPE-tN 8ULKHEA0 JACKS MIXER 2 IZO VAC OUTDOOR BULKHEAD SEALED ENCLOSURE Fig; 2.10. Complete front-end diagram. IF INJECTION AND MATCHING NETWORK (MICROSTRIP ON TEFLON) 50 n 3.5 GHz 50 A 4 5 MHz PORT 3.5 GHz BANDPASS FILTER 3 % BANDWIDTH (MICROSTRIP ON TEFLON) AVANTEK APT-4013 THIN FILM 2 - 4 GHz POWER AMPLIFIER AIG CUSTOM VARACTOR X3 FREQUENCY MULTIPLIER ^ 50 a <<? 10.5 GHz 10 MW (a> 10.5 GHz PROGRAMMABLE IF ATTENUATOR TEXSCAN PA-51 28vDC YIF ANZAC AM 107 LOW NOISE 1-100 MHz AMPLIFIER so a f5> 45 MHz TRQ 922 v HARMONIC MIXER BIAS JTL u n ANT. PORT UG 385/U FLANGE ATTENUATOR POWER SUPPLY ALL CONNECTORS SMA T ATTENUATOR CONTROL SIGNAL MIXER BIAS MONITOR /IN. SIGNAL ' BIAS CONTROL CIRCUIT f 1 F i g . 2 . 1 1 . Detailed block diagram of one channel. 56 F i g . 2.12. IF/LO dip l e x e r s , LO amplifiers and frequency m u l t i p l i e r s . 57 receiver front end with the IF preamplifier and attenuator assembly removed i s shown i n F i g . 2.13. The complete front end i s shown i n F i g . 2.14. 2.3.3.3 Harmonic Mixers The most important components i n the front-end are the harmonic mixers and accordingly these were selected f i r s t . The required characteristics of the mixers were: V-band RF signal range, 45 MHz IF frequency and harmonic mixing. The two mixers which were seriously considered for this system were the TRG 922-V and the Hughes 47434H-1000. These two mixers have very similar conversion loss specificat ions. The Hughes mixer, however, requires s ignif icant ly higher LO power for lowest conversion loss . The Hughes mixer incorporates a s i l i c o n Schottky barrier diode which is not normally-replaceable i n the f i e l d . The TRG mixer uses a gallium-arsenide diode mounted in a field-replaceable Sharpless wafer mount. Both mixers have satisfactory IF frequency ranges. The TRG mixer was chosen because of i t s lower LO power requirement, f i e l d replaceable diode and because the TRG mixer was s l i g h t l y less expensive. 2.3.3.4 Mixer Specifications The specifications of the TRG 922-V harmonic mixers relevant to the front-end c i r c u i t description and receiving system operation are given i n Table 2.4. F i g . 2.13. Front-end without IF preamplifiers and attenuators. 59 F i g . 2.14. Complete front-end. 60 TABLE 2.4 TRG-922-V Harmonic Mixer Specifications; Conversion loss Conversion loss Harmonic number 21 39-42 dB 10 28 dB 9 26 dB 8 24 dB 7 22-23 dB 6 18 dB LO frequency 8.2-12.4 GHz LO power 10 mw Typ. LO port Impedance 50 fi LO/IF Isolation 25 dB Min. IF Bandwidth 10 MHz to 500 MHz IF Port Impedance 50 fi RF VSWR 2:1 Typ. Bias Requirements -0.7 V @ 2 mA Typ. Max. diode current 4 mA 2.3.3.5 IF/LO Diplexer IF/LO diplexers are required to interface the Sc ient i f i c Atlanta model 1750 receiver to the TRG 922V harmonic mixers. The receiver was intended to be used with mixers employing a single coaxial connection to the mixing diode to provide the LO injection and to remove the IF s i g n a l . The TRG 922V mixers are constructed i n the more common configuration employing separate LO and IF ports. The design of the IF/LO diplexer c i r c u i t i s documented here because 61 t h i s type of r e c e i v i n g system and mixer configuration i s very useful and t h i s type of diplexer has low i n s e r t i o n l o s s , i s e a s i l y r e a l i z a b l e i n m i c r o s t r i p and has not, to our knowledge, been described elsewhere. The design objective f o r the diplexer was a well-matched, low-loss connection between corresponding ports at the IF and LO frequencies. I t i s important to have a well-matched, low-loss connection between the IF preamplifier output port and the receiver LO/IF cable because a mismatch or loss associated with t h i s connection w i l l reduce the re c e i v i n g system s e n s i t i v i t y . A well-matched connection at the LO frequency i s also required to ensure r e l i a b l e operation of the receiver l o c a l o s c i l l a t o r source and to minimize LO loss through the coa x i a l connection from the r e c e i v e r . The l o c a l o s c i l l a t o r i n the receiver i s operated at approximately the V-band s i g n a l frequency divided by twenty-one, which, i n t h i s case, i s 3.5 GHz. Other components of the system do not allow operation except i n a narrow two or three percent bandwidth around the center frequency of 73.5 GHz. Therefore, the IF/LO diplexer c i r c u i t f o r t h i s system i s required to operate only over a s i m i l a r percentage bandwidth. Referring to F i g . 2.11, the s p e c i f i c requirements of the IF/LO diplexer are: (a) to provide a matched connection with minimum loss from the receiver port to the LO m u l t i p l i e r chain input over a bandwidth of a few percent centered at 3.5 GHz. and (b) to provide a minimum-loss, matched connection from the IF si g n a l port to the receiver port at 45 MHz. 62 The requirement f o r minimum-loss connections precludes the p o s s i b i l i t y of a d i r e c t i o n a l coupler type network f o r LO i n j e c t i o n or IF removal, as i s often employed i n IF/LO d i p l e x e r s . Fortunately, since the frequency d i f f e r e n c e between the LO and IF i s large and because narrowband operation i s acceptable, a simple microstrip transmission l i n e c i r c u i t could be designed to meet the network requirements. This c i r c u i t was designed h e u r i s t i c a l l y and i t s operation v e r i f i e d a n a l y t i c a l l y . The IF/LO diplexer consists of an IF i n j e c t i o n and matching c i r c u i t and a l o c a l o s c i l l a t o r bandpass f i l t e r both r e a l i z e d i n m i c r o s t r i p . The connection of these components i s shown i n F i g . 2.11. The IF i n j e c t i o n and matching c i r c u i t was designed to provide a low-loss, matched connection f o r the IF s i g n a l to the receiver without s i g n i f i c a n t l o s s or mismatch to the LO s i g n a l . The LO bandpass f i l t e r prevents los s to the IF s i g n a l and ensures that only the desired 3.5 GHz LO s i g n a l i s applied to the power a m p l i f i e r . The operation of the IF i n j e c t i o n and matching c i r c u i t , shown i n F i g . 2.15 can be explained using conventional transmission l i n e a n a l y s i s . The input admittance at planes A-A of the 25 fi open c i r c u i t shunt stubs i s given by; 1 • Y A " TT = - j z L t g * = J V a n 3 * w h e r e - 25 0 , (2.1) assuming n e g l i g i b l e transmission l i n e attenuation and n e g l i g i b l e r a d i a t i o n from the open-circuit terminations. At each node there are two shunt stubs, e f f e c t i v e l y i n p a r a l l e l . The combined admittance at each node i s therefore given by Y g = 2Y A = j2Yj tan U (2.2) RX PORT TO RECEIVER 2.08 (50 A) r NODE 2 t n D r 2I (25 n! T 2.72 I 1 A r (25 n) IF PORT TO MIXER IF PORT 15.02 T" 2.72 | | HH LO PORT TO 3.5 GHZ BANDPASS FILTER ALL DIMENSIONS IN MILLIMETRES CONNECTORS ARE SUA F i g . 2.15. IF i n j e c t i o n and matching c i r c u i t , LO 64 Each stub i s a quarter wavelength long at the LO frequency. I f the transmission l i n e wavelength at 3.5 GHz Is designated AgLo*the admittance YB at a frequency, f , or wavelength, Xg, can be rewritten as: = j . 0 8 tan (-J • - ~ ) LO This admittance appears i n p a r a l l e l with the admittance looking i n t o plane C-C, which w i l l be referred to as Yt> The t o t a l admittance at node 1 i s therefore: Y 3 = Y c + Y f i (2.4) This admittance, Y3, w i l l be transformed by the s e c t i o n of 50 ft l i n e between node 1 and node 2 which i s also one quarter wavelength long at ^L0» The admittance at node 2 now becomes: Y_ + j .02 tan (J I ) J LO Y = Y n + .02 jr-4 .02 + j Y tan (J | ) LO F i n a l l y , looking into plane D-D the admittance i s : Y A + j.02 tan {-} f ) (2.5) Y = .02 J^J .02 + j Y 4 tan [j j ) 2 f T A L 0 (2.6) LO One of the problems i n designing the matching network i s that Y J F , the admittance looking into the output port of the IF attenuator, i s unknown i n 65 the v i c i n i t y of f T ^ . Even i f the admittance YTT, were known, the admittance J LO IF at plane C-C, i . e . Yc» would not be known unless the exact length of the coaxial connection between the mixer preamplifier and the IF port i s also determined. For this reason, the IF injection and matching network must have a very low sensi t ivi ty to the value of Y o This i s accomplished i n part by using low Impedance lines for the shunt quarter-wave stubs. At frequen-cies around f^o, t n e admittance YB w i l l be very large and thus w i l l reduce the effect of Yc which appears in p a r a l l e l . The quarter-wave section between nodes 1 and 2 w i l l further reduce the unknown effect of Yc by transforming the admittance at node 1 to a low admittance at node 2, which w i l l be small compared to Y B . The result is that, regardless of Yc, the admittance at node 2 i s large, ensuring the admittance at plane D-D i s small . The very low admittance at plane D-D w i l l cause almost no ref lect ion on the LO l ine to the LO port at 3.5 GHz. To ver i fy the operation of the IF Injection and matching c i r c u i t theoretical ly , a computer program was written i n the BASIC language. The program was used to predict the VSWR on the local osc i l la tor l ine over the local osc i l la tor frequency range of the receiver. The results are shown graphically in F i g . 2.16. Different values of Yc between + j l 0 2 5 and -i l O 2 5 mhos produced no significant change in the VSWR over the frequency range 2 to 4 GHz. The predicted response of this network shows a more than adequate bandwidth. The effect of the IF injection and matching c i r c u i t on the 45 MHz IF signal can be analyzed in the same manner up to plane D-D. In this case Y T F is known to be approximately 50 ft at 45 MHz. The difference i n the 67 analysis a r i s e s when the e f f e c t of the impedance looking to plane E-E at 45 MHz i s considered. This admittance, YE, must be very low at 45 MHz to prevent I F s i g n a l mismatch. To ensure that YR i s small, the 3.5 GHz bandpass f i l t e r i s placed at the output of the LO port. The bandpass f i l t e r topology described by Cohn [ 2 . 1 1 ] chosen because i t was a tran s f e r function zero at dc, and presents almost an open c i r c u i t at 45 MHz. This small admit-tance i s transformed by the length of 50 fi l i n e from the bandpass f i l t e r to plane E-E r e s u l t i n g i n a small capacitive susceptance at plane E-E. Thus the e f f e c t of the I F i n j e c t i o n and matching network at 45 MHz i s j u s t to add a small c a p a c i t i v e susceptance at nodes 1 and 2 and at plane E-E. The predicted e f f e c t of these shunt susceptances i s to produce a small VSWR on the I F l i n e . The resultant VSWR on the I F l i n e w i l l be 1.4 i f the distance from the f i l t e r to plane E-E i s approximately 15 cm. This value increases only to VSWR = 1.6 i f the distance increases to 25 cm. The m i c r o s t r i p substrate chosen f o r the f a b r i c a t i o n of the I F i n j e c t i o n and matching c i r c u i t and LO bandpass f i l t e r i s a copper-clad t e f l o n f i b r e g l a s s m a t e r i a l . This material was chosen because i t i s e a s i l y machinable and has a comparatively low d i e l e c t r i c constant (Er = 2 . 5 5 ) . A low d i e l e c t r i c constant makes c i r c u i t elements p h y s i c a l l y larger ( r e s u l t i n g i n l e s s stringent f a b r i c a t i o n tolerances), and reduces the e f f e c t s of dispersion caused by the d i e l e c t r i c inhomogeneity. Unfortunately, the lower d i e l e c t r i c constant also r e s u l t s i n decreased open c i r c u i t resonator Q due to r e l a t i v e l y large r a d i a t i o n l o s s e s . The choice of the substrate thickness was determined by the open-c i r c u i t resonator 0. Both c i r c u i t s include o p e n - c i r c u i t quarter wave or h a l f 68 wave microstrip lines - which are referred to as open c i r c u i t resonators. Microstrip resonator 0 is determined by conductor loss , d i e l e c t r i c loss and radiation l o s s . These losses have been calculated for the copper and tef lon-fibreglass laminate over the frequency range of interest using equations i n [2.5] and [2.6]. The results show that the radiation losses are dominant and that the conductor losses are much larger than the d i e l e c t r i c losses. The open-circuit resonator Os were found to be comparable for the available sub-strate thicknesses of 10 and 30 mils i n the frequency and impedance ranges required. The 30 mil substrate thickness was chosen because i t would result i n larger c i r c u i t dimension and correspondingly lower fabricat ion tolerances. The laminate used was GX-6098-22-030-55 by 3M Company. Single microstrip characteristic impedances were calculated using Hammerstad's synthesis equations [2.7]. The l ine geometries were corrected for conductor thickness in the IF injection and matching c i r c u i t using Wheeler's method [2.8], Corrections for dispersion using Getzinger's equa-tions [2.9] at the LO frequency yielded increases i n effect ive d i e l e c t r i c constant of approximately 1% for 25 ft l ines and 0.5% for 50 ft l i n e s . A correction for the T-junction discontinuity using Hammerstad's method [2.7] resulted in only a 300 ym increase in the T-shunt arm length. The stub-length correction due to the open c i r c u i t discontinuity capacitance was determined from [2.10] and [2.5], The f i n a l dimensions for the IF injec -tion and matching c i r c u i t on the specified laminate are given i n F i g . 2.15. Cohn's bandpass f i l t e r topology was chosen for the L0 f i l t e r to satisfy the requirement of high input impedance at the IF frequency. The 69 bandpass f i l t e r was designed to have a 5% bandwidth, second order, Butterworth response. The coupled microstrip even and odd mode impedances were calculated from Cohn [2.11]. The microstrip widths and spacings were derived from Garg and Bahl's coupled microstrip analysis equations [2.12], A BASIC language computer program was written to determine the s t r ip widths and spacings i tera t ively from the mode impedances. To correct for the unequal phase veloci t ies of the two modes the procedure described by Kojfez and Govind [2.13] was employed. Open c i r c u i t end-correction was calculated from [2.10]. The f i n a l dimensions for the 3.5 GHz bandpass f i l t e r are shown i n F i g . 2.17. The microstrip substrate which was available was clad i n 2 ounce copper (thickness =71 microns). This thickness of copper would normally require that a correction be applied to the dimensions in F i g . 2.17 to account for the capacitance between the ver t i ca l edges of adjacent conductors. In addition, under-etching problems were also anticipated with this conductor thickness in the region of the f i r s t gap which has a spacing of only 0.2896 mm. To circumvent these problems the copper thickness on the upper side of the laminate was pre-etched to approximately 12 microns before the photoresist was applied. The etched microstrip c i rcui ts were mounted i n custom fabricated aluminum boxes. Several small machine screws and a s i l v e r loaded adhesive were used to mount the substrates and ensure a low-inductance ground connection. Coaxial connections were made to the 50 fi microstrip transmission lines by threading SMA bulkhead jacks into the boxes so the center conductors of the connectors aligned exactly with the copper 50A INPUT I • 2.115 III! 50 A OUTPUT ALL DIMENSIONS IN MILLIMETRES CONNECTORS ARE SMA Fig. 2.17. 3.5 GHz microstrip bandpass fil t e r . o 71 conductors. The dimensions of the boxes were chosen by using the rule -of -thurab that the case walls should be more than three times the conductor width and more than f ive times the substrate thickness from the microstrip conduc-tors [2.14], [2.5]. The completed IF injection and matching unit i s shown i n F i g . 2.18 and the LO bandpass f i l t e r i s shown In F i g . 2.19. The IF inject ion and matching c i rcui t assemblies were tested by meas-uring the VSWR looking to the receiver port. Measurements were made with the LO port terminated with 50 ft and the IF port open-circuited, short-circuited and terminated i n 50 ft. A 50 ft slotted coaxial l ine was used to measure the VSWR over the range 2 - 4 GHz. The effect of the impedance presented to the IF port could only be noticed at the lowest frequencies ( i . e . close to 2 GHz) and even then i t had a very small effect on the receiver port VSWR. F i g . 2.16 shows the measured VSWR for each of the two IF inject ion and matching units together with the calculated VSWR. The measured values are s l i g h t l y higher than those calculated. This is attributed to the effects of the coaxial-to-microstrip discontinuities and to the residual VSWR of the measurement system. This residual VSWR is also shown i n F i g . 2.16. The measured values were obtained without resorting to any tuning of the etched c i r c u i t and show that the IF injection and matching c i r c u i t performed very well and had much greater than the required bandwidth. The insertion loss of the IF injection and matching c i rcui t was measured to be 0.5 dB. Testing of the two 3.5 GHz bandpass f i l t e r s was accomplished by measuring the f i l t e r insertion loss between 3.2 and 3.8 GHz. The results , which again did not require post-fabrication tuning, are shown In F i g . 2.20 72 F i g . 2.19. 3.5 GHz bandpass f i l t e r p h o t o g r a p h . Frequency (GHz) F i g . 2.20. 3.5 GHz bandpass f i 1 t e r performance . 74 along with the theoretical , lossless response. Microstrip losses, which produce f i n i t e resonator Q's , account for the 2 dB f i l t e r insertion l o s s . Agreement between calculated and measured results i s considered to be extrem-ely good. Some difference between the two units was observed and can be attributred to fabrication tolerances ( i . e . underetching, copper thickness) and die lec t r i c permittivity variat ion. It was noticed that when the bandpass f i l t e r enclosure l i d was in place a notch i n the f i l t e r response occurred at about 3.52 GHz. Because of the "sharpness" of the notch and the adequate distance from the c i r c u i t to the l i d , resonances of the enclosure were investigated. The Inner dimensions of the aluminum enclosure are d = 51.1 mm, b = 76.2 mm and a = 24.5 mm, ( F i g . 2.19). Resonances occur i n rectangular enclosures at frequencies given by: f „ " c nm £ resonant (_L_)2 + (H-) 2 + ( 5 _ ) 2 (2.7) • 4 d ; V 2b ; K2aJ for either TE or TM modes. By exhaustive search, the nm£ =110 resonant frequency was found to be 3.53 GHz which i s within measurement error of the observed notch. The effect of this resonance was eliminated by placing a small piece of microwave absorbing foam on the inner side of the enclosure l i d . 2.3.3.6 Local Osci l lator Frequency Mult ipl ier The receiver front-end incorporates local osc i l la tor frequency multiplier c i rcui ts to reduce harmonic mixing conversion l o s s . The harmonic 75 mixing process r e l i e s on the nonlinear mixer diode j u n c t i o n to produce har-monics of the l o c a l o s c i l l a t o r s i g n a l . The l o c a l o s c i l l a t o r frequency i s chosen so that one of i t s harmonics mixes with the s i g n a l frequency to produce a s i g n a l at the IF frequency. The harmonic generation e f f i c i e n c y of the mixer diode decreases monotonically as the harmonic number Increases. This r e s u l t s i n increasing mixer conversion l o s s with Increasing l o c a l o s c i l -l a t o r harmonic number ( r e f . Section 2.3.3.4). A preliminary i n v e s t i g a t i o n i n t o the operation of the TRG mixers at high harmonic numbers showed unaccep-ta b l y high conversion l o s s . The TRG mixers were modified s l i g h t l y at the f a c t o r y by increasing the si z e of the l o c a l o s c i l l a t o r coupling capacitors to te s t the f e a s i b i l i t y of mixing using the twenty-first harmonic of a 3.5 GHz l o c a l o s c i l l a t o r . The r e s u l t i n g conversion l o s s was between 39 and 42 dB. This conversion los s was unacceptable because of the high s e n s i t i v i t y r e -quired to accurately measure crosspolar s i g n a l l e v e l s . A tradeoff between conversion loss and c i r c u i t r e a l i z a b i l i t y r e s u l t e d i n the s e l e c t i o n of a times three frequency m u l t i p l i e r . Referring to the mixer s p e c i f i c a t i o n s , Section 2.3.3.4, a conversion l o s s of 18-26 dB can be achieved using a l o c a l o s c i l l a t o r i n X-band, and mixing with the 6th to 9th harmonic. An i n v e s t i g a t i o n of these harmonic numbers showed that the most f e a s i b l e mixer harmonic number was the 7th, r e q u i r i n g a times three frequency m u l t i p l i e r , and r e s u l t i n g i n a predicted 22-23 dB conversion l o s s . I t also may have been possible to s e l e c t a times four m u l t i p l i e r and mix with the f i f t h harmonic. This would have resulted i n a f u r t h e r 5 dB reduction i n conversion l o s s , but was decided against because the r e s u l t a n t 14.7 GHz s i g n a l would have been above the recommended l o c a l o s c i l l a t o r range of the 76 mixer. The s i x t h harmonic was not usable because i t would have required operating the receiver l o c a l o s c i l l a t o r at 4.08 GHz, near the absolute upper l i m i t of i t s range (4.1 GHz), where r e l i a b l e phase-locking i s not po s s i b l e . C i r c u i t s to u t i l i z e the eighth or ninth harmonic were r e a l i z a b l e but these harmonics would r e s u l t i n higher conversion losses than the seventh. The frequency m u l t i p l i e r c i r c u i t s accept a 3.5 GHz input and produce a 10.5 GHz output at a l e v e l of 13 dBm f o r each mixer. The 13 dBm output includes a maximum 3 dB budget f o r cable l o s s and mismatch to r e s u l t i n 10 dBm minimum at each mixer LO port. A frequency m u l t i p l i e r i n t h i s frequency range uses the nonlinear j u n c t i o n capacitance of a s i l i c o n varactor or step recovery diode to produce the harmonic s i g n a l . The m u l t i p l i e r input, output and bias c i r c u i t s have to be c a r e f u l l y matched to the diode c h a r a c t e r i t i c s to r e s u l t i n s t a b l e , e f f i c i e n t operation. F a b r i c a t i o n and t e s t i n g of e f f i c i e n t and stable harmonic m u l t i p l i e r s i n th i s frequency range requires t e s t equip-ment which was not av a i l a b l e i n the E l e c t r i c a l Engineering Department. For t h i s reason commerically b u i l t m u l t i p l i e r c i r c u i t s were purchased. Due to the many possible combinations of m u l t i p l i e r frequencies and power l e v e l s and t h e i r inherent narrow bandwidths, m u l t i p l i e r c i r c u i t s have to be custom f a b r i c a t e d . The s p e c i f i c requirements and small quantities involved i n t h i s order made i t very d i f f i c u l t to f i n d a s u p p l i e r . The A.I. Grayzel, Inc. Company which s p e c i a l i z e s i n frequency m u l t i p l i e r s was able to supply a device to our s p e c i f i c a t i o n s at a good p r i c e and with an acceptable d e l i v e r y time. Design tradeoffs i n v o l v i n g e f f i c i e n c y and bandwidth were negotiated d i r e c t l y with the company's c i r c u i t designers. 77 2.3.3.7 Frequency Mul t ip l ie r Specifications and Testing The manufacturer's specifications for the A . I . Grayzel model OX-3.5 frequency multipliers are given in Table 2.5. TABLE 2.5 A . I . Grayzel OX-3.5 Frequency M u l t i p l i e r Specifications Input frequency Output frequency Input power required for 20 mW output Bandwidth The three frequency multipliers (one i s a spare) were tested by supplying an input power of 150 mW at frequencies between 3.45 and 3.55 GHz and measuring the X-band power output. Results of this test are plotted i n F i g . 2.21. The results of a second test with different 3.5 GHz input powers is shown in F i g . 2.22. These tests showed that none of the three multipliers met the manufacturers specified power output. The manufacturer suggested that the cause of the reduced output might be either that the generator or load impedance presented to the c i rcui ts was not matched or that the genera-tor produced an unexpected output waveform. Subsequent tests including attenuator pads (to ensure matched impedances) and different signal sources did not improve the multiplier performance. 3.5 GHz 10.5 GHz 135 mW 2 % 78 003 ' • i i , 1 i . . 3.^8 3.50 3.52 3.5A 3.56 Frequency (GHz) F i g . 2.21. Frequency m u l t i p l i e r f requency response . F i g . 2.22. Frequency m u l t i p l i e r conversion l o s s . 80 Because the multipliers were sealed and time constraints did not i n i -t i a l l y permit returning them to the manufacturer, the p o s s i b i l i t y of supply-ing a higher input power to the multipliers was investigated. Power inputs of up to 500 mW were considered safe by the manufacturer. Fortunately, the amplifiers chosen during the design phase to provide the 3.5 GHz input to the mult ipl iers , did have enough extra gain and power output capability to make this solution possible. M u l t i p l i e r , s e r i a l no. 002, was eventually returned to the manufac-turer for repair and realignment in mid 1981. Its subsequent performance is also shown i n Figs . 2.21 and 2.22. 2.3.3.8 Local Osci l lator Power Amplifier Power amplifiers are included In the front-end to supply the 3.5 GHz drive level for the frequency mul t ipl iers . The two-channel front-end is mounted adjacent to the receiving antenna and is connected to the receiver v i a two 35 metre long coaxial cables. Low-loss 7/8 inch, a i r - d i e l e c t r i c cable i s used to minimize signal attenuation. These cables have a measured attenuation of 4 dB at the LO frequency. With the maximum LO output from the receiver, 16 mW of LO drive is available at the input to the front-end. The expected insertion loss of the IF injection and matching c i r c u i t and LO band-pass f i l t e r i s about 1 dB and 3 dB respectively. This results i n an 8 dBm maximum Input to the LO power amplifier . To provide the design 135 raW m u l t i -p l ier input l e v e l , the power amplifier required a minimum gain of 14 dB. The Avantek APT-4013 thin-f i lm power amplifier met these specifications with best economy. These devices have a minimum gain of 18 dB and a power output at 81 saturation of 25 dBm over a frequency range of 2-4 GHz. This extra gain and output capacity made i t possible to use the frequency m u l t i p l i e r s , which di d not perform according to t h e i r design s p e c i f i c a t i o n s , i n one of the p o s s i b l e LO chain configurations which are discussed i n the next s e c t i o n . 2.3.3.9 LO Frequency M u l t i p l i e r C i r c u i t Configurations Three c i r c u i t configurations, shown i n F i g . 2.23, were investigated f o r the LO frequency m u l t i p l i e r chain. The receiver provides two LO output connectors as shown i n F i g . 2.9. A front panel adjustable attenuator i s included to set the output l e v e l at each connector. In c i r c u i t s (a) and (b) of F i g . 2.23 only one LO connection i s used with the m u l t i p l i e r s , a m p l i f i e r s and a two-way power d i v i d e r to provide LO signals f o r both mixers. These configurations have the advantage of r e q u i r i n g fewer a m p l i f i e r and m u l t i p l i e r modules. C i r c u i t (a) which uses a 10.5 GHz power d i v i d e r , requires only one a m p l i f i e r and m u l t i p l i e r but when t h i s c i r c u i t was tested, however, there was only 35 dB i s o l a t i o n between channels. The low IF/LO i s o l a t i o n s p e c i f i c a t i o n of the mixers (Section 2.3.3.4) prompted an i n v e s t i g a t i o n i n t o whether the f i r s t IF s i g n a l was being coupled between mixers through the LO connections even though no 45 MHz s i g n a l could be observed on the LO c a b l e s . A t e s t was performed by adding sections of X-band waveguide between the power d i v i d e r and mixer LO ports. This waveguide would not allow any 45 MHz s i g n a l s to propagate out from the mixer LO ports. The i s o l a t i o n between channels d i d not improve. As a r e s u l t the presence of 45 MHz sidebands on the 10.5 GHz LO s i g n a l was suspected. No spectrum analyzer was a v a i l a b l e to v e r i f y t h i s i g . 2.23. LO frequency m u l t i p l i e r chain c i r c u i t c o n f igurations. 83 suspicion. To test this theory one of the outputs from the 10.5 GHz power divider was used as the input to a single ended X-band waveguide mixer with a coaxial IF connection. The mixer IF port was connected to the second IF channel of the receiver. This resulted i n an indicated signal level i n the second channel which was 40 dB below that in the channel with the harmonic mixer and V-band input, thus verifying the presence of 45 MHz sidebands on the LO signal . This indirect modulation of the LO signal was probably due to the changing impedance of the mixer diode over a cycle of the IF waveform. This problem could l i k e l y have been alleviated by including isolators after the power divider , but this would not have been cost effect ive . Circuit (b) uses a 3.5 GHz power divider , one amplifier and two f r e -quency mult ipl iers . This c i rcui t would be less susceptable to 45 MHz modula-tion of the LO signal because of the reverse Isolation of the mul t ip l ie rs . It was not usable however, because the unexpectedly high conversion loss of the multipliers meant there was insuffic ient amplifier output to drive two mult ipl iers . (The previous c i rcui t had a similar disadvantage.) The i n -creased cost of an amplifier with sufficient gain and output negated any advantage of this c i rcui t over c i rcui t (c) . In comparison with c ircui ts (a) and (b), c i rcui t (c) , which employs two amplifiers and two mult ipl iers , has extremely high channel-to-channel i sola t ion and the added advantage of being able to use the front panel attenuators to set the individual mixer LO levels (and thus easily compensate for the differences in multiplier eff ic iency . ) To provide 10 mW at the mixer LO port i n this configuration, the amplifier driving multiplier 002 (before 84 repair) must supply close to 25 dBm (multiplier 003 was not used). For these reasons c i r c u i t (c) was chosen for the f i n a l front-end design. 2.3.3.10 Mixer Bias Circuits The front-end includes a mixer bias c i r c u i t to bias each mixer diode at the optimum point on i t s V-I characteristic for minimum conversion loss . These c i r cui t s supply a dc output voltage which is adjustable from zero to approximately - I V . To protect the mixer diodes (which are extremely expen-sive) against operator errors and c i r c u i t f a i l u r e , an overcurrent shutdown i s provided. The current shutdown threshold i s adjustable from 0 to 4 mA. Most of the active components In this c i r c u i t are duplicated to reduce the prob-a b i l i t y of diode damage even i f a component in the mixer bias c i r c u i t f a i l s . Reverse voltage protection diodes are included to protect the mixer diodes against reverse voltage damage i n the event of a fa i lure of the positive power supply. Voltage and current meters are included in each bias current as an aid i n mixer bias adjustment. The mixer diode voltage is coupled through an isolat ion resistor to an external jack on the bias c i r c u i t enclo-sure. These signals are applied to analog input ports on the data acquisi -tion system. By monitoring the mixer diode voltage, any changes i n either the bias or LO signal applied to the mixer can easily be detected. A schematic of one mixer bias c i rcui t is shown in F i g . 2.24. 2.3.3.11 D i g i t a l l y Programmable IF Attenuators In order to increase the receiving systems dynamic range, a d i g i t a l l y programmable attenuator, Texscan model PA-51, i s included in each IF signal 10 K Fig. 2.24. Mixer bias circuit schematic. co 86 path. In any receiving system, dynamic range i s limited at high signal levels by saturation or non-linearity and at low signal levels by the noise l e v e l . In this system, each receiver channel must sequentially monitor a copolar and a crosspolar signal l e v e l . The gain of each receiver channel was adjusted for maximum sensi t iv i ty (with the programmable attenuator set at minimum) for best crosspolar measurement s e n s i t i v i t y . During copolar signal measurement the programmable attenuator reduces the IF signal level to prevent receiver saturation. The model PA-51 attenuator i s programmable from 0 to 63 dB in 1 dB steps and switches i n 6 ms. Switch contacts i n the polarization switch were used to control the attenuator (refer to F i g . 2.5 and 2.11). When the data was analyzed, software was used to correct for the reduced receiver copolar gain. 2.3.3.12 IF Preamplifier Low noise IF preamplifiers are included i n the front end to improve sensi t iv i ty and thus increase signal-to-noise ratio during crosspolar signal measurements. The front end single-sideband noise figure is given by [2.15]: where: F = L ( F T T , + t - 1) ( 2 * 8 ) F.E. C V IF m L = mixer conversion loss (power ratio) c ? = total IF noise figure (power ratio) IF t = mixer noise temperature ratio m The total IF noise figure i s that of the IF amplifier cascade and can be approximated by F - 1 2 nAMF F I F ~ F l s t J F + G ( 2 ' 9 ) The mixer noise temperature ratio is related to the mixer noise figure by: FM= LC * Cm ( 2' 1 0> The expression for the front end noise figure cannot be evaluated direc t ly because manufacturers do not quote mixer noise figures for harmonic mixers i n this frequency range. An estimate of the mixer noise temperature ratio can be derived from equations appearing i n [2.16] and [2.17], The single sideband mixer noise figure for the case of a r e s i s t i v i t y terminated image i s given by [2.16]: FM = r c ^ ( L c - 2> + 2 * L c - t m . L c (2.11) where T D = diode noise temperature (°K) TQ = ambient temperature (°K) This expression is derived from the equations i n [2.16] and does not agree with the equation for mixer noise figure In [2.17]. The authors of both references discuss the discrepancies in these mixer noise figure equations and i t is not obvious which is precisely correct. However, the differences 88 i n the two expressions w i l l not produce a significant error i n the following analysis . Solving for t y i e l d s : T t = i [ -£ (L_ - l ) + 2] (2.12) m L C T o c References [2.16], [2.17] and [2.18] state that for an ideal Schottky diode: T0 T D ~ T~ (°K) ( 2 , 1 3 ) This value i s probably very optimistic for this type of application [2.19]. [2.20] but w i l l be used i n an attempt to ascertain the relative contribution of the IF preamplifier to the front-end noise f igure . Using this expression for T„, t can be rewritten as: D' m t = 0.5 + m I, ! _ (2.14) This expression for t m can now be substituted into the expression for the front-end noise f igure, (2.8), to y i e l d , F F E = 1 + V F I F ~ ° ' 5 ) ( 2 * 1 5 ) The equation i l lus t ra tes the relative effect of the IF preamplifier noise f i g u r e . The f i r s t stage of IF gain in the Scient i f i c Atlanta receiver uses a 40235 transistor . This device is not characterized for noise figure at the IF frequency but extrapolation of i ts specifications indicates i t s noise figure is in the v i c i n i t y of 3.3.dB at 45 MHz. Lower noise figures are now 89 possible at 45 MHz. The low noise amplifier selected to be used as an IF preamplifier is the Anzac Electronics AM-107-8408. This amplifier has i o dB gain and a 1.5 dB maximum noise figure over a frequency range of 1-100 MHz. The 10 dB gain w i l l reduce the noise contribution of the f i r s t IF stage i n the receiver to approximately 0.3 dB. The total IF noise figure is then 1.8 dB, an approximate improvement of 1.5 dB. This improvement in IF noise figure results i n a 2.0 dB improvement in front-end noise figure at a very low cost. 2.3.4 Frequency Counter An EIP model 351C microwave frequency counter was used to continuously measure the 3.5 GHz receiver LO frequency. This was done to monitor the millimetre-wave klystron frequency, which is exactly twenty-one times the receiver LO frequency plus or minus the 45 MHz IF frequency. Because the klystron was free-running, changes i n i t s supply voltages, case temperature and cavity tuning a l l affect i t s operating frequency. Changes i n the m i l l i -metre frequency can result in changes in the received signal levels due to the frequency sensitive behaviour of many components in the experimental system. To ensure that frequency changes did not corrupt data during an event and to be able to compare data and system behaviour over longer per-iods, seven BCD digi ts of frequency data from the counter were continuously recorded along with the other experimental data. 90 2.3.5 Receiving System Performance 2.3.5.1 Calculated Sensitivity The noise figure of the receiving system front-end is given by: F p E = 1 + L c ( F I p - 0.5) (2.15) From Section 2.3.3.12 the total IF noise figure i s : F T „ = 1.5 = 1.8 dB (2.16) Ir The mixer conversion loss with the local osci l la tor chain described i n Section 2.3.3.6 was estimated from the manufacturer's catalogue, to be 22-23 dB. However, the measured mixer conversion loss in the front-end with a 10 mW LO l e v e l , was 26 dB with a measurement accuracy of ±1 dB. Using these values, the front-end single-sideband noise figure i s calculated to be also 26 dB. This value of noise figure would be applicable to the calculation of a receiving system sensi t ivi ty i f this front-end were used in a single-conversion non-radiometer type receiver with no image band noise rejection [2.15]. However, with the Scient i f ic Atlanta model 1751 receiver, an additional sensi t iv i ty degradation results because there Is also no second-conversion image-noise rejection. This problem w i l l be i l lus t ra ted using the frequency domain representation in F i g . 