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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 in 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 B a s i l Peters  In  presenting  requirements of  British  it  freely  agree for  this for  available  that  I  understood  that  financial  by  his  that  of  or  her or  DE-6  (3/81)  Ct^JL  ~i ,  copying  publication be  of  Columbia  the  s h a l l make  the  I of  further this  thesis  head of It  this  allowed without  Sue  i9 82-  Library  by  of  University  representatives.  s h a l l not  ^<-<sc-  the  and s t u d y .  extensive  The U n i v e r s i t y o f B r i t i s h 1956 Main M a l l Vancouver, Canada V6T 1Y3  Date  at  the  permission.  Department  fulfilment  may b e g r a n t e d  copying  gain  degree  reference  for  purposes  or  partial  agree  for  permission  scholarly  in  an a d v a n c e d  Columbia,  department for  thesis  my  is thesis my  written  ABSTRACT  This thesis describes the design, construction and r e s u l t s of an accurate, 73 GHz, over a 1.8  dual-polarized atmospheric propagation experiment conducted  km t o t a l length radar path.  The millimetre-wave equipment  consisted of a switched-polarization transmitter and a two-channel r e c e i v i n g system which included a phase-compensated crosspolar c a n c e l l a t i o n network and a novel, high-performance microstrip IF/LO diplexer.  Meteorological  instru-  mentation consisted of an improved e l e c t r o s t a t i c disdrometer, a raingauge network with high temporal and s p a t i a l resolution and a three-vector anemometer. A comprehensive experimental model was developed to predict the system crosspolar discrimination (XPD) This model was the e f f e c t s of:  response during a wide v a r i e t y of conditions.  used to analyze, f o r what i s believed to be the f i r s t time, orthomode transducer  port mismatches, the frequency response  and error s e n s i t i v i t y of crosspolar c a n c e l l a t i o n systems and the range of possible cancelled system XPD  responses during r a i n .  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 c a n c e l l a t i o n network.  The a p p l i c a t i o n of the  experimental model resulted i n far more accurate determinations of path  XPD  than would have been otherwise p o s s i b l e . The cancelled XPD  r e s u l t s showed a reasonable c o r r e l a t i o n to  horizontal wind v e l o c i t i e s and agreed with model predictions for e f f e c t i v e  ii  mean canting angles ranging between 0 and 6 ° .  The frequent observation of  negative d i f f e r e n t i a l attenuations and e r r a t i c uncancelled XPDs led to the conclusion that drops along the path often d i d not have consistent shapes and canting angles. tions.  This i s believed to be due to extremely v a r i a b l e wind condi-  Copolar attenuations considerably lower and higher than expected from  the standard predictions were observed.  The higher attenuations are s a t i s -  f a c t o r i l y explained as r e s u l t i n g from v e r t i c a l wind conditions and are correlated to the predictions from a proposed model which includes the e f f e c t s of constant v e r t i c a l wind v e l o c i t i e s .  iii  TABLE OF CONTENTS  Page  Abstract  »  i i  Table of Contents  iv  List of Figures .  xv  List of Tables. 1.  2.  xxix  Introduction  1  1.1  2  Spectrum Demand  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  Millimetre-Wave Experimental System 2.1  « .  26  Comparison of Dual-Polarization Measurement Methods. . . . .  26  2.2 Transmitting System 2.2.1  29  Klystron and Supply  29  2.2.2 Reference Signal and Calibrated Attenuator  33  2.2.3  34  Feedline and Pressurization  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 S w i t c h i n g Methods . . . . . .  2.2.4.2  P o l a r i z a t i o n Switch and  2.2.4.3 2.2.5  . . . . .  Specifications  Testing  P o l a r i z a t i o n Switch Subsystem  . . . .  S i g n a l L e v e l s i n t h e T r a n s m i t t i n g System. . . .  R e c e i v i n g 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 U n i t s  2.3.3  Two-Channel F r o n t End 2.3.3.1  Basic Mixer Considerations  2.3.3.2  Front-End C i r c u i t D e s c r i p t i o n  2.3.3.3  Harmonic M i x e r s  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 D i p l e x e r .  2.3.3.6  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  2.3.3.7  Frequency M u l t i p l i e r and  . . . .  Specifications  Testing  2.3.3.8  Local  O s c i l l a t o r Power A m p l i 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 C i r c u i t s .  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  2.3.5  Receiving System Performance  90  2.3.5.1  Calculated S e n s i t i v i t y  90  2.3.5.2  Measured Receiving System S e n s i t i v i t y . . .  93  2.3.5.3  Receiving System Small-Signal Performance  96  2.3.5.4  Receiving System Isolation and  2.3.5.5  .  .  89  Frequency Response  98  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 i n this Experiment.  2.5.1.3  RF v s . IF Cancellation  2.5.1.4  Crosspolar Cancellation C i r c u i t Description  . . . .  120 120  122  2.5.2  Antenna Mounting and Rain Shields  124  2.5.3  Antenna Alignment  127  Page 2.9 3.  Data Acquisition System. . . . . . . . . .  Meteorological Instrumentation. 3.1  134  . . . .  . . . . . . . .  136  Raingauge Network  136  3.1.1  Path-Rainrate  Measurement  3.1.2  Rain Gauge Types.  3.1.3  Rain Gauges  3.1.4  Raingauge Locations  144  3.2  Raindrop Size Measurement.  147  3.3  Raindrop Size Transducer Methods . . . . . . . . .  147  3.3.1  148  Optical Methods . .  136 . . . . . . . . . . .  138  . . . . . . . . . .  141  . . . . . . . . . . .  3.3.1.1  Optical Scanning Methods.  . . . .  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  3.3.2  152  Electromechanical Methods 3.3.2.1  148  152  Moving C o i l i n Magnetic F i e l d Method.  153  3.3.2.2  Piezoelectric  Method  153  3.3.2.3  Other Electromechanical  3.3.2.4  Factors A f f e c t i n g the Accuracy of  Disdrometers.  Electromechanical Methods  . . .  .  154  155  3.3.3  E l e c t r o s t a t i c Methods  155  3.3.4  Comparison of Methods  157 vii  Page  4.  3.4  Disdroraeter Transducer  159  3.5  Disdrometer  168  3.6  Disdroraeter System T e s t R e s u l t s  173  3.7  Disdrometer  177  3.8  Anemometer  3.9  Temperature Measurement.  Calibration  T h e o r e t i c a l l y P r e d i c t e d Propagation 4.1  5.  Electronics  * •  183  .  186  Parameters  187  M e t e o r o l o g i c a l Inputs  188  4.1.1  Rainrate  • •  4.1.2  Drop S i z e D i s t r i b u t i o n s  190  4.1.3  Drop Shape.  193  4.1.4  C a n t i n g Angle  4.1.5  Rain Temperature  198  4.1.6  Spatial Uniformity  199  4.2  S c a t t e r i n g Amplitudes  4.3  C a l c u l a t e d Propagation  . . . . .  189  194  199 Parameters  4.3.1  P r i n c i p a l Plane A t t e n u a t i o n s and  4.3.2  Propagation  200 Phase S h i f t s  Parameters f o r Canted Raindrops  . . . .  201 205  4.4  E f f e c t s of V e r t i c a l Wind on C o p o l a r A t t e n u a t i o n  216  4.5  Backscatter Calculation  220  D u a l - P o l a r i z e d Experimental 5.1  »  Model . .  225 227  P r e v i o u s Work viii  Page 5.2  S i m p l i f i c a t i o n s , Approximations and Assumptions. . . . . . «  227  5.3  Notation and Units  229  5.4  System Descriptive Equations  5.5  Analysis Without the Crosspolar Cancellation Network . . . . 5.5.1  «•  235  Contribution of Antenna XPD's to Clear Weather Crosspolar Signal Level  5.5.2  238  Effect of Reflected Signals on the Clear Weather Crosspolar Signal Level . . . . . . . . 5.5.2.1  Basic OMT Operation  5.5.2.2  Calculated Results and Comparisons  243 .  to Experimental Data. 5.5.2.3 5.6  244  248  System XPD Improvement Using Mismatches  . .  257  Crosspolar Cancellation Network Operation i n Clear Weather.  258  5.6.1  S e n s i t i v i t y 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  5.7  237  270  Model Predicted System XPD Performance 5.7.1  Effects  of P o l a r i z a t i o n  Insensitive  A t t e n u a t i o n or Phase S h i f t . 5.7.2  E f f e c t s o f Antenna XPD Angle  ix  273  . . . . . . . .  274 275  Page 5.7.3  Effects of D i f f e r e n t i a l Attenuation and Phase S h i f t  5.7.4  6.  6.2  278  Effects of Antenna XPD Magnitudes  Experimental Results. 6.1  . . . . . . .  282  ...<.  285  Preliminary Discussion  285  6.1.1  Disdrometer Data. . . . . . . . . . . . . . . . . . .  286  6.1.2  Receiving System Noise Levels  291  6.1.3  D i f f e r e n t i a l Attenuation Calculations  . . .  291  Experimental Results for 81.11.30.10  292  6.2.1  Attenuation Data f o r 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 , 0.23-0.26 h . . . . .  306  6.2.1.3  Attenuation During T , 0.27-0.29 h  311  6.2.1.4  Attenuation During T , 0.31-0.34 h . . . . .  314  6.2.1.5  Attenuation During T , 0.72-0.74 h  317  6.2.1.6  Attenuation During T , 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  0.87-0.89 h . . . . .  320  6.2.1.9  Attenuation During T , 0.89-0.93 h . . . . .  327  6.2.2  2  3  4  5  g  ?  8 >  g  XPD and D i f f e r e n t i a l Attenuation Data for 81.11.30.10 6.2.2.1  .  327  XPD and D i f f e r e n t i a l Attenuation During T  1 Q  ,  0.62-0.72 h x  334  Page 6.2.2.2  XPD and D i f f e r e n t i a l Attenuation During .  339  T^^j 0»78"~0«85 ti» » • • • > • • » • • • > • * •  339  T , n  6.2.2.3  6.2.2.4  0.72-0.78 h . . «  XPD and D i f f e r e n t i a l Attenuation During  XPD and D i f f e r e n t i a l Attenuation During T^^> 0o88~0»93  6.2.2.5  XPD and D i f f e r e n t i a l Attenuation During T j , 0.93—0.99 h .  6.3  342  • •>•••••••••*••  342  . . . » » » » . » » . « •  Experimental Results f o r 81.11.30.18  345  .  6.3.1  Attenuation Data for 81.11.30.18.  6.3.2  XPD and D i f f e r e n t i a l Attenuation Data  357  . . . . . . . . .  357  for 81.11.30.18 6.4  Experimental Results f o r 81.11.30.19 6.4.1  6.4.2  367  . . . .  377  Attenuation Data f o r 81.11.30.19 6.4.1.1  Attenuation During l»  0.24-•0.28 ll • • • • •  377  6.4.1.2  Attenuation During T ,  0.28-•0.33 tl • • * • •  382  6.4.1.3  Attenuation During 3> 0.33--0.43 h .  6.4.1.4  Attenuation During T V  0.47--0.53 \l m  6.4.1.5  Attenuation During  T  0.53--0.55 l l # • • * • •  385  6.4.1.6  Attenuation During  T  0.55--0.59 ll • • • • •  392  6.4.1.7  Attenuation During  0.59--0.71 ll • • • • •  395  6.4.1.8  Attenuation During  0.71- -0.83 h.  395  T  2  T  XPD and D i f f e r e n t i a l  5>  T  6'  8«  • • • • •  •  *  •  • • • •  385 385  A t t e n u a t i o n Data  395  for 81.11.30.19 xi  Page 6.4.2.1  XPD and D i f f e r e n t i a l Attenuation During T , 0.71-0.83 h o . . .  405  8  6.4.2.2  XPD and D i f f e r e n t i a l Attenuation During T , 0.83-0.99 h .  407  g  6.5  Experimental Results f o r 81.11.30.21  410  6.5.1  417  6.5.2  Attenuation Data for 81.11.30.21 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 , 0.89-0.99 h . . . „ .  421  3  XPD and D i f f e r e n t i a l Attenuation Data f o r 81.11.30.21 6.5.2.1  426  XPD and D i f f e r e n t i a l Attenuation During T , 0.65-0.80 h  , . .  4  6.5.2.2  XPD and D i f f e r e n t i a l Attenuation During T , 0.80-0.99 h . . .  433  5  6.6  426  Experimental Results for 81.11.30.22  436  6.6.1  436  Attenuation Data f o r 81.11.30.22 6.6.1.1  Attenuation During  6.6.1.2  Attenuation During  6.6.1.3  Attenuation During  6.6.1.4  444 0.13-0.26  ti •  • • • •  444  0.26-0.31  ti •  •  • • •  452  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 , 0.54-0.63  ti •  • • • •  457  T  3'  7  xii  Page  6.6.2  6.6.1.8  A t t e n u a t i o n During T , 0.63-0.66 h . . „ . .  464  6.6.1.9  A t t e n u a t i o n During T , 0.66-0.73 h . . . . .  464  g  g  XPD and D i f f e r e n t i a l  A t t e n u a t i o n Data  f o r 81.11.30.22 6.7  Experimental 6.7.1  6.7.2  464  R e s u l t s f o r 80.05.22.10  . . . . . . . . . . . .  A t t e n u a t i o n Data f o r 80.05.22.10  471  6.7.1.1  A t t e n u a t i o n During T , 0.20-0.25 h . . . . .  477  6.7.1.2  A t t e n u a t i o n During T , 0.25-0.31 h  482  6.7.1.3  A t t e n u a t i o n During T , 0.31-0.35 h  482  6.7.1.4  A t t e n u a t i o n D u r i n g T^, 0.42-0.47 h . . . . .  485  6.7.1.5  A t t e n u a t i o n During T , 0.48-0.61 h  485  6.7.1.6  A t t e n u a t i o n D u r i n g T , 0.61-0.75 h  485  x  2  3  5  6  XPD and D i f f e r e n t i a l  Attenuation Results  f o r 80.05.22.10 6.7.2.1  490  XPD and D i f f e r e n t i a l  Attenuation  During  T j - T , 0.20-0.25 h  497  3  6.7.2.2  XPD During T , 0.25-0.31 h and 2  T , 0.31-0.35 h  497  3  6.7.2.3  XPD and D i f f e r e n t i a l  Attenuation  During  T , 0.61-0.75 h  497  6  6.8  Experimental  R e s u l t s f o r 81.06.18.15 .  6.8.1  A t t e n u a t i o n Data f o r 81.06.18.15  6.8.2  XPD and D i f f e r e n t i a l  Experimental  510  A t t e n u a t i o n Data  f o r 81.06.18.15 6.9  504  . . . . . . . .  R e s u l t s f o r 81.11.14.07 xiii  510 523  Page 6.9.1  6.9.2  A t t e n u a t i o n 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  A t t e n u a t i o n During T , 0.65-0.77 h . . . . .  