2.25. In the single conversion case, the RF and I F signal spectrum are shown in F i g . 2.25(a) and 2.25(b) respectively. I f the IF signal in F i g . 2.25(b) were to be detected, the desired signal would be corrupted by noise from frequencies within the IF passband downconverted from both the signal and image channels. Because 91 t 1 I 1 sig LO image 73.50 GHz 73.5*»5 GHz 73.590 GHz (a) RF signal spectrum e 1 eve 1 Noise level 45 MHz 1st IF BW (= 7 MHz) (b) First IF spectrum t 1 '1 Noise level 1 » « IF LO image 45 MHz 45.001 MHz ^5.002 MHz (c) Second conversion spectrum Noise level 1 KHz-2nd IF BW (30 Hz) (d) Second IF spectrum Fig. 2 . 2 5 . Receiver: signal, IF, L0 and noise in the frequency domain. 92 nothing i s done to reject the image band noise the IF signal-to-noise ratio i s reduced by 3 dB. This i s the reason single sideband mixer noise figures are approximately 3 dB higher than double sideband mixer noise figures [2.15], [2.17], [2.21]. In a typical double-conversion receiving system, the noise figure would be unchanged because a f i r s t IF bandpass f i l t e r would be provided to attenuate the second-conversion image noise. In the model 1751 receiver no such f i l t e r i s included because the 1 kHz second IF frequency is too low to make such f i l t e r i n g prac t i ca l . (This second IF frequency was chosen because 1 kHz i s a widely used standard frequency and thus makes the receiver compatible with different detection systems.) The f i r s t and second IF spectrum diagrams i n Figs . 2.25(c) and 2.25(d) show how In this case an additional doubling of noise power occurs before signal detection. To be able to use standard equations to convert the noise figure to s e n s i t i v i t y this extra noise component w i l l be accounted for by using an "effect ive" receiving system noise figure of 29 dB. The noise contribution of the receiver, referred to i t s input, can also be expressed as an effective input noise temperature, T g using [2.15]: T = T (F-1) e o (2.17) where T = 290°K. From (2.17) this receiver has a noise temperature of T £ -o 2.3 • 10 5 o K. The equivalent input noise power of the receiver can be calculated using this noise temperature and the receiver predetection noise bandwidth. The predetection bandwidth is determined by the second order f i l t e r s in the 93 d i g i t a l amplitude measurement units . The 30 Hz - 3 dB bandwidth of these f i l t e r s corresponds to a noise equivalent bandwidth of approximately: B n = 44 Hz [2.22]. Equation 2.18 relates the equivalent input noise power, P n , to these quantities: P = kT B (2.18) n e n where k = Boltzman's constant - 1.38 • 10~ 2 3 J / ° K . Thus, for this receiver P - 1.4 • 10~ 1 6 W = -129 dBm. n 2.3.5.2 Measured Receiving System Sensit ivity An attempt was made to measure the equivalent input noise power of the receiving system by using a spectrum analyzer to observe the f i r s t IF signal after the receiver IF amplifier . Because of the high gain of the receiver IF amplifier , there i s no sensi t ivi ty reduction due to noise contributions of the following stages. A resolution bandwidth of 30 Hz was used for the measurements to approximate the receiver predetection bandwidth. However, the noise band-width of the Gaussian f i l t e r s i n the analyzer are approxi-mately 1.2 times their 3 dB bandwidths [2.23], necessitating a noise level measurement correction of -0.7 dB. An additional correction of +2.5 dB is required when observing random noise to correct for the spectrum analyzers average l e v e l indication and logarithmic compression [2.23]. Thus the "indicated" signal-to-noise ratio on the spectrum analyzer was 1.8 dB higher than that for the complete re-ceiving system with the same input s ignal . 94 Figure 2.26 i s a photograph of the spectrum analyzer display for a -100 dBm Input signal at 73.5 GHz. When measuring noise levels on a spectrum analyzer, the average noise l e v e l i s usually displayed by adjusting the video f i l t e r bandwidth to be one-hundredth or less of the resolution bandwidth [2.23]. This procedure could not be followed for this measurement because the minimum video f i l t e r bandwidth was 10 Hz. As a r e s u l t , the average noise l e v e l can only be estimated. From several observations s i m i l a r to F i g . 2.26, the approximate signal-to-noise r a t i o i s 24 dB ±3 dB. After Including the correction f a c t o r s , this corresponds to an equivalent input noise power for the receiving system of -122 dBm. With the uncertainty i n the measured conversion loss and noise l e v e l and the estimates i n the calculated noise f i g u r e , and because of the numerous possible impedance mismatches, this value was considered to be i n reasonable agreement. Another possible cause for the discrepancy between the calculated and measured receiving system s e n s i t i v i t i e s i s l o c a l o s c i l l a t o r noise. Because the mixers used i n the front-end are single-ended, they w i l l have very low LO noise r e j e c t i o n . Any LO noise sidebands at frequencies plus or minus 45 MHz from the center of the LO spectrum w i l l combine with the LO center frequency and produce an IF output. This w i l l result i n an unexpectedly higher noise l e v e l i n the previously described t e s t . Due to the very high s e n s i t i v i t y of this receiver, even i f a spectrum analyzer could be used to monitor the 73.545 GHz multiplied LO signal at the mixer diode, these noise sidebands would probably not be observable. The potential for this type of s e n s i t i v i t y degradation could be eliminated by using a much higher f i r s t IF frequency. f CENTER = 45 MHz Scan width = 100 Hz/div. Resolution bandwidth = 30 Hz Video f i l t e r = 10 KHz Scan time = 10 s V e r t i c a l scale = 10 dB/div. Signal into receiver i s 73.5 GHz § -100 dBm. F i g . 2.26 Spectrum analyzer display of 1st IF s i g n a l . 96 2.3.5.3 Receiving-System Small-Signal Performance At low input-signal levels , the measurement accuracy of the receiving system is corrupted by noise. The complete receiving system was tested by applying a known signal level to the mixer inputs. F i g . 2.27 shows the i n -dicated d i g i t a l signal levels for each channel with 0 dB corresponding to a -40 dBm input l e v e l . The average value, and minimum and maximum indicated values for a 1.0 sec. sampling period are shown. During these tests i t was extremely d i f f i c u l t to prevent signal leak-age into the front-end. This problem was also observed during similar tests i n [2.24]. Radiation from the klystron and waveguide flanges resulted i n a significant ambient signal l e v e l . Signal Ingress into the front-end resulted i n a higher indicated noise l e v e l , greater nonlinearity and larger peak-to-peak fluctuations. To reduce the ambient level and front-end ingress, the front-end was shielded and moved as far away from the klystron as prac t i ca l . In addition, a l l waveguide junctions were v isual ly Inspected after connection and then wrapped i n metal f o i l . These measures reduced the undesired signal level by more than 20 dB but the indicated noise levels were s t i l l 5 to 6 dB higher than when the front end was mounted on the roof. For this reason the actual receiving system performance i s actually 5 to 6 dB better than indica-ted in F i g . 2.27. The results from tests performed on the bench (F ig . 2.27) indicate that average indicated levels of the receiving system are linear to with ± 0.3 dB for input levels down to -95 dBm. At this input l e v e l , peak-to-peak noise fluctuations are 1.0 dB or less . (When the system was instal led on the roof, similar performance was obtained for -100 dBm.) The effect of these c c H H A B INDICATION 73.5 GHz Signal l e v e l (dBm) • .27. Receiving system small s i g n a l performance on the bench. 98 fluctuations i n Indicated signal level can be reduced by averaging during data analysis . The nonlinearity at low signal levels was l i k e l y due to signal ingrees. This front end is approximately 30 dB more sensitive than the Scient i -f i c Atlanta model 13-50A mixer, but an exact comparison has not been made. 2.3.5.4 Receiving System Isolation and Frequency Response The measured channel-to-channel isolat ion of the complete receiving system was greater than 75 dB. This i s the measurement l imit imposed by saturation i n the channel with the signal applied (without IF attenuation) and noise level i n the other channel. F i g . 2.28 shows a typical response of the complete receiving system to input frequencies between 73.0 and 73.5 GHz. The frequency response of the receiving system is mainly determined by the frequency multipliers and mixers. Changing the position of the mixer backshort tuning adjustment w i l l s igni f i cant ly al ter the receiving system frequency response. 2.3.5.5 Front-end Alignment The following procedure is followed to align the front end for a new receiver frequency. 1. Adjust the LO level for 10 mW at the mixer LO port. CAUTION: Do not exceed 20 mW LO level or the mixer diode may be damaged. LO level i s adjusted by the receiver front panel LO attenuator or by placing a fixed pad with SMA connectors on the LO amplifier input. F i g . 2.29 shows a typical variation in mixer conversion loss for various LO levels . F i g . 2 . 2 8 . R e c e i v i n g system frequency response. F i g . 2.29. E f f e c t of LO l e v e l on convers ion l o s s . 101 2. Adjust the mixer bias level for maximum signal indicat ion. CAUTION: Do not exceed 4 mA diode current. F i g . 2.30 shows a typical variat ion i n signal and noise level for various mixer bias conditions. (These results would be changed for different LO levels and tuning positions.) Because the noise level i s re la t ively constant, i t i s permissible to adjust for maximum signal level only. The optimum bias setting i s very dependent on LO drive l e v e l . 3. Adjust the mixer waveguide backshort for maximum signal indica t ion . The maxima for the backshort closest to the diode w i l l give the widest frequency response. 4. Repeat steps 2 and 3. 2.4 Propagation Path The radar propagation path for this experiment i s located on the campus of the University of B r i t i s h Columbia. Antennas for both transmitting and receiving are mounted on the roof of the E l e c t r i c a l Engineering bui lding . The antennas are separated by a horizontal distance of 20 metres to prevent any stray coupling. The reflector is mounted on the roof of the Gage Towers building 880 metres away. This provides a total path length of 1.76 km. Fig 2.31, from [2.1], shows the path d e t a i l s . F i g . 2.32 i s a photograph showing the path looking from the reflector toward the antennas. 2.5 Antennas and Orthomode Transducers TRG model V822 Cassegrain parabolic antennas are used for both transmitting and receiving. These antennas are 61 cm i n diameter and have Mixer d iode c u r r e n t (mA) i g . 2 . 3 0 . E f f e c t o f mixer b i a s c u r r e n t on f r o n t - e n d performance. ANTENNAS Fi g . 2.31. Propagation path d e t a i l s . Fig . 2.32. Propagation path photogra 105 machined aluminum ref lec tors . Corrugated, conical , scalar feed horns are incorporated for polarization insensitive characteristics , high aperture efficiency and low sidelobe levels [2.25]. Dual-linear polarization cap-a b i l i t y is realized by including orthomode transducers which interface to the c i rcular waveguide ports on the feedhorns. The orthomode transducers for these antennas were specially manufactured to yield the highest possible polarization i s o l a t i o n . The manufacturers specifications for the two anten-nas assemblies are included in Table 2.6. Crosspolar isolat ion performance, measured by the manufacturer, for the complete antennas is shown i n F i g . 2.33. TABLE 2.6 TRG V822 Antenna Specifications at 73.5 GHz. Serial no. 22 Serial no. 23 On axis gain through port cross port 50.6 dB 50.6 dB 50.9 dB 50.9 dB VSWR through port cross port 3 dB Beam Width through port cross port Sidelobe levels (max.) through port cross port 1.07 1.09 0.45c 0.A6C -23 dB -22 dB 1.12 1.11 0.45c 0.45c 21 dB 21 dB Additional tests were made on the orthomode transducers to supplement the manufacturer's p olarization isolat ion data. This was accomplished by F i g . 2.33. Antenna c r o s s p o l a r i s o l a t i o n p e r f o r m a n c e . 107 connecting the two orthomode transducers "back-to-back" through t h e i r c i r -c u l ar waveguide ports as shown i n F i g . 2.34. I s o l a t i o n between the two per-pendicular p a i r s of rectangular waveguide ports were measured using a power meter with the unused ports of the transducers terminated with matched loads. The t e s t r e s u l t s , (which are corrected for the source and power meter f r e -quency response) for frequencies between 73.0 and 73.6 GHz, are shown i n F i g . 2.35. The copolar i n s e r t i o n losses of the two orthomode transducers were found to be s l i g h t l y d i f f e r e n t . The average i n s e r t i o n l o s s f o r the s t r a i g h t arm - s t r a i g h t arm connection was 0.8 dB l e s s than for the cross arm - cross arm connection. This f a c t introduced some uncertainty i n t o the manufacturers antenna gain s p e c i f i c a t i o n s , which are i d e n t i c a l for each arm - an u n l i k e l y r e s u l t In view of the d i f f e r e n t i n s e r t i o n l o s s e s . The crosspolar i s o l a t i o n between ports was also found to be d i f f e r e n t . This i s l i k e l y due to the d i f f e r e n t ways the p o l a r i z a t i o n i s o l a t i o n was r e a l i z e d i n the cross and through arras. I t i s also possible that the d i f f e r -ences between the two i s o l a t i o n s i s p a r t l y due to a s l i g h t p o l a r i z t i o n o r i e n t a t i o n mismatch between the transducers f o r one of the p o l a r i z a t i o n s , i . e . the output p o l a r i z a t i o n s may not be exactly perpendicular. This could not be investigated because the c i r c u l a r flanges had l o c a t i n g pins which prevented the p o l a r i z a t i o n o r i e n t a t i o n s between the transducers from being varied i n t h i s test configuration. When a s i m i l a r test of crosspolar i s o l a t i o n for the two back-to-back orthomode transducers was made using the r e c e i v i n g system instead of the power meter, a very d i f f e r e n t frequency response was observed. This T R A N S M I T O R T H O M O D E T R A N S D U C E R T E S T S I G N A L T H R O U G H A R M R E C E I V E ORTHOMODE T R A N S D U C E R M A T C H E D T E R M I N A T I O N C R O S S A R M Fig. 2.34. Orthomode transducer test configuration. 109 28 r 46 I I I I I 1 —1 73.05 73.15 73.25 73.35 7 3 . ^ 5 73.55 Frequency (GHz) F i g . 2 . 3 5 . Orthomode t ransducer t e s t r e s u l t s w i t h matched t e r m i n a t i o n s . 110 difference prompted several new isolation-frequency response tests under s l i g h t l y different conditions. It was discovered that even very small mismatches occurring on the rectangular ports of the orthomode transducers produced large changes i n the measured i s o l a t i o n . As an example, F i g . 2.36 shows the response which was obtained by deliberately mismatching the unused cross arm of the transmit orthomode transducers and repeating the test shown i n F i g . 2.34. The mismatch was produced by placing a waveguide E-H tuner between the matched termination and the transmit transducer cross arm port. A second test was performed using the receiving system with a variable attenuator before one mixer and an isolator ahead of the second mixer as shown in F i g . 2.37. The crosspolar i sola t ion without the isolator and with no attenuation shows a similar result to F i g . 2.36. The improvements which result with the addition of the isolator and with 10 dB and 20 dB attenuation are shown i n F i g . 2.38. This observed degradation of performance due to even sl ight mismatches is the reason a l l ports of both orthomode transducers are connected through isola tors . The theoretical explanation of the mechanism believed to be responsible for this impedance sensitive behaviour of the OMT i s presented i n Section 5.5.2. 2.5.1 Crosspolar Cancellation Network The impetus for the investigation of methods to improve the crosspolar measurement range at 73 GHz resulted from several factors: 1. Theoretically predicted levels of XPD near 73 GHz are very high. Published calculations predict XPD values around 40 - 50 dB for 20 dB I l l 28 r 73.05 73.15 73.25 73.35 73.'.5 73.55 Frequency (GHz) F i g . 2.36. Orthomode transducer test r e s u l t s with one port mismatched. 112 TEST SIGNAL MATCHED TERMINATION ORTHOMODE TRANSDUCERS i VARIABLE ATTENUATOR F R O N T END TO RECEIVER F i g , 2.37-..'-Orthomode transducer test with the r e c e i v i n g system front-end. 113 73.05 73.15 73 .25 73.35 7 3 . ^ 5 Frequency (GHz) F i g . 2.33. Test r e s u l t s f o r F i g . 2.37. 114 copolar fades. The probability of a 20 dB or greater copolar fade on the UBC path is very low (approximately 10 min/year). 2. Even with the excellent performance of the specially fabricated orthomode transducers (OMT), careful alignment could not yield simultaneous i s o l a -tions on both channels of greater than approximately 34 dB and 36 dB. These isolations i n this frequency range are extremely high but s t i l l do not result i n easily interpreted XPD data for most r a i n f a l l events. Measurements taken without the crosspolar cancellation network have con-firmed that system XPD's w i l l only be a few dB different that the clear weather values, (refer to Chapter 6). 3. It is possible with certain combinations of OMT port terminations and antenna and feed alignments to have clear weather, system isolations higher than 34-36 dB for one polarization over narrow frequency ranges. Unfortunately this appears to be accompanied by very poor isolat ion i n the other channel. Simultaneous improvement i s not possible because adjusting port terminations and alignments does not provide suffic ient degrees of freedom. A complete explanation of the effects of OMT port terminations and alignment are found in Section 5.5.2 and 2.5.3 respec-t i v e l y . 2.5.1.1 XPD Improvement Methods There are two basic methods which have been used to improve the XPD of microwave or millimetre-wave systems. These techniques are most commonly referred to in the l i terature as orthogonalization and cancellation. (Other terms which- have been used to describe cancellation methods are cross 115 coupling [2.26], [2.27] and the matrix method [2.28]). Both techniques req-uire four independently variable parameters to completely correct a dual-polarized l i n k . Orthogonalization uses a rotatable d i f f e r e n t i a l phase shif ter and a rotatable d i f f e r e n t i a l attenuator i n a circular waveguide. XPD improvement is accomplished in essentially the same way in which a depolari -zing medium, ( i . e . rain) decreases XPD. Cancellation techniques incorporate two direct ional couplers, an attenuator and a phase shifter for each channel to be corrected. The undesired depolarized signal i s cancelled by vector subtraction of a sample of the perpendicularly polarized copolar s i g n a l . Both basic methods may be applied s ta t i ca l ly or adaptively. Static XPD improvement is.used to increase clear-weather XPD by compensating for the crosspolar signals due to the f i n i t e isolat ion of the system's orthomode transducers and antennas and is usually employed to improve the XPD measure-ment range in propagation experiments. In an adaptive application, an elec-tronic control system - usually including a microprocessor - varies the four XPD - improvement - network parameters to continually correct for depolariza-tion resulting from anomalous propagation conditions. A l l of the available references on adaptive systems applied these techniques to s a t e l l i t e l i n k s . The orthogonalization method for XPD improvement was f i r s t proposed by T . S . Chu [2.29], [2.30]. This method requires a d i f f e r e n t i a l phase shif ter and d i f f e r e n t i a l attenuator which can be oriented at any desired angle bet-ween horizontal and v e r t i c a l . The rotatable d i f f e r e n t i a l phase shifter transforms the general dual-polarized signal - which i s comprosed of two non-orthogonal, e l l i p t i c a l l y - p o l a r i z e d components - into l inear ly polarized non-116 orthogonal waves. These l inear ly polarized waves can then be made orthogonal by a suitable d i f f e r e n t i a l attenuation applied at the correct angle between horizontal and v e r t i c a l . A network to l i t e r a l l y f u l f i l l these requirements can only be constructed i n circular waveguide and, therefore, must be instal led immediately after the feedhorn on the receiving antenna. The major disadvantage of this technique i s the d i f f i c u l t y of fabricating and adjusting the network and the fact that the network must precede the receiver front-end and therefore w i l l reduce sensi t ivi ty [2.31], [2.26]. The advantage of this method, however, is that i t w i l l probably produce the widest operating bandwidth because the entire c i rcui t is fabricated within a single, short section of waveguide [2.27]. Kannowade [2.32] has further analyzed the Chu type orthogonalization network for adaptive correction on s a t e l l i t e l i n k s . He has also proposed a method of real izing a Chu type orthogonalization in a rectangular waveguide network instal led after the orthomode transducer. This i s accomplished by incorporating two networks for coordinate rotation each of which is constructed from two 3-dB couplers and a phase shi f ter . Different ial phase shif t and attenuation are accomplished by applying different amounts of phase shif t and attenuation to signals i n each separate signal path. No example of an actual application of the Chu method could be found i n the l i tera ture . This i s because at lower microwave frequencies - where almost a l l existing systems operate - a simplification of this technique i s prac t i ca l . Depolarization at lower frequencies is mainly due to d i f f e r e n t i a l phase shif t [2.31]. If d i f f e r e n t i a l attenuation can be ignored, Williams [2.33] has shown that a suboptimal orthogonalization c ircuit can be realized 117 w i t h on ly two c o n t r o l l a b l e parameters . Th is theory was used to f a b r i c a t e a 4/6 GHz o r t h o g o n a l i z a t i o n c i r c u i t from two p o l a r i z e r s (which ac t as a d i f f e r -e n t i a l phase c o r r e c t i v e ne twork ) , three r o t a r y j o i n t s and an orthomode t r a n s -ducer [ 2 . 3 3 ] . The c i r c u i t was e l e c t r o n i c a l l y c o n t r o l l e d v i a two m o t o r s . A c t u a l o p e r a t i o n or a s a t e l l i t e l i n k [2 .34] showed that t h i s adapt i ve system was capable of m a i n t a i n i n g a system XPD of b e t t e r than 25 dB f o r r a i n r a t e s as h i g h as 130 mm/hr. U n c o r r e c t e d , the l i n k XPD was as low as 10 dB f o r the same maximum r a i n r a t e . A s i m i l a r s i m p l f i c a t i o n of the Chu o r t h o g o n a l i z a t i o n method may be p r a c t i c a l near 35 GHz, where d e p o l a r i z a t i o n i s almost e n t i r e l y due to d i f f e r -e n t i a l a t t e n u a t i o n [ 2 . 2 6 ] . In t h i s c a s e , the subopt imal network would o n l y r e q u i r e a r o t a t a b l e d i f f e r e n t i a l a t t e n u a t i o n . No examples of t h i s type of XPD improvement c o u l d be found i n the l i t e r a t u r e . Evans and Thompson [2 .35] were p robab ly the f i r s t to p u b l i s h a d e s -c r i p t i o n of a c a n c e l l a t i o n network to improve XPD i n a microwave sys tem. The b a s i c - c a n c e l l a t i o n techn^ue, which has been used i n v a r i o u s a p p l i c a t i o n s , i s accompl ished by the v e c t o r s u b t r a c t i o n of a s u i t a b l y a t tenuated and phase -s h i f t e d sample of the undes i red s i g n a l f rom the channel p r e v i o u s l y c o n t a i n i n g both the d e s i r e d and undes i red s i g n a l s . In microwave c a n c e l l a t i o n networks , d i r e c t i o n a l c o u p l e r s are u s u a l l y used to sample the undes i red s i g n a l and t o i n j e c t the c a n c e l l a t i o n s i g n a l v e c t o r . Th is technique can be a p p l i e d a t R F , IF and i n some systems, even at baseband. The advantages of c a n c e l l a t i o n over o r t h o g o n a l i z a t i o n are t h a t c a n c e l l a t i o n : i s e a s i e r to implement, uses r e a d i l y a v a i l a b l e components, i s e a s i e r to a d j u s t manual ly or e l e c t r o n i c a l l y and can be implemented a f t e r 118 amplification i n systems where the coupler insertion loss would be objectionable [2.26]. Cancellation techniques can also be readily applied to single or dual-polarization systems. Evans and Thompson [2.35] instal led a single-channel cancellation network on an 11.6 GHz, 1.6 km experimental l ink at the University of Essex, England. The network was used to improve the clear weather system isolat ion from around 40 dB to 55-60 dB. No details of the c i rcui t realization were given. Results were shown for an " a r t i f i c i a l " precipitation event and the authors note that "the variation of the crosspolar signal for the cancelled l ink are consistent, whereas, for the uncancelled l i n k , the addition of the system and atmospheric phasors yields a signal which fluctuates around the clear weather value." The published results also seem to show some d r i f t i n the clear-weather crosspolar signal levels , especially on the cancelled l i n k . Sobieski [2.36] has described a switched polarization experiment at 12 GHz over a 2 km l ink at the Universite Catholique de Leuvain, Belgium. The construction of this experiment was not complete when [2.36] was written, but the authors intended to incorporate a two-channel cancellation network to improve the XPD measurement range. An alternative c i rcui t realization for use at IF frequencies was proposed. This cancellation network used four 3 dB hybrid junctions and four attenuators but no phase shi f ter . Dilworth [2.26] has reported a single-channel adaptive cancellation network instal led on the 11.6 GHz l ink at the University of Essex, England. The network included two 10 dB couplers, a PIN diode attenuator and a varactor phase-shifter, a l l fabricated i n microstrip. This c i rcui t increased the clear weather linear XPD from 40 dB to 60 dB, which was the system noise 119 f l o o r . Dilworth and Evans [2.37] have recently published results where this cancellation network was used adaptively to correct circular polarization on the same experimental l i n k . A microcomputer was used to control the cancel-la t ion network by searching for the minimum crosspolar signal l e v e l . This system was able to maintain an XPD of better than 40 dB even during a r a i n -induced, 10 dB copolar fade. O ' N e i l l [2.38] has described a receiving system including a single channel cancellation network designed for propagation measurements using the European Orbital Test S a t e l l i t e . This 11.7 GHz c i rcui t used the standard configuration of two directional couplers, an attenuator and a phase s h i f t e r , to s t a t i c a l l y improve the clear weather XPD. The only results presented i n this paper were those or iginal ly presented by Evans and Thompson [2.35]. Dintelmann [2.39] has published a description of a 12 GHz cancellation network i n an Orbital Test Satel l i te propagation experiment underway at the Research Institute of the Deutsche Bundesport, Darmstadt, F .R .G. Single channel cancellation networks for linear and circular cancellation networks are described. In this experiment cancellation is used s t a t i c a l l y to improve the XPD measurement range. Murphy, in this thesis, [2.40] has reported a single channel cancella-tion network i n a fixed polarization 30 GHz propagation experiment on a 1.02 km l ink at University College, Cork, Ireland. This reference does not include any discussion of the construction, operation or performance of the cancellation network. The XPD results indicate that a clear weather average XPD of 52-56 dB was obtained. Some results seem to indicate that the cross-polar signal level drifted over a considerable range. 120 2.5.1.2 XPD Improvement in this Experiment A single channel crosspolar cancellation network was chosen for XPD improvement in this experiment. Cancellation was selected instead of ortho-gonalization because rotatable d i f f e r e n t i a l attenuators and phase shifters with the necessary degree of control would have been exceedingly d i f f i c u l t to fabricate . Only one channel was equiped with a cancellation network because i t was hoped that OMT port termination impedance and antenna and feed a l ign-ment could be used to improve the XPD level on the other channel. This would allow comparison to be made between the XPD response of cancelled and uncan-celled systems. No information is lost by not cancelling both channels because the off diagonal elements in the dual-polarized transmission matrix are equal (See Chapter 4). In addition, i f only one cancellation network was i n s t a l l e d , i t would be possible to s ignif icant ly reduce the length of wave-guide required to interconnect the directional couplers, attenuator and phase s h i f t e r . Short interconnections are desirable to increase the operating bandwidth, as discussed in Section 5.6.2. 2.5.1.3 RF v s . IF Cancellation In a l l of the previously discussed experiments, where cancellation networks were actually installed in working systems, cancellation was per-formed at the propagating-signal frequency. Theoretically, cancellation could also be applied in the IF sections of a receiver which had two separate IF channels. The advantages of IF cancellation are that: - there would be no reduction in receiving system s e n s i t i v i t y . 121 - necessary components such as couplers, attenuators and phase s h i f t e r s would be f a r l e s s expensive, at the lower frequency. - f l e x i b l e - c o a x i a l rather than waveguide interconnections can be used, and - the e l e c t r i c a l length of interconnections i n terms of the c a n c e l l a t i o n frequency would be much shorter, r e s u l t i n g i n a larger operating bandwidth, as discussed i n Section 5.6.2. The only disadvantage of IF c a n c e l l a t i o n i s that phase or gain d r i f t i n e i t h e r channel of the receiving system preceding the c a n c e l l a t i o n network w i l l t r a n s l a t e d i r e c t l y to a c a n c e l l a t i o n network error [2.27], An analysis of the c a n c e l l a t i o n error due to phase and gain errors or d r i f t s i s given i n Section 5.6.1. The advantages of IF c a n c e l l a t i o n prompted an i n v e s t i g a t i o n into the gain and phase s t a b i l i t y of the r e c e i v i n g system front-end. Considerable operating experience with the front-end, both i n s t a l l e d i n the experimental system and on the bench, has shown that the gain s t a b i l i t y was very good. Ty p i c a l gain v a r i a t i o n s on the bench, a f t e r a warm up period, are one or two tenths of a dB f o r periods over an hour. Gain v a r i a t i o n s when the front-end i s i n s t a l l e d i n the system are s l i g h t l y l a r g e r , presumably due to s c i n t i l l a -tions ( f o r short term v a r i a t i o n s ) and temperature changes (for long term v a r i a t i o n s ) . The gain v a r i a t i o n s are n e g l i g i b l e f or propagation measurements and may even have been to l e r a b l e i n an IF c a n c e l l a t i o n system. However, i t was discovered that the front-end had an unacceptable AM-FM conversion f a c t o r . A 0.1 dB change i n the front-end gain induced by a small adjustment i n the receiver LO output was found to r e s u l t i n an approximate 10 to 15 degree phase s h i f t i n that channel. This phase s h i f t 122 appeared to be due to the l o c a l o s c i l l a t o r frequency m u l t i p l i e r s , but the. harmonic mixers may also have been p a r t i a l l y responsible. The phase s h i f t i s believed to be due to a change i n the m u l t i p l i e r or mixer diode impedance r e s u l t i n g from the small amplitude v a r i a t i o n . This i s not e n t i r e l y unexpec-ted, however, because both devices are designed to operate under maximally non-linear conditions. From Section 5.1.6 i t i s obvious that t h i s degree of AM-PM conversion would r e s u l t i n unacceptable crosspolar s i g n a l l e v e l d r i f t In an IF cancelled system. For t h i s reason i t was decided to perform the crosspolar c a n c e l l a t i o n at 73 GHz. 2.5.1.4 Crosspolar Cancellation C i r c u i t Description The single-channel millimetre-wave crosspolar c a n c e l l a t i o n c i r c u i t was designed to provide the greatest possible degree of t u n a b i l i t y and the l a r g e s t obtainable operating bandwidth. These design c o n s t r a i n t s were imposed by the desire f o r maximum measurement range and the unavoidable f r e -quency: d r i f t of the free running millimetre-wave source. A high degree of t u n a b i l i t y i s necessary to be able to adjust the c i r c u i t f o r almost t o t a l c l e a r weather crosspolar s i g n a l c a n c e l l a t i o n . Large c a n c e l l a t i o n c i r c u i t bandwidth i s desirable to reduce the changes i n the clear-weather crosspolar-s i g n a l baseline due to source frequency d r i f t and ambient temperature changes. Cancellation network t u n a b i l i t y i s determined by the a d j u s t a b i l i t y of the attenuator and phase s h i f t e r . (The e f f e c t s of small adjustment errors on crosspolar c a n c e l l a t i o n i s discussed i n Section 5.6.1). Bandwidth i s l i m i t e d by the t o t a l phase v a r i a t i o n with frequency between the undersired-crosspolar and c a n c e l l a t i o n signals at the j u n c t i o n of the combining coupler. 123 The most s i g n i f i c a n t source of th i s phase v a r i a t i o n i s the e l e c t r i c a l length of the s i g n a l path between the sampling and combining d i r e c t i o n a l coupler ports. (This i s described i n d e t a i l i n Section 5.6.2). The d i r e c t i o n a l couplers incorporated i n the crosspolar c a n c e l l a t i o n c i r c u i t were s p e c i f i e d on the basis of the uncorrected c l e a r weather cross-polar i s o l a t i o n . If the e n t i r e experimental system was aligned f o r best crosspolar i s o l a t i o n f o r only one p o l a r i z a t i o n , the i s o l a t i o n f o r the other p o l a r i z a t i o n was t y p i c a l l y i n the range between 25 and 30 dB. Using 25 dB as a worst case estimate and considering the i n s e r t i o n l o s s of the attenuator, phase s h i f t e r and the waveguide interconnections, r e s u l t e d i n the s e l e c t i o n of 10 dB couplers f o r both the sampling and combining d i r e c t i o n a l couplers. " I d e n t i c a l " couplers are used to equalize the v e r t i c a l and h o r i z o n t a l i n s e r -t i o n loss of the c a n c e l l a t i o n network. The couplers used are Microwave Associates MA-655. These couplers have an i n s e r t i o n l o s s of approximately 0.8 dB, which w i l l r e s u l t i n a corresponding reduction i n r e c e i v i n g system s e n s i t i v i t y . A d j u s t a b i l i t y was the major c r i t e r i o n applied i n the s e l e c t i o n of the attenuator and phase s h i f t e r . Devices chosen were the Demornay Bonardi DBB-410 and DBB-910, r e s p e c t i v e l y . These components are almost i d e n t i c a l mechanically and incorporate micrometer drive tuning which w i l l provide the maximum degree of a d j u s t a b i l i t y . The attenuator i s adjustable from 0 to 40 dB with a 0.5 dB Insertion l o s s . The phase s h i f t e r i s adjustable over a range greater than 360° and has a maximum i n s e r t i o n l o s s of 1.25 dB at 360° phase s h i f t . The physical length between the waveguide flanges on each of these components i s 14.6 cm. 124-The mechanical layout of the crosspolar c a n c e l l a t i o n network was designed to minimize the length of the waveguide connections between the c i r c u i t elements and thus maximize the bandwidth. This was accomplished by attaching the couplers d i r e c t l y to the front-end input ports and by mounting the attenuator and phase s h i f t e r as p h y s i c a l l y close to the couplers as p o s s i b l e * The t o t a l physical length of the waveguide c i r c u i t between the two coupler j u n c t i o n s , including the length of the attenuator, phase s h i f t e r , coupler arms and interconnections, i s approximately 93 cm. F i g . 2.39 i s a schematic of the crosspolar c a n c e l l a t i o n network. 2.5.2 Antenna Mounting and Rain Shields F i g . 2.40 i s a photograph of the transmitting antenna showing i t s r a i n s h i e l d and mounting method, the r e c e i v i n g antenna i s i d e n t i c a l . The antenna mounts are f a b r i c a t e d from heavy gauge mild s t e e l and angle i r o n stock. The mounts are attached to the concrete r a i l i n g around the b u i l d i n g roof. The extreme r i g i d i t y of these mounts insures there w i l l be no antenna d e f l e c t i o n even during severe wind conditions. 1 The shortest possible c o i n - s i l v e r XtfR-15 waveguide interconnections were fab r i c a t e d by f i l l i n g the waveguide sections with a low melting temperature metal a l l o y before bending. F i l l i n g the waveguide with s o l i d metal before bending s i g n i f i c a n t l y reduces the minimum p r a c t i c a l bend radius and therefore the t o t a l length of the interconnection. The metal a l l o y i s removed a f t e r bending by heating the waveguide se c t i o n and then f l u s h i n g i t with very hot water. R E C E I V I N G A N T E N N A ' O R T H O M O D E T R A N S D U C E R P H A S E C O M P E N S A T I O N W v 10 d B DIRECTIONAL C O U P L E R (INSERTION) r V A R I A B L E A T T E N U A T O R 10 d B D I R E C T I O N A L C O U P L E R ( S A M P L E ) F R O N T E N D E N C L O S U R E N 1 I I C R O S S P O L A R M I X E R I C O P O L A R M I X E R F i g . 2.39. Crosspolar c a n c e l l a t i o n network. F i g . 2.42. Reflector photograph. 127 A poly-vinyl-chloride (PVC) rain shield covers the top half of each antenna to prevent rain accumulation on the antenna components. The mounting stress of the PVC shield i s distributed by connecting i t to an aluminum ring with numerous small fasteners. PVC was chosen for i t s toughness and d u r a b i l i t y . With this mounting method, these shields have survived several large wind storms without damage. The shields did not cause any measurable change i n the antenna gain or introduce any observable pointing error. It i s important not to allow rain to accumulate on the antenna ref lec tor , subreflector or feedhorn to prevent a reduction i n crosspolar i s o l a t i o n . Several experimenters have reported crosspolar isolat ion reduction due to rain accumulation [2.41], [2.42], [1.80], [1.85]. 2.5.3 Antenna Alignment The antennas are f i r s t aligned for maximum copolar signal level and then for minimum crosspolar signal l e v e l . After a coarse alignment of both antennas and the ref lector , the copolar signal was maximized by i tera t ively adjusting the antenna azimuth and elevation. The polarization angle of the antennas Is most easily adjusted by loosening the set screws in the col lar which secures the feedhorn and then rotating the entire feedhorn and orthomode transducer assembly. The transmitted polarizations were f i r s t adjusted to be exactly ver t ical and horizontal by using a small bubble l e v e l . Then the receiving antenna feed assembly was rotated to the angle which gave the minimum crosspolar signal l e v e l . 128 129 At this point;the antenna azimuth and elevations were readjusted. The purpose of this second adjustment was to ensure that the antennas were pointed with the crosspolar n u l l aligned exactly with the ref lec tor . The maximum gain of the copolar lobe nominally corresponds to the n u l l i n the crosspolar lobe and crosspolar levels typical ly increase at pointing angles deviating from this nul l [2.43], [2.44], [1.80]. It i s not unusual however, for the pointing angle corresponding to the crosspolar n u l l to be s l i g h t l y different from the pointing angle for maximum copolar gain [2.45]. [2.46], [2.47], [2.48]. In this case, the most desirable alignment is for minimum crosspolar l e v e l . F i g . 2.33 shows that the best i sola t ion does occur for angles s l i g h t l y off axis for the antennas used i n this experiment. To determine the precise antenna alignment for best system XPD, i t i s necessary to examine the XPD through a range of frequencies. The theoretical explanation for the reason why i t i s not suffic ient to examine system XPD at one frequency is given i n Chapter 5. F i g . 2.41 shows the system XPD's measurer! for three s l i g h t l y different transmit-antenna azimuth adjustments. The f i n a l antenna alignment involved a tradeoff between copolar and crosspolar signal levels to yield the maximum system XPD. 2.6 Reflector The one metre square, f la t reflector used as the radar path target i s shown in F i g . 2.42. It is constructed from a sheet of 9.5 mm thick plate glass supported by an angle-iron frame. A coating of "Scotchtint" , a plast ic loaded with metallic part ic les , was used to make the surface reflect ive [2.1]. A PVC rain shield with an aluminum frame was instal led on the 130 reflector to prevent water accumulation which may cause depolarization (as discussed in Section 2.5.2). The calculated 3 dB beamwidth of the reflector radiation pattern is approximately 0 . 2 1 ° [2.50], This angular displacement corresponds to an approximate deflection of only 3.7 mm at the top of the ref lector . To prevent wind deflection of the ref lector , two s tabi l iz ing struts were instal led on the upper reflector corners. These tubular struts are adjustable to allow proper strut tensioning after reflector alignment. A test was performed to verify that the received signal levels were from the reflector and not due to reflections from the building on which the reflector was mounted or antenna coupling. This was accomplished by comparing received signal levels for the reflector aligned and misaligned. The copolar levels were 34-38 dB lower for various misaligned reflector positions. Cross-polar levels were observed to be at least 30 dB lower for reflector misalignment. A more accurate measurement could not be made for the crosspolar levels because of limitations imposed by the receiver s e n s i t i v i t y . Some of the measured signal when the reflector was misaligned may have been from a minor lobe on the reflector radiation pattern. This i s l i k e l y because the reflector mount only allowed reflector misalignments of a few degrees. This was not investigated further because the minimum 30 dB change in level was sufficient to ensure accurate results even during deep fades. 1 3 1 2.7 Transmission Loss After the antennas and r e f l e c t o r s were aligned, a comparison was made between the cal c u l a t e d and measured transmission los s between the transmitting and rec e i v i n g antenna ports. This was done to v e r i f y the antenna and r e f l e c t o r alignments and to be sure that there were no s i g n i f i c a n t antenna-feedline mismatches. A p r e r e q u i s i t e f o r the c a l c u l a t i o n of the transmission loss i s the v e r i f i c a t i o n of operation i n the f a r f i e l d of the antennas and r e f l e c t o r . The boundary between the near f i e l d region and the f a r f i e l d region f o r a 2D2 r a d i a t i n g aperture i s commonly estimated to occur at a distance R = — — -where D = aperture diameter or square side-dimension [ 2 . 4 9 ] . At the operating frequency, the f a r f i e l d of the antennas begins at a distance of approximately 1 8 0 m and the f a r f i e l d of the r e f l e c t o r begins at about 5 0 0 m. When considering the antenna and r e f l e c t o r together i t i s not necessary to have them separated by the sum of t h e i r near f i e l d d i s t a n c e s . Instead, to ensure the two aperture systems can be described by f a r f i e l d approximations. J a s i k [ 2 . 5 0 ] suggests the approximation: d > l A 2 x a A x A 2 ( 2 . 1 9 ) X / A + 6Aj • A + A where Ai = aperture area. For one antenna (Aj = 0 . 2 9 2 m2) and the r e f l e c t o r ( A 2 = 1 m2) the required separation i s d = 3 7 0 meters. Therefore, f a r f i e l d approximations can s a f e l y be used f o r t h i s system. 132 The angle between the normal to the r e f l e c t o r and either of the antennas i s only 0.651°. For th i s angle, the projected area of the r e f l e c t o r along the antenna axis i s i n s i g n i f i c a n t l y smaller than the r e f l e c t o r p h y s i c a l area. Therefore the antenna w i l l be assumed to occupy the same l o c a t i o n perpendicular to the r e f l e c t o r . The two way path loss or "basic transmission l o s s " [2.51] at 73.5 GHz i s given by: 4Tt(2r) 2 L ^ H = 10 l o g 1 ( ) [ ~ ] (2.20) The e n t i r e r e f l e c t o r surface i s well within the f i r s t Fresnel zone at t h i s distance because the v a r i a t i o n i n path length from the center of the r e f l e c t o r to one of i t s corners i s approximately one sixteenth of a wavelength [2.52]. Therefore, the r e f l e c t o r gain can be calculated from [2.50]: 2 ARFF 2 GREF - 1 0 l o « 1 0 [ - X r - ] ( 2 ' 2 1 ) = -5.1 dB The atmospheric loss due to molecular absorption i s nominally 0.3 dB/km at t h i s frequency (see F i g . 1.2 and [2.53]) or about 0.5 dB for the t o t a l path, but t h i s value w i l l depend on the atomospheric water vapour content, which i s quite v a r i a b l e . The s p e c i f i e d antenna port VSWR are less than 1.12. This produces a transmission loss of 0.014 dB which i s n e g l i b l e . Thus the t o t a l transmission loss i s : 133 LTOT L^^E G r X ~ G r E F + L a t m o s (2.22) = 134.7 - 50.6 - 50.9 - (- 5.1) + 0.5 = 38.8 dB The transmission loss was measured by connecting a c a l i b r a t e d attenuator between the model 13-50A mixer and the f e e d l i n e port normally connected to the transmitting antenna. This i s possible because t h i s mixer was connected to the receiver v i a a long f l e x i b l e c o a x i a l cable. This method has the advantage that the loss and mismatch i n the transmitting antenna f e e d l i n e and mixer c o a x i a l cable are automatically included i n the measurement. When 43 dB of attenuation was inse r t e d , the receiver indicated the same s i g n a l l e v e l as when th i s mixer was connected d i r e c t l y to the r e c e i v i n g antenna. There i s an estimated t 2 dB uncertainty i n t h i s measurement due to attenuator accuracy and possible impedance mismatch. The c a l c u l a t e d transmission loss i s 4.2 dB less than the measured value. Experimental uncertainty cannot account f o r the t o t a l d i f f e r e n c e . The extra l o s s i s probably due to a combination of r e f l e c t o r imperfections, r e f l e c t o r misalignment, waveguide flange mismatch, mixer mismatch, e r r o r i n the s p e c i f i e d antenna gains, and uncertainty i n the atmospheric water vapour content. 2.8 Fade Margin Using the measured path loss and a usable receiver s e n s i t i v i t y of --100 dBm, the copolar s i g n a l fade margin i s approximately 65 dB. This can 134 be extended to approximately 70 dB i f averaging times of ten seconds or over are used during data analysis . It i s more d i f f i c u l t to estimate a crosspolar measurement fade margin because of the uncertainty in the crosspolar baseline and because the crosspolar level increases with respect to the copolar level during deep fades. If a crosspolar baseline 40 dB below the copolar baseline is assumed and depolarization is ignored ( i . e . worst case) there would s t i l l be at least a 25 dB fade margin. 2.9 Data acqusition system In this experiment a minicomputer based data acqusition system samples, preprocesses and records the experimental data. This system is an extension of the one described in [2.1]. The original data acqusition system ran on the department's NOVA 840 minicomputer under the RDOS disk operating system. The software for this system was modified to be able to operate using the core resident RTOS (Real Time Operating System). Using RTOS, the data acquisition system can be operated on either the NOVA 840 or a smaller, more available , SUPERNOVA system. After preprocessing, the data is recorded on one half inch, 9-track magnetic tape. Data analysis is then performed on the main university computing f a c i l i t i e s . The following data is recorded from peripheral instruments in d i g i t a l form once per second: - channel A and B received signal levels - local osc i l la tor frequency - r e a l time A sixteen channel A/D converter i s used to sample the f o l l o w i n g parameters once per second: - three wind v e l o c i t y vectors temperature - p o l a r i z a t i o n state - mixer diode voltages - k l y s t r o n power output The status of the f i v e raingauges are sampled 16 times per second. Hardware and software provisions also e x i s t to record sixteen drop s i z e categories once per second. 136 3. METEOROLOGICAL INSTRUMENTATION 3.1 Raingauge Network 3.1.1 Path - Rainrate Measurement To be able to make accurate comparisons between observed propagation phenomena and meteorological conditions i t i s imperative that the path rainrate be sampled with sufficient spatial and temporal resolution. In two reviews by Crane [3.1], [3.2] he concludes that the lack of agreement between measured propagation and meteorological conditions was, up to that time, primarily due to inadequate r a i n f a l l observations. Fedi [3.3] and Fedi and Mandarini [3.4] have analyzed the errors due to raingauge spacing and integration time for a similar experiment. Watson [3.5], Hogg [3.6],Barsls and Samson [3.7], and Bodtmann and Ruthroff [3.8] have also discussed the importance of raingauge spacing and integration time in propagation experiments. High spatial and temporal resolution is required for path rainrate measurements because r a i n f a l l is not uniform, but instead, occurs i n " c e l l s " of f i n i t e horizontal extent. Rain cel ls vary in extent from a few kilometers up to approximately twenty kilometres. Within a rain c e l l , rainrates may only be uniform over distances of a few hundreds of metres. Rain ce l ls can also change morphologically over periods of a few seconds and travel horizontally at speeds approaching the wind veloci ty . F i g . 3.1 from [3.6], gives two examples of rain c e l l structure and temporal change. Small rain ce l l s and rapidly changing point r a i n f a l l rates are characteristic of heavy r a i n f a l l or thundershower a c t i v i t y . Medium and l ight r a i n f a l l i s typical ly much more 137 : Cf- _ J ! I ° I Z 3 km (Top) Plot of rainfall-rate con-tours (in millimeters per hour), showing two rain cells on the Bedfordshire rain-gauge network; (bottom) contours 2 min-utes later. (Top) Plot of rainfall-rate contours (in millimclers per hour) showing several rain cells, on the JJoImdel, New Jersey, rain-gaii':c network; (bottom) contours 10 seconds later. Fig. 3.1. Rain c e l l examples, from [3.6]. 138 uniform h o r i z o n t a l l y and changes much more slowly. Further data on r a i n c e l l s i s a v a i l a b l e i n [3.9]. To be able to characterize the rainrate along a path with reasonable accuracy i t i s necessary to have rainguage spacings of a few hundred metres and i n t e g r a t i o n times of a few tens of seconds. Crane [3.1] suggests spacings of "several hundred metres". Fedi and Mandarini [3.4] have estima-ted the spread of attenuation values which they expected for a propagation experiment at 30 GHz using raingauges with a 730 sq.cm. c o l l e c t i n g area spaced at 100 m and 1 km and with i n t e g r a t i o n times of 10 sec and 60 sec. Their r e s u l t s are shown i n F i g . 3.2. 3.1.2 Rain Gauge Types The two basic types of non-disdrometer r a i n gauges which have been used i n propagation experiments are the tipping-bucket and c a p a c i t i v e . A tipping-bucket r a i n gauge c o l l e c t s water i n a funnel and d i r e c t s i t to a small two chambered bucket. When a quantity of water equal to the gauge " t i p - s i z e " has accumulated the weight of the water causes the bucket to t i p and empty, allowing the second chamber to s t a r t f i l l i n g . An e l e c t r i c a l s i g n a l i s generated as the bucket t i p s . A capacitive r a i n gauge works by d i r e c t i n g the water from a c o l l e c t i n g funnel between two p a r a l l e l plates which form the electrodes of a capacitor. The r e s u l t i n g change i n capacitance i s usually monitored as a s h i f t i n the frequency of an o s c i l l a t o r c i r c u i t incorporating the capacitor. Capacitive r a i n gauges have been used by several i n v e s t i g a t o r s at B e l l Laboratories [3.-10], [3.11], [3.12] and by Fedi and h i s coworkers [3.13], 139 40 13 o g 20 h f = 30 GHz 10 sec t h e o r e t i c a l .*=100 m 100 Rainrate (mm/h) 200 F i g . 3.2. Attenuation spread f o r d i f f e r e n t raingauge spacing and i n t e g r a t i o n times. 140 [3.3]. The basic advantage of these rain gauges is their quasi-instantaneous response and their a b i l i t y to measure extremely high rain rates. Fedi and Merlo [3.13] have shown the superior response of capacitance gauges compared to tipping-bucket rain gauges for rainrates between 100 and 400 mm/hr. The disadvantages of the capacitive type gauges are their periodic maintenance requirements [3.10] and i n a b i l i t y to measure low rainrates. Freeny and Gabbe [3.11] report satisfactory readings only above 10 mm/hr. Fedi [3.3] using a s l i g h t l y improved version, has obtained results down to 5 mm/hr with only small reductions in accuracy. Capacitive rain gauges were tried i n an earl ier study at UBC but were abandoned because of their poor performance at low rain rates [2.1]. The tipping-bucket rain gauge is "simple, re l iable and requires a minimum of maintenance" [3.3] but has the disadvantage of averaging the rainrate over the period between t i p s . Tipping-bucket gauges have been used i n propagation experiments by Goldhirsh [3.14], Blevis , Dohoo and McCormick [3.15]., Fedi [3.3], Skerjanec and Samson [3.16] and Ippolito [3.17], The t ip size of the gauges used i n these experiments were: 0.25 mm [3.15], [3.16], [3.17] and 0.2 mm [3.3]. This results in an integration time at 50 mm/hr of 18 and 14.4 seconds respectively. These periods are compatible with the limits described in Section 3.1.1, but unfortunately lower rainrates have correspondingly longer integration times. Fedi [3.3] has analyzed the expected error of capacitive and t ipping-bucket raingauges at various rainrates. The analysis showed that the gauges he used had very similar accuracies for higher rainrates and that the tipping bucket gauges were more accurate for lower rainrates. Segal [3.9] also 141 includes a discussion of raingauge accuracy. F i g . 3.3 from [3.9] shows the effect of horizontal windspeed on gauge catch e f f i c i e n c y . The reduction i n co l l e c t i o n e f f i c i e n c y i s due to wind turbulence around the gauge carrying drops away from the c o l l e c t i n g aperture. 3.1.3 Rain Gauges The previous considerations i n conjunction with the extremely low probability of intense r a i n f a l l i n Vancouver (see F i g . 3.4 from [3.9]) led to the selection of tipping bucket ra i n gauges for t h i s experiment. To reduce the problems of integration-time averaging, rain gauges with a very small t i p size (0.05 mm of rain) were constructed. The f i r s t version of these 920 cm2 c o l l e c t i n g area r a i n gauges i s described i n [2.1]. These r a i n gauges had a t i p size which was adjustable to a minimum of 0.05 mm. However, at t h i s t i p size these gauges suffered some inaccuracy due to water retention i n the bucket. This problem was all e v i a t e d by incorporating a new bucket geometry and by the inclusion of several small b a l l bearings i n a cavity i n the lower portion of the bucket. These b a l l bearings r o l l from one end of the bucket to the other as the bucket t i p s . This results i n a rapid and fo r c e f u l t i p , greatly reducing the water retained i n the bucket. This extremely small t i p size results i n an integration time of only 3.6 seconds at 50 mm/hr. and : acceptable integration times down to a few mm/hr. ( I t i s not possible to put an exact lower l i m i t on the acceptable integration time because at low r a i n -rates the rate-of-change of point rainrate i s also greatly reduced.) A small permanent magnet attached to the bucket opens and closes a glass encapsulated reed switch as the bucket t i p s . The c i r c u i t which F i g . 3.3. P r e c i p i t a t i o n gauge catch e f f i c i e n c y as a function of h o r i z o n t a l windspeed, from [3.9.] 143 F i g . 3.4. P r o b a b i l i t y of exceeding a s p e c i f i e d r a i n r a t e i n Vancouver, from [3.9.] 144 interfaces the rain gauges to the data acquisition system is described in [2.1]. The accuracy of the rain gauges is determined by the t ip size accuracy and the t i p interval sampling period. The average t ip size accuracy -measured by allowing a large, known volume of water to pass through the gauge and recording the number of tips - is better than ± 1% for a l l gauges. Sampling of the rain gauge t ip interval is done sixteen times a second by the data acquisit ion system. At low rain rates the total measurement•error i s almost entirely due to the t ip size accuracy. At higher rain rates the sampling interval is the larger source of error . At 50 mm/hr rainrate the total error i s below ± 2.7%. A photograph of one rain gauge with i t s cover removed is included as F i g . 3.5. 3.1.4 Raingauge Locations Rainrate i n this experiment is measured by a network of f ive rain gauges spaced along the propagation path. These rain gauges are located on building rooftops at the locations shown i n F i g . 2.31. This spacing (approximately 220 metres) should give adequate spatial resolution for v i r t u a l l y a l l rainstorms in this climatic region. The rain gauge signals are transmitted to the data acquisition system on dedicated half-duplex telephone l i n e s . 3.2 Raindrop Size Measurement To be able to accurately correlate observed 73 GHz attenuation and meteorological conditions, the rain drop size distr ibution must also be measured. Most propagation studies have compared attenuation observations to 1 4 5 F i g . 3.5. Raingauge with cover removed. 146 calculated values based on the "standard" rain-drop size distributions referred to as the Laws and Parsons, Marshall and Palmer and Joss et a l distr ibutions . These distributions seem to provide reasonable agreement for most observations on an average basis, especially at the lower frequencies. However, some experimenters have made attenuation observations, especially in the millimetre frequency range, which do not appear to f a l l within the l imits calculated from these distributions [3.18], [3.19], [3.20], [3.4]. Some of the discrepancies between measured and calculated attenuation are undoubtably due to the natural, wide variation i n rain drop size dis t r ibut ion . Crane [3.2], Keizer et a l . [3.21], Goldhirsh [3.22], Watson [3.5], Emery and Zavody [3.23] and others have commented on the large v a r i a b i l i t y of drop size dis tr ibutions . Simultaneous measurement of the drop size dis t r ibut ion , especially including the smaller drops, is far more important i n the upper millimetre range than at the lower millimetre and microwave frequencies. For shorter wavelengths, the effect of the smaller drops i s more important because of the increased diameter-to-wavelength r a t i o . In the lower millimetre range, near 35 GHz, the drop size distr ibution has only a small effect on the attenuation [3.24], [3.25], [3.4]. However, in the range between 50 and 100 GHz the sensi t ivi ty of attenuation to drop size distr ibution is very high [3.21], [3.24], [3.2], [1.58], [1.85]. For these reasons, the measurement of drop size distr ibution has been given careful consideration i n the design of this experiment. 147 3.3 Raindrop s i z e transducer methods The three basic transducer mechanisms considered f o r real-time measurement of raindrop sizes were: o p t i c a l , electromechanical and e l e c t r o -s t a t i c . A c a r e f u l search of the l i t e r a t u r e uncovered references to two modern electromechanical methods, a wide v a r i e t y of o p t i c a l schemes and two e n g l i s h language references to e l e c t r o s t a t i c methods. No comprehensive comparison of the d i f f e r e n t methods has been published. A review of the disdrometer transducer methods i s included here to show why the e l e c t r o s t a t i c method was chosen for further i n v e s t i g a t i o n . 3.3.1 Optical Methods Opt i c a l methods r e l y on e i t h e r : scanning, arrays of sensors, l a s e r s c i n t i l l a t i o n c o r r e l a t i o n , beam e x t i n c t i o n or s c a t t e r i n g . O p t i c a l methods, with the exception of the l a s e r c o r r e l a t i o n method, have the advantage that the drop siz e i s measured d i r e c t l y , without r e l y i n g on simultaneous knowledge or assumptions about the drop v e l o c i t y or d i r e c t i o n of t r a v e l . However, the scanning and array methods may require c o r r e c t i o n for drop geometry and o r i e n t a t i o n ( i . e . canting angle). An a d d i t i o n a l advantage of the o p t i c a l methods, with the exception of the l a s e r method, i s that wind w i l l not degrade the operation of the transducer. A l l o p t i c a l methods s u f f e r some operating problems due to the large v a r i a t i o n s i n ambient l i g h t l e v e l . The scanning, array and l a s e r methods also have high e l e c t r o n i c hardware overheads associated with s i g n a l processing. 148 3.3.1.1 Optical Scanning Methods O p t i c a l scanning methods would u t i l i z e e i t h e r t e l e v i s i o n - t y p e cameras or f l y i n g - s p o t scanners. Conventional t e l e v i s i o n cameras were considered not s u i t a b l e because scanning rates were not adequate to record a drop f a l l i n g at i t s terminal v e l o c i t y . Even i f an imaging tube could be scanned f a s t enough (even i n one dimension), the hardware requirements f o r u l t r a - h i g h speed, real-time d i g i t i z a t i o n and image processing would be p r o h i b i t i v e f o r t h i s experiment. Flying-spot scanner type equipment could probably be constructed with adequate scan rates but the p r a c t i c a l problems associated with high l e v e l s of ambient l i g h t seem to preclude t h e i r use. No examples of d i s d r o -meters using e i t h e r of these approaches were found i n the l i t e r a t u r e . 3.3.1.2 Optical Array Methods Methods using arrays of photodetectors are the most promising of the f e a s i b l e o p t i c a l methods. The basic operation depends on the drop p a r t i a l l y occluding the l i g h t from a source which would normally have f a l l e n unob-structed on the elements of a photodetector array. The d i f f i c u l t y with t h i s method i s f a b r i c a t i n g the array of detectors. To have the required r e s o l u -t i o n , the e f f e c t i v e spacing between array elements would need to be less than the minimum measurable drop diameter ( i . e . preferrably l e s s than 250 microns). This precludes the p o s s i b i l i t y of an array f a b r i c a t e d from d i s -crete photodetectors unless a lens or f i b r e o p t i c system was also i n c o r -porated. A preliminary i n v e s t i g a t i o n showed the lens system would be quite large and probably require s p e c i a l f a b r i c a t i o n . The disadvantages of the 149 f i b r e o p t i c system are the d i f f i c u l t y of construction for large arrays and large i n d i v i d u a l f i b r e beamwidths. Ex c e l l e n t monolithic photodetector arrays with good r e s o l u t i o n are a v a i l a b l e . The major problem i s that the l i n e a r s i z e of the arrays i s l i m i t e d . This w i l l mean that the c o l l e c t i n g area using a s i n g l e array w i l l u s u a l l y be too small to obtain a s t a t i s t i c a l l y v a l i d sample of the raindrop d i s t r i b u t i o n [3.26]. The arrays cannot be l i n e a r l y concatenated to form a l a r g e r array because of the integrated c i r c u i t packages used. Conceivably, several arrays could be staggered to form a l a r g e r array, but t h i s would only be acceptable i f the drops f e l l v e r t i c a l l y . It i s however, probably s t i l l f e a s i b l e to use a large number of arrays i n reasonably close proximity and combine t h e i r measured raindrop histograms to improve the r e l i a b i l i t y of the s t a t i s t i c a l sample. A small integrated o p t i c a l array has been used by Cunningham [3.27] to make measurements on a v a r i e t y of hydroraeteors. The problem of the small sample s i z e was a l l e v i a t e d i n t h i s case by o r i e n t i n g the array v e r t i c a l l y , and a f f i x i n g i t to the e x t e r i o r of a j e t a i r c r a f t , thus considerably i n c r e a s -ing the number of drops sampled per unit time. Knollenberg [3.28] has constructed an o p t i c a l array f o r hydrometeor s i z e measurement using o p t i c a l f i b e r s and d i s c r e t e photodetectors. In t h i s method, one end of each o p t i c a l f i b e r i s placed i n a l i n e a r array and the other end i s connected to a photomultiplier tube. There are obvious problems associated with the f a b r i c a t i o n of large arrays using t h i s method, even i f smaller photodetectors could be employed. This type of array was used f o r 150 sampling from aircraft where the small linear array extent is not a d i s -advantage. 3.3.1.3 Laser S c i n t i l l a t i o n Correlation Method Raindrop size measuring apparatus employing an expanded laser source and v e r t i c a l l y separated sensors has recently been developed by Wang et a l [3.29] [3.30]. This technique has the unique property of measuring the average raindrop size distribution over a path of up to 200 meters i n length. A medium power cw laser is optical ly expanded to a 20 cm beam diameter and oriented horizontally along the path. The receiver consists of two horizon-t a l l inear photodetectors separated v e r t i c a l l y by a few centimetres. The s c i n t i l l a t i o n i n the outputs of the two sensors, due to the passage of drops through the beam, are correlated in an analog c i r c u i t . The correlator output for different correlation delays is then proportional to the number of drops which travelled the vert ical distance between the sensors in the correlation delay time. Unfortunately this technique rel ies on the assumption of a time-invariant monotonic relationship between drop-size and vert ical veloci ty . As a result , changes in drop vert ical velocity due either to vert ical wind veloci t ies or turbulence w i l l produce a distorted raindrop size histogram. The error in calculated drop size due to a change in drop ver t ical velocity can be determined from the known drop size terminal velocity relationships [3.31]. As an example a 1 m/s updraft would produce an approximate error in diameter of 23% for a 3 mm drop and 40% for a 5 mm drop. 151 Vertical wind velocities w i l l also produce v e r t i c a l l y correlated optical s c i n t i l l a t i o n which w i l l result i n a correlator noise output. The other disadvantage of this method is the high cost of the laser source and expander. 3.3.1.4 Optical Scattering and Extinction Methods One of the f i r s t real-time raindrop measurement systems was a photo-elec t r ic raindrop spectrometer constructed by Mason and Ramanadham [3.32], This disdrometer measured the l ight scattered by a drop as i t f e l l near an intense source. The scattered l ight at an angle of 20 degrees off -axis was collected i n a telescope-type lens system and directed to a photomultiplier tube. The drops were then electronically sorted into eight size categories. Dingle and Shulte [3.33] constructed a disdrometer similar to the one des-cribed by Mason and Ramanadham. In this reference the theory for an optimum scattering type instrument is presented. The instrument was calibrated with drops from 0.72 mm to 3.13 mm i n diameter. The resulting calibration curve shows that the output pulse height is proportional to the drop diameter squared. Very recently, Klaus [3.34] has reported a similar photoelectric d i s -drometer. In this case the degree of extinction of a beam i s used to deter-mine the drop size . This system uses solid-state diode sources and detectors and a microprocessor to sort the drops into eight categories. A serious l imitat ion of both these analog optical systems is the change i n the small-signal sensi t ivi ty of the photodetectors with changes i n ambient l ight l e v e l . This is particularly troublesome during periods of rain 152 when the ambient l ight level can be quite variable [3.31]. This type of system could conceivably be improved by using narrow bandwidth optical f i l -ters and higher intensity l ight sources. Dingle and Shulte [3.33] have also designed a " l ight shield" which improved the operation of, their scattered l ight disdrometer to some extent. 3.3.2 Electromechanical Methods The disdrometers most commonly used in propagation studies are the electromechanical types which convert the Impact from a drop as i t f a l l s on the sensor to an electronic s ignal . The mechanical to e lec t r ic energy con-version is accomplished using either a moving c o i l In a stat ic magnetic f i e l d , piezoelectic transducers or a conventional audio microphone. 3.3.2.1 Moving C o i l i n Magnetic F ie ld Method The disdrometer using a moving c o i l in a magnetic f i e l d was described by Joss and Waldvogel [3.35], Georgii and Jung [3.36], and Rowland [3.37]. It has been used in studies by Waldvogel [3.38], Joss, Thams and Waldvogel [3.39], Brewer and Kreuels [3.40] and Keizer, Snieder, and Haan [3.41]. The construction of the coil-magnet transducer is very similar to a conventional acoustic loudspeaker. A collecting surface, usually 50 cm 2 , i s connected to the moving c o i l . The collecting surface is designed to have a low mass for maximum signal output. The c o i l i s situated i n the a i r gap of a permanent magnet. The momentum of the drop causes a displacement of the c o i l thus producing an electr ic signal at the c o i l terminals. 153 In some models, a second coil-magnet assembly is also included. In this case, the c o i l i s energized with an amplified, f i l t e r e d form of the signal from the f i r s t c o i l . This produces negative feedback which can then be used to modify the sensor response time. 3.3.2.2 Piezoelectric Method The piezoelectric disdrometer was probably f i r s t described by Flach [3.42], It was subsequently adapted and expanded upon by Rowland; [3.37 ]. The Flach type piezoelectric disdrometer uses a sol id acryl ic clyinder with a beveled top. The cylinder and a piezoelectric transducer are then bonded to a brass block. The Impact of the drop on the top of the cylinder causes an acoustic wave to travel through the cylinder to the transducer. Rowland instead cast the transducer in a solid block of epoxy and thus eliminated the brass block. The piezoelectric disdrometer has been used by Goldhirsh [3.22], [3.43] and Rowland, Bennett and M i l l e r [3.44]. 3.3.2.3 Other electromechanical Disdrometers Other electromechanical disdrometers have been constructed using con-ventional audio microphones. Kinnell [3.45] used a dynamic microphone, Katz. [3.46] a condenser microphone and Cunningham [3.47] a carbon microphone. These instruments couple the displacement of a larger membrane to the micro-phone using air or a f l u i d . None of these instruments were satisfactory but they did lead to the design of the other electromechanical transducers des-cribed previously. 154 3.3.2.4 Factors Affecting the Accuracy of Electromechanical Methods Rowland [3.37] has compared the two basic types of electromechanical disdrometer transducers. The coil-magnet transducer gave an output peak voltage proportional to D^ *'' and the piezoelectric proportional to D^*-*. The range of measurable drop sizes is ultimately limited on the upper end by amplifier saturation and on the lower end by various noise sources. This large value of diameter exponent w i l l mean the smallest measurable drop size w i l l be larger for electromechanical transducers than for transducers with a pulse proportional to a lower power of the drop diameter (assuming similar noise l e v e l s ) . The major disadvantage of electromechanical transducers is their sensi t ivi ty to drop ver t i ca l veloc i ty . Rowland also investigated the res-ponse of these sensors to drops f a l l i n g below terminal veloc i ty . He found the response of the transducers was reasonably well predicted by the quan-t i t y : mv2/Djwhere ra = drop mass, v = velocity and D = drop diameter. This , is to a f i r s t approximation, the average force applied to the sensor during the period of drop c o l l i s i o n [3.37]. Rowland used this function to produce a correction factor for drops f a l l i n g at ver t i ca l speeds other than their s t i l l a i r terminal veloci ty . However, to be able to use this correction, actual drop ver t ica l velocity must be known. This requires simultaneous knowledge of the ver t ica l wind speed and the drop direction of travel with respect to the sensor. Kinnell [3.48] has examined the effects of drop shape, drop velocity and impact location on the Joss-Waldvogel disdrometer. This investigation found a discontinuity in the response of the transducer associated with drop 155 veloc i ty . No definite conclusions regarding the cause or effect of this discontinuity were given. Variations i n the position of the drop impact on the target were observed to cause a change in transducer output which was described as "quite large" . The drop shape was also found to introduce a significant uncertainty i n transducer reponse. Kinnell concludes that "variations i n factors such as rain drop velocity and raindrop shape genera-ted by a i r movements might produce unacceptable errors in the measurement of raindrop size by the disdrometer under some r a i n f a l l conditions". . . A further disadvantage of the coil-magnet transducers is their susceptability to wind-produced acoustic noise. This problem is accentuated by the requirement of a low mass, large area collecting surface. Wind shielding i s only par t ia l ly effective i n reducing this problem and can i t s e l f introduce errors when drops are not f a l l i n g almost v e r t i c a l l y . 3.3.3 Electrostatic Methods Electrostatic methods work by f i r s t arranging for a drop to a r t i f i -c i a l l y accumulate a charge which is related to the drop size and then measuring this charge as the drop impacts on a conductor at ground potent ia l . The only detailed english language reference to electrostatic measurement of rain-drop sizes which could be located was a paper by Lammers [3.49]. An ear l ier paper by Keiley and Millen [3.50] described a similar electrostatic technique to measure cloud-drop s izes . A Lamraers-type disdrometer was b u i l t and used by Sander [1.84], [3.51]. A unit developed by Sander was also used by Humpleman and Watson -[1.85]. 