535  6.9.1.3  A t t e n u a t i o n During T , 0.77-0.84 h  539  ?  3  XPD and D i f f e r e n t i a l A t t e n u a t i o n Data f o r 81.11.14.07 6.9.2.1  539  XPD and D i f f e r e n t i a l A t t e n u a t i o n  During  T j , 0.56-0.65 h 6.9.2.2  XPD and D i f f e r e n t i a l A t t e n u a t i o n T , 3  7.  8.  548 During  0.77-0.84 h  548  Conclusions  553  7.1  Millimetre-Wave  Equipment.  554  7.2  M e t e o r o l o g i c a l Instrumentation  555  7.3  E x p e r i m e n t a l Model  555  7.4  Experimental  556  Results  7.4.1  XPD R e s u l t s  556  7.4.2  C o n c l u s i o n s Regarding Drop Shape and C a n t i n g A n g l e .  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  7.4.4  F u t u r e Work  on CPA.  .  556 557 559  560  References  xiv  LIST OF FIGURES Page F i g . 1.1.  Geosynchronous s a t e l l i t e i n orbit and planned . . . .  3  Fig.  Atmospheric attenuation due to molecular absorption .  5  1.2.  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.  P o l a r i z a t i o n switching methods  36  F i g . 2.5.  P o l a r i z a t i o n switch subsystem schematic .  AO  F i g . 2.6.  P o l a r i z a t i o n switch subsystem photograph. . . . . . .  Al  F i g . 2.7.  P o l a r i z a t i o n switch control unit schematic  A3  F i g . 2.8.  Receiving system block diagram  A6  F i g . 2.9.  Receiver block diagram  A8  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 d i p l e x e r s , LO amplifiers and frequency m u l t i p l i e r s . . . . . . . . . . . . . . . .  56  F i g . 2.13.  Front-end without IF preamplifiers and attenuators. .i t  .  58  . •  59  v  .  F i ? . 2.1 A.  Complete front-end  F i g . 2.15.  IF i n j e c t i o n and matching c i r c u i t  F i g . 2.16.  IF i n j e c t i o n and matching c i r c u i t performance  F i g . 2.17.  3.5  F i g . 2.18.  IF i n j e c t i o n 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  .  GHz microstrip bandpass f i l t e r .  xv  63 . . . .  . . . . . . . . .  66 70  Page F i g . 2.21.  Frequency m u l t i p l i e r frequency response  . . . . . . .  78  F i g . 2.22.  Frequency m u l t i p l i e r conversion l o s s .  .  79  F i g . 2.23.  LO frequency m u l t i p l i e r chain c i r c u i t configurations.  82  F i g . 2.24.  Mixer bias c i r c u i t schematic  85  F i g . 2.25.  Receiver: s i g n a l , I F , LO and noise i n the frequency domain.  91  F i g . 2.26.  Spectrum analyzer display of 1st IF s i g n a l . . . . . . .  95  F i g . 2.27.  Receiving system small signal performance on the bench.  97  F i g . 2.28.  Receiving system frequency response  F i g . 2.29.  E f f e c t of LO l e v e l on conversion loss  F i g . 2.30.  Effect of mixer bias current on front-end  . . . .  99 100  performance  102  F i g . 2.31.  Propagation path d e t a i l s  103  F i g . 2.32.  Propagation path photograph  F i g . 2.33.  Antenna crosspolar i s o l a t i o n performance.  F i g . 2.34.  Orthomode transducer test configuration  F i g . 2.35.  . .  105  . . . . . .  106 .  108  Orthomode transducer test results with  F i g . 2.38.  matched terminations Orthomode transducer test results with one port mismatched . . . . . . . . . . . Orthomode transducer test with the receiving system front-end. Test results for F i g . 2.37. .  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 d i f f e r e n t antenna alignments . . . . .  128  F i g . 2.42.  Reflector photograph  126  F i g . 2.36. F i g , 2.37.  xvi  109 Ill 112 113  Page F i g . 3.1.  R a i n c e l l examples.  137  F i g . 3.2.  A t t e n u a t i o n spread f o r d i f f e r e n t  raingauge 139  s p a c i n g and i n t e g r a t i o n times 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 f u n c t i o n o f 142  h o r i z o n t a l windspread F i g . 3.4.  P r o b a b i l i t y of e x c e e d i n g a s p e c i f i e d i n Vancouver.  F i g . 3.5.  Raingauge w i t h cover removed  145  F i g . 3.6.  Disdrometer t r a n s d u c e r g r i d  160  F i g . 3.7.  Disdrometer t r a n s d u c e r dimensions  165  F i g . 3.8.  Disdrometer t r a n s d u c e r w i t h cover removed  166  F i g . 3.9.  Complete d i s d r o m e t e r t r a n s d u c e r  167  F i g . 3.10.  Disdrometer system b l o c k diagram  169  F i g . 3.11.  Transducer p r e a m p l i f i e r  170  F i g . 3.12.  Peak d e t e c t o r  172  F i g . 3.13.  Peak p u l s e amplitude vs g r i d v o l t a g e f o r  rainrate  143  174  d i f f e r e n t drop diameters F i g . 3.14.  Peak p u l s e amplitude vs. R^  F i g . 3.15.  P u l s e p e r i o d vs. R  F i g . 3.16.  Apparatus  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  F i g . 3.18.  175  n  i n  .  f o r c r e a t i n g small drops. . . . .  176 178 179  Square r o o t of p u l s e 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 p u l s e a m p l i t u d e . . . . . .  181  F i g . 3.20.  Anemometer photograph  184  F i g . 3.21.  Anemometer p r o p e l l e r a n g u l a r response xvii  185  . 9. Pa  e  F i g . 4.1.  Canting angle as a function of size and height. . . .  195  F i g . 4.2.  Magnitude of p r i n c i p a l plane attenuation vs. rainrate.  203  F i 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 . .  204  F i g . 4.4.  Geometry for canted drop calculations  . . . . . . . .  206  F i g . 4.5.  D i f f e r e n t i a l attenuation vs. rainrate and canting angle . . . . . . . . . .  210  D i f f e r e n t i a l phase s h i f t vs. rainrate and canting angle  211  F i g . 4.7.  Magnitude of T  212  F i g . 4.8.  Angle of T  F i g . 4.9.  XPD vs. rainrate for horizontal p o l a r i z a t i o n . . . . .  214  F i g . 4.10.  XPD vs. CPA for horizontal p o l a r i z a t i o n . . . . . . .  215  F i g . 4.11.  Horizontal CPA vs. rainrate for 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 .  219  F i g . 5.1.  Experimental system signal flow diagram  226  F i g . 5.2.  Contribution of antenna XPDs to clear weather crosspolar signal at the front-end input  241  F i g . 5.3.  Orthomode transducer construction  245  F i g . 5.4.  OMT model options . . . . . . . . .  247  F i g . 5.5.  Mismatched transmit OMT signal flow diagram  249  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. .  251  Crosspolar signal l e v e l at plane D-D f o r XPD =XPD x=37dB and one mismatch with return loss = lOdB  253  F i g . 4.6.  F i g . .5.7.  TX  F i g . 5.8.  2 1  2 1  vs. rainrate  vs. r a i n r a t e  213  and operation . . .  R  Crosspolar signal l e v e l at plane D-D f o r XPD = XPD =37dE and A 6 = 150° TX  RX  x p D  xviii  254  Page F i g . 5.9.  E f f e c t of crosspolar cancellation network amplitude e r r o r s .  F i g . 5.10.  E f f e c t of crosspolar cancellation network  ^  . . . . .  phase errors  261  F i g . 5.11.  Clear weather cancelled system XPD v s . frequency. . .  267  Fig.  Effect of phase compensation on cancelled system XPD.  271  5.12.  F i g . 5.13.  E f f e c t s of d i f f e r e n t i a l attenuation on system XPD  F i g . 5.14.  for no path depolarization Effects of d i f f e r e n t i a l attenuation on system XPD for path XPD = 40 dB<0°  276 277  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 v e l o c i t y , 10 s avg. for 81.11.30.10  294  F i g . 6.2.2(b)  Horizontal wind v e l o c i t y , 30 s avg. for 81.11.30.10  295  F i g . 6.2.3(a)  V e r t i c a l wind v e l o c i t y , 30 s avg. and N (0.5)/N (1.0) f o r 81.11.30.10 . B  296  D  F i g . 6.2.3(b)  V e r t i c a l wind v e l o c i t y , 60 s avg. for 81.11.30.10  F i g . 6.2.4(a)  Signal l e v e l s f o r horizontal p o l a r i z a t i o n transmitted, 10 s avg. f o r 81.11.30.10  F i g . 6.2.4(b)  Signal l e v e l s f o r horizontal p o l a r i z a t i o n transmitted, 30 s avg. for 81.11.30.10. .  F i g . 6.2.5  Signal l e v e l s for v e r t i c a l p o l a r i z a t i o n transmitted, 2 s avg. for 81.11.30.10 . xv ix  297 .  298 299  ...  Page F i g . 6.2.6  CPA during T  F i g . 6.2.7  Drop d i s t r i b u t i o n s f o r  308  F i g . 6.2.8  CPA during T  309  F i g . 6.2.9  Drop d i s t r i b u t i o n f o r T  F i g . 6.2.10  CPA during T  F i g . 6.2.11  Drop d i s t r i b u t i o n s f o r T  F i g . 6.2.12  CPA during  315  F i g . 6.2.13  Drop d i s t r i b u t i o n s f o r  316  F i g . 6.2.14  CPA during T  318  F i g . 6.2.15  Drop d i s t r i b u t i o n s f o r T  F i g . 6.2.16  CPA during T  F i g . 6.2.17  Drop d i s t r i b u t i o n s f o r T  F i g . 6.2.18  CPA during T  F i g . 6.2.19  Drop d i s t r i b u t i o n s f o r T  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 f o r Tg  326  F i g . 6.2.22  CPA during T  328  F i g . 6.2.23  Drop d i s t r i b u t i o n s f o r T  F i g . 6.2.24  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 , 30 s avg. f o r 81.11.30.10  F i g . 6.2.25(a) F i g . 6.2.25(b)  .  1  307  2  3  .  2  . . . .  312 313  3  5  6  319  5  ......... '  321 322  fi  323  ?  g  310  .  y  . . . g  .  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 2 s avg. f o r 81.11.30.10  324  329 .  330 331  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 30 s avg. f o r 81.11.30.10  332  F i g . 6.2.26  D i f f e r e n t i a l attenuation f o r 81.11.30.10.  335  F i g . 6.2.27  XPD during T  338  H  1 0  xx  Page Fig. 6.2.28  XPD during T  n  Fig. 6.2.29  XPD during T  1 2  .  341  Fig. 6.2.30  XPD during T  1 3  . . .  343  Fig. 6.2.31  XPD during T j  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  Horizontal wind velocity, 10 s avg. for 81.11.30.18  349  Horizontal wind velocity, 99 s avg. for 81.11.30.18  350  Vertical wind velocity, 10 s avg. for 81.11.30.18 . . . . .  351  Vertical wind velocity, 30 s avg. for 81.11.30.18  352  Drop distributions for T j , 0.0-0.04 h  353  Drop distributions for T , 0.23-0.27 h  354  Drop distributions for 0.35-0.39 h  355  Fig. 6.3.3(b) Fig. 6.3.3(c) Fig. 6.3.4(a) Fig. 6.3.4(b) Fig. 6.3.5 Fig. 6.3.6 Fig. 6.3.7 Fig. 6.3.8 Fig. 6.3.9 Fig. 6.3.10  R  R  H  340  H  . . .  Drop distributions for T. , 0.83-0.87 h Signal levels for horizontal polarization transmitted, 10 s avg. for 81.11.30.18.  344  : . .  356 358  Signal levels for vertical polarization transmitted, 10 s avg. for 81.11.30.18  359  Fig. 6.3.11  CPA during T , 0.32-0.40 h  360  Fig. 6.3.12  CPA during T , 0.40-0.45 h xxi  361  5  2  Page F i g . 6.3.13  CPA during T , 0.48-0.54  362  F i g . 6.3..14(a)  XPD for horizontal transmitted p o l a r i z a t i o n , 10 s avg. f o r 81.11.30.18  363  XPD f o r horizontal transmitted p o l a r i z a t i o n , 99 s avg. for 81.1.1.30.18  364  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 81.11.30.19  365  F i g . 6.3.14(b) F i g . 6.3.15(a)  F i g . 6.3.15(b)  y  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 , 99 s avg. 81.11.30.18 .  366  F i g . 6.3.16  D i f f e r e n t i a l attenuation for 81.11.30.18. . . . . . .  368  F i g . 6.4.1  Rainrates f o r 81.11.30.19  369  F i g . 6.4.2(a)  Horizontal wind v e l o c i t y , 10 s avg. for 81.11.30.19 Horizontal wind v e l o c i t y , 30 s avg. for 81.11.30.19  F i g . 6.4.2(b) F i g . 6.4.3(a) F i g . 6.4.3(b)  F i g . 6.4.4 F i g . 6.4.5  371  V e r t i c a l wind v e l o c i t y , 10 s avg. for 81.11.30.19 .  372  V e r t i c a l wind v e l o c i t y , 30 s avg. and N (0.5)/N (1.0) for 81.11.30.19  373  V e r t i c a l wind v e l o c i t y , 60 s avg. for 81.11.30.19  374  Signal l e v e l s f o r horizontal p o l a r i z a t i o n transmitted, 10 s avg. f o r 81.11.30.19.  375  D  F i g . 6.4.3(c)  370  D  Signal levels f o r v e r t i c a l p o l a r i z a t i o n transmitted, 10 s avg. f o r 81.11.30.19. . . . . . . .  376  F i g . 6.4.6  CPA during T  380  F i g . 6.4.7  Drop d i s t r i b u t i o n s f o r T ^ . . . . ".'  381  F i g . 6.4.8 F i g . 6.4.9  CPA during T Drop d i s t r i b u t i o n s forng  383 384  F i g . 6.4.10  CPA during T  386  1  £  3  xxi i  Page F i g . 6.4.11  Drop d i s t r i b u t i o n s f o r T  F i g . 6.4.12  CPA during  F i g . 6.4.13  Drop d i s t r i b u t i o n s for  F i g . 6.4.14  CPA during T  F i g . 6.4.15  Drop d i s t r i b u t i o n s f o r T  F i g . 6.4.16  CPA during T  F i g . 6.4.17  Drop d i s t r i b u t i o n s f o r T  F i g . 6.4.18  CPA during T  F i g . 6.4.19  Drop d i s t r i b u t i o n s f o r T  F i g . 6.4.20  CPA during T  F i g . 6.4.21  Drop d i s t r i b u t i o n s f o r Tg  F i g . 6.4.22(a)  XPD for horizontal transmitted  3  . . . . „  .  387 388  .  . . . . . . .  5  R  389 390  . .  391 . . . . . . . . . . . .  6  393 394  6  396  y  397  ?  398.  g  399 polarization,  10 s avg. for 81.11.30.19 F i g . 6.4.22(b)  XPD for horizontal transmitted 30 s avg. for 81.11.30.19  F i g . 6.4.23(a)  XPD f o r v e r t i c a l transmitted 10 s avg. for 81.11.30.19  polarization,  F i g . 6.4.23(b)  XPD f o r v e r t i c a l  polarization,  transmitted  polarization,  30 s avg. for 81.11.30.19  .  400  .  401 402  .  403  F i g . 6.4.24  D i f f e r e n t i a l attenuation f o r 81.11.30.19  404  F i g . 6.4.25  XPD during T g , 0.71-0.83 h  408  F i g . 6.4.26  XPD during T , 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 v e l o c i t y ,  F i g . 