156 The instrument described by Lammers basically consisted of two fine horizontal wire grids separated horizontally by a small distance. The top grid was connected to a 300 V positive dc supply. A high impedance amplifier was connected between the bottom grid and ground. The grids were constructed from para l le l strands of 0.05 mm tungsten wire spaced 0.75 mm apart. This instrument had a 25 cm2 collecting area. Lammers found that this instrument produced a pulse amplitude propor-2.32 t ional to D * and yielded high signal-to-noise ratios even for drops as small as 1 mm diameter. Experiments with this transducer did show that the drops had time to completely discharge as they passed through the lower g r i d . This i s important to ensure that the pulse amplitude is not dependent on how many grid wires the drop contacts. High-speed photographic observa-tions of drops as they passed through the grids showed some drop breakup, but this did not cause "much variation" i n the output s ignal . The explanation given by Lammers as to how the transducer functioned was basical ly that the drop acquired a charge by conduction as i t passed through the upper grid and deposited this charge i n the lower g r i d , resulting i n a pulse from the amplifier . The electrostatic instrument described by Keiley and M i l l e r [3.50] was designed for measurements of cloud-drop size distr ibutions . Drops sampled by this instrument were directed through a small conducting o r i f i c e by a high velocity air stream. They then impacted on a sol id conducting target which was connected to an amplifier . A potential difference of 400 V was main-tained between the o r i f i c e and target plate. The 200 micron diameter 157 sampling o r i f i c e of this instrument was not a disadvantage because i t was used on the e x t e r i o r of an a i r c r a f t . The voltage pulse produced by th i s instrument was approximately proportional to the drop diameter squared. In t h i s instrument the sampled drop does not contact the conducting o r i f i c e . Keiley and M i l l e r believed that the pulse was due to a hemispherical induced charge acquired by the drop as i t crossed the a i r gap. The actual pulse was believed to r e s u l t from the c a n c e l l a t i o n of the charge on one side of the drop as i t struck the target. This instrument was s e n s i t i v e enough to measure drop sizes down to 4 microns. 3.3.4 Comparison of Methods An exact quantitative comparison between drop s i z e measurement methods i s not possible because comparable data are not a v a i l a b l e f o r d i f f e r e n t methods. A summary of the major advantages and disadvantages are given below: - O p t i c a l scanning methods are e i t h e r too slow or p r o h i b i t i v e l y expensive and s u f f e r from ambient l i g h t problems. - O p t i c a l array methods have the advantage of d i r e c t s i z e measurement but have inadequate sampling sizes and require c o r r e c t i o n f o r drop o r i e n t a t i o n and canting angle. - Laser c o r r e l a t i o n has the advantage of measuring the path average d i s t r i b u t i o n but suffers from the disadvantage that drop v e l o c i t y i s a c t u a l l y being observed. This method i s also very expensive. 158 - Linear o p t i c a l methods ( i . e . s c a t t e r i n g and extinction) are simple and inexpensive but have s e n s i t i v i t y and ambient l i g h t l e v e l problems. - The two electromechanical methods are very well documented and are easy to implement but have the disadvantage that the transducer pulse i s proportional to D^*^ to D^*^ and drop v e l o c i t y squared. This r e s u l t s i n a low s e n s i t i v i t y to small drops. These instruments also have errors due to drop shape, angle of incidence and impact l o c a t i o n . - The e l e c t r o s t a t i c method i s simple and r e l a t i v e l y easy to construct but i s not well documented. It produces a pulse approximately proportional to drop diameter squared and seems to o f f e r e x c e l l e n t s e n s i t i v i t y to small drops. No data was a v a i l a b l e on the errors due to drop v e l o c i t y , shape, angle of incidence or impact l o c a t i o n . I n t u i t i v e l y , these sources of e r r o r should be less serious than f o r the electromechanical methods. These considerations led to the s e l e c t i o n of the e l e c t r o s t a t i c method fo r further i n v e s t i g a t i o n i n t h i s experiment. The p o t e n t i a l f o r improved s e n s i t i v i t y was p a r t i c u l a r l y a t t r a c t i v e because of the short wavelength being studied and the recent speculations i n the l i t e r a t u r e that higher than pre-dicted attenuations i n the higher millimetre range ( i . e . above 40 GHz) were p a r t l y due to under-estimating the number of small drops^ as discussed i n Section 3.2. It was also hoped that the e l e c t r o s t a t i c method would be l e s s prone to the types of errors which degrade the accuracy of the e l e c t r o -mechanical transducers. 159 3.4 Disdrometer Transducer The electrostat ic disdrometer transducers constructed for this experi-ment are based on the instrument described by Lammers [3.49], The f i r s t disdrometer b u i l t was very similar to the one reported i n [3.49], This instrument and i t s associated electronics are described i n [3.52], [3.53]. Experience accruing from the construction and operation of this f i r s t ins t ru-ment resulted i n several improvements to the basic design. These improve-ments were incorporated i n a second generation transducer. The f i r s t transducer bui l t had a 25 cm2 sampling area and grids formed from double layers of horizontal wires with 0.45 mm horizontal spacing. This double layer grid system was also used by Lammers and results from the method used to form the gr ids . Because of the small spacing between the wires, the most feasible way to construct the grids i s by winding the wire on a frame similar to the one shown i n F i g . 3.6, producing a double layer structure. The grid spacing was reduced from the 0.75 mm used by Lammers to 0.45 mm to improve the minimum measurable drop s ize . The diameter of the Individual grid wires was reduced from the 0.05 mm used by Lammers to 0.038 mm to reduce drop breakup. Nichrome wire was used because i t was readily available and corrosion resis tant . The basic operating limitations of this transducer were found to result from movement of the grid wires and the double grid structure. Move-ment or o s c i l l a t i o n of the grid wires resulted i n a time varying change i n the capacitance of the grids which i n turn produced an output from the transducer preamplifier . Significant motion of the grid wires resulted from: the passage of the drop through the grids , high wind veloci t ies and building Tungsten Wi re P o l y c a r b o n a t e Frame Copper Bar F i g . 3.6. Disdrometer transducer g r i d . o 161 v i b r a t i o n . Passage of the drop through the grids resulted i n a decaying sin u s o i d a l output from the transducer a f t e r the main pulse. This did not seem to s e r i o u s l y a f f e c t the main pulse accurcy but did s i g n i f i c a n t l y i n -crease the t o t a l period of the pulse due to a s i n g l e drop and hence the minimum period between drops for accurate r e s u l t s . Grid motion due to wind was not u s u a l l y as detrimental as g r i d motion due to b u i l d i n g v i b r a t i o n . The b u i l d i n g v i b r a t i o n was apparently caused by the movement of large numbers of students between classes and a large v e n t i l a t i o n fan motor on the roof. These undesired signals could not be reduced by f i l t e r i n g because they were r e l a t i v e l y broadband and occupied frequencies s i m i l a r to the major s p e c t r a l components of the desired pulse. The double g r i d structure was a disadvantage because i t r e s u l t e d i n greater drop breakup and increased water r e t e n t i o n . It was observed that a f t e r a period of operation i n actual r a i n there were small droplets of water attached to the g r i d wires. The amount of water was considerably l a r g e r on the lower grids l a y e r s . This was believed to be due to the in c r e a s i n g drop breakup and s p l a t t e r r e s u l t i n g from the drop passage through each successive g r i d l a y e r . Retained water on the upper g r i d r e s u l t s i n reduced disdrometer accuracy because a part of the drop captured by the upper g r i d w i l l not d i s -charge on the lower g r i d 5 r e s u l t i n g i n a reduced output f o r that drop. In a d d i t i o n , i f t h i s water i s dislodged by a subsequent drop, the I n d i c a t i o n f o r that drop w i l l be l a r g e r . Water retained on the lower g r i d i s not thought to be detrimental. Another problem with the f i r s t disdrometer was leakage currents between the upper and lower g r i d s . After long periods of operation 5the 162 baseline or dc output l e v e l of the transducer preamplifier often d r i f t e d . When the transducer was cleaned i n alcohol and drie d , t h i s problem disappear-ed. This seemed to ind i c a t e that a high resistance leakage path had'been established along the surface of the g r i d frame, and was probably due to contaminants entering the transducer with the r a i n and a buildup of moisture. The design of the second disdrometer transducer a l l e v i a t e d the problems discussed previously, increased the sampling s i z e and further r e -duced the g r i d conductor spacing. The sampling area of the transducer was increased to 50 cm 2 i n order to reduce the period of time required f o r a s t a t i s t i c a l l y v a l i d drop d i s t r i b u t i o n sample. (A 50 cm 2 sampling area i s also used on almost a l l electromechanical disdrometers.) The major improvement incorporated i n the second disdrometer was an improved g r i d s t r u c t u r e . These grids used a sing l e layer of more c l o s e l y spaced wire with f a r greater wire tension. Grid wire spacing was fu r t h e r reduced to 0.234 mm to f a c i l i t a t e the measurement of smaller drops. This g r i d spacing i s believed to be very close to the minimum p r a c t i c a l spacing f o r grids of th i s area. A sing l e g r i d layer was used to reduce breakup, s p l a t t e r and water ret e n t i o n . The maximum possible wire tension was used to minimize the g r i d movement and to increase the natural o s c i l l a t i n g frequency of the g r i d v i b r a t i o n s . Maximum wire tension i s also necessary for best wire spacing uniformity. The wire chosen for the g r i d was 0.038 mm tungsten. This choice involved a tradeoff between the smallest possible diameter-to reduce breakup-and the highest possible t e n s i l e strength-to allow maximum wire tension. 1 6 3 Tungsten was chosen over other metals because i t i s corrosion r e s i s t a n t , has very high t e n s i l e strength and was a v a i l a b l e i n the diameter range required. F i g . 3.6 shows the g r i d frame and the method of winding the wire. Polycarbonate was chosen f o r the frame because i t i s i n s u l a t i n g , extremely strong and e a s i l y machinable. Frame r i g i d i t y was found to be extremely important because the combined forces of the approximately four hundred wires - each of which i s under a tension close to the breaking point of the wire -tends to deform the g r i d near the center. This deformation would, then r e s u l t i n a reduction i n the wire tension and spacing uniformity i n the middle of the g r i d . A copper bar i s bonded into a s l o t on each side of the frame to provide an e l e c t r i c a l contact between the wires and a connection to the g r i d . Slots f o r each wire were machined in t o the polycarbinate and copper bar using the thread c u t t i n g f a c i l i t i e s on a l a t h e . A f t e r the threads were cut, a 9.4 cm x 9.4 cm area was m i l l e d through the frame. The g r i d area i s l a r g e r than the sampling aperture to ensure that drops entering the aperture at an angle pass through both g r i d s . The distances from the g r i d wires to the g r i d mounting holes were increased to reduce the p r o b a b i l i t y of surface leakage between g r i d s . In addition, nylon, rather than metal, supports were used between g r i d s . The most d i f f i c u l t process i n the g r i d f a b r i c a t i o n was a c t u a l l y wind-ing the wire onto the frames. I n i t i a l attempts to wind the wire onto the frames by hand were not s a t i s f a c t o r y because of the extreme d i f f i c u l t y of maintaining uniform wire tension. If the winding were to be done by hand i t was estimated that each g r i d would probably require two men f o r approximately one day. The method f i n a l l y devised to wind the grids used a lathe to slowly 164 rotate the frame and an automatic wire tensioning mechanism. This reduces the time for f a b r i c a t i n g one g r i d to less than one man-day. Afte r the g r i d was wound, the wires were bonded with epoxy to the frame along the e n t i r e outside edge. Then another piece of polycarbonate sheet, cut to the same dimensions as the frame, was bonded to the top of the frame to further secure the wires. One set of the two layers of wires were then cut away to leave a si n g l e layer of wires on the frame. This elaborate method of securing the wires was found to be necessary to prevent the high wire tension from causing bond f a i l u r e a f t e r the wires were cut. The two g r i d assemblies and supporting structure are mounted i n the aluminum housing shown i n F i g . 3.7 and F i g . 3.8. The grids are located near the top opening to ensure that drops passing through the aperture pass through both g r i d s and that water does not splash back up to the grids from the drain grating on the bottom of the housing. To prevent water accumula-t i o n on the housing top, the top slopes towards the sides of the u n i t . Splashing into the aperture i s reduced by a l i p around the opening and an expanded metal g r i d s l i g h t l y above the housing top. (The ef f e c t i v e n e s s of these splash reduction methods has not been experimentally v e r i f i e d . ) A removable l i d i s provided to protect the g r i d sides from dust and h a i l when the disdrometer i s not i n use. Connections to the grids are v i a type-N jacks mounted on the side of the housing. F i g . 3.9 shows the complete disdrometer transducer. 7.1 9.4 26.7 A l l measurements i n centimetres Fig. 3.7. Disdrometer transducer dimensions. 166 167 168 3.5 Disdrometer Electronics The interconnection of the disdrometer transducer, preamplifier, peak detector and microprocessor i s shown i n F i g . 3.10. A 300 V primary battery, Eveready 493 or Mallory M722 supplies the dc voltage to the upper gr id . Batteries are used for the grid and preamplifier supplies because power supplies are neither as convenient nor as safe for operating this type of device i n wet conditions. Power supplies i n the v i c i n i t y of the transducer also tend to induce 60 Hz noise onto the lower transducer gr id . The 0.005 pF capacitor connected from the upper grid to ground was found to reduce the susceptability of the transducer to 60 Hz electrostatic interference. The transducer preamplifier, shown i n F i g . 3.11, converts the flow of charge from the lower grid to ground into a buffered voltage pulse. This charge produces a voltage across the amplifier input resistance shown as R i n F i g . 3.10. R. i s essentially equal to R, in F i g . 3.11. A discrete JFET i n I i s used as the f i r s t stage in the preamplifier because this device results i n better low frequency noise performance than can be obtained with monolithic operational amplifiers . Metal f i l m resistors are used i n the f i r s t stages of the preamplifier to reduce thermal noise contributions. Capacitor Cj is provided for testing the preamplifier using a signal generator. In normal operation this capacitor is shorted. When driven by a signal generator, the voltage gain of the preamplifier is adjustable from approximately 0.5 to 15. At a gain setting of 2.4 the amplifier has a 3 dB frequency response from 0.1 Hz to 1.8 MHz. The preamplifier is mounted i n a gasketed die cast box and mounted direct ly on the transducer housing using a type N plug-plug adapter. 300 V DISDROMETER TRANSDUCER PEAK DETECTOR A/D CONVERTER MICRO-PROCESSOR r t 0 DATA OUTPUT PEAK DETECTOR RESET F i g . 3.10. Disdrometer system block diagram. INPUT F i g . 3.11. Transducer p r e a m p l i f i e r . o 171 The peak detector, shown i n F i g . 3.12, stores the peak value of the preamplifier output pulse. This c i r c u i t was designed to have a f a s t r e s -ponse, low overshoot and high dynamic range. More than adequate holding time i s provided f o r the A/D conversion of the stored pulse. The microprocessor resets the peak detector a f t e r A/D conversion. The 12 b i t A/D converter converts the pulse amplitude to a d i g i t a l quantity f o r input to the micro-processor. Pulses are then sorted into up to sixteen s i z e categories. The microprocessor outputs the number of drops i n each category which were de-tected during the sample i n t e r v a l s . Two d i f f e r e n t schemes were used to record the microcomputer data out-put. At f i r s t , the microcomputer was i n t e r f a c e d to the data a c q u i s i t i o n minicomputer. The number of drops was transferred each second and recorded on the magnetic tape along with a l l the other experimental data. This method worked well and was used to produce the data reported i n [3.53]. The d i s -advantage of t h i s method was the high software and computing costs associated with processing the large amounts of data recorded. Because only short periods of disdrometer data were a c t u a l l y analyzed and because i n t e g r a t i o n times of up to one minute (depending on rainrate) are required f o r a s t a t i s -t i c a l l y v a l i d sample, a semimanual method was adopted to handle the d i s d r o -meter data. The microcomputer i s now i n t e r f a c e d d i r e c t l y to a hardcopy p r i n t e r . A hardware timer, which i s manually synchronized to the data a c q u i s i t i o n system, i s used to define sample and p r i n t periods. At the end of the sample period, the microcomputer p r i n t s out the number of drops i n each s i z e category. Drop size data i s then analyzed with the a i d of a pro-grammable c a l c u l a t o r . ALL DIODES ARE IN458 F i g . 3.12. Peak detector. ho 1 7 3 3.6 Disdrometer System Test Results The e f f e c t s of various disdrometer c i r c u i t parameters were i n v e s t i -gated i n an attempt to experimentally optimize the disdrometer system. F i g . 3.13 shows the peak pulse amplitudes f o r various drop sizes with d i f f e r e n t g r i d voltages. With preamplifier voltage gains of only 1 to 2 the preampli-f i e r saturated on the largest drops when using a 600 V battery. Because the s e n s i t i v i t y of the transducer i s l i m i t e d by the time varying capacitance produced by g r i d movement, a la r g e r g r i d voltage did not improve the tr a n s -ducer s i g n a l to noise r a t i o . For these reasons no advantage could be r e a l -ized by using more than one 300 V battery to power the upper g r i d . The s e l e c t i o n of the preamplifier input r e s i s t a n c e , R i n , involves a tradeoff between the pulse amplitude and pulse period. F i g . 3.14 shows that larger values of R^n are desirable because they produce large pulse amplitudes. However, larger values of R^n also r e s u l t i n longer pulse periods as shown i n F i g . 3.15. The pulse period i s defined here as the time from the s t a r t of the pulse to when the preamplifier output s e t t l e s to the noise l e v e l . The pulse period i s l i n e a r l y r e l a t e d to the value of R^ n« This i s mainly due to the time constant of the transducer capacitance-amplifier input resistance product. In a r a i n f a l l of 50 mm/hr the average i n t e r v a l between drop a r r i v a l s i n a 50 cm 2 area i s approximately 35 msec. As a r e s u l t the value of R^n was chosen to be 100 Mfi, which provides an acceptable pulse amplitude and a pulse period of approximately 16 msec. 174 1.4 0 200 400 600 800 1000 1200 Grid voltage (Volts) F i g . 3.13. Peak pulse amplitude vs gr i d voltage f or d i f f e r e n t drop diameters. 120 r-F i g . 3.15. Pulse period vs R. . 177 3.7 Disdrometer Calibration The disdrometer was calibrated by measuring the peak pulse amplitude of drops of known size and ve l o c i t y . Large drops were formed by dripping water through nozzles of various cross sections. Small drops were formed with a s p e c i a l l y constructed apparatus, shown i n Fig. 3.16, which directed a variable a i r flow around a vibrating hypodermic needle. By using different combinations of needle diameter, a i r flows, vibration frequency and vibration amplitude, drops as small as 0.5 mm could be formed. The drop sizes were determined by weighing a number of drops collected i n a very small container. Drop v e l o c i t i e s were controlled by varying the distance each drop f e l l . The c a l i b r a t i o n results for drops at terminal ve l o c i t y are shown i n Fig. 3.17. This same data i s shown i n Fig. 3.18 but here the square root of the pulse amplitude i s plotted against drop s i z e , resulting i n an almost l i n e a r curve. A least squares exponential curve f i t to this data results i n the r e l a t i o n s h i p : VPEAK - °' 0 2 7 ° 2 " 6 2 ( 3 " X ) where V i s i n volts and D i s i n mm. From the results gathered from several si m i l a r c a l i b r a t i o n s , i t has been found that the exact relationship between the peak pulse amplitude and drop size depends on the preamplifier bandwidth and time constant. The effects of drop velocity on the peak pulse amplitude for various size drops i s shown i n Fig. 3 . 1 9 . This graph shows that the peak response was l i n e a r l y related to the drop ve l o c i t y . 178 VARIABLE FREQUENCY AMPLIFIER GENERATOR VALVE F i g . 3.16. Apparatus for creating small drops. F i g . 3.17. Disdrometer c a l i b r a t i o n f o r drops at terminal v e l o c i t y . 1.75 o I ; 1 1 1 1 ' 1 0 l 2 3 4 5 ° Drop diameter (mm) F i g . 3.18. Square root of pulse amplitude vs drop diameter. F i g . 3.19. E f f e c t of drop v e l o c i t y on pulse amplitude. 182 This e l e c t r o s t a t i c disdroraeter system has an output pulse proportional 2 62 to D and l i n e a r l y r e l a t e d to drop v e l o c i t y . In comparison, the e l e c t r o -3.5 3.7 mechanical disdrometers produce pulses proportional to D to D and v e l o c i t y squared. These dif f e r e n c e s make the e l e c t r o s t a t i c disdrometer advantageous f o r measuring small drops and less susceptible to wind v e l o c i t y e r r o r s . An a d d i t i o n a l advantage over electromechanical devices i s the f a c t that the output pulse i s independent of impact l o c a t i o n on the transducer. The disadvantages of t h i s disdrometer a r i s e from the deleterious e f f e c t s of r e s i d u a l water r e t e n t i o n . After a period of operation i n act u a l r a i n , the upper g r i d often accumulates small water dro p l e t s . These are the r e s u l t of extremely small drops which have inadequate v e l o c i t i e s to escape the hydrostatic a t t r a c t i o n of the g r i d wires and from larger drops s t r i k i n g the edge of the transducer housing and splashing onto the g r i d . When these water droplets are dislodged, there w i l l be an erroneous transducer output. In t h i s experiment, t h i s problem was overcome by p e r i o d i c a l l y blowing the upper g r i d dry. This could e a s i l y be accomplished automatically with a s e r i e s of small a i r j e t s i n s i d e the transducer housing. A second problem with t h i s transducer arises when the en t i r e g r i d frame structure Is saturated with small water droplets. This only occurs a f t e r several hours of operation but when a leakage path i s established between the g r i d s , the e n t i r e system saturates and the disdrometer must be completely d r i e d . If the disdrometer was f i t t e d with a i r j e t s , t h i s problem would probably be overcome a l s o . The disdrometer system a c t u a l l y used i n t h i s experiment would measure drops down to 0.3 to 0.35 mm i n diameter. Drops were sorted into the t h i r -teen "standard" drop categories used i n most experiments. 183 3.8 Anemometer Three components of the wind velocity vector were continually measured on the roof of the Elec t r i ca l Engineering building. The anemometer assembly is mounted on top of a 8 m tower as shown i n F i g . 3.20, to reduce reading inaccuracies due to turbulence near the building. Wind direction i s conver-ted to an analog signal using a three-phase syncro c i rcui t described i n [2.1]. Horizontal and 60° elevation wind velocity are measured using pro-pellers and dc generators manufactured by the R.M. Young Co. The model 8078 generators used have a 2.40 V output at 1800 rmp. Model 21281 propellers were selected because of their low threshold and large low speed response. These four-blade propellers are made from expanded polystyrene beads, are 23 cm i n diameter and have a 30.6 cm effective pitch. Their threshold is between 0.1 and 0.2 m/s and they are calibrated at 9.18 m/s horizontal for 1800 rpm. The horizontal and 60° elevation wind speed are used to calculate the ver t i ca l wind speed during data analysis. This method alleviates the low speed problems which would arise due to propeller threshold and generator bearing f r i c t i o n i f the propeller was mounted v e r t i c a l l y . If the anemometer propeller angular response was i d e a l , the ver t i ca l wind velocity would be given by: V60° ~ VH0RIZ C O S 6 ° ° ..... VERT sin 60 6 The measured angular response of the propellers from the manufacturers specifications, is shown in F i g . 3.21. Using the data from this graph, the actual ver t i ca l wind is calculated from: F i g . 3.20. Anemometer p h o t o g r a p h . 180 240 300 0 60 120 180 Wind angle 9 (Deg) F i g . 3.21. Anemometer p r o p e l l e r angular response. 186 V 60° - 0.40 V. HORIZ V, VERT 0.82 (3.3) 3.9 Temperature Measurement A commercial temperature probe, B & K Precision TP-28, was used to monitor the ambient air temperature. This unit provides an output of 10 mV per °C or ° F . Boiling water and ice were used to calibrate the device before use. The temperature transducer output was connected to one of the analog channels on the data acquisition system for continuous recording. 4. THEORETICALLY PREDICTED PROPAGATION PARAMETERS The purpose of t h i s chapter i s to use e x i s t i n g t h e o r e t i c a l methods to pr e d i c t the propagation parameters f o r d i f f e r e n t r a i n conditions. Results of these c a l c u l a t i o n s w i l l be used as Inputs to the experimental model described i n the next chapter and compared to the measured propagation data. The p r e d i c t i v e procedures require that the parameters of the r a i n medium, i n c l u d -ing r a i n r a t e , r a i n drop s i z e d i s t r i b u t i o n , r a i n temperature, canting angle and drop shape, be s p e c i f i e d . From the drop shape and temperature, the complex s c a t t e r i n g amplitude f o r each drop s i z e can be c a l c u l a t e d . For a s p e c i f i c drop si z e d i s t r i b u t i o n , the s c a t t e r i n g amplitudes are then used to c a l c u l a t e the attenuation and phase s h i f t at d i f f e r e n t rainrates f o r waves l i n e a r l y p o l a r i z e d along the drop major and minor axes (or p r i n c i p a l planes). From these intermediate r e s u l t s and an assumed canting angle, i t i s then possible to c a l c u l a t e the v e r t i c a l and h o r i z o n t a l copolar attenuation and phase,shift, d i f f e r e n t i a l attenuation, d i f f e r e n t i a l phase s h i f t and XPD s f o r both p o l a r i z a t i o n s . I t was necessary to c a l c u l a t e these propagation parameters because crude approximations and i n t e r p o l a t i o n s would have been needed to compare the dual-polarized r e s u l t s of t h i s experiment to published propagation data. The following i s a b r i e f survey of the previously published t h e o r e t i c a l r e s u l t s . Chu [4.1], i n one of the e a r l i e r papers i n t h i s area, did include graphical r e s u l t s a p p l i c a b l e i n t h i s frequency range. The problem i s that p r a c t i c a l constraints mean that data can only be presented f o r a few d i f f e r e n t r a i n c o n d i t i o n s . For example, t h i s reference includes a graph showing 188 d i f f e r e n t i a l phase s h i f t , but only at rainrates of 5, 25 and 100 mra/h and f o r one drop s i z e d i s t r i b u t i o n . Data are also presented f o r XPD at the same ra i n r a t e but only f o r a simultaneous 20 dB copolar fade and one canting angle. Recently, Evans [4.2] and Holt and Evans [4.3] have published r e s u l t s showing XPD f o r both p o l a r i z a t i o n s vs. CPA f o r 57, 94 and 137 GHz but, unfortunately, data are only presented f o r a constant canting angle of 2° and one drop d i s t r i b u t i o n . In another recent paper, Neves and Watson [4.4] have published comprehensive calculated r e s u l t s i n c l u d i n g s c a t t e r i n g amplitudes, XPD at d i f f e r e n t canting angles, d i f f e r e n t i a l attenuation and d i f f e r e n t i a l phase at 36.5 GHz. Oguchi [4.5] has also published tables of s c a t t e r i n g amplitudes, p r i n c i p a l - p l a n e complex propagation constants and XPD f o r d i f -ferent canting angles at 34.8 GHz. The development of t h i s chapter w i l l follow the natural sequence of the p r e d i c t i v e c a l c u l a t i o n s . Accordingly, the meterological inputs to the c a l c u l a t i o n s w i l l be discussed f i r s t . Then, the s c a t t e r i n g amplitude data w i l l be presented. These two sets of information w i l l then be used to compute the propagation parameters at the frequency of i n t e r e s t f o r a v a r i e t y of r a i n c o n d i t i o n s . 4.1 Meterological Inputs To predict the macroscopic propagation properties of a transmission path, assumed to contain s p a t i a l l y uniform r a i n , i t i s necessary to sum the e f f e c t s of each i n d i v i d u a l drop along the path. This requires a knowledge of the microscopic r a i n properties i n c l u d i n g the number of drops of each s i z e 189 per u n i t volume (drop s i z e d i s t r i b u t i o n ) the drop shape, the drop o r i e n t a t i o n (canting angle) and r a i n temperature. Lack of information about these micro-scopic r a i n properties i s the largest source of uncertainty i n p r e d i c t i n g propagation parameters. Because i t i s so d i f f i c u l t to accurately measure some of these microscopic r a i n parameters i n natural r a i n , i t i s often necessary to resort to models or estimates. This u s u a l l y means that the pr e d i c t i v e c a l c u l a t i o n s must be performed f o r a range of assumed r a i n condi-t i o n s . The r e s u l t i n g range of values can then be compared to the measured propagation conditions with the hope of being able to match the observations to a consistent set of r a i n parameters. 4.1.1 Rainrate Rainrate i s the most r e a d i l y measured r a i n parameter and therefore i s convenient to use as the prime i n d i c a t o r of the r a i n medium condition when comparing predictions and observations. Because r a i n r a t e i s extremely v a r i -able, the p r e d i c t i v e c a l c u l a t i o n s must be performed f o r a wide range of values. The upper l i m i t on the ra i n r a t e used i n these c a l c u l a t i o n s was determined by the highest expected r a i n r a t e i n t h i s l o c a t i o n . Propagation parameters were calculated f o r the following r a i n r a t e s : 1.25, 2.5, 3.75, 5.0, 6.25, 7.5, 10, 12.5, 15, 17.5, 20, 25, 30, 40 and 50 mm/h. Since a l l of the propagation parameters are smoothly varying functions of r a i n r a t e , i n t e r p o l a -t i o n can be used between these values i f necessary. 190 4 . 1 . 2 Drop S i z e D i s t r i b u t i o n Even though a v a r i e t y of methods have been used t o s tudy r a i n d r o p s i z e d i s t r i b u t i o n s , t h e i r wide v a r i a b i l i t y i n n a t u r a l r a i n means that a s e l e c t i o n of d i s t r u b t i o n s must be used i n p r e d i c t i v e c a l c u l a t i o n s . The " s t a n d a r d " d i s t r i b u t i o n s which are w i d e l y used f o r p ropagat ion p r e d i c t i o n s are t h e : Joss et a l . Thunderstorm, Widespread and D r i z z l e [ 4 . 6 ] , M a r s h a l l and Palmer [4 .7 ] and Laws and Parsons [ 4 . 8 ] . A negat ive e x p o n e n t i a l d i s t r i b u t i o n I s u s u a l l y used to c h a r a c t e r i z e a l l of these d i s t r i b u t i o n s except the Laws and Parsons (where a n e g a t i v e e x p o n e n t i a l does not a c c u r a t e l y f i t the t a b u l a t e d d a t a ) . The b a s i c form of these d i s t r i b u t i o n s i s g i v e n by : N D (D ,R) = ^ e " ^ ( 4 . 1 ) where: • A = o R " 3 a n d : : N(D,R) i s the number of drops per m 3 i n the s i z e category between D-0 . 5 mm and D + 0 . 5 mm at a g i ven r a i n r a t e , R. R i s the r a i n r a t e i n mm/h. D i s the e q u i v o l u m e t r i c drop s i z e d iameter i n mm. a , 3 are cons tants N q was o r i g i n a l l y cons idered a constant [ 4 . 6 ] , [ 4 . 7 ] , but Harden, Norbury and White [4 .9] have po in ted out that the o r i g i n a l Joss et a l d i s t r i -bu t ions d i d not s a t i s f y the r a i n r a t e i n t e g r a l e q u a t i o n . In o ther words, i f the drops d e s c r i b e d by the d i s t r i b u t i o n at a c e r t a i n r a i n r a t e were cons idered 191 to be f a l l i n g at their terminal velocity i n s t i l l a i r , the rainrate calcula-ted from the sum of the drops of a l l sizes did not agree with the rainrate used i n the dis t r ibut ion . Olsen [4.10] proposed that N q be renormalized as a function of R so that the distributions did satisfy the rainrate integral equation over a certain range of rainrates. Olsen indicated that the largest discrepancy with the rainrate equa-tion was for the Joss Thunderstorm dis t r ibut ion. Neves and Watson [4.4] and Shkarofsky [4.11] have recently used the renormalized Joss Thunderstorm d i s t r i b u t i o n . Shkarofsky, however, does not use the renormalized versions for the other distr ibutions, presumably because Olsen has indicated that the greatest rainrate discrepancy is for the Joss Thunderstorm dis t r ibut ion . To test whether i t was necessary to use the renormalized distributions In this work, sample calculations of 74 GHz copolar attenuation were performed using both normalized and unnormalized distr ibutions . The test calculations showed that the largest attenuation differences were for the thunderstorm d i s t r i b u -tion but that the two drizzle distr ibution attenuations were also s i g n i f i -cantly different . For this reason, i t was decided to use the renormalized distributions exclusively for the following calculations. To avoid confusion with the unnormalized distr ibutions , these distributions w i l l be referred to as the Joss/Olsen Thunderstorm, etc. The renormalized distributions and their range of greatest v a l i d i t y for the new values of N q are given below [4.10]: 1. Joss/Olsen Thunderstorm: 192 N (D,R) = 1.31 10 3 R 0 * 0 8 4 exp (-3.0 DR °" 2 1) (4.2) r a i n r a t e : 25-150 mm/hr 2. Marshall and Palmer or Joss/Olsen Widespread: 3 0 021 —0 21 N D(D,R) = 6.62 1 0 J R U * U ^ exp(-4.1 DR U , Z i ) (4.3) r a i n r a t e : 1-50 mm/hr 3. Joss/Olsen D r i z z l e : N D(D,R) = 3.38 1 0 4 R _ 0 , 0 3 exp(-5.75R~ 0 , 2 1) (4.4) r a i n r a t e : 0.25-5 mm/hr The Laws and Parsons d i s t r i b u t i o n was not used because i t cannot be accurately described by a negative exponential d i s t r i b u t i o n . This means that c a l c u l a t i o n s can only be performed at the r e l a t i v e l y few rainrates where the tabulated drop d i s t r i b u t i o n s are given [4.8]. The Marshall and Palmer d i s t r i b u t i o n c l o s e l y f i t s the Laws and Parsons data except f o r the small drop sizes [4.11]. Calculated 74 GHz attenuation values f o r the Laws and Parsons d i s t r i b u t i o n s would be between the values f o r the Joss Thunderstorm and Marshall and Palmer d i s t r i b u t i o n s [4.10]. The drop s i z e diameter categories used i n these c a l c u l a t i o n s are 0.5 mm i n t e r v a l s centered on 0.5, 1, 1.5, ... 6.5 mm. These categories were used by Laws and Parsons and appear to have been adopted as a standard by the majority of inves t i g a t o r s since. Because these i n t e r v a l s are separated by only 0.5 mm, i t i s important to remember that the number of drops per unit volume i n these categories i s one half the value of N , as conventionally defined, which i s the number i n a 1 mm width s i z e category. 193 Implicit in the relationship between the standard drop size d i s t r i b u -tions and their corresponding rainrates, i s the assumption of zero ver t i ca l wind veloc i ty . Nonzero ver t i ca l wind velocit ies can s ignif icant ly alter the raindrop size distr ibution above the ground. The effects of ver t i ca l wind veloci t ies on copolar attenuation are analyzed i n Section 4.4. 4.1.3 Drop Shape The most accurate description of the shape of f a l l i n g water drops appears to be the one developed by Pruppacher and Pitter [4.12]. A water drop f a l l i n g in a i r assumes a shape so that the internal and external forces at the surface of the drop are i n equilibrium. The aerodynamic forces are symmetrical about a ver t i ca l axis through the center of drop mass for a drop f a l l i n g i n s t i l l a i r . As a result , the drop shape is symmetrical around this axis . Pruppacher and Pit ter accurately determined the drop's asymmetric oblate spheroidal shape by solving a pressure balance equation at the surface of the drop. Oguchi [4.5] used the techniques described by Pruppacher and Pit ter to calculate the deformation (or eccentricit ies) for the Laws and Parsons drop s izes . Oguchi concluded that the propagation parameters calcu-lated at frequencies up to 34.8 GHz using Pruppacher-Pitter drop shapes did "not d i f f e r too much" from those calculated ear l ier for oblate spheroids. The scattering amplitudes used i n the following calculations are for the Pruppacher-Pitter drop eccentr ic i t ies . The largest uncertainties in the appl icabi l i ty of the Pruppacher-Pitter drop shape arise from the assumption that the a i r surrounding the drop is not in a state of turbulence and the fact that drop col l i s ions are 194 ignored. Warner [4.13] has calculated that drops col l ide every few seconds i n heavy r a i n . He also states that drop osci l lat ions can persist for several seconds. Warner concludes that "raindrops are l i k e l y to take on a variety of shapes and orientations" and that "they are unlikely to follow closely a mean orientation or canting angle". Haworth and McEwen [4.14] have recently used a 20 GHz bis ta t ic scatter l ink to study the Doppler spectrum of the i n -coherent forward scattered signal from r a i n , hoping to detect drop vibrat ions . They conclude that "suggestive but not conclusive evidence for the detection of drop vibrations has been presented. . . " . 4.1 .4 Canting Angle As a raindrop f a l l s , ver t ica l wind gradients cause the orientation of the drops axis of symmetry (or minor axis) to shif t from v e r t i c a l . The angle between the axis of symmetry and ver t i ca l i s called the canting angle. Brussaard [4.15], explained that this wind gradient is caused by f r i c t i o n with the ground and results in a decreasing wind speed with decreasing height i n the region below 1 km i n height. The ver t ica l wind gradient i s influenced by the height above ground, wind speed and type of t e r r a i n . Brussard's model for canting angle also showed a theoretical relationship between drop size and canting angle. F i g . 4.1, from [4.15] shows Brussaard's predictions for canting angle as a function of drop size and height above ground for a horizontal wind speed of 15 m/s. Maher, Murphy and Sexton [4.16] later developed a theoretical model to explain the distr ibution of canting angles based on the effects of wind 195 0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 DROP DIAMETER (mm) F i g . 4.1. Canting angle as a function of s i z e and height. 1.96 gusting. Their model provided an explanation of the simultaneous observation, of drops with p o s i t i v e and negative canting angles. Very l i t t l e data e x i s t from the d i r e c t measurement of canting angles. The most notable i n v e s t i g a t i o n of canting angle was c a r r i e d out by Sanders [4.23] using a "raindrop camera". In th i s study 463 photographs from two storms were c o l l e c t e d and the canting angles were measured using a pr o t r a c t o r . Results f o r the two storms showed that about 40% of the drops had a canting angle i n excess of 15° and about 25% had negative canting angles i n excess of -15°. These t h e o r e t i c a l models and l i m i t e d experimental observations i n d i c a t e that drops have a d i s t r i b u t i o n of canting angles i n natural r a i n . The t h e o r e t i c a l models to predict canting angles include many variables> some of which are almost as d i f f i c u l t to measure as the canting angle i t s e l f . For these reasons i t i s not, at present, possible to make meaningfulljr accurate estimates of canting angle d i s t r i b u t i o n s f o r use i n propagation predictions.. As a r e s u l t , most experimental i n v e s t i g a t o r s have simply used a v a r i e t y of constant or " e f f e c t i v e " canting angles i n c a l c u l a t i o n s for comparisons with experimental data, even though t h e o r e t i c a l models have now been developed which can use more complicated canting angle models. Watson [4.17] discusses t h i s problem of r e l a t i n g measurements to canting angle s t a t i s t i c s . As a s o l u t i o n , Watson has defined an "equivalent mean, canting angle as that value of canting angle i n a constant-canting-angle r a i n f a l l model required to give an equivalent c r o s s p o l a r i z a t i o n to that measured i n the rainstorm." This d e f i n i t i o n w i l l be used i n th i s experiment. In t h i s study, propagation para-meters were calculated for constant or equivalent mean canting angles of 1, 197 2 , 3 , 4, 6 , 8, 1 0 , 15, 2 0 , 3 0 and 45° (which i s equivalent to the c i r c u l a r p o l a r i z a t i o n case f o r any canting angle.) Some q u a l i t i t i v e improvement on the assumption of a constant canting angle can be made by considering the r e s u l t s of Oguchi [4.5] and Kobayashi [4.18]. These two papers show graphs of crosspolar i s o l a t i o n [XPI] (which, f o r p r a c t i c a l purposes i s equal to XPD [4.19], [4.18]) as a function of the canting angle standard d e v i a t i o n . Both graphs use the p r i n c i p a l plane attenuations calculated by Oguchi [4.5], but f o r some reason, which Is not r e a d i l y apparent, the two sets of r e s u l t s d i f f e r by a small amount. The r e s u l t s show that XPI (or XPD) w i l l improve f o r increasing standard devia-t i o n . Oguchi states that "when the standard deviation exceeds 3 0 ° , cross-p o l a r i z a t i o n f a c t o r s tend to improve as compared with those calculated f o r equioriented raindrops." He also concludes that "the r e s u l t s show that the canting angle of the equioriented model i s replaced by the e f f e c t i v e canting angle and the d i f f e r e n t i a l propagation constant i s reduced by a multiplying f a c t o r . An example of the c a l c u l a t i o n s based on the measured canting-angle d i s t r i b u t i o n by Sauders [1971], shows that the c o r r e c t i o n to the d i f f e r e n t i a l propagation constant i s 48%, and the c r o s s - p o l a r i z a t i o n f a c t o r f o r c i r c u l a r p o l a r i z a t i o n , c a l c ulated at 34.8 GHz for a rainrate of 50 mm/h and for a propagation path of 1 km, improves about 7.5 dB as compared with that for equioriented model." Chu [4.1] also used a constant multiplying factor to cor r e c t r e s u l t s calculated f o r a constant canting angle model. A recent review by Olsen [4.20] includes a survey of methods used i n p r e d i c t i v e calcu-l a t i o n s to account for canting angle d i s t r i b u t i o n s . These r e s u l t s i n d i c a t e that the c a l c u l a t i o n s f o r a constant canting angle w i l l be a worst-case condition compared to a distr ibution with the same mean but they could probably be corrected i f adequate canting angle information were available. 4.1.5 Rain Temperature Kinzer and Gunn [4.21] have published a comprehensive study which showed that raindrops can be much cooler than the surrounding a i r due to evaporation. They conclude that the drop temperature i s within a few tenths of a degree Celcius of the temperature indicated by a venti l lated wet bulb thermometer, regardless of drop s i z e . It turns out, however, that i n the higher mil l imetric range, the effect of drop temperature does not s ignif icant -ly effect the calculated attenuations. Olsen [4.10] has published results which indicate that the difference i n attenuation for rain temperatures between 0 and 20°C are negligible i n the frequency range above approximately 50 GHz. He concludes that " i t i s only for frequencies below about 15 GHz where temperature variations have a significant effect on the calculated value of A [attenuation], and even then the effect is not large" . Rogers and Olsen [4.22] have published a graph showing the variation i n 70 GHz attenuation for rain temperatures between -5°C and 40°C. these results indicate that attenuation over the approximate range of 3°C to 23°C i s , for a l l practical purposes, identical to the attenuation at the 20°C reference temperature. For this reason i t appears to be possible to use any reasonable value for drop temperature in the frequency range used in this experiment. The scattering parameters used in the following calculations are for a drop temperature of 20°C. 199 4.1.6 Spatial Uniformity It was shown i n Section 3.1.1 that the rainrate during natural rain i s not uniform horizontally . This w i l l also mean that the drop distr ibution and canting angle w i l l vary along a long propagation path. To include the effects of this horizontal meterological v a r i a b i l i t y on long paths, i n v e s t i -gators have used synthetic storm models and distributions of rain parameters within individual rain cel ls when predicting propagation effects , e .g . [1.85], [4.4], [4.24]. Fortunately, in this experiment, the physical length of the radar path i s only 900 m. It is therefore reasonably accurate to assume, for calcula-tion purposes, that the meteorological conditions along this path are uniform and can be characterized by the path average rainrate calculated from the f ive raingauges. When making comparisons to individual rain events, the v a l i d i t y of this assumption can easily be checked by comparing the results from the individual raingauges along the path. 4.2 Scattering Amplitudes The forward scattering amplitudes presented i n this sect ion 2 were calculated using a f i e l d point-matching program developed by Dissanayake and Watson [4.25] using the following conditions: 1. Frequency = 74 GHz. 2. Pruppacher-Pitter drop shape eccentr ic i t ies . 2Provided by Dr. P .A. Watson, University of Bradford, U.K. 3. Drop temperature = 20°C. 4. Refractive index = 3.6994 + j2.1824. 5. Angle of incidence = 90° ( i . e . terres t r ia l path). 6. Laws and Parsons drop s izes . The scattering complex amplitudes under these conditions for the drop principle planes are shown i n Table 4.1. Table 4.1 Forward Scattering Amplitudes at 74 GHz Drop ST(o) S I I (o ) Diameter (mm) 0.5 1.67648 . 1 0 - 2 - j5 .81169 . lO - 2 1.69305.10"2 - j5 .84513 . lO - 2 1.0 3.70110 . l O - 1 -j3.43414 - l O - 1 3.81541 .10" 1 - j 3.46684.10"1 1.5 1.03925 - j 2.98682*10"1 1.07658 - j 2.74903.10"1 2.0 1.68310 -13.79032 .10" 1 1.77801 -j 3.14879 . l O " 1 2.5 2.60981 ~j4.39117 « 1 0 - 1 2.80529 - j 2.26872.lO" 1 3.0 3.56138 -j4.89027 » 1 5 - 1 3.88261 -j 1.05223 .10" 1 3.5 4.71177 -j6.19467 *10 _ 1 5.21626 +j 9.11839 . l O - 2 4.0 5.9625 -j7.0845 .10" 1 6.6288 +J3.5173.10 - 1 4.5 . 7 .3685 -j8.49.10~ 1 8.240 +J6.571.10 - 1 5.0 8.932 -19.65 ' l O - 1 9.953 +j 1.013 5.5 10.6 - j l . 0 6 11.8 +11.39 6.0 12.4 - j l . l 13.8 +J1.8 6.5 14.0 , - j l . 2 15.9 +J2.4 4.3 Calculated Propagation Parameters In this section, the scattering amplitudes w i l l be used to calculate the copolar attenuation and phase s h i f t , d i f f e r e n t i a l attenuation, di f feren-t i a l phase s h i f t , and XPD's for a l l of the meteorological conditions d i s -cussed i n Section 4.1. The f i r s t step in the procedure i s to calculate the principal plane attenuations and phase s h i f t s . Principal plane complex attenuations ( i . e . magnitude and phase) would be equal to the copolar attenuations f o r v e r t i c a l and ho r i z o n t a l l i n e a r p o l a r i z a t i o n s i f a l l drops had zero canting angle. In t h i s case, when a l l the drops are aligned and the transmitted p o l a r i z a t i o n s are i n the drop p r i n c i p a l planes, there w i l l For nonzero canting angles, the transmitted p o l a r i z a t i o n i s l i n e a r l y transformed to be p a r a l l e l with the drop p r i n c i p a l planes. A f t e r propagation through the a n i s o t r o p i c medium, the vectors are retransformed to y i e l d the received v e r t i c a l and h o r i z o n t a l s i g n a l s . This procedure r e s u l t s i n the elements of the medium transmission matrix ( i . e . the propagation parameters assuming i d e a l antennas). From these r e s u l t s the d i f f e r e n t i a l attenuation and phase s h i f t and the XPDs f o r both p o l a r i z a t i o n s can be d i r e c t l y c a l c u l a -ted. 4.3.1 P r i n c i p a l Plane Attenuations and Phase S h i f t s v The basic method f or c a l c u l a t i n g the attenuation and phase s h i f t f o r l i n e a r p o l a r i z a t i o n p a r a l l e l to the drop major and minor axes i s a t t r i b u t e d to Van de Hulst [4.26]. From [4.1], the equations are: also be no s i g n a l d e p o l a r i z a t i o n . A. I, II = 0.434 TT Drop siz e s I RefSj I X ( 0 ) }ND . AD .. (dB/km) (4.5) e. i , i i = -36 Drop sxzes I Im{ST jj_(0) }N^« AD .. (deg/km) (4.6) where: - S I,II are from Table 4.1 202 - N D are from (4.2) - (4.4) - AD = 0.5 as discussed i n Section 4.1.2 - the summation i s over the Laws and Parsons drop sizes (Section 4.1.2) For a zero canting angle the subscripts I and II are applicable for v e r t i c a l and horizontal polarizations, respectively. Hogg and Chu [4.27] note that the relationship between (4.5) and the tradit ional Medhurst [4.28] method for calculating copolar attenuation can be shown by the following relationship between the extinction cross section, Q, and the forward scattering function: Q = -f- Re {S(0)} (4.7) Figs . 4.2 and 4.3 show the magnitudes and angles of the principal plane attenuations vs rainrate for the three drop size distributions d i s -cussed i n Section 4.1.2. The values calculated from (4.5) were compared to the results from Olsen'.s [4.9] A = aR equation. Values for a and 3 for 74 GHz were obtained by l inear interpolation of Olsen's published values at 70 and 80 GHz. Com-parisons were made for the rainrates i n Section 4.1.1 which were i n the range of the rainrates used i n the regressions by Olsen for each of the drop size distributions i n Section 4.1.2. The average value of and A^j agreed with Olsen's results to within 3.7%, 6%, and 4.3% (percent of dB difference) for the Joss/Olsen Drizzle , M & P or Joss/Olsen Widespread and Joss/Olsen Thunderstorm distr ibutions , respectively. The largest differences were a l l at the largest val id value of rainrate for each dis tr ibution, indicating that some of the difference is l i k e l y due to increasing error in the regression 203 F i g . 4.2. Magnitude of p r i n c i p a l plane attenuation, vs. r a i n r a t e . 204 140 Drop s i z e d i s t r i b u t i o n s : 1. Joss/Olsen D r i z z l e 2. Joss/Olsen Widespread or M & P 3. Joss/Olsen Thunderstorm 120 A, I I 100 80 60 A. I I 40 AT 20 TLT _J 50 10 20 30 Rainrate (mm/h) 40 Fi g . 4.3. Angle of p r i n c i p a l plane attenuations vs. r a i n r a t e . 205 performed by Olsen. The agreement between the two sets of c a l c u l a t i o n s i s considered to be very good. 4 . 3 . 2 Propagation Parameters f or Canted Raindrops The propagation parameters f o r a r a i n medium composed of drops with a constant canting angle are calculated by transforming the transmitted polar-i z a t i o n Into the drop p r i n c i p a l planes, applying the p r i n c i p a l plane complex attenuations and then retransforming the p o l a r i z a t i o n s back into v e r t i c a l and ho r i z o n t a l components. The geometry f o r t h i s c a l c u l a t i o n i s shown i n F i g . 4 . 4 . The transformation from v e r t i c a l and h o r i z o n t a l p o l a r i z a t i o n to the p r i n c i p a l plane d i r e c t i o n s (I and II) i s given by: I _ E _ I I cos <{> sm <J> s i n (j) cos <j> E„ V _H ( 4 . 8 ) The reverse transformation, from the p r i n c i p a l planes to v e r t i c a l and ho r i z o n t a l i s : cos <{> - s i n <J> s i n <j> COS (J) E _ I E _ I I (4 .9 ) I f the subscripts TX and RX are used to designate the transmitted and received s i g n a l s r e s p e c t i v e l y and T^ and T 2 are used to describe the complex attenuations over the transmission path, then the e f f e c t of the r a i n medium on waves l i n e a r l y p olarized i n the I and II d i r e c t i o n s can be described by: 206 F i g . 4.4. Geometry for canted drop c a l c u l a t i o n s . RX II 0 0 TX (4.10) E RX II TX The off-diagonal elements of this matrix are zero because no depolarization occurs for signals l inear ly polarized i n the principal planes. Similarly , the path transmission matrix for ver t i ca l and horizontal polarizations can be written: E. RX RX 11 L21 12 L22 TX H, TX (4.11) Using (4.8)-(4.10) to describe equation (4.11) Ev RX EH _ RX cos $ sin <j> - s i n <j> cos <j> T1 0 0 T, cos - s i n <J> sin (j) cos <j> TX _ H TX (4.12) Solving for T ^ yie lds : 2 2 T l l = T l C O S ^ + T2 s i n * 2 2 T22 = T l S l n * + T2 C O S * T 1 2 = T 2 1 = ( T 2 - T l ) sin2tj) (4.13) (4.14) (4.15) These equations for T are equivalent to those given by Neves and Watson [4.4] except that they formally use the ensemble average along the path of the canting angle. The differences are the substitution of cos2<|<j)|>, sin^jc})^ and <sin2<J>> for the corresponding terms present in 208 (4.13)-(4.15). The formal use of the ensemble average is rigorously correct but i s not used here to simplify notation and because only constant canting angles are actually used i n the following calculations. with positive and negative canting angles tend to cancel. This is the basic mechanism which explains the results of Oguchi [4.5] and Kobayashi [4.18] which show XPI improvements for large canting angle standard deviations (ref. Section 4.1.4). It i s also important to note that i f the sign of mean canting angle changes, the angles of T , ? w i l l change by 1 8 0 ° . from positive and negative canting angles cancel, the depolarized signals resulting from the two way propagation of a radar path w i l l not cancel. This can be readily shown by resolving the signal transmitted into the anisotropic rain medium into components para l le l to the drop axes, which l i e i n the principal planes of the medium. The two way propagation of the path, in the +Z and -Z directions, w i l l y ie ld results identical to (4.13)-(4.15) for the same total path length, assuming a homogeneous rain medium along the path. Using (4.13)-(4.15), the following, direct ly measurable, propagation parameters can be defined: From (4.15) i t can be seen that the depolarizing contribution of drops It should be pointed out that even though depolarization contributions Different ia l attenuation = 20 l o g ( | T „ | - | T . | ) (4.16) (4.17) (4.18) 209 XPD R = 20 log It i s Important to note that the copolar attenuations ( T J J and T 2 2 ) are l i n e a r l y r e l a t e d to the propagation path length, assuming uniform r a i n . It i s , therefore, also possible to express d i f f e r e n t i a l attenuation and d i f f e r e n t i a l phase on a per kilometer basis. However, because T j 2 i s a vector, rather than s c a l a r , d i f f e r e n c e , i t i s not pos s i b l e to p r e c i s e l y express T^ 2, and therefore XPDs, on a per unit length basis. ( I t should be mentioned that there i s an approximation f o r XPD which uses a "small argument approximation" that r e s u l t s i n an expression for XPD that i s l i n e a r l y r e l a t e d to path length [4.20].) For t h i s reason, the following r e s u l t s f o r T 1 2 and XPDs are given f o r the 1.8 km path length used i n t h i s experiment. The following graphs show a representative sampling of the propagation parameters calculated at 74 GHz for the meteorological conditions described i n Section 4.1. D i f f e r e n t i a l attenuation, d i f f e r e n t i a l phase, magnitude of T 1 0 , angle of T „, and XPD vs rainrate are shown i n F i g s . 4.5, 4.6, 4.7, 4.8 and 4.9 r e s p e c t i v e l y . XPD^ vs CPA^ i s shown i n F i g . 4.10. It i s very i n t e r e s t i n g to note that the XPD vs ra i n r a t e r e l a t i o n , shown i n F i g . 4.9 i s almost t o t a l l y independent of drop s i z e d i s t r i b u t i o n . This occurs because the higher CPA for the d i s t r i b u t i o n s with smaller drops i s almost p e r f e c t l y compensated by a lower value of T 1 2 as shown i n F i g s . 4.2 and 4.7. J l [22 (4.19) 210 1.2 a o I u u td •rf a u <4-l •H 1.0 0.8 0.6 0.4 0.2 Drop s i z e d i s t r i b u t i o n s : •1. Joss/Olsen D r i z z l e 2. Joss/Olsen Widespread or M & P 3. Joss/Olsen Thunderstorm Canting angle in brackets 20 30 Rainrate (mm/h) 40 50 F i g . 4.5. D i f f e r e n t i a l attenuation vs. r a i n r a t e and canting angle. 211 DD QJ •U <+-l - H 43 CO OJ w Ji •H 4J a OJ S-J U H • r l Q Drop s i z e d i s t r i b u t i o n s : 1. Joss/Olsen D r i z z l e 2. Joss/Olsen Widespread or jM & P 3. Joss/Olsen Thunderstorm Canting angle i n brackets 20 30 Rainrate (mm/h) 1 (20°) V \ 1 (10°) X 1 (2°) 2 (20°) 3 (20°) 2 (10°) 2 (2°) 3 (10°) 50 3 < 2°> F i g . 4.6. D i f f e r e n t i a l phase s h i f t vs. r a i n r a t e and canting angle. 212 100 90 Drop s i z e d i s t r i b u t i o n s : •1. Joss/Olsen D r i z z l e 2 . Joss/Olsen Widespread or M & P 3. Joss/Olsen Thunderstorm Canting angle i n brackets Path length = 1.8 km 80 70 60 50 1 (2") 3 (6°) 40 30 10 20 30 Rainrate (mm/h) 40 50 Fig. 4.7. Magnitude of T vs. rainrate. 12 213 to o CD rH 60 100 i -50 U 0 r--50 U -100 Drop size distributions: • — 1. Joss/Olsen Drizzle — •2. Joss/Olsen Widespread or jM & P — 3. Joss/Olsen Thunderstorm Canting angle in brackets Path length = 1,8 km -150 -200 10 JL 20 30 Rainrate (mm/h) 40 "50 F i g . 4.8. Angle of T v s . rainrate.. 214 Drop s i z e d i s t r i b u t i o n s : •1. Joss/Olsen D r i z z l e 2. Joss/Olsen Widespread or M & P 3. Joss/Olsen Thunderstorm Canting angle i n brackets Path length = 1.8 km I I ! I ! I 0 10 20 30 40 50 Rainrate (mm/h) F ig . 4.9. XPD vs . rainrate for horizontal polarizations. 2 1 5 Drop s i z e d i s t r i b u t i o n s : 1. Joss/Olsen D r i z z l t Widespi Thunderstorm _L 10 20 30 40 Horizontal copolar attenuation (dB) 1 (2°) 2 (2°) 3 (2°) 1 (6°) 2 (6°) 3 (6°) 50 F i g . 4.10 . XPD vs. CPA for ho r i z o n t a l p o l a r i z a t ion, 216 4.4 Effects of Vert ical Wind on Copolar Attenuation Vert ical components of wind velocity can signif icantly affect attenua-tion by changing the drop size distr ibution above the ground [4.28], The distr ibution i s altered because the ver t i ca l wind equally affects the d i f -ferent f a l l veloci t ies of drops of different s izes . In this section, the effects of a constant ver t i ca l wind velocity component on CPA w i l l be estima-ted i n terms of the change in the attenuation/measured-rainrate re la t ion . A l l other propagation parameters w i l l , of course, also be similarly affected by a change in the drop size d is t r ibut ion . There are at least two known causes for ver t i ca l wind v e l o c i t i e s . Semplak and Turrin [4.29] state that "the c lass ica l picture for ver t i ca l wind movement at the interface of the cold front i s updrafts associated with the retreating warm system and downdrafts i n the advancing cold f ront" . The second cause of ver t i ca l wind i s changes i n topography. From Caton [4.30], " . . . lee-wave ver t i ca l velocit ies of order 1 m s e c - 1 may occur over a sub-stantial azimuth sector to at least 20 km downstream of even small h i l l s 100 m high. The wavelength of such waves is typical ly 5-16 k m . . . " In s t i l l a i r , drops f a l l at a terminal velocity at which the forces of gravity and aerodynamic drag are in equilibrium. Terminal veloci t ies for the standard drop sizes are given in Table 4.2 from [4 .31]: 217 Table 4.2 Drop Terminal V e l o c i t i e s i n S t i l l A i r Drop Diameter (mm) Terminal V e l o c i t i e s (m/s) 0.5 2.06 1.0 4.03 1.5 5.40 2.0 6.49 2.5 7.41 3.0 8.06 3.5 8.53 4.0 8.83 4.5 9.00 5.0 9.09 5.5 9.13 6.0 9.14 6.5 9.14 For cases where there i s a constant v e r t i c a l wind v e l o c i t y , the steady-state v e r t i c a l f a l l v e l o c i t y i s given by: V = V - V (4.20) w I ^ E L m where p o s i t i v e v e r t i c a l wind v e l o c i t i e s are defined to be upward. To estimate the e f f e c t s of a v e r t i c a l wind v e l o c i t y , i t w i l l be assumed that the v e r t i c a l wind only occurs at heights below the r a i n c e l l and that the v e r t i c a l wind has a constant v e l o c i t y to heights well above the microwave path. These are reasonable assumptions when the v e r t i c a l wind i s created by topographical changes but are of course not s t r i c t l y v a l i d f o r v e r t i c a l winds associated with weather f r o n t s . For th i s v e r t i c a l wind model, the drop s i z e d i s t r i b u t i o n leaving the r a i n c e l l i s the same as would be measured on the ground i n the absence of v e r t i c a l wind. It w i l l also be assumed that the: depth of the v e r t i c a l wind region i s s u f f i c i e n t f o r the 218 drops to reach their steady state v e l o c i t i e s . Under these assumptions, the actual rainrate measured at the ground w i l l not be altered but the drop size distr ibution i n the ver t i ca l wind region w i l l be changed. It should be mentioned that some other Investigators [3.4], [4.32] appear to have approached this problem from the opposite point of view and assumed that the effect of ver t i ca l wind i s to change the rainrate measured on the ground. This approach is not believed to be as r e a l i s t i c as the one described here because of the equal change i n the ver t i ca l veloci t ies for drops of different s izes . Because the drop size distr ibution is inversely proportional to the drop veloci ty , the value of for each drop size in the presence of v e r t i c a l wind i s now given by: VDRQP ( D ) N (D) = N (D) ' I A*? (4.21) This calculation may only be val id for ver t i ca l wind veloci t ies up to the smallest s t i l l a i r drop velocity considered ( i . e . 2.06 m/s). At higher up-ward wind v e l o c i t i e s , the drop motion would also be upward and then this simple model would predict a constantly increasing number of drops near the top of the ver t i ca l wind region. Horizontal CPAs for distributions calculated from (4.21) at several wind veloci t ies are shown in F i g . 4.11. For this analysis, i t has been assumed that the drop size distr ibution above the ver t i ca l wind region is described by the Joss/Olsen Widespread or Marshall and Palmer d is t r ibut ion . Even though the ver t ica l wind model used here is probably a simplificat ion of 219 F i g . 4.11. H o r i z o n t a l CPA vs. r a i n r a t e f o r d i f f e r e n t v e r t i c a l wind v e l o c i t i e s . the actual conditions during natural ra in , the results in F i g . 4.11 are considered to be suff i c ient ly accurate for v e r t i c a l velocities below 2 m/s for comparison to experimental resul ts . These results i l lus t ra te the Import-ance of measuring ver t i ca l wind velocit ies i n propagation experiments. 4.5 Backscatter Calculation Because a radar path is used i n this experiment, a component of the received signal w i l l result from backward scattering from the rain volume common to both antenna beams. The rain backscattered copolar s ignal , refer-red to as rain c lut ter , Is a l imit ing factor i n radar systems and accordingly has been studied theoretically and experimentally by several investigators. A calculation of the rain backscatter for this path w i l l be made to estimate the relative level of this undesired signal compared to the signal returned from the reflector at the end of the path. The type of radar configuration used i n this experiment i s referred to as a bis ta t ic radar because the transmitting and receiving antennas are not collocated. Rain backscatter for a bis ta t ic radar can be calculated from [ 4 . 3 3 ] : 3 V o ( 6) e -aR, - aR. ( 4 . 2 2 ) 4TTX2 R 2 R 2 2 where: P , P are the received and transmitted powers. A^, A ,^ are the antennas' effective areas R , R„ are the ranges to the rain volume common to the antenna beams 3 is the scattering cross section per unit volume V i s the s c a t t e r i n g volume of. 0) gives the angular properties of the s c a t t e r i n g process and -oR i s the atmospheric attenuation e In t h i s experiment, the ranges and antenna e f f e c t i v e areas are equal. The sc a t t e r i n g d i r e c t i o n i n t h i s case i s n e g l i g i b l y d i f f e r e n t from d i r e c t l y back-V7ard, so o( 8) can be ignored i f the backscatter cross s e c t i o n i s used f o r g. Therefore, ignoring attenuation, t h i s equation can be rewritten f o r t h i s experiment as: c u l t to c a l c u l a t e exactly because of the complicated geometry of the volume and because small errors In the assumed pointing angles w i l l r e s u l t i n large changes i n t h i s volume. An a d d i t i o n a l complication a r i s e s i n t h i s experiment because of the proximity of the b u i l d i n g on which the r e f l e c t o r i s mounted. On top of t h i s b u i l d i n g , a penthouse s h i e l d s the r a i n volume behind and above the r e f l e c t o r from both antenna beams. The r a i n volume behind and below the r e f l e c t o r i s shielded by the top f l o o r of the b u i l d i n g . Therefore, only the common r a i n volume i n front of the r e f l e c t o r can backscatter a s i g n a l . The f i r s t point common to both antenna 3 dB beamwidths i s approximately 660 m from the antennas. (If the buil d i n g were not there, the f a r t h e r common point would be about 1300 m. from the antennas). The antenna 3 dB beamwidths are about 6.8 m i n diameter at the r e f l e c t o r . This r e s u l t s i n a common volume i n 6 V (4.23) The volume common to the 3 dB beamwidths of the two antennas i s d i f f i -222 front of the reflector or approximately 3000 m 3 . (Without the building this would have been approximately 11000 m 3 ) . Calculated backscatter cross sections for frequencies between 20 and 100 GHz have recently been published, by Crane [4.34]. These calculated results appear to agree well with the experimental results published by Currie, Dyer and Hayes [4.35] and Dyer and Currie [4.36]. Crane's calculated backscatter cross sections per unit volume at 73 GHz are appoximately 1.0 • 10" 3 m - 1 and 1.1 • 1 0 - 3 m - * for the Laws and Parsons and Marshall and Palmer drop size distr ibutions , respectively, at a rainrate of 50 mm/hr. Using these results the l inear ly polarized, copolar backscatter can be calculated using (4.23). The results for this calculation, which ignores attenuation, predicts a received, rain backscattered signal approximately 92 dB below the transmitted signal at the antenna ports for a rainrate of 50 mm/h. Attenuation was ignored i n this calculation to allow a simplified comparison to be made between the received rain backscatter and reflector signals . Because of the geometry of the antenna beams' common volume, the major portion of the rain backscatter w i l l originate within a short distance of the ref lec tor . As a result the rain backscatter and reflector signal w i l l experience very similar attenuations. This allows a direct comparison to be made between the calculated rain backscatter and the transmission loss c a l -culation in Section 2.7. The calculated transmission loss including the reflector was approximately 39 dB, or 53 dB higher than the rain backscat-tered signal at a rainrate of 50 mm/h. 223 Another way to compare the signals from the rain and reflector is to compare the two scattering cross sections. For the rain volume, the scatter-ing cross section i s about 3 m 2 at 50 mm/h. The scattering cross section for a square f l a t plate with an edge dimension of "a" can be calculated from [2.50]: (4.24) Equation (4.24) gives a scattering cross section for the reflector of 7 .5*10 5 m 2 , or about 54 dB larger than the 50 mm/h rain cross section. It is not possible to accurately estimate the magnitude of the depolarized backscatter at this frequency because very l i t t l e i s known about this phenomena. Shimabukuro [4 .33] states that "The scattered wave i s nearly completely polarized over the entire range of scattering angles. There is a slight depolarization at angles away from the forward and backscatter direc -tions, with the maximum depolarization occuring near 6 = 9 0 ° . " The only references which could be located containing quantitive information on depolarized backscatter were by Tsang and Kong [ 4 . 3 7 ] , Oguchi [4 .38] and Shupyatsky [4 .39 ] . The f i r s t two of these references discuss aspects of the theory and do not contain any results which are direc t ly applicable to this problem. However, the results i n Tsang and Kong [4 .37] do indicate that the depolarization cross section is much smaller than the copolar cross section for general random media. Results in [4 .39] indicate that, i n general, the depolarized backscattered signal is at least 30 dB below the copolar back-scattered s ignal . 224 The r e s u l t s i n t h i s section show conclusively that copolar backscatter from r a i n i s not a source of error f o r the radar path used i n t h i s e x p e r i -ment. While the s i t u a t i o n f o r depolarized backscatter i s f a r l e s s c e r t a i n , the a v a i l a b l e evidence indicates that t h i s e f f e c t i s much smaller than the copolar backscatter and therefore w i l l not be a source of uncertainty i n the experimental data. 225 5. DUAL-POLARIZED EXPERIMENTAL MODEL This chapter describes a general theory and an experimental model developed to analyze the performance of a practical dual-polarized atomo-spheric propagation l ink including a crosspolar cancellation network. The major functions of this experimental model are to predict the dual-polarized l ink XPD performance and to separate, as far as possible, the depolarized signals resulting from the f i n i t e antenna/OMT isolations and the atmospheric propagation path. This type of analysis i s especially important when comparing measured and predicted XPDs i n this frequency range because the level of the rain depolarized signal is usually lower than the signal due to the uncancelled clear weather system isola t ion . The basic idea of analyzing the XPD performance of a dual-polarized l ink by vector addition of a l l of the depolarized signals is not new and some references to previous work i n this area are included i n the next section. However, the model presented here has been extended to include a crosspolar cancellation network and the important effects of mismatches on the OMT ports. This model also incorporates a number of s implif icat ions, approxima-tions and a more descriptive notation which makes i t easier to apply i n a practical s i tuation. Since they are not important in this experiment, the effects of antenna alignment errors and Faraday rotation are not included i n this model. A signal flow diagram for the dual-polarized experimental system to be described by this model is shown i n F i g . 5.1. A number of simplifications, approximations and assumptions which were used to arrive at this system FIG. 5.1 EXPERIMENTAL SYSTEM SIGNAL FLOW DIAGRAM 227 diagram are discussed in Section 5.2. The symbols and notation i n F i g . 5.1 are defined in Section 5.3. The equations describing the signals throughout the experimental system are discussed in Section 5.4. The rest of this chapter i s devoted to the results and practical implications of the experi-mental model. 5.1 Previous Work Several investigations have previously discussed some aspects of the problem of separating the antenna and path depolarized signals . Shkarofsky [5.1] and Shkarofsky and Moody [5.2] have included the effects of hydro-meteors, antenna isolat ions , antenna misalignment and Faraday rotation i n the XPD analysis of s a t e l l i t e l i n k s . Nowland and Olsen [5.3] have developed a simplified analysis of XPD including the same effects as discussed i n the two previous references. Dintelmann [2.39] has investigated some aspects of the performance of dual-polarized links including crosspolar cancellation net-works. Evans and Thompson [2.35] and Delogne and Sobieski [5.4] have pre-sented graphs showing the error bounds on XPD measurements for conventional, uncancelled dual-polarized experimental systems. 5.2 Simplifications, Approximations and Assumptions In order to reduce the complexity of the algebraic manipulations, only a single , f ixed, transmitted polarization i s included i n the model. To f a c i l i t a t e the reading of the following equations, the two polarizations w i l l be referred to as the copolar and crosspolar, rather than ver t i ca l or h o r i -zontal as Is usually the case. These simplifications can be made without 228 loss of gen e r a l i t y up to the point where the actual meteorological parameters are substituted i n t o the equations. To make the following analysis f e a s i b l e , i t i s necessary to make some assumptions.and approximations. Most of these s i m p l i f i c a t i o n s cause small losses, phase s h i f t s and r e f l e c t i o n s to be ignored. Where i t i s f e l t to be necessary, a short explanation i s included with the reasons why these approximations are j u s t i f i a b l e . Assumptions and approximations: 1. - the magnitude of the r e f l e c t e d signals throughout the c a n c e l l a t i o n network can be ignored. This i s reasonable because the coupler ports are connected to eit h e r the well matched antenna ports or the i s o l a t o r s preceding the mixers. 2. - the e f f e c t s of signals due to the f i n i t e d i r e c t i v i t y of the d i r e c t i o n a l couplers are not s i g n i f i c a n t . Even f o r r e l a t i v e l y low d i r e c t i v i t i e s , t h i s assumption i s v a l i d e i t h e r because of the f i r s t assumption or because the undesired coupled s i g n a l i s very much smaller than the desired s i g n a l . 