6.5.3(a)  for 81.11.30.21 V e r t i c a l wind v e l o c i t y , for 81.11.30.21  H  R  g  10 s avg.  30 s avg.  xxiii  412 413  Page Fig. 6.5.3(b)  Fig. 6.5.4  Fig. 6.5.5  V e r t i c a l wind v e l o c i t y , 60 s a v g . for 81.11.30.21  414  Signal l e v e l s f o r horizontal transmitted p o l a r i z a t i o n , 10 s a v g . f o r 8 1 . 1 1 . 3 0 . 2 1  .  415  Signal l e v e l s f o r v e r t i c a l transmitted polarization,  10 s avg. f o r 8 1 . 1 1 . 3 0 . 2 1  Fig. 6.5.6  CPA d u r i n g  . . .  Fig. 6.5.7  Drop d i s t r i b u t i o n s  Fig. 6.5.8  CPA d u r i n g T  Fig. 6.5.9  Drop d i s t r i b u t i o n s  Fig. 6.5.10  CPA d u r i n g T  Fig. 6.5.11  Drop d i s t r i b u t i o n s  Fig. 6.5.12  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  Fig. 6.5.13  10 s a v g . f o r 8 1 . 1 1 . 3 0 . 2 1 XPD f o r v e r t i c a l t r a n s m i t t e d  .  416 419 420  forT  1  422  2  for T  423  2  424  3  for T  425  3  polarization, .  427  polarization,  10 s a v g . f o r 8 1 . 1 1 . 3 0 . 2 1  428  Fig. 6.5.14  D i f f e r e n t i a l attenuation f o r 81.11.30.21  430  Fig. 6.5.15  XPD  H  during  431  Fig. 6.5.16  XPD  V  d u r i n g T^.  Fig. 6.5.17  XPD  H  during T  5  435  Fig. 6.5.18  XPD  H  during T  g  435  Fig. 6.6.1  Rainrates  Fig. 6.6.2  Wind d i r e c t i o n  Fig. 6.6.3  H o r i z o n t a l wind v e l o c i t y , 10 s a v g . and  Fig. 6.6.4(a)  N (0.5)/N (1.0) ratio for81.11.30.22. V e r t i c a l wind v e l o c i t y , 30 s a v g . for 81.11.30.22 D  .  .  .  f o r 81.11.30.22 10 s a v g . f o r 8 1 . 1 1 . 3 0 . 2 2  D  xxiv  432  437 438  439 440  60 s avg.  Page  F i g . 6.6.4(b)  V e r t i c a l wind v e l o c i t y , for 81.11.30.22  F i g . 6.6.5  Signal levels for horizontal transmitted p o l a r i z a t i o n , 10 s avg. for 81.11.30.22  442  F i g . 6.6.6  Signal levels for 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 81.11.30.22 . . . . . . .  443  F i g . 6.6.7  CPA during T j  448  F i g . 6.6.8  Drop d i s t r i b u t i o n s f o r T  449  F i g . 6.6.9  CPA during T  450  F i g . 6.6.10  Drop d i s t r i b u t i o n s for T  F i g . 6.6.11  CPA during T  F i g . 6.6.12  Drop d i s t r i b u t i o n s f o r T  F i g . 6.6.13  CPA during  455  F i g . 6.6.14  Drop d i s t r i b u t i o n s f o r T^  456  F i g . 6.6.15  CPA during T  458  F i g . 6.6.16  Drop d i s t r i b u t i o n s f o r T  F i g . 6.6.17  CPA during T  F i g . 6.6.18  Drop d i s t r i b u t i o n s f o r T  F i g . 6.6.19  CPA during T  F i g . 6.6.20  Drop d i s t r i b u t i o n s f o r T  F i g . 6.6.21  CPA during T  F i g . 6.6.22  Drop d i s t r i b u t i o n s f o r T  F i g . 6.6.23  CPA during T  F i g . 6.6.24  Drop d i s t r i b u t i o n s for T  F i g . 6.6.25  XPD for v e r t i c a l  441  l  2  a  2  451  . . .  .,  .  5  5  453 454  3  459  . . .  460  6  &  461  . . . .  462  ?  463  ?  465  8  g  466  . . .  467  g  468  g  transmitted  polarization,  10 s avg. f o r 81.11.30.22 . F i g . 6.6.26  .  D i f f e r e n t i a l attenuation f o r 81.11.30.22 xxv  .  469 470  Page 472  Fig.  6.7.1  Rainrates for 80.05.22.10  Fig.  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  Fig.  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 .  Fig.  6.7.3  H o r i z o n t a l wind v e l o c i t y , for 80.05.22.10  Fig.  Fig.  Fig.  6.7.4  6.7.5  6.7.6  V e r t i c a l wind v e l o c i t y , for 80.05.22.10  473 . . .  .  . .  474  10 s a v g . 475  10 s a v g . 476  Signal levels for horizontal transmitted 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  Signal levels for v e r t i c a l transmitted 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  Fig.  6.7.7  CPA d u r i n g T j  483  Fig.  6.7.8  CPA d u r i n g T  2  484  Fig.  6.7.9  CPA d u r i n g T  3  486  Fig.  6.7.10  CPA d u r i n g T  4  487  Fig.  6.7.11  CPA d u r i n g T  Fig.  6.7.12  CPA d u r i n g T g  Fig.  6.7.13  XPD f o r v e r t i c a l t r a n s m i t t e d 10 s a v g . f o r 8 0 . 0 5 . 2 2 . 1 0  Fig.  6.7.14  488  5  489 polarization, 492  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  Fig.  6.7.15  D i f f e r e n t i a l attenuation for 80.05.22.10  494  Fig.  6.7.16  XPD  V  for T ^ T g  498  Fig.  6.7.17  XPD  R  for T -T  499  Fig.  6.7.18  XPD  V  for T  2  Fig.  6.7.19  XPD  V  for T  3  . . .  Fig.  6.7.20  XPD  y  for T  &  .  x  3  500 501 502 xxvi  Page F i g . 6.7.21  XPD  F i g . 6.8.1  R a i n r a t e s 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 a v g . f o r 81.06.18.15  506  F i g . 6.8.3  H o r i z o n t a l wind v e l o c i t y ,  R  for T  503  £  10 s a v g .  f o r 81.06.18.15 F i g . 6.8.4(a)  507  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 81.06.18.15 F i g . 6.8.4(b)  508  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 F i g . 6.8.5(a)  Signal  509  levels f o r horizontal  polarization  t r a n s m i t t e d 10 s avg. f o r 81.06.18.15 F i g . 6.8.5(b)  Signal  levels f o r horizontal  511  polarization  t r a n s m i t t e d , 30 s avg. f o r 81.06.18.15 F i g . 6.8.6  Signal  levels for vertical  512  polarization,  10 s avg. f o r 81.06.18.15 . . .  513  F i g . 6.8.7  CPA d u r i n g 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  polarization,  10 s avg. f o r 81.06.18.15 . ., F i g . 6.8.8(b)  XPD f o r h o r i z o n t a l  transmitted  515 polarization  30 s avg. f o r 81.06.18.15  516  F i g . 6.8.9  XPD  F i g . 6.8.10  XPD f o r v e r t i c a l t r a n s m i t t e d  R  during  518 polarization  10 s avg. f o r 81.06.18.15  520  F i g . 6.8.11  XPD  521  F i g . 6.8.12  D i f f e r e n t i a l a t t e n u a t i o n d u r i n g 81.06.18.15 . . . . .  522  F i g . 6.9.1  R a i n r a t e s 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  H o r i z o n t a l wind v e l o c i t y ,  V  during T  1  f o r 81.11.14.07  10 s a v g .  . 526 xxv i i  F i g . 6.9.A  V e r t i c a l wind v e l o c i t y , for 81.11.14.07 .  30 s avg.  F i g . 6.9.5(a)  Signal levels f o r horizontal p o l a r i z a t i o n transmitted, 10 s avg. for 81.11.14.07. .  F i g . 6.9.5(b)  Signal levels f o r horizontal p o l a r i z a t i o n 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 p o l a r i z a t i o n 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 ( a )  F i g . 6.9.10  CPA during T ( b )  F i g . 6.9.11  CPA during T  F i g . 6.9.12  CPA during T ( a )  F i g . 6.9.13(a)  XPD f o r horizontal transmitted p o l a r i z a t i o n , 10 s avg. for 81.11.14.07 . . . .  F i g . 6.9.13(b)  XPD f o r horizontal transmitted 30 s avg. f o r 81.11.14.07  F i g . 6.9.14  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 81.11.14.07 . . .  F i g . 6.9.15  D i f f e r e n t i a l attenuation f o r 81.11.14.07. .  F i g . 6.9.16  XPD f o r T j . . . . . . .  F i g . 6.9.17  XPD f o r 7  F i g . 6.9.18  XPD f o r T  3  F i g . 6.9.19  XPD f o r T  3  ....  . . . . . .  2  . .  2  3  • •  ,  . . . ,  3  H  V  1  R  V  xxviii  polarization,  LIST OF TABLES 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  Summary of WARC-79 allocations above 40 GHz . . . . . .  Page 6  DBB-614-LE2 electromechanical DPST waveguide switch waveguide switch s p e c i f i c a t i o n s . . . . . .  39  Transmitting system s i g n a l l e v e l s  44  - S c i e n t i f i c Atlanta model 1751 receiver s p e c i f i c a t i o n s .  50  TRG 922-V harmonic mixer s p e c i f i c a t i o n s  60  A . I . Grayzel OX-3.5 frequency m u l t i p l i e r specifications  77  TRG V822 antenna s p e c i f i c a t i o n s at 73.5 GHz  105  Forward scattering amplitudes at 74 GHz  200  Drop terminal v e l o c i t i e s i n s t i l l a i r . . . . . . . . .  217  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 on cancelled and uncancelled systems. . . . . . .  279  Table 5.2  Range of possible system XPDs f o r d i f f e r e n t antenna XPD angles  281  Table 5.3  Range of possible system XPDs f o r d i f f e r e n t antenna XPD magnitudes  283  Summary of attenuation data f o r 81.11.30.10  302  Summary of XPD and d i f f e r e n t i a l attenuation data f o r 81.11.30.10  336  Summary of attenuation data f o r 81.11.30.19 . . . . . . .  378  Summary of XPD and d i f f e r e n t i a l attenuation data f o r 81.11.30.19 -  406  Summary of attenuation data for 81.11.30.21 . . . . . .  418  Summary of XPD and d i f f e r e n t i a l - a t t e n u a t i o n data f o r 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  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  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 f o r 81.11.14.  Table 6.9.2  Summary of XPD and d i f f e r e n t i a l data f o r 81.11.14.07  XXX  attenuati  ACKNOWLEDGEMENTS  I would l i k e foremost, to acknowledge the c o n t r i b u t i o n , encouragement and moral s u p p o r t o f D r . M.M.Z. K h a r a d l y whose wealth of knowledge p r a c t i c a l and t h e o r e t i c a l microwave t e c h n i q u e s and c r i t i c a l make t h i s p r o j e c t  about  i n s i g h t helped  successful.  I am a l s o v e r y g r a t e f u l t o D r . P e t e r Watson, of the U n i v e r s i t y of B r a d f o r d , U.K. f o r p r o v i d i n g  the forward s c a t t e r i n g amplitudes on which t h e  c a l c u l a t i o n s i n Chapter 4 a r e based. Mr.  Jack S t u b e r , f o r m e r l y  made s e v e r a l c o n t r i b u t i o n s  o f the E l e c t r i c a l E n g i n e e r i n g machine shop,  t o t h i s work, i n c l u d i n g the c o n s t r u c t i o n o f : t h e  antenna and r e f l e c t o r mounts and s h i e l d s , r a i n g a u g e s , d i s d r o m e t e r and numerous waveguide s e c t i o n s . Mr. James J o h n s t o n , who was a t e c h n i c i a n i n o u r l a b was a l s o v e r y h e l p f u l i n : the f i n a l d i s d r o m e t e r c a l i b r a t i o n , microcomputer preparation  of t h i s  s o f t w a r e and  report.  I would a l s o l i k e t o s p e c i a l l y thank G a i l Schmidt  f o r typing  this  report. Mr. Tony Leugner,  o f the E l e c t r i c a l E n g i n e e r i n g Department was  e x t r e m e l y h e l p f u l by s e r v i c i n g the d a t a a c q u i s i t i o n minicomputer by c o n s t r u c t i n g  t h e d i s d r o m e t e r p r e a m p l i f i e r and mixer b i a s  Many members of the departmental  system and  circuits.  technical staff, including:  A l MacKenzie, C h r i s S h e f f i e l d , Derek Daines, Dave F l e t c h e r , and W a l l y W a l t e r s , p r o v i d e d i n v a l u a b l e a s s i s t a n c e a t one time o r another the course of t h i s work.  xxxi  during  A s s i s t a n c e i n t h e development of the f i r s t  v e r s i o n of the d i s d r o m e t e r  was p r o v i d e d by: Mike Koombes, Vince Loney and W i l l i a m Wong. The  software  f o r data h a n d l i n g and p r e s e n t a t i o n was developed  by:  Ian Vogelesang, B r i a n Thompson, Peter Chun, L i s b e t h S e e l e y , E r i c MInch, Andrew M i l n e , Ramon V a l e r d a , Ho Jun Lee and Len Smart. The  Postgraduate  S c h o l a r s h i p I r e c e i v e d from the N a t u r a l S c i e n c e s and  Engineering Research C o u n c i l i s a l s o g r e a t f u l l y  acknowledged.  Funds f o r t h i s p r o j e c t were p r o v i d e d by the Communications Center,  Ottawa, under t h e f o l l o w i n g DSS c o n t r a c t s : OSU77-00056,  Research  0SU77-000261,  0SU78-00012, 0SU79-00009, 0SU80-00129, 0SU81-00057, and by the N a t u r a l S c i e n c e and E n g i n e e r i n g Research C o u n c i l under g r a n t 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 i n t e r e s t i n the application of the millimetre-wave bands [1.1]-[1.12] and orthogonal p o l a r i z a t i o n frequency reuse [1.6]/ [1.13]-[1.15]. systems employing  Many new  atmospheric propagation of the higher microwave and m i l l i -  metre frequencies are now being developed.  The main uses planned f o r these  higher frequencies are wideband t e r r e s t r i a l and s a t e l l i t e communication l i n k s , (both analog and d i g i t a l ) and a variety of radar applications.  Milli-  metre-wave systems are also rapidly becoming p r a c t i c a l because of advances i n higher frequency s o l i d - s t a t e components and integrated c i r c u i t technologies. To be able to e f f e c t i v e l y apply the millimetre frequencies and the techniques of p o l a r i z a t i o n frequency reuse, accurate information about the e f f e c t s of atmospheric propagation, e s p e c i a l l y during r a i n , must be available to system designers.  The mathematical methods for predicting the important  atmospheric propagation parameters during r a i n are f a i r l y well developed l i t t e controversy p e r s i s t s about the basic theory. of these mathematical  and  However, the usefulness  models i s limited because very l i t t l e i s known about  some of the meteorological parameters necessary for accurate predictive calculations.  There have also been a s i g n i f i c a n t number of reported  experimental measurements which do not appear to agree with the basic t h e o r e t i c a l predictions based on simultaneous meteorological observations. In most instances, t h i s i s probably due to inaccurate or incomplete meteorological instrumentation or inadequacies i n the meteorological or  2  experimental models.  