3. - a l l signals are t o t a l l y coherent. Only very small v a r i a t i o n s from i d e a l coherency occur due e i t h e r to atmospheric turbulence or to multiple s c a t t e r i n g . 4. - the planes A-A and B-B of F i g . 5.1 are the 3-port d i r e c t i o n a l coupler reference planes and the s i g n a l coupled out of the main l i n e i s 10 dB lower i n amplitude at planes A-A and B-B. It i s also assumed that no 229 s i g n i f i c a n t phase v a r i a t i o n with frequency occurs as a r e s u l t of the coupling at these reference planes. 5. - the phase s h i f t introduced by the phase s h i f t e r has n e g l i g i b l e v a r i a -t i o n with frequency over the bandwidth considered. 6. - the t o t a l length of the waveguide c i r c u i t between the d i r e c t i o n a l coupler -10 dB ports can be considered as a section of uniform waveguide i n c l u d i n g the attenuator loss and phase s h i f t e r angle. 7. - the XPD of the antennas are independent of the atmospheric conditions i . e . near f i e l d antenna e f f e c t s can be ignored. 8. - the c l e a r weather attenuation and XPD of the propagation path are assumed to be zero and i n f i n i t e , r e s p e c t i v e l y . 9. - the waveguide losses before the d i r e c t i o n a l couplers and the through-l i n e losses of the couplers can be modelled as a reduction i n receiving system s e n s i t i v i t y and otherwise ignored. 10. - the amplitude of the crosspolar s i g n a l depolarized to the copolar p o l a r i z a t i o n can be ignored. 5.3 Notation and Units The notation used i n the following section was designed to reduce the number of times the symbol d e f i n i t i o n s would have to be consulted. This i s accomplished i n part by including the following d e s c r i p t i v e subscripts. Subscript d e f i n i t i o n s : CP -copolar s i g n a l , i . e . signa l of the same l i n e a r p o l a r i z a t i o n ( v e r t i c a l or horizontal) as was o r i g i n a l l y transmitted. 230 XP -crosspolar s i g n a l , i . e . l i n e a r p o l a r i z a t i o n orthogonal to CP. CN - c a n c e l l a t i o n s i g n a l , r e f e r r i n g to the s i g n a l i n the attenuator - phase s h i f t e r l i n e of the ca n c e l l a t i o n c i r c u i t . CW - c l e a r weather, value of a s i g n a l or quantity under cl e a r weather conditions. TX,RX -Transmitting and Receiving. When r e f e r r i n g to s i g n a l s , designates signals propagating on the path at the "output" of the transmitting antenna and at the "input" to the r e c e i v i n g antenna r e s p e c t i v e l y . When r e f e r r i n g to antenna para-meters TX and RX r e f e r to the i n d i v i d u a l antennas. PATH -value of attenuation, phase s h i f t or XPD r e s u l t i n g from the s i g n a l propagation over the path. FE -front-end r e f e r s to s i g n a l at the input to the receiving system. These q u a n t i t i e s are those recorded by the data a c q u i s i t i o n system. The u n i t s used i n the following analysis are, whenever p o s s i b l e , those usu a l l y associated with the i n d i v i d u a l q u a n t i t i e s . For example: attenuations are i n dB, angles are i n degrees and s i g n a l l e v e l s are i n dB r e l a t i v e to the cl e a r weather l e v e l of the received copolar s i g n a l . These f a m i l i a r units and conventions are used when discussing data and analysis r e s u l t s and provide the most natural a s s o c i a t i o n with the actual measurement system. However, i n 231 the actual equations, where complex voltages are used, s i g n a l representation i n dB i s not convenient. To solve t h i s problem, a superscript V i s used, when necessary, on the attenuations and XPD s to designate a voltage r a t i o . For example, i n the case of X P D : XPD indicates the value i n dB and XPD^ i s the same value as a voltage r a t i o , i . e . .Hl/2 X P D V =A - X P D 10 1 0 - X P D 10 2 0 J 6 i A s i m i l a r s i t u a t i o n a r i s e s when angles are written i n the form e " t and i n t h i s case the angle i s assumed to be i n radians. The symbol E i s used to designate signals which are complex voltages, i . e . signals having a magnitude and angle. Symbol d e f i n i t i o n s : Tf'CPCW - r e f e r s to the clear-weather complex voltage of the copolar received s i g n a l at the input to the reference plane D-D of F i g . 5 . 1 . E r j p c w * s t l i e ^ dB reference throughout the following a n a l y s i s . E -the general received copolar s i g n a l at D - D , i . e . D during anomolous propagation conditions. E - r e f e r s to the normalized signal generated by the CP, s millimetre source. This s i g n a l Is normalized to include the c l e a r weather transmission l o s s , i . e . antenna gains and dispersive path l o s s . r e f e r s to the copolar s i g n a l at the "output" of the transmitting antenna, i . e . at the path "input". - r e f e r s to the copolar s i g n a l at the "input" to the receiving antenna a f t e r propagating the path, -the copolar s i g n a l at the output of reference junctions A-A, i . e . the copolar s i g n a l at the front-end input, - r e f e r s to the cl e a r weather crosspolar received s i g n a l at the input of the reference j u n c t i o n B-B. -r e f e r s to the same crosspolar s i g n a l under anamolous atmospheric conditions, - r e f e r s to the crosspolar s i g n a l at the "output" of the transmitting antenna. This s i g n a l i s due only to XPD T X. - r e f e r s to the crosspolar s i g n a l at the receiving antenna input, -the s i g n a l at the output of reference junction B-B, i . e . the t o t a l s i g n a l i n t o the crosspolar channel of the front-end. This w i l l be the measured s i g n a l l e v e l of the crosspolar channel, - r e f e r s to the copolar s i g n a l at the reference 233 plane A-A which i s coupled through the sampling coupler - 10 dB output, i . e . the c a n c e l l a t i o n s i g n a l before attenuation or phase s h i f t i n g but a f t e r the - 10 dB coupling, - r e f e r to the c a n c e l l a t i o n s i g n a l at the input to B the coupled port at reference junction B-B. This i s the attenuated and phased s h i f t e d version of E„ x, and includes the e f f e c t of both d i r e c t i o n a l C N A couplers. XPD^.XPD^ -re f e r s to the crosspolar d i s c r i m i n a t i o n of the V V XPD_ ,XPD transmitting and receiving antennas (inc l u d i n g the orthomode transducer) i n dB and as a voltage r a t i o . These are for the transmitted p o l a r i z a t i o n considered. 8 Y t m , 6 -refers to the angle of the phase s h i f t added to X P D T X X P D ^ the crosspolarized s i g n a l a f t e r I t i s depolarized by the antennas. The angle i s r e l a t i v e to the copolar s i g n a l and includes any path length differences through the antenna for the two p o l a r i z a t i o n s . AG>VDR -refers to the d i f f e r e n c e between QVT)T. and 0 XPD X P D T X X P D ^ i . e . A 0 x p u = © X P D ~ °XPD ' AIQ - r e f e r s t o t h e p a t h l e n g t h d i f f e r e n c e w h i c h causes r e f e r s to the magnitude r a t i o of the path depolarized s i g n a l at the r e c e i v i n g antenna with respect to the copolar s i g n a l at the transmitting antenna. This i s equal to the magnitude of T 1 2 i n the previous chapter. •refers to the phase differ e n c e between the path depolarized s i g n a l at the receiving antenna and the copolar s i g n a l at the transmitting antenna. This i s equal to the angle of T 1 2 . •total system XPD i n c l u d i n g the e f f e c t s of the antennas and path f o r cl e a r weather and i n general r e s p e c t i v e l y . •excess path loss i n (dB) and s c a l a r voltage r a t i o , r e s p e c t i v e l y for the copolar p o l a r i z a t i o n , i . e . due to anamolous propagation only, • e l e c t r i c a l path length i n degrees f o r the copolar p o l a r i z a t i o n . • s i m i l a r l y f o r the crosspolar p o l a r i z a t i o n . •total attenuation i n dB and as a voltage r a t i o , r e s p e c t i v e l y , of the c i r c u i t connected between the - 10 dB coupler ports, i n c l u d i n g the attenuator phase s h i f t e r loss and waveguide l o s s . 235 -angle of the phase s h i f t introduced by the phase s h i f t e r i n degrees. - t o t a l phase s h i f t between reference planes A-A and B-B through the c a n c e l l a t i o n c i r c u i t excluding a, PS. - t o t a l phase s h i f t between reference planes A-A and B-B through the c a n c e l l a t i o n c i r c u i t . e. 'D-A'UD-B -the phase s h i f t r e s u l t i n g from the waveguide connection between reference planes DD-AA and DD-BB r e s p e c t i v e l y . 5.4 System Descriptive Equations A s i g n a l flow diagram for the experimental system in c l u d i n g most of the previous symbols was shown i n F i g . 5.1. The following equations r e s u l t d i r e c t l y from the previous d e f i n i t i o n s and F i g . 5.1. The s i g n a l l e v e l s at the input to the front-end i n terms of the signa l s at the rec e i v i n g antenna orthomode transducer ports i s given by: 1 •0 E X P _ FE V J ° T 0.1'A,e A 1 (5.1) This matrix completely describes the e f f e c t s of the crosspolar c a n c e l l a t i o n network under the assumptions i n Section 5.2. The s i g n a l vectors at the re c e i v i n g antenna ports can be expressed i n terms of the transmitted s i g n a l by: 236 JCP D vpnV J 9 X P D K X X P D R X e j 0XPD V TX X P D T X 6 > J Q C P A c p e J0CPXP .V J0XP TCPXPE C^P6 CP, 0 (5.2) These three matrices describe the e f f e c t s of the r e c e i v i n g antenna, path and transmitting antenna. One more matrix i s required to include the phase s h i f t s of the waveguide connections between the reference planes D-D, A-A and B-B. This phase s h i f t w i l l be important when analyzing the behaviour of the crosspolar c a n c e l l a t i o n network. (There i s also a loss associated with these connec-tions but i t i s n e g l i g i b l e . ) The re c e i v i n g system i n t h i s experiment does not respond to the phases of the signals entering the front-end. For t h i s reason, only the magnitudes of the copolar vector a f t e r plane A-A and the crosspolar vector a f t e r plane B-B are relevant. Accordingly, the phase s h i f t s a f t e r plane A-A i n the copolar l i n e and plase B-B i n the crosspolar l i n e w i l l be ignored. Thus, the following matrix includes a l l of the impor-tant phase s h i f t s necessary to describe the signals a f t e r the receive antenna OMT: 237 — — o 0 CP. XP. (5.3) In summary, these equations and the model in F i g . 5.1 describe the complex vector signals entering the receiver front-end i n terms of the normalized transmitted s ignal . The general solution for the received signals is given by the product of the five matrices in equations (5.1), (5.2) and (5.3). It should be noted that these expressions do not contain any terms not necessary for the practical "engineering" description of the experimental system. In the following sections, every effort w i l l be made to consider only the equations necessary to analyze the system behaviour which is the topic of that section. Further assumptions and intermediate results w i l l be used whenever possible to prevent unnecessary mathematical complexity. 5.5 Analysis Without the Crosspolar Cancellation Network Without the crosspolar cancellation network, the signals at the input of the receiver w i l l be E and E . In this case, the experimental system CPD XPD i s described entirely by (5.2). Solving (5.2) for the received signals y i e l d s : Av -10CP ECPd E c p g A c p e (5.4) 238 v rAv j 0 C P v J G X P D R X E X P n = E C p J A C P e X P D R X e -i o ^ ® Y P D if) , V J UCPXP , TX 4V J U X P i , c ' • CPXP 6 XPD T Xe A ^ e J ( 5 . 5 ) 5 . 5 . 1 Contribution of Antenna XPD's to Clear Weather Crosspolar Signal Level Both the transmitting and rec e i v i n g antennas contribute to the cross-polar s i g n a l entering the receiver front-end. Reciprocity arguments show that the magnitude of the XPD coupling should be the same for transmitting or rec e i v i n g using a p a r t i c u l a r antenna. The two antennas and orthomode trans-ducers are i d e n t i c a l l y constructed but minute mechanical d i f f e r e n c e s , e s p e c i a l l y i n the r e l a t i v e angular o r i e n t a t i o n of the side arm port and p o l a r i z i n g septum w i l l cause differences i n the i n d i v i d u a l antennas XPD values, as seen i n Section 2 . 5 . In addition, small v a r i a t i o n s i n the angular alignment of the antenna assemblies and orthomode transducers w i l l s i g n i f i -cantly a f f e c t the i n d i v i d u a l XPD's as discussed i n Section 2 . 5 . 3 . It would be exceedingly d i f f i c u l t to quantify the complex XPDs of the antennas used i n t h i s experiment even using the most advanced millimetre wave measurement systems. The major d i f f i c u l t y would be i s o l a t i n g the e f f e c t s of the antenna XPD angles ( i . e . 0 v r > r i and QVT>r. ) from that of the free-space X P D R X X F U T X measurement set-up. Even measurements of the magnitude of the antenna XPD contain a s i g n i f i c a n t uncertainty i n t h i s frequency range for antennas with XPDs as high as those used i n t h i s experiment. 239 For these reasons, the following analysis must use a range of values f o r the complex antenna XPDs. Reasonable estimates of the XPD magnitude range can be made based on the manufacturers s p e c i f i c a t i o n s , measurements made on the orthomode transducers connected back-to-back and measurements made on the complete antennas i n s t a l l e d i n the measurement system. It i s reasonable to assume that the differences between the angles of the two complex antenna XPD's can be any value between 0 and 360°. This i s because path length differences of the order of a few millimetres can i n t r o -duce r e l a t i v e phase s h i f t s of up to 360°. In add i t i o n , these length depen-dent phase s h i f t s w i l l be a function of the operating frequency which i s adjustable. The following a n a l y s i s , based on the r e s u l t s of the preceding s e c t i o n , w i l l demonstrate how the i n t e r a c t i o n of the complex antenna XPD's can r e s u l t i n a wide range of values f o r the received crosspolar s i g n a l l e v e l s . In c l e a r weather conditions, i t can be assumed that T^p^p i s i n f i n i t e , A^ p and A are zero and that 0 =0 and can, therefore, a l l be ignored i n t h i s XP V»P A r section of the a n a l y s i s . Under these assumptions (5.5) can be rewritten: V }QXPJ)RX V J ° X P D T X EXP = EXP = E C P J X P D R X * + X P D T X e 1 ( 5 ' 6 ) D r c, S Equation (5.6) shows that during c l e a r weather, i n the system without a crosspolar c a n c e l l a t i o n network, the crosspolar s i g n a l entering the front-end has only two components, one r e s u l t i n g from each antenna. To q u a n t i t i v e l y investigate the implications of (5.6) i t w i l l be assumed that: 240 1. XPDTX = 3 7 D B 2. XPD D V = 33, 35, 37, 39, 41 dB 3. 0 < AG x p D < 360° F i g . 5.2 i l l u s t r a t e s how the c l e a r weather crosspolar s i g n a l l e v e l at the front-end input depends on the magnitudes and angles of the i n d i v i d u a l antenna XPDs. This graph shows that the received c l e a r weather crosspolar s i g n a l l e v e l can vary between 6 dB higher than the i n d i v i d u a l antenna XPD's to i n f i n i t y , depending on the r e l a t i v e XPD magnitudes and angles. The l a r g e s t range of crosspolar s i g n a l l e v e l s occurs f o r the case when the magnitudes of the i n d i v i d u a l XPDs are equal. The angle A<=xpn=®xpD ~®XPD W 1 H r e s u l t from the d i f f e r e n t path TX RX lengths traversed by the two crosspolar s i g n a l components. Most of t h i s d i f f e r e n t i a l path length w i l l o r i g i n a t e i n the OMTs and w i l l depend on the precise l o c a t i o n of the depolarizing elements i n the OMTs. ( I t i s possible that d e p o l a r i z a t i o n occurs at more than one l o c a t i o n within the OMT and that the i n d i v i d u a l OMT t o t a l XPDs r e s u l t from the a d d i t i o n of more than one depolarized signal.) In t h i s frequency range, the waveguide wavelengths are of the order of 5 ram. For these reasons i t i s not possible to make an ac-curate estimate of AO from mechanical measurements of the OMTs. However, even though i t i s reasonable to assume that t h i s angular difference is.any-where between 0 and 360°, i t can be s a f e l y assumed that the path length d i f -ference i s less than a few wavelengths. This i s because the physical dimen-sions of the OMTs could not r e s u l t i n path length d i f f e r e n c e s greater than a few m i l l i m e t r e s . 241 g. 5.2. C o n t r i b u t i o n of antenna XPDs t o c l e a r weather c r o s s p o l a r s i g n a l a t t h e f r o n t - e n d i n p u t . 242 Because A Q ^ results from a path length difference, this angle w i l l be a function of the operating frequency. If the physical path length difference creating A 0 x p D i s denoted AfcQ the change in A 0 x p n at two different frequencies w i l l be given by: f 2 ( 0 X P D T X " Q x P D R X ) | f 1 ~ ( G X P D T X " QX™J = ( S ( f l ) - 3(f2)]A* 0 (5.7) From (5.7) i t is seen that the x-axis i n F i g . 5.2 could be replaced by a frequency scale i f AJl^ was known. Alternately, i f the variation i n the crosspolar signal level with frequency was measured, i t would be possible to calculate the effective A £ Q . F i g . 2.35 i s an example of this type of measurement. Both curves i n this graph show a frequency response similar to that predicted by F i g . 5.2. However, a simple analysis w i l l show that these responses cannot be sa t is -f a c t o r i l y explained from the results i n this section. This i s because these variations could only result from longer path lengths than those which could arise within the OMT s. To demonstrate this conclusion, i t w i l l be assumed that the path length different results from both OMTs is less than or equal to 2 cm. Using a 2 cm d i f f e r e n t i a l path length and assuming the path length difference occurs i n rectangular waveguide propagating the T E 1 Q mode, (5.7) predicts a 360° change i n AG^pp for a frequency change from 62.8 to 75 GHz. This frequency change is much larger than that shown in F i g . 2.35 and there-243 fore the observed e f f e c t must be due to another cause. In the next section i t w i l l be shown that the v a r i a t i o n i n crosspolar l e v e l i n F i g . 2.35 probably a r i s e s from a mismatch within the back-to-back OMT c i r c u i t . The k l y s t r o n used i n t h i s experiment can be tuned over a frequency range from approximately 73.0 to 74.5 GHz. Over t h i s frequency range (assuming T E 1 0 mode), the change i n AO^p^ i s approximately 15°. F i g . 5.2 shows that t h i s w i l l r e s u l t i n a change of only a few dB i n the crosspolar s i g n a l l e v e l . Accordingly, i n the following sections, the e f f e c t of changes i n AQ^pjj due to frequency v a r i a t i o n over the k l y s t r o n tuning range ( i . e . i n Figs. 2.35, 2.36 and 2.38), w i l l be ignored. 5.5.2 E f f e c t of Reflected Signals on the Clear Weather  Crosspolar Signal Level The experimental r e s u l t s presented i n Section 2.5 showed that the frequency v a r i a t i o n of the crosspolar s i g n a l l e v e l at the front-end input was very dependent on the impedance connected to the orthomode transducer rec-tangular ports. No references to t h i s phenomenon could be found i n the l i t e r a t u r e and the antenna manufacturers did not have any explanation for these observations. It i s believed that this impedance s e n s i t i v e behaviour of the dual-polarized system can be explained using the model depicted i n F i g . 5.1 with some a d d i t i o n a l c l a r i f i c a t i o n of the orthomode transducer operation. 244 5.5.2.1 Basic OMT Operation Attempts to find OMT references with a mathematical description of their operation or mention of this mismatch sensitive behaviour have been unsuccessful. The OMT references which were located [5.5], [5.6], [5.7] contained only empirical discussions of OMT operation. F i g . 5.3 shows the construction of the OMTs used in this experiment. This figure shows the basic OMT components and principals of operation [5.6]. Some aspects of the orthomode transducer operation w i l l be quickly reviewed here to explain the expansion of the model required for this section of analysis . For s implic i ty , only the transmitting antenna OMT effects w i l l be considered i n this section. However, because the OMTs operate reciprocal -l y , the entire discussion i n this section applies equally well to the receiv-ing OMT or to the combined pair of OMTs. If the transmitting signal i s applied to the through arm port on the transmit OMT, almost a l l of this s i g -nal w i l l leave the OMT via the antenna port unaffected by the septum and polarized in the copolar direct ion. Because the cross arm (or side arm) port is beyond cutoff for this polarization, v i r t u a l l y none of this copolar signal i s coupled to the cross arm port. Small mechanical imperfections, p r i n c i p a l -ly in the alignment of the conducting septum, w i l l create a small depolarized signal propagating i n the circular waveguide within the OMT. This signal i s generally considered to leave the OMT v ia the antenna port . However, the cross arm port, which is located after the septum in the direction of propa-gation, should also couple this depolarized waveguide mode. Measurements made on the OMTs used in this experiment showed that t h i s , indeed, did occur Fig. 5.3. Orthomode transducer construction and operation. 246 and that the crosspolar s i g n a l amplitude at the side arm and antenna ports were approximately equal. (Exact comparison could not be made because these measurements could only be performed with the OMTs back-to-back and the signals due to each OMT cannot be separated i n t h i s configuration.) If the transmitted s i g n a l i s applied to the cross arm port, a s i m i l a r s i t u a t i o n occurs. In t h i s case, approximately h a l f of the crosspolar s i g n a l generated at the r e c t a n g u l a r - c i r c u l a r waveguide ju n c t i o n propagates unimpeded past the septum i n t o the through arm port. This e f f e c t can be included i n the model of F i g . 5.1 i n two ways, depending on the d i r e c t i o n a l properties a t t r i b u t e d to the summing junctions i n the OMT model. The d i r e c t i o n a l properties of these summing junctions were not previously considered because they are unimportant i f the experimental system i s p e r f e c t l y matched. I f the summing junctions i n the OMT models are V ^ ^ XPD assumed to be d i r e c t i o n a l , the depolarized s i g n a l of amplitude XPD e only couples to the antenna port. In t h i s case, the OMT model requires an ad d i t i o n a l coupling element and d i r e c t i o n a l summing junction which w i l l . account f o r the s i g n a l leaving the cross arm. This model configuration with the two coupling c o e f f i c i e n t s , XPD and XPD , i s shown i n F i g . 5.4(a). If the summing junction i s considered to be b i d i r e c t i o n a l , the OMT can be modelled as shown i n F i g . 5.4(b). Model (a) i s more general and can include d i f f e r e n t couplings i n each d i r e c t i o n . Model (b) i s simpler and more c l o s e l y describes the ac t u a l OMT operation. For these reasons, model (b) w i l l be used and i t w i l l be assumed that the OMT summing junctions i n F i g . 5.1 are b i d i r e c t i o n a l . It should also be noted that the XPDs (power) i n model (a) should be double that i n model (b ) . However, to s i m p l i f y the equations and Copolar Rectangular ports Crosspolar JG X P D e X P D T X 2 T X X X P D e X P D T X e D i r e c t i o n a l y summing junction ^ Copolar Antenna port Crosspolar (a) Copolar Rectangular ports Crosspolar X P D i 9J 6 X P D T X T X Copolar Ant enna port Crosspolar (b) F i g . 5.4. OMT model options. 248 to conform to the usual definit ion of XPD, i t w i l l be assumed that the signal t ravel l ing i n each direction from the bidirectional junction has amplitude X P D J . 5.5.2.2 Calculated Results and Comparisons to Experimental Data If the crosspolar rectangular port i s mismatched, another crosspolar signal component w i l l be propagated i n the direction of the receiver. The signal flow diagram for the mismatched transmit OMT model is shown i n F i g . 5.5. A complex reflect ion coefficient T^, completely describes the mismatch connected to the rectangular crosspolar OMT port. E is the reflected X P R signal at the OMT-load junction travell ing in the direction of the receiving antenna. Plane C-C located at the bidirectional junction w i l l be used as a loca l reference. The reflected signal w i l l propagate through plane C-C with negligible coupling i n the "direction" of the copolar OMT ports ( i . e . the reflected signal behaves l ike a transmitted signal injected into the side arm port) . Now, the crosspolar signal at the output of the transmit antenna, designated E' , contains two components described by: X F T X J 0XPD ~ J 2 ^ R E X P T X = ^ T X 6 = XPD^X e i A (1 + T Le K ) (5.8) The angle of the second signal component with respect to the f i r s t at plane C-C i s : 249 Copolar "CPC F i g . 5.5. Mismatched transmit OMT s i g n a l flow diagrams. 250 0 R ^ Arg[T L] " 2 6^ (5.9) where i s the length of the waveguide connection between the OMT j u n c t i o n and the load represented by T^. In p r a c t i c e , JL^  i s much longer than several wavelengths and accordingly, Arg[V ] v a r i a t i o n s with frequency can be ignored .Li f o r p r a c t i c a l purposes. The e f f e c t s of the mismatch w i l l be i l l u s t r a t e d by c a l c u l a t i n g a new, e f f e c t i v e complex XPD which Includes the r e f l e c t e d s i g n a l generated at the J.X crosspolar rectangular OMT port. Previously, i . e . without any mismatch: V J 0 X P D T X ^ T X XPD!L e ™ = = — — (5.10) CP g Now, the e f f e c t i v e transmit antenna XPD designated XPD^. i s described by: m Solutions to (5.8),(5.9) and (5.11) are presented g r a p h i c a l l y i n F i g . .5.6. The e f f e c t i v e XPD magnitude i s given i n dB and the change i n the ix angle of the XPD is plotted as: 6 ( W f x " V , ~ °* P DTX C 5 ' 1 2 ) Fig. 5,6 illustrates how the magnitude of the mismatch and distance from the OMT junction to the mismatch can change the e f f e c t i v e OMT complex XPD. This graph shows that as the magnitude of the r e f l e c t i o n c o e f f i c i e n t on the unused rectangular port increases, the peak-to-peak v a r i a t i o n of the 253. Return l o s s (dB) F i g . 5.6. E f f e c t of a mismatch at the crosspolar rectangular OMT port on the e f f e c t i v e transmit OMT complex XPD. 252 total OMT XPD also increases. The case where the return loss is 0 dB represents the situation which occurred when the transmit OMT was connected to the polarization switch without isolators as discussed in Section 2.2.4.3. For a 0 dB return loss , F i g . 5.6 shows that the OMT XPD can be degraded by up to 6 dB. However, early tests on the complete experimental system showed that the severe mismatch on the transmit OMT caused by the polarization switch could degrade the system XPD by more than 6 dB (Section 2.2.4.3). This can be explained by solving (5.6) after substituting the new value of the tran-smit OMT given by (5.8) and (5.11). The solutions of these equations assum-ing equal antenna XPDs of 37 dB and a mismatch return loss of 10 dB (VSWR = 1.92) are shown i n F i g . 5.7. Another set of solutions for the assumptions that the antenna XPDs are 37 dB and - 0 v r > r i = 150° are X P D T X X P D R X shown i n F i g . 5.8. These graphs show that mismatches can change the system XPD by considerably larger values depending on the exact values of the complex crosspolar signal vectors. It i s interesting to note that i n F i g . 5.8, the largest peak-to-peak variation in the crosspolar signal level occurs, i n this case, when the return loss i s 5 dB because the reflected signal is approximately the same magnitude as the sum of the antenna depolar-ized signals . The largest degradation s t i l l occurs for a 0 dB return l o s s . In the case of a mismatch on the receive OMT copolar rectangular port, the effect on the system XPD i s , of course, very similar to the results In F i g s . 5.7 and 5.8 but the mechanism is s l i g h t l y different than that shown i n F i g . 5.5. A mismatch on this copolar port w i l l result i n a reflected copolar 253 40 80 120 160 200 240 280 320 Angle of reflected signal at reference plane C-C (Deg.) Fig. 5.7. Crosspolar signal level at plane D-D for XPD„X=XPD r=37dB and one mismatch with return loss = lOdB. R x ' 254 255 signal t ravell ing toward the transmitter. As this signal passes through the receive OMT i t w i l l be depolarized and w i l l result in approximately equal signals leaving v i a the "c ircular" and rectangular crosspolar ports. The signal leaving v i a the antenna feedhorn can be safely ignored. However, the signal leaving the crosspolar rectangular port w i l l add to the other cross-polar signal components entering the front-end. For the same ref lect ion coefficient and OMT XPD, this signal vector w i l l have the same magnitude entering the front-end as the signal caused by a mismatch on the transmit OMT crosspolar rectangular port. It i s extremely d i f f i c u l t to quantitively compare the results of this section to a practical situation because a l l mismatches throughout the system w i l l additively create effects similar to those shown i n Figs . 5.7 and 5.8. Values could be chosen for this model which would generate results acceptably close to the experimental data shown i n Figs . 2.35, 2.36 and 2.38. However, this would not be very meaningful because the model contains enough para-meters to generate numerous solution sets which would f i t the experimental data. If measuring apparatus were available to more completely characterize the individual components, accurate model parameters could be determined. Nevertheless, some meaningful conclusions regarding the operation of the experimental system can be made with the aid of the results of this sec-t i o n . F i g . 2.35 presents the experimental results for the back-to-back OMT connection with terminations which were thought to be well matched. But this graph, especially the lower curve, shows a frequency response similar to those i n Figs . 5.7 and 5.8. This response is believed to be due to the fact that the Hughes 44894H thermistor mount used In the crosspolar level 256 measurement (connected to the OMT through arm i n this case) has a specified VSWR of only 2:1 (return loss = 9.5 dB). F i g . 5.7 shows very similar v a r i a -tions i n crosspolar level for AO^^ i n the range 1 2 0 ° - 1 5 0 ° with a 10 dB return loss and appears to explain the lower curve of F i g . 2.35. The smaller crosspolar variations i n the upper curve could result either from the addi-t ion of two vectors or a reduction i n the reflection caused by the thermistor mount due to some conjugate mismatch inherent i n the receive OMT cross arm. F i g . 2.36, where the transmit OMT cross arm was deliberately mismatch-ed gives a response of the form shown i n F i g . 5.8 for a return loss around 5 dB. The frequency response of F i g . 2.36 shows that the reflected signal angle (0_) varies over approximately 180° over the frequency range 73.18-73.45 GHz, (a similar 180° frequency range occurs i n F i g . 2.35). Over this frequency range, the change i n the TE^^ mode 6 i s 7.0. Using (5.9), this gives £ , the distance from the combining reference plane to the mismatch as R approximately 22 cm. This distance i s reasonable for the c i rcui t topology actually used to make the measurements. An exact correlation cannot be made due to the uncertainty of the location of the combining reference plane with-i n the back-to-back OMT c i r c u i t . F i g . 2.38 shows the variation of crosspolar signal level with frequency for the back-to-back OMTs connected to the front-end. The mixers in the front-end have a specified input VSWR of 2:1 typical (this w i l l depend on the backshort tuning). With no isolat ion between the receive OMT and the front-end, large variations in the crosspolar level are observed. The v a r i a -tion with frequency in this case is more rapid than i n the previous cases. This is due to the. longer e lec t r i ca l path lengths between the OMT and the 257 mismatches and may also par t ia l ly be due to the addition of more than one reflected signal vector. With reasonable degrees of isolat ion between the OMT and the front-end, the crosspolar signal level shows very l i t t l e variation with frequency. This ver i f ies that the cause of the crosspolar signal variation with frequency is explained by the analysis presented in these sections. 5.5.2.3 System XPD Improvement Using Mismatches This impedance sensitive behaviour of the OMTs can actually be used benef ic ia l ly to increase the "uncancelled" system clear weather i sola t ion at one frequency. Several methods were explored to change the OMT port mis-matches i n attempts to Improve the system i s o l a t i o n . It was found that even with the Isolators instal led between the mixers and OMTs, the mixer backshort tuning and LO drive level would affect the system i s o l a t i o n . The most con-venient method of adjusting the uncancelled system isolat ion was found to be a combination of operating frequency and copolar mixer LO adjustment. For certain combinations of antenna alignment and operating frequency, i t was possible to improve the uncancelled system XPD from around 35 dB to 45 dB by s l i g h t l y reducing the copolar mixer LO drive l e v e l . The required LO reduc-t ion only resulted i n a few tenths of a dB reduction in copolar s e n s i t i v i t y . This method was successfully used during data acquisition for the results showing approximately 45 dB isolat ion on the "uncancelled" polarizat ion. This technique has limited practical application, however, because of the d i f f i c u l t y of determining the advantageous combinations of antenna alignment, backshort tuning, LO level and operating frequency. 258 5.6 Crosspolar Cancellation Network Operation i n Clear Weather The theory presented in this section w i l l be used to analyze the operation of the crosspolar cancellation network, examine the effects of amplitude and phase errors, and determine the cancellation frequency response - a l l under clear weather conditions. The previous sections introduced two pairs of crosspolar signal vectors, one pair due to the "matched" OMTs and a second pair resulting from mismatches on the OMT ports. These four signals are each actually the vector sum of more than one signal resulting from the same basic mechanism. The complex sum of these coherent signals propagates toward the front-end along the crosspolar signal path up to plane D-D i n F i g . 5.1. Without the crosspolar cancellation network, this vector sum would be the clear weather received crosspolar s i g n a l . The magnitude of this signal under different conditions is shown i n Figs . 5.7 and 5.8. In summary, i t was shown that the crosspolar signal vector entering plane D-D, and thereafter junction B-B along the crosspolar signal l i n e , can have any magnitude shown on Figs . 5.7 and 5.8 and any angle between 0 and 3 6 0 ° . If the crosspolar cancellation network is adjusted so that the second signal entering the combining junction at plane B-B has exactly the same magnitude but opposite phase as the previously described s ignal , then the net signal leaving junction B-B, in the direction of the front-end, w i l l be zero. Thus, perfect crosspolar signal cancellation can be achieved at one frequency under any clear weather conditions assuming the crosspolar cancellation network attenuation and phase can be adjusted with suff ic ient accuracy. In practice, however, i t can be d i f f i c u l t to maintain the necessary cancellation 259 signal phase and amplitude accuracy because of frequency shifts and ambient temperature variat ions . 5.6.1 Sensitivity to Amplitude and Phase Errors The f i r s t step i n analyzing the operating characteristics of the crosspolar cancellation network is to quantify the sensi t ivi ty of the receiv-ed crosspolar signal to phase and amplitude errors. F i g . 5.9 shows the change i n the crosspolar signal level at the front-end input for an error i n the adjustment of the crosspolar cancellation c i rcui t attenuation. Curves are given for uncorrected system isolations of 30, 35, 40 and 45 dB. This graph shows that the sensi t ivi ty of the crosspolar signal level to amplitude errors Increases for lower levels of uncorrected system Isolation. F i g . 5.10 is a corresponding plot for phase errors . It shows a similar increase in error sensi t iv i ty at lower uncorrected system isolat ions . The receiving system average noise level corresponds to a crosspolar signal level of approximately 65-70 dB below the copolar signal l e v e l , ( ref . Section 2.8). From Figs . 5.9 and 5.10 i t can be seen that to achieve a suff ic ient level of cancellation to ensure that the crosspolar signal level i s below the noise level the adjustment errors must be maintained below ± 0 . 3 dB and ±1 .9 degrees for an uncorrected system isolat ion of 35 dB. 5.6.2 Cancelled System Frequency Response To be able to analyze the frequency response of the cancelled systemsj the mathematical expression for the crosspolar signal entering the front-end 260 C r o s s p o l a r c a n c e l l a t i o n n e t w ork a t t e n u a t o r a d j u s t m e n t e r r o r (dB) F i g . 5.9. E f f e c t o f c r o s s p o l a r c a n c e l l a t i o n network a m p l i t u d e e r r o r s . 261 Crosspolar c a n c e l l a t i o n network phase s h i f t e r adjustment error (Deg.) F i g . 5.10. E f f e c t of crosspolar c a n c e l l a t i o n network phase e r r o r s . 262 must be derived. The matrix (5.1) describes the signals entering the f r o n t -end i n terms of the signals at the reference planes A-A and B-B. Equation (5.3) r e l a t e s the signals at plane D-D to the received signals at the d i r e c -t i o n a l coupler junctions (planes A-A and B-B). The s i g n a l set at the r e c e i v i n g antenna OMT ports (plane D-D) i s described i n general by (5.2) with the modifications introduced i n Section 5.5.2 to include the e f f e c t s of mismatches on the OMT ports. Because c l e a r weather operation i s again being considered, the s i m p l i f y i n g assumptions made f o r (5.6) are s t i l l a p p l i c a b l e . Thus, the c l e a r weather signals at the front-end input are, i n t h i s case, described by: JCP FE XP. FE 0 V j 0 T 0.1A*e A "jo, 'D-A D-B 'CP. JXP D (5.13) where the possible range of values f o r the s i g n a l s at plane D-D has been analyzed f o r c l e a r weather conditons i n Section 5.5. Solving (5.13) f o r the crosspolar s i g n a l at the front-end input y i e l d s : JXP. A 6 + EXP, (f) = E c p (0.1)A> " " " + E„_ e (5.14) FE D ' D If the crosspolar c a n c e l l a t i o n network i s adjusted f o r t o t a l c a n c e l l a t i o n at a frequency f ^ , (5.14) becomes: 3©r ' X P F F / ° (fJ = 0 = E c p (0.1)A A e V ^VS-A* D 'D-B (5.15) 263 The solutions to (5.15) are: | E C P J 0.1 Al (5.16) and ( A r g [ E c p J + + e^_A) - (ArgfE ) + 6 ^ ) - 180° D D (5.17) which describe the conditions necessary f o r complete c a n c e l l a t i o n , i . e . the c a n c e l l a t i o n s i g n a l must have equal amplitude and opposite phase. The frequency s e n s i t i v e behaviour of the cancelled system w i l l be analyzed by solving (5.14), (5.16) and (5.17) a f t e r making the following s i m p l f i c a t i o n s : f o r p r a c t i c a l purposes, the attenuator loss can be assumed to be constant over the frequency range under consideration. - the c l e a r weather, copolar, received s i g n a l l e v e l w i l l also be assumed here to be constant over t h i s frequency range. - because the path length differences which give r i s e to the d i f f e r e n c e between Arg[E ] and Arg[E ] are small compared to other path length differences, i t w i l l be assumed that the change i n these angles are n e g l i -g i b l e over the frequency range of i n t e r e s t . (Similar arguments were applied i n Sections 5.5.1 and 5.5.2). These angles can be completely ignored i n the frequency response c a l c u l a t i o n by considering t h e i r f i x e d values as a minute change i n the length of the waveguide connections between A-D and B-D. - from the symbol d e f i n i t i o n s , the t o t a l phase s h i f t i n the c a n c e l l a t i o n 264 c i r c u i t (6L.) i s the sum of the phase s h i f t e r phase s h i f t ( 0 p s ) and the phase s h i f t through the waveguide connection between the planes A-A and B-D - i t w i l l also be assumed that the phase s h i f t through the phase s h i f t e r i s independent of frequency. (This i s not s t r i c t l y true but the phase s h i f t change with frequency w i l l be n e g l i g i b l e compared to the change i n the phase 0 ). Now, using the symbol E ^ N which represents the c a n c e l l a t i o n s i g n a l at B plane B-B (and includes the e f f e c t of both couplers): l ECNJ " ' EXP n ( V l " l ECP l ( 0 ' 1 ) AI ( 5 ' 1 8 ) B D D which according to the previous assumption, i s constant with frequency. This allows (5.14) to be rewritten as: j 0 p _ j ( 0 + 0 ) j© ECP ( f ) = ' ECN • e e + l EXP < f ) ' e ( 5 - 1 9 ) FE B D j e To consolidate the e terms, t h i s may be rewritten: E ( f ) e = |E ( f ) | e + |E |e e e A r F E D B (5.20) Because the phase of the crosspolar s i g n a l entering the front-end i s not important, t h i s equation may be rewritten: j°ps ^(Qz+ V A " VB> | E x p |(f) I -FE lECN I + 'EXP ( f ) ' e 6 (5.21) where QJ)_k and Q^_ B are, of course, also functions of frequency. Thus, 265 the magnitude of the crosspolar signal in the cancelled system can be cal-culated at any frequency by the complex addition of a scalar constant and a vector dependent on frequency. The angle between these two vectors is given by: W f ) - GPS + V f ) + V f ) - W f ) ( 5 - 2 2 ) Therefore the constant angle 0 is equal to: if O OPS - 1 8 0 ° - W - W V + V B ( V ( 5 - 2 4 ) The three angles 0^ , a n <* ®n-jj c a n a _ _ ^ e e xP r e s s e <* f n radians, by equations of the form: e.(f) = 0 5(f ) + [$(f) - e(f )U (5.25) SI SL o o 2TT where £ is the appropriate length, i.e. SL, D^-A o r ^D-B A R U * ^ = X ~ * ^ N E R E _ g fore, (5.22) can be rewritten: 0 D I F(f) = 0 p s + 0^(fo) + [g(f) - 3(f Q)]A + W V + [ P ( f ) " g ( f o ) ] V A ~ W f o > " U ( f ) " e ( f o ) ] V B ( 5 " 2 6 ) Substituting (5.24) into (5.26): 0 D I F(f) = T T + [3(f) - 3 ( f o ) U 0 (5.27) where: ^ ^ + V A " V B ( 5 ' 2 8 ) and now (5.21.) can be written: 266 1V= I*™ ! e j ° + K p ( f ) | e ° C V X PD (5.29) Equation (5.29) gives the magnitude of the crosspolar signal at the front-end input at any frequency i n terms of measurable quantities . The results from these equations can now be compared to actual measurements made with the crosspolar network connected to the front-end. F i g . 5.11 shows the results of a frequency response measurement made on the bench with the OMTs connected back-to-back and the crosspolar cancel-la t ion network connected to the front-end. The experimental set-up was i d e n t i c i a l to F i g . 2.37 without the isolator and variable attenuation but with the crosspolar cancellation network connected as shown in F i g . 2.39. The f i r s t measurement was made with the cancellation network attenuator at maximum attenuation to determine the uncancelled system XPD. This value varied between 32 and 37 dB over the measurement frequency range. This magnitude and rate of XPD variation indicates that the entire system was f a i r l y well matched i n this configuration ( i . e . compared to F i g . 2.38). The crosspolar cancellation network was then adjusted for a n u l l at 73.125 GHz and the second set of measurements were made. The calculated values of XPD were obtained using (5.29) with: -|E ( f )| are the values of XPD for the uncancelled system. D -|E I = 36 dB which is the value of uncancelled XPD at 73.125 GHz. C N B -£Q = l + ~ \)-B = 7 7 C m w n : * - c n r e s u l t e d from Z = 91 cm ± 1 cm (the length of the waveguide connection between the two directional 267 F i g . 5.11. Clear weather cancelled system XPD vs. frequency; 268 coupler junctions through the c a n c e l l a t i o n network) and £p_g ~ ^ T J _ ^ = 14 c m « t 1 cm (the differ e n c e i n the length of the waveguide connection between the OMT ports and the d i r e c t i o n a l coupler "input" p o r t s ) . and - B calculated f o r WR-15 waveguide. The agreement between the measured and ca l c u l a t e d cancelled system frequency responses i s considered to be very good. Both curves show d i f -ferences between the maximum and minimum XPD values which r e s u l t from changes i n the uncancelled system XPD magnitude. Differences between the two curves presumably r e s u l t from: small changes i n angles not due to waveguide lengths, small mismatches and small frequency dependent amplitude changes i n the OMTs, couplers, attenuators and front-^end. The t y p i c a l peak-to-peak v a r i a t i o n i n the free running k l y s t r o n frequency i n a one hour period i s approximately 3.5 MHz. This i s the c a l -culated average of the difference between the maximum and minimum frequency values recorded by the data a c q u i s i t i o n system over s e v e r a l , t y p i c a l one hour periods. Many records show much smaller v a r i a t i o n s but some also show l a r g e r v a r i a t i o n s , probably due to d i f f e r e n t changes i n ambient temperature. The s p e c i f i e d temperature c o e f f i c i e n t of the k l y s t r o n i s -1.0 MHz/°C t y p i c a l . This v a r i a t i o n i n the k l y s t r o n frequency could cause the cancelled system c l e a r weather XPD to d r i f t to approximately 55-60 dB, from a value below the noise l e v e l , over a t y p i c a l one hour period. This e f f e c t can be compounded by the f a c t that i t i s possible to have cumulative k l y s t r o n frequency d r i f t s over longer periods due to a consistent change i n the ambient temperature. Operational experience with the c a n c e l l a t i o n network 269 also uncovered changes i n the cancelled XPD level which could not be accoun-ted for by frequency d r i f t . For this reason the effects of temperature variation on the cancellation network were also investigated. 5.6.3 Cancelled System Temperature D r i f t It is also possible to use the previously derived theoretical results to estimate the change i n the cancelled system XPD due to temperature var ia -t i o n . Equations (5.27) to (5.29) show how the lengths of the waveguide connections associated with the cancellation network can affect the cancelled system XPD. The net c r i t i c a l length, was measured to be 93 cm for the network topology used i n the v i c i n i t y of the receiving antenna and front end. Coin s i lver waveguide i s used for these interconnections. The linear co-eff ic ient of thermal expansion for s i lver is 1 9 . 1 • 1 0 - 6 / ° C over the tempera-ture range 0 - 1 0 0 ° C . This w i l l result in a net change i n ZQ of approximately 0.018 mm/°C. At 73 GHz this w i l l translate to a change in the cancellation c i r c u i t angle of approximately 1.3 d e g r e e s / ° C . From F i g . 5.10, i t can be seen that a change i n the ambient temperature of a few °C can result in significant changes In the crosspolar signal l e v e l . It i s also l i k e l y that other components i n the crosspolar cancellation network or associated m i l l i -metre-wave c i r c u i t r y have significant temperature coefficients which could also affect the cancelled system XPD. Unfortunately, no specifications for temperature effects are available for these devices. 270 5.6.4 Phase Compensation of the Crosspolar Cancellation Network The previous theory indicates that the frequency and temperature dependence of the cancelled system XPD can be improved by selecting the lengths of the important waveguide connections i n the v i c i n i t y of the cross-polar cancellation network. From (5.28) and (5.29) i f £ Q = 0, then the XPD frequency variation is only due to the variation in the uncancelled system XPD and the frequency variation of the c i rcui t components. In addition, i f £Q = 0 the temperature dependent XPD variation w i l l result only from the temperature effects on the millimetre-wave components, i . e . the attenuator, phase s h i f t e r , etc. and not the change i n the waveguide lengths. It Is a simple matter to set ^ = 0 by selecting the length of the waveguide connection £_ „ ( i . e . the connection between the receiving antenna OMT crosspolar port and the cancellation network summing coupler) to be equal to the sum of the lengths ^ D _ ^ and £ ( i . e . the connections between the OMT copolar port and sampling coupler and total length between the coupler junctions, respectively) , as shown i n F i g . 2.39. To test the efficacy of this phase compensation scheme, a 93 cm length of WR-15 waveguide was added to the length, £ • . This length was c a l c u l -ated, after measuring the relevant waveguide lengths i n the c i r c u i t , to give £ - 0. . F i g . 5.12 shows the measured XPD for the uncancelled, cancelled but not phase corrected and cancelled and phase corrected systems. The improve-ment was less than what was hoped for but the phase compensation section did result i n an approximate increase of 100% in the useful bandwidth. The reason that the phase compensated response is not f la t is that even though the major source of the frequency sensitive response was the length £ R , other 271 73.20 73.30 73.40 Frequency (GHz) 73.50 F i g . 5.12. E f f e c t of phase compensation on uncancelled system XPD 272 c i r c u i t components also produce v a r i a t i o n s with frequency. Also shown i n F i g . 5.12 i s the predicted XPD l e v e l ( i . e . 48 dB) f o r a c a n c e l l a t i o n network imbalance of approximately 1 dB or 7 Deg. ( r e f . Fi g s . 5.9 and 5.10). This e f f e c t can e a s i l y explain the phase compensated response. For example, the uncancelled system XPD does show a 1 dB v a r i a t i o n within the frequency range where the compensated response degrades to approximately 48 dB. While the bandwidth improvement of approximately 100% i s very bene-f i c i a l , the o v e r a l l improvement i n the s t a b i l i t y of the c a n c e l l a t i o n appears to be much greater. This extra improvement i s thought to be due to the temperature compensation e f f e c t discussed i n Section 5.6.3. Before the phase compensation section was added, i t was occasionally necessary to readjust the c a n c e l l a t i o n network every hour or so to maintain the system XPD below 55 dB. With phase compensation, the XPD l e v e l has often remained i n the 60 dB range f o r many hours and does not usually require adjustment a f t e r the warm up period. 5.7 Model Predicted System XPD Performance In t h i s s e c t i o n , the previously described experimental model w i l l be used to predict the system XPD response during r a i n . I t w i l l be shown that f o r a given set of meteorological conditions, a range of system XPD values could possible be observed. This a p p l i c a t i o n of the model allows a more accurate comparison to be made between the t h e o r e t i c a l l y predicted and measured XPD during r a i n . This type of mathematical procedure i s very important when measuring XPD i n the shorter millimetre range because path XPD values are usually more 273 than the uncancelled system c l e a r weather i s o l a t i o n . As a r e s u l t , the observed system XPD during r a i n can be very d i f f e r e n t than that predicted f o r i d e a l antennas because of the addition of the path and antenna/OMT depolar-ized s i g n a l s . The observed system XPD can vary over a range of values f or a f i x e d path d e p o l a r i z a t i o n depending on the r e l a t i v e phases of the depolarized s i g n a l s . Even though the t h e o r e t i c a l methods can predict the r e l a t i v e phase of the path d e p o l a r i z a t i o n , t h i s uncertainty cannot be resolved because the angles of the antenna depolarized signals are not known. The use of the model i s also e s s e n t i a l to predict the change i n the measured system XPD due to path d i f f e r e n t i a l attenuation and phase s h i f t . It w i l l be shown that f or d i f f e r e n t measurement system configurations, the d i f -f e r e n t i a l attenuation and phase s h i f t also cause a change i n the system XPD because of t h e i r r e l a t i v e e f f e c t on the transmit antenna depolarized s i g n a l . This e f f e c t would cause an apparent change i n XPD even f o r the case of equi-oriented drops with zero canting angle. For t h i s reason, i t i s important to take i n t o consideration t h i s e f f e c t when comparing XPD predictions and measurements. The basic procedure to be followed i n t h i s section i s to use the model to c a l c u l a t e the possible system XPD values f o r a range of the unknown de-p o l a r i z a t i o n angles. The model inputs are a set of predicted path propaga-t i o n parameters and estimated values f o r the antenna XPDs. Values f o r the magnitudes of the antenna depolarized signals w i l l be estimated from previous measurements and the observed c l e a r weather system XPD. In some cases, i t i s also possible to estimate the difference between the antenna XPD angles from the c l e a r weather system i s o l a t i o n and the antenna XPDs i n F i g . 2.33. Path 274 propagation parameters are calculated f o r a set of assumed meteorological conditions using the techniques described i n Chapt er 4. These data are then used as the input f o r a model implementation program written f o r an HP-41-CV programmable c a l c u l a t o r . The program outputs the si g n a l l e v e l s throughout the measurement system and XPD values f o r cancelled or uncancelled systems. This basic method was also used i n the next chapter when experimental data are compared to t h e o r e t i c a l p r e d i c t i o n s . In the following sections, example predictions w i l l be used to demon-s t r a t e the use of the model and to show the i n t e r r e l a t i o n between the path propagation parameters and the experimental system. The e f f e c t s of path attenuations and phase s h i f t s on the measured XPD w i l l be i l l u s t r a t e d . An example showing the range of XPD values possible f o r cancelled and uncancel-l e d systems w i l l also be discussed. A complete, rigorous i n v e s t i g a t i o n of the r e l a t i o n s h i p between the path propagation parameters and the measured system XPD, as predicted by the model under a l l propagation conditions, would be extremely tedious. Instead, the r e s u l t s i n the next chapter also include discussions of the experimental model i n conjunction with actual experimental data. 5.7.1 E f f e c t s of P o l a r i z a t i o n Insensitive Attenuation or Phase S h i f t s Sample model c a l c u l a t i o n s show that a p o l a r i z a t i o n i n s e n s i t i v e path attenuation or phase s h i f t w i l l have no e f f e c t on the cancelled or uncancel-led system XPD, as would be expected i n t u i t i v e l y . Even though a p o l a r i z a t i o n i n s e n s i t i v e attenuation or phase s h i f t could only occur for the u n r e a l i s t i c case of s p h e r i c a l r a i n drops, i t i s necessary to v e r i f y that the p o l a r i z a t i o n 275 I n s e n s i t i v e portions of the path propagation do not a f f e c t the measured XPD. When performing these c a l c u l a t i o n s i t i s Important to remember that these attenuations and phase s h i f t s must also be included i n T^p^p. 5.7.2 E f f e c t s of D i f f e r e n t i a l Attenuation and Phase S h i f t Path d i f f e r e n t i a l attenuation and phase s h i f t cause a change i n the system XPD because of t h e i r e f f e c t on the transmit antenna depolarized s i g n a l . The system XPD can increase or decrease depending on whether v e r t i -c a l or h o r i z o n t a l p o l a r i z a t i o n i s transmitted. F i g . 5.13 shows the model predicted e f f e c t s of d i f f e r e n t i a l attenuation f o r several system configura^-tions with no path depolarizaton. Because the model uses copolar and cross-polar p o l a r i z a t i o n s , d i f f e r e n t i a l attenuation i s p o s i t i v e and negative f o r v e r t i c a l and h o r i z o n t a l transmitted p o l a r i z a t i o n s , r e s p e c t i v e l y . The l a r g e s t v a r i a t i o n due to d i f f e r e n t i a l attenuation occurs f o r the cancelled system. This would appear at f i r s t glance, to be a disadvantage of the c a n c e l l a t i o n system, but F i g . 5.14 shows that f o r the case where there i s a path depolar-i z e d s i g n a l , the cancelled system gives a much more accurate response. (The s u p e r i o r i t y of the cancelled system w i l l also be demonstrated i n further model predictions.) F i g . 5.14 shows that for both the cancelled and uncancelled systems, the XPD v a r i a t i o n due to d i f f e r e n t i a l attenuation i s lower f o r higher trans-mit antenna XPDs. For t h i s reason, the antenna/OMT assembly with the s l i g h t -l y better i s o l a t i o n was used f o r the transmit antenna i n t h i s experiment. 276 Fig. 5 .13. Effects of differential attenuation on system XPD for no path depolarization. 277 l I I U -0.5 0 0.5 1.0 D i f f e r e n t i a l a t t e n u a t i o n (dB) -1.5 T i g . 5.14. E f f e c t s o f d i f f e r e n t i a l a t t e n u a t i o n on system XPD f o r p a t h XPD = 40 dB ^10° 278 These graphs show that f o r accurate comparisons between predicted and measured XPD, i t i s necessary to include the e f f e c t s of d i f f e r e n t i a l attenua-t i o n on the system XPD. Path d i f f e r e n t i a l phase w i l l produce s i m i l a r r e s u l t s . To i l l u s t r a t e , and to compare the e f f e c t s of d i f f e r e n t i a l attenua-t i o n and phase, a r e a l i s t i c set of path propagation parameters w i l l be used. For t h i s example, the following meteorological conditions w i l l be assumed: ra i n r a t e = 10 mm/h, Joss/Olsen Widespread drop s i z e d i s t r i b u t i o n , canting angle = 2°, path length =1.8 km., h o r i z o n t a l transmitted p o l a r i z a t i o n and antenna XPDs = 40 dB J_ 0° . For t h i s set of conditions., the path XPD i s pre-dic t e d to be 54.3 dB. Table 5.1 shows the system XPD response f o r cancelled and uncancelled systems with no d i f f e r e n t i a l attenuation or phase s h i f t , d i f f e r e n t i a l attenuation only included, d i f f e r e n t i a l phase only included and both included. These r e s u l t s show that, f o r t h i s case, the e f f e c t of d i f f e r -e n t i a l phase i s l e s s than the e f f e c t of d i f f e r e n t i a l attenuation f o r both cancelled and uncancelled systems. 5.7.3 E f f e c t s of Antenna XPD Angle The l a r g e s t uncertainty i n XPD measurement i s due to the unknown r e l a -t i v e angles between the antenna/OMT and path depolarized s i g n a l s . The model shows that a r a i n depolarized s i g n a l can cause the measured uncancelled system XPD to increase or decrease depending on t h i s r e l a t i v e angle. This e f f e c t has been demonstrated t h e o r e t i c a l l y by Evans and Thompson [2.35] and Delogne and Sobieski [5.4]. Experimental observations of system XPD improve-ment during r a i n , presumably due to t h i s e f f e c t , have been observed and 279 System XPD (Measured) Ignoring d i f f e r e n t i a l attenuation and phase shif t Including d i f f e r e n t i a l attenuation only Including di f ferent ia l phase shif t only Including both d i f f e r e n t i a l attenuation and phase shif t Uncancelled 34.8 34.5 34.8 34.5 dB Cancelled 54.3 56.5 54.6 57.2 dB Copolar atten = 11.28dB j_ - 1 0 6 . 1 ° D i f f . atten.=-.43 dB D i f f . phase=1.25 Deg Path XPD = 54.3 dB Table 5.1 Effects of Dif ferent ia l Attenuation and Phase Shift Cancelled and Uncancelled Systems. Meteorological conditions: Path length = 1.8 km R = 10 mm/h = 2° T x = Horiz. Joss/Olsen Widespread drop size distr ibution X P D T X " X P D R X = 40 dB l_ 0° Clear weather uncancel-led isolat ion = 34 dB 280 commented on by De Lange, Dietrich and Hogg [1.74] and seem to appear but were not discussed in Shimba and Morita [1.81]. For an experimental system with constant antenna XPD angles, i t is possible to observe system XPD increases or decreases because the angle of ^CPXP ^ * e * ^12^ c a n c n a n S e depending on the canting angle. Equation (4.15) shows that the angle of the depolarizing element i n the transmission matrix w i l l change by 180° for opposite canting angle signs. In actual ra in , the angle of T , shown i n F i g . 4.8, depends on rainrate and dropsize d i s t r i b u -ter XP tion and is quite variable . As a result , when analyzing this effect , i t Is necessary to consider a l l relative angles between the path and antenna/OMT depolarized signals . To demonstrate this effect for the cancelled and uncancelled systems used i n this experiment, the system XPD response for the meteorological conditions used i n the previous section w i l l be predicted again. In this case, the antenna XPI) angles w i l l be varied to i l l u s t r a t e the range of possible measured XPD values. The maximum and minimum XPD values were determined by incrementing the antenna XPD angles by n degrees for the same set of path propagation parameters. Table 5.2 shows the range of XPD values for different sets of antenna XPD angles. Again, i t is important to note that the same range of values could occur i f the antenna XPDs were held constant and the path depolariza-tion angle varied. These results again show the reduced uncertainty when using the crosspolar cancellation network. The uncertainty when using the cancellation network is due to d i f f e r e n t i a l attenuation and phase s h i f t . For the uncancelled system, a very large range of system XPD values is possible. 281 Antenna XPD Angles (DEG) Uncancelled System Clear Weather XPD (dB) Uncancelled System XPD range (dB) Cancelled System XPD range (dB) 1. / X P DRX * / X P D T X -24.5 + 23.2 + n n 34 33-34.6 52.1-57.2 2. / X P DRX " / X P D T X -24.5 23.2 + n 34-NOISE LEVEL 34.6-52.2 52.1-57.2 3. / X P DRX * /XPD^ = 24.5 + 23.2 n 34-NOISE LEVEL 34.6-56.9 56.8 4. / X P D R X = /XPD^ = 204.5 23.2 + n 34-NOISE LEVEL 33-56.9 52.1-57.2 5. / X P D R X -/XPD,^ = 24.5 + 203.2° n 34-NOISE LEVEL 33-52 .2 52.2 6. / X P D R X = _/XPDTX = 150 + n n 45.7 42.5-48.9 52.1-57.2 Antenna XPD magnitudes = 40 dB Meteorological conditions given i n Table 5.1 Path XPD = 54.3 dB Table 5.2 Range of Possible System XPDs for Dif f e r e n t Antenna XPD Angles. 282 Case 1 i n Table 5.2 i s for the s i t u a t i o n where the antenna depolarized s i g n a l s are i n phase at plane D-D. This i s l i k e l y to be very close to the actual s i t u a t i o n when cl e a r weather i s o l a t i o n s are observed to be about 34 dB. Case 6 represents the s i t u a t i o n where a c l e a r weather XPD improvement has been obtained by a l t e r i n g the r e l a t i v e antenna XPD angles. This i s thought to be s i m i l a r to the s i t u a t i o n s when received OMT mismatches were used to improve the c l e a r weather system XPD. 5.7.4 E f f e c t s of Antenna XPD Magnitudes Table 5.3 shows the range of XPD values f o r the s i t u a t i o n i n case 1 of Table 5.2 but with d i f f e r e n t antenna XPD magnitudes. These r e s u l t s show that the uncertainty i n the cancelled system XPD decreases as the transmit antenna XPD increases. The re c e i v i n g antenna XPD has no e f f e c t because the c a n c e l l a -t i o n network can compensate for the r e c e i v i n g antenna without degradation due to d i f f e r e n t i a l attenuation and phase. For the uncancelled system, the system XPD i s c l o s e r to the path XPD f o r higher antenna i s o l a t i o n s . The range of possible XPD values increases f o r higher i s o l a t i o n s i n t h i s case because the r e l a t i v e magnitude of the path depolarized s i g n a l has increased. This trend would of course reverse i f the path XPD was smaller than the c l e a r weather system XPD. These r e s u l t s show that i n cancelled systems, i f the a v a i l a b l e anten-nas have d i f f e r e n t i s o l a t i o n s the higher i s o l a t i o n antenna should be used f o r transmitting. In t h i s experiment tbe transmit antenna XPDs are a few dB higher than those f o r the receive antenna. 283 Antenna XPD magnitudes (dB) Uncancelled Clear weather System XPD (dB) Uncancelled System XPD (dB) Cancelled System XPD (dB) XPD T X = 40 dB 34 33-34.6 52.1-57.2 X P D R X = 4 0 d B X P D R X = 4 0 d B 35 33.9-35.6 52.5-56.5 XPD^ = 42 dB XPD^ = 42 dB 36 34.8-36.8 52.5-56.5 XPD^ =42 dB Table 5.3 Range of Possible System XPDs f o r D i f f e r e n t Antenna XPD Magnitudes. ft 284 P r a c t i c a l applications of the experimental model developed i n t h i s chapter w i l l be included i n the next chapter i n conjunction with the a c t u a l experimental observations. 285 6. EXPERIMENTAL RESULTS 6.1 Preliminary Discussion During the period t h i s experimental system was being developed, several hundred hours of data were recorded. Only si n g l e p o l a r i z a t i o n CPA and r a i n r a t e , however, were observed during the early phases of t h i s project. Dual-polarized, uncancelled XPD measurements were made l a t e r . F i n a l l y , when the crosspolar c a n c e l l a t i o n network was added and the f i n a l version of the disdrometer system operational, many hours of complete data were recorded. For the majority of t h i s time, however, rainr a t e s were below 5 mm/h (as predicted by F i g . 3.4). At low r a i n r a t e s , i t i s more d i f f i c u l t to make accurate XPD measurements (due to small changes from the clear weather value) and r a i n r a t e measurements (because of raingauge averaging). In addition, reasonably high rainrates were often accompanied by low wind v e l o c i t i e s which re s u l t e d i n path XPD values too high to be accurately measured. The number of data f i l e s which could be completely analyzed and i n -cluded i n t h i s report was l i m i t e d by the f i n i t e monetary resources a v a i l a b l e and the great deal of time required to thoroughly analyze each hour of data. Most of the f i l e s were subjected to a preliminary a n a l y s i s . The majority of these showed very s i m i l a r r e s u l t s , with high path XPDs and CPAs i n agreement with the "standard" p r e d i c t i o n s , e s p e c i a l l y during periods with low wind v e l o c i t i e s . For t h i s reason, the f i l e s which were chosen to be presented i n t h i s report contain either comparatively low path XPDs and/or CPAs beyond the range of the "standard" predictions. 286 Eight d i f f e r e n t data periods w i l l be analyzed i n Sections 6.2-6.9. Each se c t i o n includes the r e s u l t s from a portion of a one hour data f i l e . These data f i l e s are described by an eight d i g i t code, e.g. 81.11.30.18 which, i n t h i s case, designates the f i l e recorded November 30, 1981. The l a s t p a i r of d i g i t s are the hour of the day during the f i r s t data sample. Most pl o t headers contain: t h i s f i l e number, the date, the f i l e s t a r t i n g time i n hours and minutes, and the data averaging period. Before analyzing the f i r s t data f i l e , a short discussion of some experimental c h a r a c t e r i s t i c s common to a l l f i l e s may be u s e f u l . 6.1.1 Disdrometer Data A l l of the drop si z e data included i n th i s report were recorded using: - the standard ( i . e . Laws and Parsons) drop diameter categories - a minimum measurable drop diameter of approximately 0.30-0.35 mm diameter and - a one minute averaging i n t e r v a l . The drop data are presented as the number density, i . e . number of drops per cubic meter i n a 1 mm drop diameter i n t e r v a l , to conform to the standard d e f i n i t i o n of Np. These values of N^ are plotted against drop diameter along with the s i m i l a r standard drop d i s t r i b u t i o n s f o r s i m i l a r r a i n -r a t e s . On these curves, and throughout t h i s chapter, the following abbrevia-tions are used f o r the standard d i s t r i b u t i o n s : JOD f o r Joss/Olsen D r i z z l e JOW for Joss/Olsen Widespread, which i s the same as the Marshall and Palmerj, 287 and JOT for Joss/Olsen Thunderstorm. Propagation data i n t e r v a l s are segmented during analysis i n t o hundred-th hour periods. Because drop data are recorded f o r one minute periods, the number of drop d i s t r i b u t i o n samples displayed on each graph w i l l vary depend-ing on where i n the hour the decimal d i v i s i o n s occurred. Some one-to-three minute gaps also occur i n the drop data because the transducer g r i d was p e r i o d i c a l l y cleared of small droplets c l i n g i n g to the wires by blowing a i r over the g r i d s . The accuracy of the disdrometer data was p e r i o d i c a l l y checked by comparison to the r a i n r a t e and water accumulation i n d i c a t e d by tipping-bucket gauge number 1, which was located about 10 m from the disdrometer. Three comparisons are shown i n F i g s . 6.1.1 to 6.1.3. T y p i c a l l y , the disdromter indi c a t e d r a i n accumulations were 5 to 8% higher than that i n d i c a t e d by the raingauge. This was at l e a s t p a r t i a l l y due to a s i m p l i f i c a t i o n i n the water accumulation c a l c u l a t i o n , which assumed a uniform d i s t r i b u t i o n of drop s i z e s i n each category. The number of drops i n the smallest category was u s u a l l y lower than expected from the standard d i s t r i b u t i o n s . To a small extent, t h i s was due to the minimum measurable drop si z e of approximately 0.30-0.35 mm i n diameter. The major portion of this discrepancy i s believed, however, to be due to the lower gauge catch e f f i c i e n c y f o r the smaller drops. F i g . 3.3 shows the reduction i n p r e c i p i t a t i o n gauge catch e f f i c i e n c y f o r d i f f e r e n t h o r i z o n t a l wind speeds. This reduction i s due to wind flows c a r r y i n g the drops up and over the gauge aperture, which i s obviously a more pronounced problem f o r smaller drops. 288 r T o t a l accumulation: Raingauge = 24.98 mm/h min. Disdrometer = 26.71 mm/h min. rt u c 5 LP I u i i — i — • r ~ j 1 I i i | i i i i i , i L _ _ i 8:42 8:44 8:46 Time 8:48 8 :50 8 :52 F i g . 6.1.1. Disdrometer-raingauge #1 comparison, Nov. 14, 1981. 289 Total accumulation: Raingauge = 39.7 mm/h min. Disdrometer = 43.3 mm/h min. Time .6.1.2. Disdrometer-raingauge #1 comparison, 290 Total accumulation: Raingauge = 36.0 mm/h min. Disdrometer = 38.1 mm/h min. L l - J I ' i "U I I I r-11:00 11:02 11:04 11:06 Time 11:08 11:10 F i g . 6.1.3. Disdrometer-raingauge #1 comparison, Nov. 30,1981. 291 6.1.2 Receiving System Noise Levels For the gains used for most data periods, the receiving system average noise levels were approximately -78 dB and -76 dB on the ver t i ca l and h o r i -zontal channels, respectively. At very low rainrates, these noise levels may have introduced inaccuracies in the cancelled XPD data as discussed i n Section 6.2.2. They also set the minimum measurable path XPD. This level was, on occasion, exceeded during high rainrates with low canting angles, as discussed i n Sections 6.4.2 and 6.9.2. 6.1.3 Different ia l Attenuation Calculations The d i f f e r e n t i a l attenuation results presented i n this chapter were calculated from the sequential samples of CPA for each polarization. For the data presented here, the polarization switching period was 15 s. During analysis, the data from one second before and two seconds after the polar-izat ion change were discarded to allow time for the receiving system to se t t le . This resulted i n 12 s of accurate data for each polarization during every 30 s of real time. Different ia l attenuation results were calculated by averaging two calculated d i f f e r e n t i a l attenution samples. Each sample was the calculated difference between 6 samples of one polarization, the next 12 samples of the other polarization and the next 6 samples of the f i r s t p o l a r i -zation. This calculation was performed starting with both polarizations, and the average value was plotted. This method eliminates calculated di f feren-t i a l attenuation errors due to linear time variations i n CPA and greatly reduces inaccuracy due to quadratic CPA changes. However, i t i s possible 292 that some inaccuracy s t i l l occurred when the CPA was changing rapidly or, increasing and decreasing, in a 30 second period. 6.2 Experimental Results for 81.11.30.10. This data f i l e i s the f i r s t of a series which were recorded on Nov. 30, 1981. As this day progressed, a wide variety of meteorological and propagation conditions were observed. Because these data contain examples of most types of anomalous propagation observed during the course of this experiment and because the entire experimental system was operating sa t i s -f a c t o r i l y and without interruption, several data f i l e s recorded on this date w i l l be thoroughly analyzed i n the following sections. The f i r s t f i l e of this series was recorded November 30, 1981 from 10:59 to 11:46. Rainrates for the individual raingauges and the path average are shown i n F i g . 6.2.1. Rainrates were reasonably uniform over the r a i n -gauge network and changed relat ively slowly. The path average rainrate during this period of widespread rain varied between 2 and 4 mm/h. During this period, the wind direction was constantly from the east and therefore blowing direct ly perpendicular to the path. The horizontal wind velocity , shown i n F i g . 6.2.2(a) on a 10 s average and i n F i g . 6.2.2(b) over a 30 s average, varied between 2 and 8.2 m/s. Vertical wind velocit ies during this period were generally posit ive, ( i . e . upward) as shown in Figs. 6.2.3(a) and (b) for 30 s and 60 s averages, respectively. The vert ical wind velocity often changed rapidly and had 30 s average values over 1.0 m/s. Signal levels for horizontal transmitted polarization are shown i n Figs. 6.2.4(a) and (b) (10 s and 30 s averages). F i g . 6.2.5 is a time series £63 L6Z 863 66Z ooe 301 pl o t of the 2 s average s i g n a l l e v e l s f o r v e r t i c a l transmitted p o l a r i z a t i o n . 6.2.1 Attenuation Data f o r 81.11.30.10, 10:59-11:41 This data f i l e contains several excellent examples of the e f f e c t s of v e r t i c a l wind on copolar attenuation. Included are periods of attenuation as low as that predicted f o r the JOT d i s t r i b u t i o n and considerably higher than predicted f o r the JOD d i s t r i b u t i o n . These occurred even though almost a l l of the measured drop d i s t r i b u t i o n s generally conformed to the JOW d i s t r i b u t i o n . S i g n i f i c a n t v a r i a t i o n did occur, however, i n the r e l a t i v e number of drops i n the smallest categories, as indicated by the r a t i o : N D(0.5)/Np(I.O) shown i n F i g . 