These factors create a d e f i n i t e need f o r accurate  millimetre-wave and dual-polarized propagation data with comprehensive raeterological  observations to v e r i f y the basic theory and to learn more  about the meteorological conditions important to these areas of atmospheric propagation.  1.1  Spectrum Demand Increasing demand f o r t e r r e s t r i a l microwave systems and the phenomenal  growth i n s a t e l l i t e  communications has s i g n i f i c a n t l y 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 a p p l i c a t i o n 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 f o r  urban areas, frequency coordination with t e r r e s t r i a l increasingly d i f f i c u l t  [1.17],  [1.18],  services has become  Frequency coordination problems w i l l  spread to higher frequencies and become even more severe f o r lower frequencies, due to the large number of new s a t e l l i t e next few years, as shown i n F i g . 1.1  [1.19].  systems planned f o r the  Since i t i s unusual f o r  channel a l l o c a t i o n s 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 i g n i f i c a n t l y revised the  18-40 GHz] (6)  18 -40 GHz (8)  |ll-17 GHz I (39)  11 -17 GHz (8) 7 -9 GHz (13)  t 7-9 GHz (4)  BELOW 6 GHz (50)  18-40 GHz (2) \  BELOW 6 GHz (54)  11-17 GHz(1)  BELOW 6 GHz (14) 1965-69  BELOW 6 GHz (23)  1970-74  1975-79  1980-84  INTERVAL  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 a l l o c a t i o n s are considered to " r e f l e c t a high l e v e l of i n t e r e s t and a c t i v i t y i n t h i s portion of the spectrum" and were "created with the objective of stimulating development of t h i s spectrum resource" [1.20].  The m i l l i m e t r e -  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 atmospheric  absorption.  F i g . 1.2, shows the  attenuation bands caused by oxygen and water vapour [1.21].  Table 1(a) from [1.20], gives the frequency l i m i t s and band designations f o r the absorption bands and windows i n the frequency range 40-275 GHz. A summary of the WARC-79 a l l o c a t i o n s , from [1.20] i s shown i n Table 1(b) to 1(e).  Complete spectrum a l l o c a t i o n s r e s u l t i n g from WARC-79 are included i n  [1.22].  1.2  M i l l i m e t r e Applications Even though a l l types of services are a l l o c a t e d i n the frequency  range above 40 GHz, the s p e c i f i c c h a r a c t e r i s t i c s of these frequencies make c e r t a i n a p p l i c a t i o n s more advantageous than others. atmospheric  propagation where millimetre-wave  Applications employing  systems have some benefit over  microwave or o p t i c a l systems include: - short haul point-to-point or l o c a l d i s t r i b u t i o n t e r r e s t r i a l l i n k s [1.26], [1.29], [1.30], [1.31],  [1.23],  [1.36].  - small, lightweight, portable communication systems [1.5], [1.24], [1.30], [1.31] , [1.32] , [1.33].  5  10  20  50 Frequency  F i g . 1.2.  Atmospheric a t t e n u a t i o n due  100  200  (GHz) to m o l e c u l a r  absorption.  350  TABLE 1(a) SUMMARY OF ALLOCATIONS ABOVE 40 GHz Total Width of Spectrum Allocated  235 GHz  Number of Services  21 0  Bands Allocated Exclusively Average Spectrum/Band: <100  GHz  2 . 5 GHz  >100  GHz  5 . 8 GHz  3.5  Average Services/Band  TABLE 1(b) ATMOSPHERIC WINDOW AND ABSORPTION BAND LIMITS Window W  Absorption Band  39.5-51.4  l A  w  51.4-66  l  66-105  2  A W  2  105-134 134-170  3 A  — " I ,  Limits (GHz)  3  170-190 190-275  7  TABLE 1(c)  Service  l  w  ALLOCATIONS TO SATELLITE SERVICES  w  l  A  A  2  2  3  W  3  A  w  4  Total  Total  Bandwdith, GHz  Amateur-Satellite  1  2  2  2  7  21.7  Fixed  4  5  3  5  17  69.5  8  44.0  10  52.5  4  2  2  Inter Mobile  3  4  Broadcasting  1  1  Radionavigation  1  2  2  1  2  1  2  4  6  44.5  TABLE 1(d) ALLOCATIONS TO SCIENTIFIC SERVICES  Service  l  W  Earth Exploration-  l  A  5  1  w  2  A  2  3  W  3  A  w  4  Total  Total  Bandwidth, GHz 2  2  2  2  4  18  1  1  1  1  2  7  2  2  2  2  4  18  69.8  Satellite 1  Radio Astronomy Space Research  Z  z  J  Z  .  —  —  •  —  -  5  1  49  69.8  TABLE 1(e) ALLOCATIONS TO TERRESTRIAL SERVICES  .Service  W  l  A  l  w  2  A  2  W  3  Fixed  6  3  7  2  4  Mobile  8  3  9  2  5  Broadcasting  1  Total  Total  7  21.7  4  6  32  124.7  4  7  38  169  2  4  3  10  53  2  6  1 1  1  w„  2  2  2  1  Radionavi gation  3  Bandwidth, GHz  Amateur  Radiolocation  A  3 2  1  2 1 1  44.5  8  - a wide variety of high resolution radar applications [1.23], [1.26],  [1.24],  [1.28].  - secure communication l i n k s operating i n absorption bands (especially at 60 GHz) [1.5],  [1.23],  [1.24],  [1.26],  - very wideband d i g i t a l l i n k s [1.25], - multichannel video systems - satellite  [1.32],  [1.31],  [1.33].  [1.35].  [1.30].  communication systems  [1.2],  [1.4],  [1.23],  [1.24],  [1.26],  [1.27]. and - radiometer, [1.26],  1.3  remote sensing and imaging systems,  [1.27],  [1.28],  [1.23],  [1.24],  [1.25],  [1.34].  Advantages and Disadvantages of Millimetre Frequencies The major factors which make millimetre frequencies advantageous i n  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 i n  p h y s i c a l l y smaller components, higher antenna gains and lower antenna beamwidths (for a s p e c i f i e d antenna aperture).  Narrow antenna beamwidths are  desirable because they ease frequency coordination problems, reduce multipath f a d i n g , lower the p r o b a b i l i t y of unauthorized reception or jamming, and y i e l d higher resolutions i n radar and radiometer systems.  Bandwidths of several  gigahertz are more e a s i l y obtainable i n 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 i n the millimetre range w i l l mean that more systems, with er bandwidths,, can be licensed i n any geographical area.  Another  high-  9  advantage of millimetre-wave systems i n high resolution radar applications Is their a b i l i t y to penetrate f o g , smoke and dust [1.23],  [1.24].  communication systems requiring a high degree of s e c u r i t y ,  In  the absorption  bands i n the millimetre range, e s p e c i a l l y at 60 GHz, are an advantage they can further reduce the p r o b a b i l i t y of unauthorized reception. [1.32],  because  [1.23],  [1.33]. The disadvantages of millimetre-wave systems are higher copolar -  attenuation (CPA) due to r a i n and molecular absorption and lower component perforraance/cost  ratios.  Attenuation due to r a i n and other hydrometeors  increases with frequency up to approximately 100 GHz. This factor  will  ultimately l i m i t 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 i s 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 r a i n attenuation, great advances are being made i n millimetre components.  1.4  Millimetre Semiconductors and Integrated C i r c u i t s 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 l e v e l s of s o l i d - s t a t e millimetre sources has been increasing at the rate of 3 dB per year 11.37],  It i s now possible to obtain 17 W peak  at 94 GHz i n 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 d i v i s i o n 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 i p l i n e mixer which yielded a t o t a l double sideband receiver noise figure of 5.8 dB at 110 GHz [1.33]. Recent advances i n millimetre frequency integrated  circuit  technologies also promise to reduce the cost of components.  Several types of  transmission l i n e structures have been demonstrated to be advantageous f o r millimetre-wave IC f a b r i c a t i o n .  These i n c l u d e :  - d i e l e c t r i c waveguide [1.43 ] , [1.44 ], [1.46 ] . - image waveguide [1.45], - f i n l i n e [1.47],  [1.46].  [1.48].  - microstrip l i n e [1.49 ], [1.50 ], [1.51 ] . - suspended s t r i p l i n e [1.41],  [1.42],  [1.52].  and - E-plane waveguide [1.53]. These techniques w i l l y i e l d large reductions i n component costs when volumes can j u s t i f y the use of modern integrated c i r c u i t production methods  1.5  [1.38].  Orthogonal P o l a r i z a t i o n Frequency Reuse Orthogonal p o l a r i z a t i o n frequency reuse can double spectrum  u t i l i z a t i o n and result i n s i g n i f i c a n t system cost reductions.  During normal  clear-weather conditions i t i s possible to transmit two orthogonal ( l i n e a r or  11  circular) polarizations  through one p a i r of antennas w i t h i n s i g n i f i c a n t  atmospheric c o u p l i n g between p o l a r i z a t i o n s . communications  T h i s can a l l o w s e p a r a t e  c h a n n e l s to occupy the same f r e q u e n c y or can be used t o  a l l e v i a t e f r e q u e n c y c o o r d i n a t i o n problems i n congested a r e a s . P o l a r i z a t i o n f r e q u e n c y r e u s e can o f f e r tremendous  c o s t 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 s h a r e a common antenna system.  In t e r r e s t r i a l systems, t o p o g r a p h i c a l  conditions  o f t e n n e c e s s i t a t e the use of l a r g e towers to support antennas. can o f t e n c o s t more than t h e systems' e l e c t r o n i c components.  These  towers  By u s i n g a  common antenna f o r two p o l a r i z a t i o n s , t h e t o t a l c o s t o f p u r c h a s i n g , s h i p p i n g , i n s t a l l i n g and m a i n t a i n i n g the antenna and tower can be g r e a t l y r e d u c e d . s a t e l l i t e systems, these economic advantages a r e even g r e a t e r  In  because  antennas a r e a l a r g e r p o r t i o n o f t o t a l system c o s t s and because mounting a d d i t i o n a l antennas on the a c t u a l s a t e l l i t e would be e x t r e m e l y e x p e n s i v e . U n f o r t u n a t e l y , some atmospheric c o n d i t i o n s can cause c o u p l i n g between p o l a r i z a t i o n s and a r e d u c t i o n i n the p a t h c r o s s p o l a r d i s c r i m i n a t i o n (XPD) and t h e r e f o r e system r e l i a b i l i t y .  A r e d u c t i o n i n path XPD can o c c u r as s i g n a l s  propagate through r a i n ( o r o t h e r hydrometeors) o r d u r i n g propagation.  multipath  M u l t i p a t h XPD r e d u c t i o n i s v e r y important i n the lower  microwave r e g i o n but because t h i s r e p o r t i s concerned o n l y w i t h m i l l i m e t r e p r o p a g a t i o n , m u l t i p a t h XPD w i l l n o t be d i s c u s s e d i n d e t a i l .  R a i n can cause a  r e d u c t i o n i n XPD because r a i n d r o p s a r e n o t s p h e r i c a l and i n the presence o f v e r t i c a l wind g r a d i e n t s can have a p r e f e r r e d a x i s o r i e n t a t i o n , o r c a n t i n g angle.  D e p o l a r i z a t i o n o c c u r s because the two p o l a r i z a t i o n s e x p e r i e n c e a  12  d i f f e r e n t i a l a t t e n u a t i o n 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  P r o p a g a t i o n Theory and  Experiment  To be a b l e to d e s i g n economical using millimetre-waves atmospheric  systems w i t h p r e d i c t a b l e r e l i a b i l i t y  or p o l a r i z a t i o n f r e q u e n c y  p r o p a g a t i o n phenomena i s r e q u i r e d .  r e u s e , a c c u r a t e knowledge of At the p r e s e n t  time,  s u f f i c i e n t , r e l i a b l e i n f o r m a t i o n i s not a v a i l a b l e on p r o p a g a t i o n a t h i g h e r f r e q u e n c i e s and  i n d i f f e r e n t geographical regions.  p r a c t i c a l atmospheric  through  advancement of  p r o p a g a t i o n knowledge r e q u i r e s a combination  t h e o r e t i c a l and e x p e r i m e n t a l The  The  investigations.  b a s i c mathematical  methods f o r p r e d i c t i n g atmospheric  r a i n are f a i r l y w e l l d e v e l o p e d .  years.  propagation  In the case of the c a l c u l a t i o n of  r a i n a t t e n u a t i o n f o r a s e t of assumed r a i n c o n d i t i o n s , the u n c e r t a i n t i e s and  of  earlier  c o n t r o v e r s i e s appear to have been r e s o l v e d i n the p a s t  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  parameters d u r i n g r a i n are l e s s mature but t h e r e appears the b a s i c t e c h n i q u e s . c a l c u l a t i o n of XPD,  few  propagation  to be agreement  Several i n v e s t i g a t o r s are c o n t i n u i n g to r e f i n e  on  the  m a i n l y by i n c l u d i n g more comprehensive m e t e o r o l o g i c a l  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  p r o p a g a t i o n d u r i n g r a i n i s a l a c k of knowledge about the m e t e o r o l o g i c a l i n p u t s 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 a t t e n u a t i o n , the number  and  s i z e s o f r a i n d r o p s at a l l p o i n t s w i t h i n the p r o p a g a t i o n path must be known. T h i s i s extremely  difficult  to p r e d i c t because v e r y l i m i t e d a c t u a l drop  size  13  d a t a a r e a v a i l a b l e and i t i s known t h a t the drop s i z e d i s t r i b u t i o n depends on r a i n r a t e - which a l s o has l a r g e temporal, -  s p a t i a l and g e o g r a p h i c a l  variations  the type of r a i n s t o r m , 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 w i t h i n a r a i n c e l l  and  other meteorological c o n d i t i o n s .  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 a d d i t i o n t o the p r e v i o u s i n f o r m a t i o n , i t i s n e c e s s a r y to know the drop shape and c a n t i n g angle  statistics.  Because o f the extreme  d i f f i c u l t y of a c c u r a t e l y measuring these parameters i n n a t u r a l r a i n , no  almost  i n f o r m a t i o n about c a n t i n g a n g l e s p r e s e n t l y e x i s t s . Radio system d e s i g n e r s i n Canada a r e v e r y f o r t u n a t e t o have a r e c e n t l y  p u b l i s h e d , d e t a i l e d study o f r a i n r a t e s t a t i s t i c s a c r o s s Canada  [1.54].  S i m i l a r d a t a , w i t h l e s s g e o g r a p h i c a l r e s o l u t i o n , have a l s o r e c e n t l y been p u b l i s h e d by Crane, showing r a i n r a t e r e g i o n s f o r a l l areas of the e a r t h [1.55],  [1.56]. While t h e s e d a t a bases g r e a t l y Improve the a c c u r a c y o f system  reliability  p r e d i c t i o n s , much more data a r e needed to be a b l e t o 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  m i l l i m e t r e p r o p a g a t i o n p r e d i c t i o n s , drop s i z e i n f o r m a t i o n i s important because the c a l c u l a t i o n s a r e v e r y much more s e n s i t i v e t o drop d i s t r i b u t i o n than i n the microwave range due to the l a r g e r drop s i z e - t o - w a v e l e n g t h  ratio.  F o r a c c u r a t e XPD p r e d i c t i o n s , the c a n t i n g angle s t a t i s t i c s a r e e s s e n t i a l . The  d i f f i c u l t y o f measuring these parameters means t h a t system d e s i g n e r s  will  not be a b l e t o a c c u r a t e l y p r e d i c t m i l l i m e t r e or d u a l - p o l a r i z e d p r o p a g a t i o n parameters, i n a g i v e n g e o g r a p h i c a l l o c a t i o n , by u s i n g a v a i l a b l e meteoro l o g i c a l s t a t i s t i c s and p r o p a g a t i o n  calculations.  Because i t i s not f e a s i b l e  to measure a l l the r e q u i r e d m e t e o r o l o g i c a l parameters a c c u r a t e l y , t h e r e i s  14  considerable Interest i n attempting to determine e f f e c t i v e r a i n conditions by comparing simultaneous propagation and measurable r a i n conditions. Experimental data on atmospheric propagation with simultaneous meterological observations are needed t o :  validate the theoretical methods,  provide p r a c t i c a l and d i r e c t l y applicable propagation data and to gain knowledge of the e f f e c t i v e 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 c a l c u l a t i o n s ,  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 u s e f u l i n a v a r i e t y of a p p l i c a t i o n s .  If adequate meteorological  information i s included with the propagation data, i t i s possible to improve predictions i n other geographical areas i f s i m i l a r , comparable meterological s t a t i s t i c s are a v a i l a b l e .  Propagation information obtained on t e r r e s t r i a l  l i n k s can also be useful i n predicting l i n k performance on s a t e l l i t e [1.8],  [1.64],  [1.65].  paths  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 i s e s p e c i a l l y great above about 40 GHz because very limited data have been published [1.9], [1.59],  [1.60],  [1.63].  [1.58],  Experimental work i s also important i n the  millimetre range because the larger drop size-to-wavelength r a t i o and freedom from multipath give most importance to d i f f e r e n t propagation problems than those which are f a i r l y well understood i n the microwave region.  In a d d i t i o n ,  15  there have been a number of cases where data from experiments, dual-polarized or millimetre frequency Investigations,  especially  did not agree with  t h e o r e t i c a l c a l c u l a t i o n s , probably because of inadequate meterological observations  [1.61],  [1.62],  of this lack of agreement  [1.64],  [1.67]-[1.73].  More, s p e c i f i c examples  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 i s included to outline the d i f f e r e n t experimental techniques, survey the experimental system performances,  and review the results obtained.  there have been several excellent tion.  At frequencies below about 18 GHz,  investigations of dual-polarized propaga-  These studies are not mentioned here for the sake of brevity and  because the important meterological conditions and propagation effects a r e , to some extent, different i n the microwave and millimetre wave frequency ranges.  There have also been several comprehensive dual-polarized s a t e l l i t e  propagation experiments at frequencies up to 30 GHz which are not dicussed here. DeLange, D i e t r i c h and Hogg have reported a 60 GHz dual-polarized experiment on a 1.03 km. l i n k at B e l l Labs, Holmdel, New Jersey [1.74].  A  switched transmitted p o l a r i z a t i o n and a switched p o l a r i z a t i o n single-channel receiver were used.  Approximate i s o l a t i o n s of 30 dB and 34 dB were achieved.  16  F i g . 4 i n t h i s reference shows a sharp, deep n u l l i n one p o l a r i z a t i o n discrimination c h a r a c t e r i s t i c  of the operating system.  (These n u l l s  are  believed to be similar to those described i n Section 2.5 of this r e p o r t . ) In the discussion of the experimental r e s u l t s ,  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 h o r i z o n t a l  p o l a r i z a t i o n was greater than i n v e r t i c a l ) .  The crosstalk  [XPD] v a r i a t i o n s  were pretty much the same for both p o l a r i z a t i o n s , with the r a t i o [XPD] becoming poorer during the deeper fade".  However, a d i f f e r e n t storm " d i d 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, i n d i c a t i n g that the attenuation of the v e r t i c a l component was greater than that of the h o r i z o n t a l component.  The fact that the crosstalk r a t i o 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 r e f e r r i n g to ( F i g . 4) system i s o l a t i o n ] which shows the clear weather operating point near  [the  +0.5  degree; a negative rotation (caused by the rain) of the v e r t i c a l component from this value would reduce the cross-coupled energy and thereby improve the ratio".  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  f o r fades greater than 30 dB". Hogg and Chu [1.75] have presented data from t h i s experiment i n the form of a graph r e l a t i n g horizontal CPA to XPD. value of XPD than expected.  These results show a lower  This is attributed to the low clear-weather,  crosspolar-discrimination l e v e l of their measuring system.  No attempt was  17  made to separate this clear weather XPD l e v e l from the atmospheric measurements. Thomas [1.76] has compared some of the 60 GHz XPD data from this experiment to h i s calculated values.  The effect of the f i n i t e experimental  system i s o l a t i o n on the measured data seems to have been considered as a simple scalar a d d i t i o n .  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 i n v e s t i g a t i o n conducted over a 13.6 km l i n k near the University of Bradford, U.K.  [1.77].  In this study, the CW transmitted s i g n a l was polarized at 4 5 ° .  Separate antennas continously monitored the v e r t i c a l and horizontal components of the received s i g n a l .  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 s h i f t and 4 5 ° c r o s s p o l a r i z a t i o n .  With this set up, the received signals w i l l  have s i m i l a r l e v e l s and high S.N.R. thus improving the accuracy of d i f f e r e n t i a l measurements.  This p o l a r i z a t i o n w i l l also y i e l d the highest levels of  depolarized s i g n a l s , but w i l l result i n a low s e n s i t i v i t y to canting angle measurements.  Also included i n this reference are e a r l i e r results f o r XPD  over the same path f o r v e r t i c a l transmitted p o l a r i z a t i o n . The r a i n instrumentation for this experiment consisted of a rapid response r a i n 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 c r o s s p o l a r i z a t i o n , 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 i n good agreement with a  18  t h e o r e t i c a l r a i n model with 3° to 4° canting angle, 2 0 ° mean modulus and 2 0 ° to 2 5 ° standard d e v i a t i o n .  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 distribution. Seraplak conducted an experiment to measure 30.9 GHz p o l a r i z a t i o n r o t a t i o n over a 2.6 km path at B e l 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 p o l a r i z a t i o n was r a p i d l y switched between plus and minus 45° with respect to vertical.  The sum and difference powers f o r both received signals was used  to calculate the p o l a r i z a t i o n r o t a t i o n . XPD (dB) = 20 l o g  1 Q  The XPD was then calculated using:  (tan a)  (1.1)  where a i s the measured p o l a r i z a t i o n r o t a t i o n .  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 p o l a r i z a t i o n rotation on cross-path wind v e l o c i t y . An e a r l i e r experiment by Semplak, also at 30.9 GHz, but over a 1.89 km path i n the same l o c a t i o n , used a s i m i l a r 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 4 5 ° and the receiver was switched between v e r t i c a l and horizontal p o l a r i z a t i o n s .  The average r e l a t i o n s h i p between the observed  copolar and d i f f e r e n t i a l attenuations agreed well with the t h e o r e t i c a l predictions.  Rainrate does not appear to have been measured i n either of  these two experiments.  19  Turner described a dual p o l a r i z a t i o n experiment at 22 GHz conducted over a 4 km l i n k i n Suffolk, England [1.80].  Two d i f f e r e n t modulation  frequencies were used, but i t was also necessary to switch the transmitted p o l a r i z a t i o n to prevent interaction between channels within the IF amplifiers.  Isolations of 29 dB and 30 dB were achieved.  Variations i n cross-  polar s i g n a l l e v e l s observed during high wind v e l o c i t i e s 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] s i g n i f i c a n t crosspolarization due to r a i n observed". However, on occasions when multipath was observed on other l i n k s i n the area, "considerable v a r i a t i o n i n crosspolar signal was seen".  Slow variations i n  crosspolar s i g n a l l e v e l s were also reported during apparently stable conditions with some i n d i c a t i o n that these effects were related to sunrise and sunset.  Suggestions as to the cause of this effect included: moisture on  radomes, multipath and variations i n r e f r a c t i v e index. Shimba and Morita conducted a crosspolarization measurement experiment on 2.9 km and 4.3 km paths i n Japan [1.81].  A s i n g l e , 19 GHz, h o r i z o n t a l l y  polarized s i g n a l was transmitted and both received p o l a r i z a t i o n s were monitored. dB.  The receiving system crosspolar discrimination was approximately 35  It i s i n t e r e s t i n g to note that the data presented i n this paper shows  two periods during rainstorms where the measured XPD increased by appoximately 10 dB.  This effect was not commented on by the authors.  Morita, Hosoya and Akeyama [1.82] reported another 19 GHz d u a l p o l a r i z a t i o n experiment at a second l o c a t i o n i n Japan over a 4 km path.  In  this experiment two d i f f e r e n t transmitted frequencies (19.3 and 19.4 GHz) and  20  switched frequency receivers were employed.  This method resulted i n very  high system i s o l a t i o n s of 46 and 56 dB. The results f o r this l o c a t i o n showed lower values of depolarization than f o r the s i m i l a r experiment cribed previously.  [1.81] des-  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 c o r r e l a t i o n between r a i n attenuation and depolarization was not necessarily h i g h " . In a l a t e r paper describing both of the previous experiments, Shimba, Morita and Akeyama [1.83] conclude that there was a high c o r r e l a t i o n between attenuation and XPD for the combined data from both experiments. scatter of XPD data points at low attenuations,  The large  including values higher than  the clear weather i s o l a t i o n , were thought to result from raindrop adherence to the radomes.  No explanation as to why the wet radomes would cause this  effect was o f f e r e d .  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 s i n g l e - p o l a r i z a t i o n millimetre  propagation experiments designed to measure r a i n attenuation.  