6.2.3(a). The v e r t i c a l wind e f f e c t s can be c l e a r l y i s o l a t e d i n t h i s f i l e because the r a i n r a t e was reasonably uniform along the path, slowly varying and r e l a t i v e l y constant over t h i s e n t i r e p e riod. A summary of the attenuation r e s u l t s f o r t h i s f i l e are given i n Table 6.2.1. A legend f o r the numbered comments for t h i s and a l l of the s i m i l a r summaries immediately follows Table 6.2.1. Period Measured Attenuation Compared to Standard Predictions Measured Drop Distribution Vertical Wind During Rain Data is in Approximate Agreement with Predictions for: Comments T l . 0.20-0.23 h Varied from JOW to greater than JOD Fig. 6.2.6 JOW, 1 Fig. 6.2.7 Decreased from +1.2 m/s to +0.2 m/s then started to increase. Fig. 6.2.3(a),(b) Rainrate = constant. Attenuation correlated with vertical wind decrease. Figs. 6.2.3(a), 6.2.4(a), 6.2.6. 3, 0.23-0.26 h Between JOD and JOW Fig. 6.2.8 JOW, 1 Fig. 6.2.9 Variable, rapidly increased, decreased and increased, avg = 0.6 m/s Fig. 6.2.3(a),(b) JOW and vert, wind 0 to +1.0 m/s Fig. 6.2.8 Ref. Section 6.2.1.2 T3 0.27-0.29 h Varied from JOD to JOT Fig. 6.2.10 Between JOW and JOT, more large drops that Tl & T2 Fig. 6.2.11 Decreased from +0.85 to -0.15 m/s Fig. 6.2.3(a) Rainrate = constant attenuation variable due to vertical wind. Figs. 6.2.3(a), 6.2.4(a), 6,2.10 3, T 0.31-0.34 h Between JOW and JOT Fig. 6.2.12 JOW, 1 Fig. 6.2.13 Relatively constant £+0.5 m/s avg. Fig. 6.2.3(a) JOT and JOW with zero vert, wind. Fig. 6.2.12 Anomolously low attenua-tion, Ref. Section 6.2.1^  T5 0.72-0.74 h Close to JOD Fig. 6.2.14 JOW, 1 & 5 Fig, 6.2.15. Increased from +0.5 to +1.15 m/s, =0.70 m/s avg. Fig, 6.2.3(a) JOW and vert, wind =+1.0 m/s Fig. 6.2.14 4, 5. Period Measured Attenuation Compared to Standard Predictions Measured Drop D i s t r i b u t i o n V e r t i c a l Wind During Rain Data i s i n Approximate Agreement with Predictions f o r : Comments 0.74-0.78 h Varied from JOW to much higher than JOD F i g . 6.2.16 B a s i c a l l y JOW, 1, but few more large drops. F i g . 6.2.17 Decreased, increased and decreased between +0.6 and +1.15 m/s F i g . 6.2.3(a) Rainrate = constant Range of attenuation due to v e r t i c a l wind. F i g s . 6.2.3(a), 6.2.4(a), 6.2.16 3 and 4 T7 0.78-0.84 h Between JOW and JOD F i g . 6.2.18 JOW, 1 F i g . 6.2.19 Rela t i v e l y constant =+0.5 m/s avg. F i g . 6.2.3(a) JOW and v e r t , wind = +0.5 m/s. F i g . 6.2.18 0.87-0.89 h JOT, lower than T y F i g . 6.2.20 JOW, 1 & 5 F i g . 6.2.21 Increased from +0.1 to 1.6 m/s F i g . 6.2.3(a) JOT and zero v e r t , wind. See comments F i g . 6.2.20 8 Ref. Section 6.2.1.8 T 0.89-0.93 h Between JOW and JOD, higher that Tg. F i g . 6.2.22 JOW, 1 Fi g . 6.2.23 Decreased from =1.0 m/s to 0 and then increased. F i g . 6.2.3(a) JOW and v e r t , wind = 0.5 m/s F i g . 6.2.22 3 Table 6.2.1 Summary of Attenuation Data f o r 81.11.30.10, 10:59-11:41 304 Legend f o r Summary Tables. 1. Number of drops i n the smallest category was a c t u a l l y larger than indicated by disdrometer because of ho r i z o n t a l wind v e l o c i t y . This i s discussed i n Section 6.1.1. 2. Actual or " e f f e c t i v e " v e r t i c a l wind v e l o c i t y appears to be approximately double measured v e r t i c a l wind v e l o c i t y . This i s discussed In Section 6.4.1.1. 3. Attenuation was unusually high because small drops were "stored" above the path by a v e r t i c a l wind flow before t h i s period and then, during t h i s period, "released" by a reduced or decreasing v e r t i c a l wind v e l o c i t y . This i s discussed i n Section 6.2.1.1. 4. Attenuation was r e l a t i v e l y high because v e r t i c a l wind was increasing or was near a peak and t h i s was increasing the number of small drops per m 3 i n the propagation path, as discussed i n Section 6.2.1.5. 5. Number of drops i n smallest or two smallest categories measured by the disdrometer were low because v e r t i c a l wind was increasing during t h i s period, t r a n s i e n t l y reducing the number of small drops f a l l i n g into the disdrometer. 6. Measured attenuation was r e l a t i v e l y low for measured path rainrate because of an unusually large number of large drops which considerably 305 increase measured ra i n r a t e but did not a f f e c t attenuation as s i g n i f i c a n t l y at t h i s frequency. 7. During t h i s i n t e r v a l the drop siz e d i s t r i b u t i o n changed r a p i d l y . Because t h i s d i s t r i b u t i o n was measured at one end of the path, the attenuation and drop s i z e data have been time s h i f t e d by up to one minute to obtain a more r e a l i s t i c c o r r e l a t i o n between the path average attenuation and the measured drop s i z e d i s t r i b u t i o n . This delay i s discussed i n Section 6.2.1.3. 8. Attenuation and number of drops i n the smallest categories were both temporarily low due to an unusually rapid increase i n v e r t i c a l wind v e l o c i t y . This v e r t i c a l wind transient temporarily reduced the number of drops f a l l i n g to the l e v e l of the propagation path, as discussed i n Section 6.2.1.8. 9. Some inaccuracy may occur when comparing XPD values during low ra i n r a t e s to t h e o r e t i c a l predictions because: - the c l e a r weather cancelled system XPD i s j u s t over 60 dB and t h i s value agrees with the t h e o r e t i c a l predictions f o r <f> = 3° at a r a i n r a t e of 2.5 mm/hr. - at low crosspolar s i g n a l l e v e l s ( i . e . close to -70 dB) the proximity of the receiver noise f l o o r can introduce errors ( e x p e c i a l l y f o r short averaging periods). 306 6.2.1.1 Attenuation During 0.20-0.23 h. During the Interval T j , F i g . 6.2.6 shows that the CPA was quite variable and at times was considerably higher than predictions for the JOD d i s t r i b u t i o n even though the measured drop sizes were i n agreement with the JOW d i s t r i b u t i o n , as shown i n F i g . 6.2.7. This i s thought to be due to the v e r t i c a l wind v e l o c i t y , which decreased rapidly from +1.1 m/s to +0.2 m/s, and then began to Increase again at the end of this period. Figs. 6.2.3(a) and 6.2.4(a) show that the attenuation was high during the decreasing v e r t i c a l wind and then decreased when the v e r t i c a l wind began to increase. I t i s believed that the high attenuation was due to a large number of small drops (which attained a reduced v e l o c i t y above the path during an immediately previous period of upward v e r t i c a l wind) being "released" as the v e r t i c a l wind decreased. When the v e r t i c a l wind increased near the end of this period, the attenuation was reduced as the drops were again temporarily "suspended" above the propagation path. 6.2.1.2 Attenuation During T 2, 0.23-0.26 h. In the i n t e r v a l T 2, the attenuation, F i g . 6.2.8, was less variable than during T p even though the variations i n the 30 s average v e r t i c a l wind v e l o c i t y , F i g . 6.2.3(a), were greater. This i s thought to be because the 1. FILE: 81.11.30.10 1 FILES TO BE PROCESSED 81.11.30 10.46 2. SECOND AVERAGE INTERVAL TIME t 0.20 0.23 308 Fig. 6.2.7. Drop distributions for T 1. FILE: 81.11.30.10 1 FILES TO BE PROCESSED 81.11.30 10.46 2. SECOND AVERAGE INTERVAL TIME « 0.23 0.26 JOW VW=1 m/s JOW VW=0 — T 1 1 1 — i 1 1 1 I — i — 1 1 1 • I 0.0 1.0 2.0 3.0 4.0 5.0 B.O 7 .0 B.O S.O 10.0 11.0 12.0 13. AVERAGE RAIN RATE(MM/HOUR1 F i g . 6.2.8. CPA d u r i n g T, 310 311 v e r t i c a l wind v e l o c i t y during T 2 increased, decreased and then increased again without s u f f i c i e n t time f o r a s i g n i f i c a n t change i n the drop s i z e d i s t r i b u t i o n at the height of the antenna beams. The 60 s average v e r t i c a l wind v e l o c i t y , F i g . 6.2.3(b), shows more c l e a r l y the general decrease during T^ and a s l i g h t l y smaller and more gradual v a r i a t i o n during T 2» 6.2.1.3 Attenuation During T ^ 0.27-0.29 h. During T 3 the attenuation, F i g . 6.2.10, again v a r i e d over a wide range, i n t h i s case, between predictions f o r the JOT, to s l i g h t l y higher than the JOD, d i s t r i b u t i o n s . The v e r t i c a l wind v e l o c i t y during t h i s period r a p i d -l y decreased from +0.85 to -0.15 m/s a f t e r a period of upward flow, F i g . 6.2.3(a), i n a manner very s i m i l a r to T j . The s l i g h t l y lower absolute values of attenuation during T 3 compared to T j were due to a l a r g e r proportion of large drops during T 3, as shown i n F i g . 6.2.11. F i g . 6.2.3(a) also shows the r a t i o : N D(0.5)/N D(1.0). This curve shows the increase i n the number of smaller drops approximately one minute a f t e r the v e r t i c a l wind decrease and attenuation increase, f o r both periods T^ and T^. The reason f o r t h i s delay i s not e n t i r e l y c l e a r , but i s believed to be due to the f a c t that the d i s d r o -meter i s at one end, which i s also the lowest point, of the path. The disdrometer i s 30 m lower than the r e f l e c t o r , F i g . 2.31. If an average v e r t i c a l wind v e l o c i t y of 1 m/s i s assumed, th i s height d i f f e r e n c e could 1. F I L E : 8 1 . 1 1 . 3 0 . 1 0 . 1 F I LES TO BE PROCESSED 8 1 . 1 1 . 3 0 10.46 2. SECOND RVERRGE INTERVAL TIME i 0.27 0.29 Fig. 6.2.10. CPA during T, 313 Fig.6.2.11. Drop distributions for T. 314 account f o r an average 30 s delay i n the a r r i v a l time of the increased number of drops i n the smallest category, at the r e f l e c t o r , compared to the d i s d r o -meter. This delay would also be considerably l a r g e r f o r the smaller drops i n t h i s category which would also have undergone the greatest degree of "storage" due to the previous upward a i r flow. I t i s also possible that there i s a general movement, during these periods, of r a i n medium change from the r e f l e c t o r end of the path towards the end of the path where the d i s d r o -meter i s located. This would probably be r e l a t e d to a southerly component of r a i n c e l l movement but t h i s i s d i f f i c u l t to v e r i f y f o r these periods because the r a i n r a t e along the path i s quite uniform. 6.2.1.4 Attenuation During T^, 0.31-0.34 h. Attenuation during period T^, F i g . 6.2.12, was anomolously low. V e r t i c a l wind during t h i s period was r e l a t i v e l y constant at +0.5 m/s, F i g s . 6.2.3(a) and (b) , which should have res u l t e d i n a s l i g h t l y increased attenua-t i o n . The drop s i z e s measured by the disdrometer during t h i s period were close to the JOW d i s t r i b u t i o n . The only possible explanation f o r t h i s low attenuation i s the r e l a t i v e l y smaller number of small drops shown i n F i g . 6.2.3(a) Immediately a f t e r t h i s i n t e r v a l . I f the theory about a delay i n the disdrometer data f o r these periods, presented i n the previous s e c t i o n , was c o r r e c t , then t h i s change i n drop d i s t r i b u t i o n might adequately explain these attenuation r e s u l t s . Fig. 6.2.12. CPA during T( r-1 316 Fig. 6.2.13. Drop distributions for T 317 6.2.1.5 Attenuation During T 5 , 0.72-0.74 h . During interval T 5 , F i g . 6.2.14 shows that the attenuation was similar to that predicted for the JOD distr ibution but the measured drop s izes , F i g . 6.2.15, generally corresponded to the JOW d is t r ibut ion . The unusually small number of drops in the smallest category i s believed to be due to the v e r t i c a l wind, which was increasing from +0.5 to +1.15 m/s during this period. It i s thought that the increasing ver t i ca l wind temporarily reduced the number of small drops f a l l i n g to the height of the disdrometer. This reduction i n the number of small drops i s clearly shown i n F i g . 6.2.3(a). The attenuation during T 5 agrees with that predicted for the JOW distr ibution and a v e r t i c a l wind velocity of +1.0 m/s. Thus, i t appears that the upward v e r t i c a l wind during this period temporarily increased the number of drops in the path while simultaneously reducing the number of drops f a l l i n g to the height of the disdrometer. Some suggestions as to the cause of this pheno-mena include: - a simple, ver t i ca l wind induced transient in the number of small drops at the location of the disdrometer - the different heights along the path - a complex, v e r t i c a l l y - c i r c u l a r , turbulent airflow along the path due to the buildings below the path, or - the ver t i ca l wind velocity near the building on which the disdrometer i s mounted further reducing the small drop catch efficiency of the disdrometer as discussed in Section 6.1.1. 1. FILE: 81.11.30.JO J FILES TO BE PROCESSED 81.11.30 10.46 2. SECOND AVERAGE INTERVAL TIME s 0.72 0.74. 319 320 6.2.1.6 Attenuation During T f i , 0.74-0.78 h . Interval Tg is another clear example of attenuation much higher than that predicted for the JOD dis t r ibut ion , F i g . 6.2.16. The highest attenua-tions occurred at 0.75 h , F i g . 6.2.4(a), at the same time as the v e r t i c a l wind decreased i n F i g . 6.2.3(a). Again, F i g . 6.2.3(a) shows an increase i n the number of small drops one minute la ter . This attenuation peak is believed to be rela t ively large because the ver t i ca l wind was steadily increasing for the 2.5 minutes before 0.75 h, resulting in a large accumula-tion of small drops. 6.2.1.7 Attenuation During T ? , 0.78-0.84 h . During T 7 , the attenuation, F i g . 6.2.18, was generally higher than that predicted for the JOW dis t r ibut ion . This is believed to be due to the re la t ively constant +0.5 m/s ver t ica l wind and possibly some small drops which were held suspended by the previously higher v e r t i c a l wind v e l o c i t y . These results agree, on the average, with predictions for the measured distr ibution and ver t i ca l wind veloc i ty . 6.2.1.8 Attenuation During T 0 , 0.87-0.89 h . o Attenuation during Tg, F i g . 6.2.20, agreed with the standard predic-tions for the JOT dis t r ibuto in . This very low attenuation was due to an extremely fast increase i n the ver t i ca l wind velocity from +0.1 to +1.6 m/s, F i g . 6.2.3(a). In this case, the disdrometer indicated the decrease i n the Np(0.5)/Np(1.0) ratio within approximately 30 s. This period is in contrast to Tg, which had higher attenuation during a period of increasing 322 Fig. 6.2.17. Drop distributions for T 1. FILE: 81.11.30.10 1 FILES TO BE PROCESSED 81.11.30 10.46 2. SECOND RVERRGE INTERVAL TIME i 0.78 0.84 324 1. FILEs 81.11.30.10 1 FILES TO BE PROCESSED 81.11.30 10.46 2. SECOND AVERAGE INTERVAL TIME i 0.87 0.89 326 r 327 v e r t i c a l wind v e l o c i t y . In t h i s case, i t i s thought that the s i g n i f i c a n t l y l a r g e r and f a s t e r v e r t i c a l wind increase was s u f f i c i e n t to temporarily reduce the number of small drops at the height of the propagation path. I t i s probable that the transient decrease i n the number of small drops was a c t u a l -l y lower than that indicated by the disdrometer because of averaging over the one minute sample period. 6.2.1.9 Attenuation During T ^ 0.89-0.93 h. During T g, F i g . 6.2.22 shows that the attenuation was higher than that predicted for the JOW d i s t r i b u t i o n . The attenuation Is not as large as that observed during Tg, even though the v e r t i c a l wind decrease at the beginning of t h i s period i s larger than during Tg. This i s thought to be because the period of upward flow preceeding the decrease was much shorter i n t h i s case, and therefore fewer drops were "stored" above the path by the upward flow. 6.2.2 XPD and D i f f e r e n t i a l and Attenuation Data f o r 81.11.30.10 The cancelled system XPD, for h o r i z o n t a l transmitted p o l a r i z a t i o n , i s shown i n F i g . 6.2.24 for a 30 s averaging period. During t h i s period, the crosspolar c a n c e l l a t i o n network provided a c l e a r weather system XPD of s l i g h t l y over 60 dB (an exact value cannot be determined because i t rained constantly during t h i s period). The uncancelled XPD, f o r v e r t i c a l transmit-ted p o l a r i z a t i o n , i s shown i n Figs. 6.2.25(a) and (b) f o r 2 s and 30 s averages r e s p e c t i v e l y . For t h i s p o l a r i z a t i o n , the c l e a r weather system XPD was approximately 33 dB. 1. FILE« 81.11.30.10 1 FILES TO BE PROCESSED 81.11.30 10.46 2. SECOND AVERAGE INTERVAL TIME t 0.89 0.93 Fig. 6.2.22. CPA during T, 329 x T. 1. FILE: 81 . J l . 3 0 . 1 0 . . 1 FILES TO BE PROCESSED 81 . 11 .30 10.46 30.SECOND AVERAGE 1 | 1 1 ! 1 1 1 1 1 0.0 0.1 0.J 0.1 0.4 0.5 0.6 0.7 0.8 0.9 TIME (HOURS) F i g . 6.2.24. XPD f o r horizontal transmitted p o l a r i z a t i o n , 30 s avg. f o r 81.11.30.10. ~i i.o 333 Both the cancelled and uncancelled XPDs show the greatest change from c l e a r weather values near the end of t h i s f i l e , during the periods of l a r g e s t h o r i z o n t a l wind v e l o c i t y . During t h i s f i l e , as during most observations from t h i s experiment, the uncancelled XPD increases and decreases from the c l e a r weather value. As an example, at 0.29 h during a r a i n r a t e maxima, both XPDs decreased. However, i n contrast, the uncancelled XPD generally i n -creased p r i o r to 0.89 h and then decreased at 0.90 h. The cancelled system XPD c o n t i n u a l l y decreased during these periods. This uncancelled system XPD behaviour i s believed to be due to changes i n the angle of Tgp^p ( i . e . T 1 2 ) « These changes i n angle r e s u l t i n the path depolarized s i g n a l adding with the antenna depolarized s i g n a l to e i t h e r increase or decrease the t o t a l system XPD. The cancelled XPD i s r e l a t i v e l y immune to these changes i n angle. I t i s believed that the path XPD d i d , i n f a c t , sharply decrease at 0.90 h as observed on the cancelled channel. This change was not c l e a r l y observed as a change from the c l e a r weather value on the uncancelled channel because i t i s believed that the h o r i z o n t a l wind transient responsible f o r t h i s path XPD minimum also changed the path XPD angle. This change i n angle caused the uncancelled XPD to change from increasing to decreasing r e s u l t i n g i n a net value close to the c l e a r weather XPD. This type of behaviour makes i t very d i f f i c u l t to compare the uncancelled XPD to model predictions during v a r i a b l e wind condit i o n s . Better examples of the phase e f f e c t s on the uncancelled XPD are included i n other sections. Some caution must be applied when comparing the cancelled XPD during low r a i n r a t e s to the model predictions because these values are close to the c l e a r weather sys.tem XPD. For example, at a r a i n r a t e of 2.5 mm/hr, the c l e a r 334 weather XPD (which would also be observed for a zero canting angle) corres-ponds to an e f f e c t i v e mean canting angle of approximately 3°. As a r e s u l t , the absolute value of the calculated canting angle i s l i k e l y smaller than the value obtained, by a d i r e c t comparison to the data during low r a i n r a t e s . The d i f f e r e n t i a l attenuation during t h i s f i l e i s shown i n F i g . 6.2.25. This p l o t shows that the d i f f e r e n t i a l attenuation was often negative ( f o r periods up to 2 minutes) i n con t r a d i c t i o n to the basic theory and drop shape assumptions. Similar negative d i f f e r e n t i a l attenuations were observed during most rainstorms over the course of t h i s experiment. While some caution i s necessary i n i n t e r p r e t i n g the d i f f e r e n t i a l attenuation data from t h i s e x p e r i -ment because of the data sampling as discussed i n Section 6.1.3, i t i s believed that these negative d i f f e r e n t i a l attenuations d i d , i n f a c t , occur. Similar negative d i f f e r e n t i a l attenuations were observed i n [1.74]. A summary of the XPD and d i f f e r e n t i a l attenuation data analyzed during t h i s f i l e i s shown i n Table 6.2.2. The legend for the comments follows Table 6.2.1. 6.2.2.1 XPD and D i f f e r e n t i a l Attenuation During T 1 Q , 0.62-0.72 h. The cancelled system XPD during T 1 Q was reasonably well correlated with the r a i n r a t e and ho r i z o n t a l wind during t h i s period, i . e . the lower XPDs occurred during the higher rainrates and h o r i z o n t a l wind v e l o c i t i e s . During t h i s period, the average h o r i z o n t a l wind v e l o c i t y was approximately 5.0 m/s, F i g . 6.2.2(b). The cancelled system XPD agrees well with the model predic-tions f o r an equivalent mean canting angle of 4°, as shown i n F i g . 6.2.27. see Period XPD Differential Attenuation Wind Velocities During Rain XPD is In Approximate Agreement with Model Predictions for: Comments T i o . 56.0-60.8 dB Peaks at-0.9dB Horiz. wind max. XPD follows <|)=40 XPD well XPD generally- at 0.66 h = 7.3 m/s. predictions ,9. correlated 0.62-0.72 decreased as during horiz. Fig. 6.2.2(a) Fig. 6.2.27 with rainrate h rainrate in- wind increase. Horiz. wind =5.0 and horiz. creased and Small and posi- m/s avg. wind varia-horiz. wind tive during Fig. 6.2.2(b) tions . increased. latter part of Figs. 6.2.2(b), period. 6.2.24, Max. pos. value and 6.2.27. occurred during horiz. wind local max. Fig. 6.2.2(a) and 6.2.26. T l l 56.0-59.3 dB Peaks at +1.2dB Horiz. wind For most of period XPD and diff. XPD min. at at a 0.75 h, generally increased <J>=4° , during peak <j>25~6°, 9. att. peaks 0.72-0.78 0.75 h. Fig. 6.2.26 from 4-7 m/s during vert. h Fig. 6.2.24 Uncancelled XPD also min. at 0.75 h. Fig. 6.2.25(a) Fig. 6.2.2(a) =5,0 m/s avg. Fig. 6.2.2(b). Moderate horiz. wind peak (6.2 m/s) and large vert, wind peak (1.2 m/s) at 0.75 h. Figs. 6.2.2(a) and 6.2.3(a) Fig. 6.2.28 and horiz. wind peaks. . . . continued Period XPD D i f f e r e n t i a l Attenuation Wind V e l o c i t i e s During Rain XPD i s i n Approximate Agreement with Model Predictions f o r : Comments T 1 2 0.78-0.85 h 57.9-59.7 dB cancelled XPD r e l . const. Fi g . 6.2.24 and 6.2.29 Uncancelled XPD has fast de-crease at 0.81 h F i g . 6.2.25(a) Varied between -0.5 to +0.4 dB Fi g . 6.2.26 Horiz. wind r e l . const. = 5.8 m/s avg. Fi g . 6.2.2(b) 4 2 5° Fi g . 6.2.29 T i 1 3 0.88-0.93 h 54.9-60.5 dB XPD min. at 0.9 h Figs. 6.2.24 and 6.2.30 Uncancelled XPD also has l o c a l min. at 0.9 h Fi g . 6.2.25(b) Rel. const. =• -0.3 dB Fi g . 6.2.26 Horiz. wind peaks at 8.2 m/s at 0.9 h Fi g . 6.2.2(a) = 5.0 m/s avg. Fi g . 6.2.2(b) large vert, wind peak j u s t before 0.9 h. <j> = 10° during h o r i z . wind max. at 0.9 h During r e s t of period <j> = 6°. Fi g . 6.2.30 Cancelled XPD correlated well with h o r i z . wind. 0.93-0.99 h 57-58.1 dB Fi g . 6.2.31 Uncancelled XPD has increased from average value F i g . 6.2.25(b) Varied -0.8 to +0.3 dB. Both extreme values occur during l o c a l h o r i z . wind peaks. Fi g . 6.2.26 = 4.3 m/s avg. Fig . 6.2.2(b) * » 6°, 9 Fi g . 6.2.31 Cancelled XPD correlated with h o r i z . wind. Table 6.2.2 Summary of XPD and D i f f e r e n t i a l Attenuation Data for 81.11.30.10, 10:30-10:46. F i g . 6 . 2 . 2 7 . XPD H d u r i n g TlQ. 339 The d i f f e r e n t i a l attenuation, F i g . 6.2.26, reached a negative value of -0.9 dB at 0.66 h during a period of rapidly increasing horizontal wind veloc i ty , F i g . 6.2.2(a). During the latter part of this period, the d i f f e r -ent ia l attenuation was positive with a range of values close to the theoreti -cal predictions. 6.2.2.2 XPD and Different ia l Attenuation During-T j , 0.72-0.78 h . The cancelled system XPD during this period also generally agreed with predictions for an effective canting angle of 4 ° . At 0.75 h, however, both XPDs rapidly decreased, Figs . 6.2.24 and 6.2.25(a). During this decrease, the horizontal wind reached a maximum of 6.2 m/s, F i g . 6.2.2(a), and the v e r t i c a l wind peaked at +1.2 m/s, F i g . 6.2.3(a). This minimum value of cancelled XPD confirmed to predictions for a 5 to 6° canting angle, F i g . 6.2.2. The plotted d i f f e r e n t i a l attenuation reached a peak value of +1.2 dB at 0.75 h, but this unusually large value must be considered suspect because of the rapid, ver t i ca l wind induced, change in the CPA. 6.2.2.3 XPD and Different ia l Attenuation for T 0.78-0.85 h . During T 1 2 > the cancelled system XPD was r e l a t i v e l y constant and agreed with predictions for an equivalent mean canting angle of 5 ° , F i g . 6.2.29. This s l ight ly larger canting angle is apparently associated with the increased horizontal wind veloci ty , which averaged about 5.8 m/s during this period. It should, however, be reiterated that the absolute value of these calculated canting angles may be too large due to the proximity of these data to the cancelled., clear-weather XPD. 1. FILEt 3 1 . 1 1 . 3 0 . 1 0 . . . . . . 1 FILES TO BE PROCESSED 81.11.30 10.46 30. SECOND RVERRGE INTERVAL TIME t 0.72 0.78 9.0 10 F i g . 6 . 2 . 2 8 . XPD H d u r i n g T. 1. FILEt 81.11.30.10 1 FILES TO BE PROCESSED 81.11.30 10.46 30. SECOND AVERAGE INTERVAL TIME t 0.78 0.8S 4>-Fig. 6.2.29. XPDH during T 1 2 > 342 The uncancelled XPD, F i g . 6.2.25(a) r a p i d l y decreased at 0.91 h, i n a manner s i m i l a r to the decrease at 0.75 h. The reasons for t h i s decrease are not c l e a r , but i t did occur at the same time as a f a s t , but r e l a t i v e l y small, decrease i n the h o r i z o n t a l wind v e l o c i t y . The d i f f e r e n t i a l attenuation during t h i s period increased from approximately -0.5 dB to +0.4 dB. Negative values occurred j u s t a f t e r and during a period of increasing h o r i z o n t a l wind and during a period of compara-t i v e l y high h o r i z o n t a l wind v e l o c i t y . 6.2.2.4 XPD and D i f f e r e n t i a l Attenuation During T ^ , 0.88-0.93 h. At 0.90 h the cancelled XPD decreased to the lowest value observed during t h i s data f i l e . This decrease coincided with the maximum h o r i z o n t a l wind during t h i s f i l e , 8.2 m/s, F i g . 6.2.2(a). It also occurred immediately a f t e r the l a r g e s t v e r t i c a l wind v e l o c i t y , which was +1.6 m/s, F i g . 6.3.3(a). During t h i s wind peak, the cancelled XPD agreed with predictions f o r a canting angle of approximately 10°. The explanation f o r the cancelled XPD behaviour during t h i s wind maxima were given i n Section 6.2.3. Tne d i f f e r e n t i a l attenuation during T^ 3 was r e l a t i v e l y constant and averaged approximately -0.3 dB. 6.2.2.5 XPD and D i f f e r e n t i a l Attenuation During T ^ , 0.93-0.99 h. During i n t e r v a l T ^ , both XPDs showed r e l a t i v e l y large changes from t h e i r c l e a r weather values, F i g s . 6.2.24 and 6.2.25(b). The cancelled system XPD data agreed with predictions f or a canting angle of approximately 6°, F i g , 6.2.31,and correlated reasonably well with the ho r i z o n t a l wind v e l o c i t y , 1. FILE* 81.11.JO.10 1 FILES TO BE PROCESSED 81111.30 10.46 30. SECOND AVERAGE INTERVAL TIME t 0.88 0.93 Fig. 6.2.30. XPD N during T. e 8-1. FILEt 81.11.30.10 1 FILES TO BE PROCESSED 81.11.30 10.46 30. SECOND AVERAGE INTERVAL TIKE t 0.93 0.99 -o-F i g . 6 . 2 . 3 1 . XPD„ d u r i n g T . , ^ 345 D i f f e r e n t i a l attenuation during varied from -0.8 to +0.3 dB, even though the rainra t e s and CPAs were only changing very slowly. The most nega-t i v e and two most p o s i t i v e maximum values a l l occurred during l o c a l maximums i n the h o r i z o n t a l wind v e l o c i t y . 6.3 Experimental Results f o r 81.11.30.18 This data f i l e was included because i t was the best example observed during t h i s experiment of the v a r i a b i l i t y of propagation phenomena which can occur during r a p i d l y changing wind conditions. Rainrates f o r th i s f i l e are shown i n F i g . 6.3.1. The i n d i v i d u a l r a i n r a t e s were r e l a t i v e l y constant on a long term basis, but were moderately va r i a b l e over short periods. Some of t h i s short term r a i n r a t e v a r i a b i l i t y i s believed to be due to varying wind v e l o c i t i e s which could a f f e c t drop v e l o c i t i e s and raingauge capture e f f i c i e n -c i e s ( F i g . 3.3). The 10 s average wind d i r e c t i o n during t h i s period was constantly from the east, as shown i n F i g . 6.3.2. Time se r i e s plots of ho r i z o n t a l wind v e l o c i t y f o r 2 s, 10 s, and 99 s averages are shown i n F i g s . 6.3.3(a), (b) and ( c ) . The 10 s average h o r i z o n t a l wind v e l o c i t y varied between 2 and 15 m/s during t h i s f i l e and was unusually v a r i a b l e . V e r t i c a l wind v e l o c i t i e s f o r t h i s period with 10 s and 30 s averages are shown i n F i g . 6.3.4(a) and (b). The v e r t i c a l wind v e l o c i t y was (sub j e c t i v e l y ) even more variable and ranged from -0.9 to +2.5 m/s with a 10 s average. Three samples of the drop siz e d i s t r i b u t i o n from t h i s f i l e are shown i n F i g s . 6.3.5-6.3.8. These are included mainly to show the unusual peak i n cc _ a a CO 1. FILE*. 81.11.30.18 1 FILES TO BE PROCESSED 81.11.30 18.46 UJ , , , 1 1 1 r- — T — a.a o.i 0.2 o.s 0.4 o.s o.e 0.7 o.s TIME (HOURS) i.o 0.9 F i g . 6 . 3 . 2 . H i n d d i r e c t i o n , 10 s a v g . f o r 8 1 . 1 1 , 3 0 . 1 8 . 1. FJLK.• HI.11.30.IB. . 1 FILES TO BE PROCESSED 81.11.30 18.46 5J F i g . 6 . 3 . 3 ( a ) . H o r i z o n t a l wind v e l o c i t y , 2 s a v g . for R l . 1 1 . 3 0 . 1 8 . 1 . riLE: 8.1.1) .30.18. 1 FILES TO BE PROCESSED 81. 11.30 18.46 F i g . 6 .3Xb). H o r i z o n t a l wind v e l o c i t y , 10 s a v g . f o r 81 .11 .30.18. 354 1000 0.1 I 1 1 ! 1 L _ I 1 I I I i i 0 1.0 2.0 3.0 4.0 5.0 Drop diameter (nan) Fig. 6.3.6. Drop dist r i b u t i o n s f o r T 0. 357 the d i s t r i b u t i o n at diameters between 3.5 and 4.5 mm. Similar d i s t r i b u t i o n peaks were observed i n [3.39], [6.1], [6.2], [6.3] and [6.4]. The four 10 s average s i g n a l l e v e l s for this f i l e are shown i n Fi g s . 6.3.9 and 6.3.10. 6.3.1 Attenuation Data f o r 81.11.30.18, 18;46-19:46 The large and extremely v a r i a b l e h o r i z o n t a l and v e r t i c a l wind v e l o c i -t i e s during t h i s f i l e resulted i n a large range of attenuation values over r e l a t i v e l y short periods. Attempts to analyze the attenuation data recorded i n t h i s f i l e i n a manner s i m i l a r to that used on other f i l e s was unsuccessful because the wind v a r i a t i o n s were too rapid to permit clear c o rrelations between attenuation and meteorological observations. Three examples of t h i s v a r i a b i l i t y are shown i n Figs. 6.3.11 to 6.3.13. During a l l of these periods, the attenuation varied over a range greater than that between the predictions f o r the JOT and JOD d i s t r i b u t i o n s . 6.3.2 XPD and D i f f e r e n t i a l Attenuation Data f or 81.11.30.18. The XPDs for ho r i z o n t a l and v e r t i c a l transmitted p o l a r i z a t i o n s f o r 10 s and 99 s averages are shown i n Fi g s . 6.3.14 and 6.3.15, (a) and (b) re s p e c t i v e l y . The 10 s average XPDs both exhibit large short term v a r i a -t i o n s , again preventing any accurate c o r r e l a t i o n s with meteorological obser-vations. Referring to the 99 s averages, however, there does appear to be a s i m i l a r long term v a r i a t i o n i n both the cancelled and uncancelled XPDs. These v a r i a t i o n s appear to be loosely correlated with the 99 s avg. h o r i -zontal wind v e l o c i t y . HH ATTENUATION (DB/KM) 4 . 0 5.0 6 .0 7 .0 e.o 3 . 0 09£ J. FILE'. 81.11.30.18 1 FILES TO BE PROCESSED 81.11.30 18.46 2. SECOND AVERAGE INTERVAL TIME t 0.48 0.54 JOD VW=0 JOT VW=0 1 1 1 1 l 1 1 l 1 1 1 I 0.0 1.0 2.0 3.0 4.0 S.O 6.0 7.0 B.O 9.0 10.0 I I . 0 12.0 AVERAGE RAIN RATE(MM/HOUR) - 1 13. F i g . 6 . 3 . 1 3 . CPA d u r i n g T. T Fig. 6.3.14(-b). XPD for horizontal polarization transmitted, 99 s avg 00 S 9 E i CC J o Wr-, IT. 1 . FILE-. 8! .11 . 3 0 . 18 . . . I F I LES TO SE PROCESSED 81 . 11 .30 18.46 99. SECOND AVERAGE 1 1 1 1—= 1 — 1 1 1 1— 0.0 0.1 0.2 0.3 0.4 O.S 0.6 0.7 J . I 0.9 TIME (HOURS) i.o F i g . 6.3.15(b). XPJi f o r v e r t i c a l t r a n s m i t t e d p o l a r i z a t i o n , 99 s avg. for 81.11.30.18. ON 367 The d i f f e r e n t i a l attenuation data i n F i g . 6.3.16 displays a wide range of values, both p o s i t i v e and negative. While these data must be i n t e r p r e t e d with the usual caution, the general s i m i l a r i t y of t h i s plot to F i g . 6.3.15(a) (which, of course, also includes the e f f e c t s of d i f f e r e n t i a l attenuation on the transmitted copolar and transmit antenna depolarized signals) means that much of the v a r i a t i o n i n F i g . 6.3.16 i s , i n f a c t , what would be observed without p o l a r i z a t i o n sampling. 6.A Experimental Results f o r 81.11.30.19. This data f i l e was recorded during a period of widespread, r e l a t i v e l y uniform r a i n of medium i n t e n s i t y and moderately high wind v e l o c i t i e s . During the l a t t e r part of t h i s f i l e , there was an i n t e r e s t i n g change i n the drop s i z e d i s t r i b u t i o n which apparently affected the XPD as well as the CPA. Rainrates f o r t h i s f i l e are shown i n F i g . 6.4.1. The path average r a i n r a t e during t h i s period varied from 3 to 13 mm/h. The wind d i r e c t i o n during t h i s f i l e was again constantly from the east, i . e . perpendicular to the path. Horizontal wind v e l o c i t i e s f o r 10 s and 30 s averages are shown i n F i g s . 6.4.2(a) and ( b ) . Over t h i s period the 10 s average h o r i z o n t a l wind varied from 4.2 to 10 m/s. V e r t i c a l wind v e l o c i t i e s are shown i n F i g s . 6.4.3(a) to (c) f o r 10 s, 30 s and 60 s aver-ages. The 30 s h o r i z o n t a l wind v e l o c i t y varied between -0.2 to +1.3 m/s. Time series plots f o r the four s i g n a l l e v e l s with 10 s averages are shown i n F i g s . 6.4.4 and 6.4.5. 1 . FILE: 81 .11.30.18. 1 FILES TO BE PROCESSED 8! . 11.30 18.46 24. SECOND AVERAGE T: cr. a: 0.0 — I 1 1 -1 1 1 1 0.1 0.2 0.3 0.4 0.5 O.E 0.7 TIME (HOURS) 'ig. 6.3.16. Differential attenuation for 81.11.30.18. F i g . 6 . 4 . 1 . R a i n r a t e s f o r 3 1 . 1 1 . 3 0 . 1 9 . J. FILE: 81.11.30.19 I FILES TO BE PROCESSED 81.11.30 i.9.46 5J '71 o CJ UJ to 10 o F i g . 6.4.2(b). H o r i z o n t a l wind v e l o c i t y , 30 s a v g . f o r 81.11.30.19. 377 6.4.1 Attenuation Data f o r 81.11.30.19, 20:20-20:34 This data f i l e includes examples of high attenuations due to v e r t i c a l wind and changes i n the drop siz e d i s t r i b u t i o n . Included are examples of v e r t i c a l wind induced attenuation c o n s i s t e n t l y higher than standard predic-tions f o r the JOD d i s t r i b u t i o n and an example of consistently decreasing attenuation with increasing rainrate due to a v e r t i c a l wind tra n s i e n t . During the l a t t e r part of this f i l e , there was a general trend to simul-taneously increasing numbers of very small and medium-large drops. Over t h i s period, the d i s t r i b u t i o n changed from close to the JOW to having more medium and large drops than the JOT d i s t r i b u t i o n . A summary of the attenuation r e s u l t s f o r t h i s f i l e are given i n Table 6.4.1. 6.4.1.1 Attenuation During T , 0.24-0.28 h During i n t e r v a l T j , the CPA, F i g . 6.4.6, was higher than that predic-ted f o r the JOD d i s t r i b u t i o n . The measured drop sizes were s i m i l a r to the JOW d i s t r i b u t i o n with a few more large drops, F i g . 6.4.7. Attenuation was higher than that predicted using standard techniques and the measured d i s t r i -bution because of the upward v e r t i c a l wind. The 30 s average wind, F i g . 6.4.3(b) was slowly increasing during T^ and had an average value of approxi-mately +0.6 m/s, F i g . 6.4.3(c). The measured data i s i n agreement with the predictions using the v e r t i c a l wind modification discussed i n Section 4.4 with a v e r t i c a l wind v e l o c i t y of s l i g h t l y greater than +1.0 m/s. This v e r t i c a l wind v e l o c i t y i s approximately double that measured by the anemometer. In most of the f i l e s with s i m i l a r , r e l a t i v e l y constant, v e r t i c a l wind v e l o c i t i e s i t was found that best agreement was obtained for an Period Measured Attenuation Compared to Standard Predictions Measured Drop D i s t r i b u t i o n V e r t i c a l Wind During Rain Data i s i n Approximate Agreement with Predictions f o r : Comments T l 0.24-0.28 h Higher than JOD F i g . 6.4.6 B a s i c a l l y JOW but few more large drops, 1 F i g . 6.4.7 5+0.6 m/s avg. F i g . 6.4.3(b), (c) JOW and v e r t , wind = +1 m/s F i g . 6.4.6 2 0.28-0.33 h Higher than JOD and s l i g h t l y higher than Tj^ F i g . 6.4.8 Agrees with JOW, 1 Fewer large drops than T. F i g . 6.4.9 Decreasing +0.6 to -0.2 m/s F i g . 6.4.3(b), (c) S l i g h t l y higher than JOW and v e r t , wind = +1 m/s F i g . 6.4.8 3 T3 0.33-0.43 h Close to JOD, lower than T 2 F i g . 6.4.10 B a s i c a l l y JOW but few more large drops F i g . 6.4.11 2 +0.7 m/s avg. F i g . 6.4.3(b) JOW and v e r t , wind = +1 m/s F i g . 6.4.10 2 0.47-0.53 h Consistently higher than JOD F i g . 6.4.12 Agrees with JOW, 1, more small drops than during T 3 F i g . 6.4.13 Generally decreasing from +1.3 to -0.1 m/s F i g . 6.4.3(b) Consistently higher than JOW and vert wind = +1 m/s F i g . 6.4.12 3 T 5 0.53-0,55 h Higher than JOD decreasing to JOW as rainrate increased. F i g . 6.4.14 B a s i c a l l y JOW but fewer drops i n two smallest cate-gories, 1, 4. F i g . 6.4.15 Increasing from -0.1 to +1.25 m/s F i g . 6.4.3(b) or -0.4 to +2.2 m/s F i g . 6.4.3(a) Between JOW and zero v e r t , wind and v e r t , wind = +1 m/s lower attenuations at 0.55 h due to increasing v e r t , wind F i g s . 6.4.3(a), 6.4.4, F i g . 6.4.14 8 as period progresses continued Period Measured Attenuation Compared to Standard Predictions Measured Drop D i s t r i b u t i o n V e r t i c a l Wind During Rain Data i s i