Most of the  experiments surveyed are the higher frequency investigations with good meteorological instrumentation. Sander reported a millimetre wave attenuation i n v e s t i g a t i o n 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 t o t a l length radar path using a corner r e f l e c t o r at the Massachusetts Institute of Technology.  Raingauges  21  and Lammers type e l e c t r o s t a t i c disdrometers were used at three locations along the path.  The disdrometers used i n the experiment had a 25 cm  sampling area and s i x size classes.  2  The author mentions that the instrument  was subsequently redesigned to have a 100 cm sample area and sixteen 2  categories,  but no d e t a i l s 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 p l o t s .  Sander concludes that "Mainly  because of the imperfections of the meteorological equipment used, but also because of the inhomogeneity of r a i n , only the s t a t i s t i c a l averages of our results v e r i f y the t h e o r e t i c a l 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 i n k at the University of Bradford, England [1.85].  Fast-response raingauges were located at each end of the path. An  e l e c t r o s t a t i c disdrometer, developed by Sander [1.84], with a sampling time of 1 min. was used to measure the dropsize d i s t r i b u t i o n .  Synthetic storm  models using the 700 mb or 850 mb pressure l e v e l e f f e c t i v e wind v e l o c i t i e s from radiosonde information were used to calculate path rainrates from the raingauge and disdrometer data.  The calculated path rainrate gave a dramatic  improvement i n the correlation with measured attenuation for i n d i v i d u a l storms compared to using either of the rainrates measured at the ends of the path.  Disdrometer evidence i s presented which indicates that the variations  i n the attenuation-calculated path rainrate r e l a t i o n are due to dropsize distributions. 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 d i s t r i b u t i o n .  In certain periods of heavy r a i n ,  attenuations were measured which were considerably lower than predicted f o r the Laws and Parsons dropsize d i s t r i b u t i o n s .  An example i s also included  which shows a t r a n s i s t i o n 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 p o l a r ized attenuation experiment over a 935 m path near The Hague, Netherlands [1.86],  [1.87].  500 m apart.  Path rainrate was measured with the raingauges spaced about  An electromechanical disdrometer with a 50 cm sample area and 2  83 second sample period was used to monitor the drop s i z e d i s t r i b u t i o n . Horizontal windspeed, wind d i r e c t i o n , pressure and humidity were also ded.  recor-  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, i n 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 r e s u l t i n g i n a predicted 0.1 to 0.2 dB/km 3  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], [1.90].  [1.89],  No meteorological data appears to have been recorded i n this  experiment.  In this i n v e s t i g a t i o n , the objective was to record data f o r a  one year period and determine l i n k r e l i a b i l i t y s t a t i s t i c s for this l o c a t i o n . Zavody and Harden have simultaneously measured v e r t i c a l attenuation at 36 GHz and 110 GHz on a 220 m path i n 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 cm sample area and 30 2  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  vs. rainrate p l o t s .  attenuation  The authors state that a " s i g n i f i c a n t number of the  measured values l i e outside the l i m i t i n g curves for this range."  An example  i s also Included i n this paper showing a reduction i n 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 i n rainrates  1.9  over 15 mm/hr.  Thesis Objectives The p r i n c i p a l objective of this work i s to develop an experimental  system to study dual-polarized atmospheric propagation near 73 GHz. This i n v e s t i g a t i o n i s part of an ongoing research program into millimetre-wave propagation which i s being supported by the Communications Research Centre, Department of Communications, Ottawa.  As an e a r l i e r part of this  research  program, a preliminary study of s i n g l e - p o l a r i z a t i o n 74 GHz copolar attenuation was conducted over the same path at the University of B r i t i s h Columbia [ 2 . 1 ] .  During this investigation, attenuation and rainrate data were  recorded for rainrates  up to 10 mm/hr.  theory of Ryde and Ryde.  Some of the equipment developed for this previous  study was retained for this project, computer interface and software, reflector.  The data were compared with the  i n c l u d i n g : most of the data a c q u i s i t i o n  parts of the raingauge network and the basic  24  o b j e c t i v e of  More s p e c i f i c a l l y , the f i r s t simultaneous m e t e o r o l o g i c a l  and  dual-polarized  are as a c c u r a t e and  as complete as p o s s i b l e .  copolar  and  attenuation  polarizations. of  describing  The  crosspolar  73 GHz  record  p r o p a g a t i o n d a t a which  These p r o p a g a t i o n d a t a  d i s c r i m i n a t i o n f o r v e r t i c a l and  second o b j e c t i v e  the XPD  t h i s work i s to  i s to c o n s t r u c t  and  include  horizontal  t e s t a model c a p a b l e  response of the e x p e r i m e n t a l system.  The  final  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 p r o p a g a t i o n o b s e r v a t i o n s terms of v a r i o u s  meteorological  wind v e l o c i t i e s , d r o p s i z e  parameters i n c l u d i n g : h o r i z o n t a l and  d i s t r i b u t i o n and  achievement of these o b j e c t i v e s  required  type of r a i n s t o r m .  the d e s i g n and  dual-polarized  millimetre-wave transmitter,  meteorological  instrumentation  f o r measuring r a i n and  A d u a l - p o l a r i z e d m i l l i m e t r e wave l i n k was the U n i v e r s i t y of B r i t i s h Columbia campus.  transmitting  and  a and  wind parameters.  e s t a b l i s h e d over a path  Different  A f t e r a b a s i c method had  of  antenna system  on  dual-polarized  e x p e r i m e n t a l methods were compared to determine which was this investigation.  vertical  The  construction  r e c e i v e r and  in  most s u i t a b l e f o r  been chosen, a p p l i c a b l e 73  r e c e i v i n g antenna systems were d e s i g n e d and  constructed  GHz with  the maximum p o s s i b l e performance compatible w i t h the budget a v a i l a b l e . Comprehensive t e s t i n g o f components, subassemblies and  the e n t i r e system  c a r r i e d out  to c h a r a c t e r i z e , as t h o r o u g h l y as p o s s i b l e , the  systems and  thus reduce the u n c e r t a i n t y  b e h a v i o u r of The  was  millimetre-wave  i n the d a t a a r i s i n g from the  nonideal  the e x p e r i m e n t a l system.  previous sections  comprehensive m e t e o r o l o g i c a l  I l l u s t r a t e d the  importance of  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 r a i n g a u g e s w i t h h i g h  accurate,  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 a l o n g the p r o p a g a t i o n path.  A f t e r a study  of measurement methods, an a c c u r a t e i n s t r u m e n t t o measure r a i n d r o p s s i z e s , r e f e r r e d t o here as a d i s d r o m e t e r , was developed.  An anemometer was i n c l u d e d  to measure t h r e e components o f the wind v e l o c i t y v e c t o r . An e x p e r i m e n t a l model was developed  t o s e p a r a t e , as f a r as p o s s i b l e ,  the e f f e c t s o f the e x p e r i m e n t a l system from the d u a l - p o l a r i z e d p r o p a g a t i o n measurements. the comparisons discrimination  T h i s model s i g n i f i c a n t l y improves  between the observed (XPD).  p r e d i c t the atmospheric  and t h e o r e t i c a l l y p r e d i c t e d c r o s s p o l a r  t e c h n i q u e s and m e t e o r o l o g i c a l o b s e r v a t i o n s t o  propagation c o n d i t i o n s .  The model i n c o r p o r a t e s  a c t u a l measurements made of the e x p e r i m e n t a l system and reduces  b e h a v i o u r o f the system The experiment  dual-polarized  the u n c e r t a i n t y i n the r e s u l t s due t o t h e n o n i d e a l components.  was designed  d a t a was as a c c u r a t e and complete budget.  the a c c u r a c y o f  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 w e l l  e s t a b l i s h e d , b a s i c mathematical  performance,  atmospheric  t o ensure  the m i l l i m e t r e wave p r o p a g a t i o n  as p o s s i b l e w i t h i n t h e a v a i l a b l e time and  These d a t a should be u s e f u l t o improve the b a s i c u n d e r s t a n d i n g of  the e f f e c t s o f the m i l l i m e t r e components and atmosphere ( e s p e c i a l l y d u r i n g r a i n ) on m i l l i m e t r e - w a v e  systems employing  atmospheric  propagation.  r e s u l t s s h o u l d a l s o 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 b a s i c p r e d i c t i o n methods. a l r e a d y known about  In summary, t h i s  experiment  theoretical  s h o u l d add t o what i s  d u a l - p o l a r i z e d and m i l l i m e t r e wave systems and improve  the a c c u r a c y of the p r e d i c t e d performances atmospheric  These  propagation.  of a v a r i e t y  of systems  employing  26  2.  MILLIMETRE-WAVE EXPERIMENTAL SYSTEM  The dual-polarized millimetre-wave system used for i n v e s t i g a t i n g atmospheric propagation c h a r a c t e r i s t i c s at 73.5  GHz used switched-  p o l a r i z a t i o n sampling and b a s i c a l l y consisted of a CW transmitter, and two channel r e c e i v e r .  radar path  A radar path was chosen because of the operational  advantages of l o c a t i n g the transmitter and receiver i n the same laboratory. Identical parabolic antennas with d u a l - p o l a r i t y feeds were used f o r transmitting and r e c e i v i n g .  Dual-polarization propagation measurements were  made by p e r i o d i c a l l y switching the transmitted signal between v e r t i c a l and horizontal p o l a r i z a t i o n s .  The two-channel receiver continually monitored  both l i n e a r p o l a r i z a t i o n s .  This resulted i n each received channel  representing a time multiplexed sample of one copolar and one crosspolar signal l e v e l .  2.1  The basic system i s shown i n F i g .  2.1.  Comparison of Dual-Polarization Measurement Methods The basic measurement methods which can be used to study l i n e a r d u a l -  p o l a r i z a t i o n propagation employ either a two-frequency dual-polarized t r a n s mitted signal or a switched-polarization transmitted s i g n a l .  In the d u a l -  frequency method, either two s l i g h t l y d i f f e r e n t frequencies - which are  close  enough to be considered as propagating i d e n t i c a l l y - or two d i f f e r e n t modulation frequencies on a common c a r r i e r frequency are transmitted with perpendicular p o l a r i z a t i o n s .  In the receiving subsystem, frequency  selective  c i r c u i t s i n both p o l a r i z a t i o n channels separate the frequencies corresponding to each o r i g i n a l l y transmitted p o l a r i z a t i o n .  This method y i e l d s four  TRANSMITTING SOURCE  27  POLARIZATION CONTROL  DEMULTIPLEXING SIGNAL REFLECTOR  VERTICAL COPOLAR SIGNAL  VERTICAL CROSSPOLAR SIGNAL  HORIZONTAL COPOLAR SIGNAL  HORIZONTAL CROSSPOLAR SIGNAL  VERTICAL TRANSMITTED POLARIZATION  HORIZONTAL TRANSMITTED POLARIZATION  -*. TIME  F i g . 2.1. B a s i c m i l l i m e t r e - w a v e  experimental  system.  28  simultaneous  s i g n a l s each c o r r e s p o n d i n g t o one  p o l a r i z a t i o n transmission matrix.  element of the d u a l -  In the s w i t c h e d - p o l a r i z a t i o n method, the  t r a n s m i t t e d s i g n a l i s s e q u e n t i a l l y switched between v e r t i c a l and p o l a r i z a t i o n and polarizations.  a two-channel r e c e i v e r c o n t i n u a l l y monitors The  s w i t c h i n g r a t e i s designed  matrix  both r e c e i v e d  to be h i g h e r than the  r e s o l u t i o n of the m e t e o r o l o g i c a l measuring equipment. received signals  horizontal  must be d e m u l t i p l e x e d t o determine  temporal  With t h i s system, the the f o u r t r a n s m i s s i o n  elements. The  s w i t c h e d p o l a r i z a t i o n scheme was  because of i t s implementation  advantages.  chosen f o r t h i s The  experiment  d u a l - f r e q u e n c y schemes r e q u i r e  e i t h e r two  s e p a r a t e t r a n s m i t t i n g s i g n a l s o u r c e s , or h i g h - l e v e l  circuits.  I f the two-source method i s used, e i t h e r the sources have to be  phase-locked  to each o t h e r or the r e c e i v e r must i n c l u d e two  l o c a l o s c i l l a t o r s , one h i g h l e v e l modulators  f o r each t r a n s m i t t i n g s o u r c e . i s used,  two  frequency  modulation  phase-locked  I f a s i n g l e source  with  s e l e c t i v e c i r c u i t s f o r each  r e c e i v e d channel are needed. It  i s very d i f f i c u l t  to r e a l i z e f r e q u e n c y 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 w i t h the h i g h i s o l a t i o n and dynamic range r e q u i r e d f o r t h i s of  experiment.  Because complex f i l t e r s a r e not f e a s i b l e a t m i l l i m e t r e  f r e q u e n c i e s , f i l t e r i n g would have to be done a t an i n t e r m e d i a t e (IF)  type  or baseband.  Filtering  at IF i s p o s s i b l e but s o p h i s t i c a t e d f i l t e r s must  be employed to a c h i e v e the n e c e s s a r y e a s i e r to b u i l d but  frequency  signal isolation.  Baseband f i l t e r s  the l a r g e dynamic range of the s i g n a l s puts  c o n s t r a i n t s on the e n t i r e r e c e i v i n g  system l i n e a r i t y ,  are  tight  (nonlinearities  before  the baseband f i l t e r s would produce i n t e r m o d u l a t i o n 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).  D u a l - f r e q u e n c y schemes a l s o r e q u i r e f o u r s i g n a l l e v e l measuring subsystems t o filter,  average, d e t e c t  and d i g i t i z e  the r e c e i v e d a m p l i t u d e s .  The switched  p o l a r i z a t i o n method r e q u i r e s a p o l a r i z a t i o n s w i t c h i n g  circuit  s i n g l e t r a n s m i t t i n g 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  received  s i g n a l l e v e l measuring subsystems a r e n e c e s s a r y .  but uses o n l y a two  The advantages o f  reduced c o m p l e x i t y and c o s t made the switched p o l a r i z a t i o n method f a r more desirable i n this  experiment.  2.2  System  Transmitting The  t r a n s m i t t i n g system b l o c k diagram i s shown i n F i g . 2 . 2 .  system c o n s i s t s of a k l 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 s u p p l y , frequency reference  coupler,  power l e v e l m o n i t o r , c a l i b r a t e d  The  isolators,  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 s w i t c h .  2.2.1  K l y s t r o n and Supply The  t r a n s m i t t i n g s i g n a l i s generated by a V a r i a n model 2101B  klystron oscillator.  The k l y s t r o n power supply  reflex  c i r c u i t s , c o o l i n g system and  l o a d i s o l a t o r were d e s i g n e d t o minimize i n c i d e n t a l f r e q u e n c y m o d u l a t i o n and t r a n s i e n t s i n the tube output. s e n s i t i v i t y Is not impaired  T h i s i s important to ensure t h a t the system  and that the r e l i a b i l i t y of the phase l o c k system  i s not reduced. The  k l y s t r o n i s extremely s u s c e p t i b l e to f r e q u e n c y modulation of i t s  output by induced v o l t a g e s changes i n l o a d impedance.  on i t s power l e a d s , s t r a y magnetic f i e l d s or For example, the modulation s e n s i t i v i t y of the  ©  0 X  ** CALIBRATED ATTENUATOR  FREQUENCY REFERENCE  WR-28 U/P—9ft FEEDLINE AND WR-I5/WR-28 ADAPTERS  >  POLARIZATION SWITCH  S IOLATORS  TO ANTENNA ORTHOMODE TRANSDUCER  t  KLYSTRON POWER SUPPLY  PRESSURATION TO RECEIVING SYSTEM  1  I p  POWER METER  TO DATA AOUISITION SYSTEM  F i g . 2.2. T r a n s m i t t i n g  system b l o c k  diagram.  o  31  tube r e f l e c t o r voltage i s approximately 3 MHz/V. I n c i d e n t a l power l i n e frequency modulation on the k l y s t r o n 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). K l y s t r o n frequency p u r i t y and s t a b i l i t y also a f f e c t the r e l i a b i l i t y of the r e c e i v e r phase lock c i r c u i t s (see Section 2.3.1). phase l o c k , r e a c q u i s i t i o n must be done manually.  If the r e c e i v e r loses  Because the experiment i s  often operated unattended, l o s s of phase lock can r e s u l t i n long periods l o s t data.  of  Loss of lock occurs when the change i n the k l y s t r o n frequency  exceeds the r e c e i v e r phase locked loop h o l d - i n range or t r a c k i n g r a t e .  This  u s u a l l y occurs on a t r a n s i e n t c o n d i t i o n caused by a power l i n e t r a n s i e n t , thermal t r a n s i e n t or "micro-arc"  w i t h i n the k l y s t r o n tube.  Micro-arcs  unavoidably occur w i t h i n tubes of t h i s type because the extremely small c a v i t i e s required f o r m i l l i m e t r e frequencies between tube elements.  r e s u l t i n high f i e l d p o t e n t i a l s  I f frequency modulation i s also present on the  k l y s t r o n s i g n a l , the receiver's a v a i l a b l e lock range and a b i l i t y to track t r a n s i e n t frequency changes i s reduced because the phase locked loop must a l s o track the p e r i o d i c frequency modulation. The k l y s t r o n power supply c i r c u i t i s shown i n F i g . 2.3. Z815C  k l y s t r o n supply was  filament supply.  The Weinschel  chosen because i t has a h e a v i l y f i l t e r e d dc  Low r i p p l e on k l y s t r o n 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 k l y s t r o n 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  t r a n s i e n t frequency excursion and help prevent i n t e r n a l p i t t i n g of the tube  REF 1  ARC SUPPRESSION NETWORK IK 2W  CATH  •A/VvV— VRE 2101 B  -1 lu WEINSCHEL 7 815 C KLYSTRON POWER SUPPLY  FILI+)  l__  ._l  FILH  BEAM  WHITE  Voltages: Reflector 1 Beam Filament  640 V 2500 V 6.3 V  F i g . 2.3. K l y s t r o n power s u p p l y  circuit,  33  elements during a r c i n g .  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 d i s c o n t i n u i t i e s i n the damaged area.  With the voltages shown i n F i g . 2.3  the  measured klystron output was 470 mW. The k l y s t r o n i s mounted on a large aluminum heat sink (Varian model VAE-2000C/2) which i s cooled by a 100 cfm blower.  The blower i s mounted  approximately one metre from the klystron and the a i r flow i s directed to tube v i a a section of 10 cm diameter f l e x i b l e p l a s t i c tubing.  the  This was  necessary to prevent modulation of the klystron output by induced 60 Hz currents and f i e l d s from the blower motor. An i s o l a t o r  i s included a f t e r the klystron because i t was observed  that even with the i s o l a t i o n provided by the feedline loss and with a measured feedline VSWR of less than 1.2:1, the klystron frequency s h i f t e d approximately 200 kHz when the p o l a r i z a t i o n was switched.  This was due to  frequency p u l l i n g as a result of small changes i n the load impedance presented to the klystron i n the d i f f e r e n t p o l a r i z a t i o n switch s t a t e s . step change i n frequency occasionally caused the receiver phase-lock to lose l o c k .  This  system  With the i s o l a t o r i n the c i r c u i t no frequency p u l l i n g could be  measured.  2.2.2  Reference  Signals and Calibrated Attenuator  The power l e v e l and operating frequency of the klystron were continually recorded to ascertain that these quantities did not d r i f t during data a c q u i s i t i o n .  The frequency reference signal i s derived from a 20 dB  d i r e c t i o n a l coupler and i s used to phase lock the receiving system to the  34  transmitted s i g n a l .  Frequency monitoring of the k l y s t r o n i s accomplished  I n d i r e c t l y by recording the receiver  l o c a l o s c i l l a t o r frequency, a multiple  of which was phase locked to the k l y s t r o n frequency. d e t a i l i n Section 2 . 3 . 4 .  The l e v e l reference  This i s explained i n  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  s i g n a l from the power meter i s connected to one of the analog Inputs of the data a c q u i s i t i o n system. A c a l i b r a t e d rotary vane attenuator i s permanently mounted i n the path of the transmitting s i g n a l 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 i s used to carry the klystron s i g n a l from the  laboratory up one f l o o r to the roof where the p o l a r i z a t i o n switch was l o c a ted.  The p o l a r i z a t i o n 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 t h e o r e t i c a l and measured attenuation of this oversize waveguide was lower than f o r the WR-15 waveguide used elsewhere i n 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 s p e c i f i e d i n [ 2 . 1 ] .  This discrepancy i s l i k e l y due to increased corrosion on the i n t e r i o r waveguide w a l l s .  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 d i r e c t i o n a l  coupler i n s t a l l e d so that the incident wave was coupled to the i n t e r n a l coupler termination, as shown i n F i g .  2.2.4 2.2.4.1  2.2.  P o l a r i z a t i o n Switching Comparison of P o l a r i z a t i o n Switching Methods Accurate measurement of crosspolarization propagation parameters i n  t h i s frequency range requires very high p o l a r i z a t i o n i s o l a t i o n and measuring system s e n s i t i v i t y .  The p o l a r i z a t i o n switch i s o l a t i o n and i n s e r t i o n loss  d i r e c t l y degrade t o t a l system i s o l a t i o n and s e n s i t i v i t y .  Switching methods  were evaluated by trading-off switch i s o l a t i o n and i n s e r t i o n loss cost and d e l i v e r y time.  against  Three basic switching schemes were compared:  Faraday r o t a t i o n , waveguide junction with absorptive single-pole single-throw (SPST) switches and single pole double-throw (SPDT) switches. are shown schematically i n F i g .  These methods  2.4.  Faraday rotation i n a section of c y l i n d r i c a l waveguide provides the most d i r e c t method of p o l a r i z a t i o n switching.  Linear p o l a r i z a t i o n rotation  i s controlled by varying the dc current through a c o i l which changes the magnetization of the f e r r i t e element i n the waveguide. i s the TRG-V145.  A device of this type  Unfortunately, this type of p o l a r i z a t i o n switch is not  applicable to this experiment because i t has only 20 dB crosspolarization isolation.  Additional i s o l a t i o n cannot be obtained by cascading because each  section would result i n a further ninety degree p o l a r i z a t i o n r o t a t i o n .  36 FARADAY ROTATION POLARIZATION SWITCH  RECTANGULAR TO CIRCULAR WAVEGUIDE ADAPTER  (a) Faraday  rotation  (b) J u n c t i o n w i t h a b s o r p t i v e SPST  (c) DPDT s w i t c h  F i g . 2.4. P o l a r i z a t i o n  s w i c h i n g methods.  switches  37  The other two basic methods, shown i n F i g . 2.4(b) and 2 . 4 ( c ) , u t i l i z e an orthomode transducer.  An orthomode transducer i s a passive r e c i p r o c a l  waveguide junction with one c i r c u l a r and two rectangular waveguide p o r t s .  A  signal with a r b i t r a r y p o l a r i z a t i o n entering the c i r c u l a r waveguide w i l l be resolved i n t o two orthogonal p o l a r i z a t i o n components which w i l l leave the junction through the rectangular ports.  Because the junction i s r e c i p r o c a l ,  i f signals are applied to the rectangular ports they w i l l leave the junction v i a the c i r c u l a r port but with orthogonal l i n e a r p o l a r i z a t i o n s .  Standard  orthomode transducers i n t h i s frequency range w i l l have losses below 1 dB and i s o l a t i o n s of 30-35 dB. Both of these schemes achieve p o l a r i z a t i o n switching by sequentially applying the transmitting signal to either the v e r t i c a l or h o r i z o n t a l port on the orthomode transducer. Fig.  2.4(b) because,  SPST switches are used i n the method shown i n  i n 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 s p l i t t e r (either a " T " junction or a 3 dB hybrid) r e s u l t i n g i n only half the available signal being applied to the antenna.  The switches must be absorptive to avoid r e f l e c t i o n s at one port of  the waveguide junction when the switch i s i n the o f f s t a t e . PIN diode switches with i s o l a t o r s and Faraday rotation attenuators were considered for the absorptive SPST switches.  Isolators are required  with the diode switches because they are unmatched i n the o f f s t a t e . t y p i c a l PIN diode switch i s the Hughes 47974VA-1000.  A  This single diode  switch has a 2.5 dB i n s e r t i o n loss and only 15 dB i s o l a t i o n .  Cascading three  similar switch sections would provide adequate i s o l a t i o n s but would also  38  y i e l d an unacceptably high i n s e r t i o n l o s s . off  Faraday attenuators achieve on-  attenuation by rotation of the waveguide p o l a r i z a t i o n either p a r a l l e l , or  perpendicular t o , a r e s i s t i v e attenator card.  A device of this type,  the  TRG-V120 has a 10 ys switching time, 1.4 dB i n s e r t i o n loss and 40 dB isolation. The only available type of SPDT switch i n this frequency range i s an electromechanical waveguide switch.  These switches use a solenoid to  p h y s i c a l l y 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 i s s p e c i f i e d at 50 dB i s o l a t i o n and 0.7  dB i n s e r t i o n l o s s . The most suitable schemes for p o l a r i z a t i o n switching i n t h i s  experiment used either the Faraday rotation attenuators and waveguide s p l i t t e r or the SPDT electromechanical waveguide switch. the f i r s t method would be at l e a s t 4.4 SPDT switch.  Insertion loss i n  dB compared to only 0.7  The i s o l a t i o n of the Faraday attenuators was also only 40 dB  compared to 50 dB for the second method.  A f i n i t e l i f e s p a n r e s u l t i n g from  mechanical wear appeared to be the only disadvantage of the switch.  dB for the  electromechanical  The SPDT electromechanical waveguide switch was chosen for this  experiment because of i t s superior s p e c i f i c a t i o n s , considerably lower cost and shorter quoted delivery time.  2.2.4.2  P o l a r i z a t i o n Switch Specifications and Testing A summary of the e l e c t r i c a l s p e c i f i c a t i o n s of the Systron-Donner model  DBB-614-LE2 waveguide switch used i n this experiment are given i n Table  2.1.  39  TABLE 2.1  DBB-614-LE2 Electromechanical DPST Waveguide Switch S p e c i f i c a t i o n s .  Insertion loss VSWR Isolation Switching time Operating l i f e s p a n  0.7 dB 1.15 50 dB min 30 ms 100 000 cycles min. 250 000 cycles typ. 28 VDC @ 50 W  Solenoid power  Measurements were made on the waveguide switch at 73.5  GHz to v e r i f y  i t s specifications.  The measured Insertion loss of the switch was below 0.7  dB i n either s t a t e .  Isolation between output ports was measured to be  between 75 and 80 dB.  2.2.4.3  P o l a r i z a t i o n Switch Subsystem The waveguide switch, i n t e g r a l power supply, and switching c i r c u i t  were assembled i n a waterproof steel enclosure and mounted adjacent to the transmitting antenna.  The schematic diagram of the p o l a r i z a t i o n switch  subsystem i s shown i n F i g . 2.5.  A photograph showing the i n t e r n a l layout and  construction i s included as F i g . 2.6. the power transistor  Referring to F i g . 2.5,  the purpose of  switch i s to reduce the current which must be remotely  switched to control the switch solenoid.  A non-resetable  electromechanical  counter i s 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 i s controlled by a control unit located near the data a c q u i s i t i o n e l e c t r o n i c s .  The schematic of the control unit i s shown i n  120 v AC 0UT0OOH BULKHEAD  OUTPUTS TO TRANSMITTING ANTENNA ORTHOMODE TRANSDUCER.  HAMMOND HPFS 2B 020 POWER SUPPLY 2 8 v © 2.0 A  INPUT FROM FEEDLINE  ELECTROMECHANICAL COUNTER 6 v COIL  -w-  CONTROL . SIGNAL >INPUT (FROM CONTROL UNIT)  - 2N3  COAXIAL CONNECTORS ARE TYPE-N BULKHEAD JACKS  POLARIZATION SWITCH STATUS ITO IF ATTENUATORS IN FRONT END)  SEALED ENCLOSURE  F i g . 2.5. P o l a r i z a t i o n  s w i t c h subsystem  schematic.  4 1  F i g . 2.6.  P o l a r i z a t i o n switch subsystem photograph.  42  Fig.  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, 10 s, 15 s, 20 s, 30 s,  1 rain. 1 min. and 4 min.  2 s, 5 s,  An LED i s provided to give  a v i s u a l i n d i c a t i o n of the switch status i n any mode.  A status signal i s  supplied for input to the data a c q u i s i t i o n system so the status of the p o l a r i z a t i o n switch can be recorded and subsequently used as a data demultiplexing s i g n a l . Isolators are i n s t a l l e d between the outputs of the p o l a r i z a t i o n 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 i s not connected to the input port.  Without the i s o l a t o r , a reactive  immittance  would be presented to the unused port on the transmitting antenna orthomode transducer.  This was found to seriously degrade the p o l a r i z a t i o n provided by  the orthomode transducer.  I n i t i a l measurements made without the Isolators  indicated that the t o t a l system p o l a r i z a t i o n i s o l a t i o n was extremely frequency sensitive and was degraded by as much as 5 to 15 dB, depending on the angle of the r e f l e c t i o n c o e f f i c i e n t presented to the orthomode transducers.  2.2.5  This effect i s discussed further i n Sections 2.5  and 5 . 5 . 2 .  Signal Levels i n 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  i d e n t i f i e d by l e t t e r s 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  T r a n s m i t t i n g System S i g n a l  REF Fig.  LOCATION  Klystron  Output  After Klystron Input to  Isolator  Feedline  Input to P o l a r i z a t i o n  Switch  26.7  B  25.3  C  23.0  D  13.5  8.4  Input to H o r i z o n t a l Ant. P o r t  8.5  i s 2 dB  difference  corrected  noted t h a t  polarizations,  dB  and  20  respectively.  insertion loss, feed-line s t r a i g h t WR-15  dB  waveguide.  antenna p o r t s .  This  waveguide  This  difference  analysis. to the  for horizontal  antenna p o r t s i s  and  T h i s i s m a i n l y due  l o s s and Up  s i g n a l transmitted with  number of bends of the  s i g n a l l o s s from the k l y s t r o n  a p p r o x i m a t e l y 18  the  h i g h e r than f o r v e r t i c a l p o l a r i z a t i o n .  i n l e n g t h s and  f o r during data  6.5  H  i t should be  polarization  to the  The  A  V e r t i c a l Output of P o l a r i z a t i o n Switch  needed to connect the waveguide s w i t c h and was  2.2  10.1  From T a b l e 2.2  i s due  out (dBm)  r  H o r i z o n t a l Output of P o l a r i z a t i o n Switch  Input to V e r t i c a l Ant. P o r t  horizontal  Levels  the  to 8 dB  vertial  to u n a v o i d a b l e component  t y p i c a l 2 dB/m c o u l d be  transmitted  insertion loss  g a i n e d i f the k l y s t r o n  of and  45  power supply were mounted on the roof I n proximity to the t r a n s m i t t i n g antenna.  This was not done because of the d i f f i c u l t i e s of p r o v i d i n g adequate  s h e l t e r f o r these components.  2.3  Receiving System The b a s i c components of the two-channel dual-conversion r e c e i v i n g  system are the millimetre-wave front-end, phase locked r e c e i v e r and d i g i t a l s i g n a l l e v e l measurement u n i t s .  A block diagram i s shown i n F i g . 2.8. Down-  conversion of the 73.5 GHz s i g n a l to the f i r s t IF frequency i s accomplished i n the millimetre-wave front-end.  To reduce s i g n a l l o s s , the front-end i s  mounted adjacent to the r e c e i v i n g antenna.  The r e c e i v e r generates the  fundamental phase-locked l o c a l o s c i l l a t o r s i g n a l and l i n e a r l y converts the f i r s t IF s i g n a l to the second IF frequency.  Local o s c i l l a t o r s i g n a l s and  f i r s t IF s i g n a l s are c a r r i e d between each channel of the f r o n t end and r e c e i v e r on a common c o a x i a l c a b l e .  The second IF s i g n a l output from the  r e c e i v e r 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 u n i t s . data a c q u i s i t i o n  2.3.1  This d i g i t a l , data i s then i n t e r f a c e d to the  system.  Receiver The r e c e i v e r used i n t h i s experiment i s a S c i e n t i f i c A t l a n t a model  1751 which was a v a i l a b l e i n the E l e c t r i c a l Engineering Department.  This  r e c e i v e r I s not i d e a l l y suited f o r the m i l l i m e t r e 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  DIGITAL AMPLITUDE DISPLAY UNIT  FROM RECEIVING ANTENNA ORTHOMODE TRANSDUCER  MM WAVE VERTICAL INPUT MM WAVE HORIZONTAL INPUT  PI I  | DUAL CHANNEL FRONT ENO  DUAL CHANNEL RECEIVER  VERTICAL SIGNAL DIGITAL DATA  , TO DATA > AOUISITION SYSTEM  SECOND IF SIGNALS  DIGITAL AMPLITUDE DISPLAY UNIT  HORIZONTAL SIGNAL ' DIGITAL DATA  Fig. 2.8. Receiving system block diagram.  4>  47  were not  s e r i o u s enough to j u s t i f y the purchase or c o n s t r u c t i o n  of  a l t e r n a t i v e equipment. Fig.  2.9  i s a s i m p l i f i e d b l o c k diagram of the model 1751  adapted from the r e c e i v e r manual.  The  the a s p e c t s of the r e c e i v e r o p e r a t i o n system o p e r a t i o n . predetection  The  r e c e i v e r was  bandwidth i n o r d e r  l o c a l o s c i l l a t o r has f o r frequency d r i f t  s i g n a l to the APC  to improve s e n s i t i v i t y .  GHz  T h i s 73 GHz  t h i s method the f i r s t  acquire  w i t h i n a few search  and  e x t e r n a l two  t h i s reason  transmitted  The  the  s i g n a l to c o r r e c t signal.  input  to  first  as the  which s u p p l i e s an  channel-front  end. MHz  By the  oscillator.  phase l o c k , the r e c e i v e r LO must be manually tuned  k i l o h e r t z of the l o c k e d  frequency.  T h i s l a c k of  To h e l p  d a t a w i l l be  to  automatic  a c q u i s i t i o n means t h a t i f the r e c e i v e r l o s e s l o c k due  r e c e i v e r i s manually r e l o c k e d .  LO  The  IF i n both s i g n a l channels i s m a i n t a i n e d e x a c t l y at reference  The  local  channel i s compared to the 45  t r a n s i e n t frequency change or l o s s of power, no the  (BWO)  and  to generate the e r r o r s i g n a l a p p l i e d to the BWO.  f r e q u e n c y of the 45 MHz To  For  s i g n a l i s the RF  backward wave o s c i l l a t o r  harmonic mixer and  oscillator  design  small e f f e c t i v e  t o the t r a n s m i t t e d  channel e x t e r n a l m i x e r .  phase of the I F s i g n a l from the APC reference  explain  s i g n a l i s a sample of the k l y s t r o n output  i n S e c t i o n 2.2.2.  i s a 2-4  designed with a very  i n both the l o c a l o s c i l l a t o r and  automatic phase c o n t r o l (APC) oscillator  to h e l p  r e l e v a n t to the f r o n t - e n d  t o be phase l o c k e d  millimetre-wave reference described  diagram i s i n c l u d e d  receiver  to a  recorded  reduce d a t a l o s s due  until  to t h i s  and  FIRST IF AMPLIFIERS  SECOND IF AMPLIFIERS  F i g . 2.9. R e c e i v e r b l o c k diagram. oo  49  o t h e r 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 l a r m system i s connected t o the t e l e p h o n e  lines.  A f t e r a m p l i f i c a t i o n i n t h e 45 MHz f i r s t  I F a m p l i f i e r , the s i g n a l i s  c o n v e r t e d by the i n t e r n a l second m i x e r and c r y s t a l - c o n t r o l l e d t h e 1 kHz second IF f r e q u e n c y .  second LO to  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 t o an i n t e r n a l a n a l o g a m p l i t u d e m e t e r i n g system and r e c e i v e r o u t p u t j a c k s . i n p u t t o the d i g i t a l  The 1 kHz second IF output i s  the  amplitude measuring u n i t s .  T h i s r e c e i v e r was d e s i g n e d to be used w i t h harmonic m i x e r s s i m i l a r t o 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 m i x e r s have a waveguide RF  i n p u t p o r t and a s i n g l e c o a x i a l c o n n e c t i o n t o t h e m i x e r d i o d e t o s u p p l y LO s i g n a l and remove the IF s i g n a l .  the  T h i s s i n g l e c o a x i a l c o n n e c t i o n to the  m i x e r r e d u c e s the c o a x i a l c a b l e r e q u i r e m e n t s and i s a d e f i n i t e advantage when the m i x e r s a r e l o c a t e d some d i s t a n c e from the  2.3.1.1  Receiver  receiver.  Specifications  A summary of the r e l e v a n t model 1751 r e c e i v e r  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  are g i v e n i n Table 2 . 3 .  50  TABLE 2.3  S c i e n t i f i c Atlanta Model 1751 Receiver Specifications  Local o s c i l l a t o r frequency  2 - 4 GHz  Local o s c i l l a t o r power output  16 dBm  F i r s t IF frequency  45 MHz 1 kHz  Second IF frequency  60 dB  Dynamic range*  ± 0 . 2 5 dB for 60 dB  Linearity*  45 MHz IF s i g n a l range greater than -110 dBm. * With S c i e n t i f i c Atlanta Model 13 series mixers.  No s p e c i f i c a t i o n s 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 r e c e i v e r .  When used alone,  the receiver e f f e c t i v e predetection bandwidth i s e s s e n t i a l l y l i m i t e d 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 u n i t s , second IF f i l t e r s i n these units determine the o v e r a l l receiver predetection bandwidth.  2.3.2  D i g i t a l Amplitude Measurement Units The S c i e n t i f i c 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 i n this unit l i m i t the entire receiver  bandwidth to 30 Hz.  predetection  For this experiment the s i g n a l averaging time was  51  selected to be 1 second.  The amplitude of the s i g n a l i s 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 i s interfaced to the data a c q u i s i t i o n system i n binary coded decimal (BCD) format,  2.3.3 2.3.3.1  Two-Channel Front-End Basic Mixer Considerations Measurement of dual p o l a r i z a t i o n propagation phenomena near 73 GHz  required a more sophisticated front-end than could be supplied by the receiver manufacturer.  Single p o l a r i z a t i o n measurements at this frequency  over the same radar path with larger antennas and using the S c i e n t i f i c 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 l e v e l above the  indicated noise l e v e l .  Due to a reduction i n receiver l i n e a r i t y at low  signal l e v e l s the useful measurement range may have been closer to 35 dB f o r that system. constraints  For this d u a l - p o l a r i z a t i o n propagation experiment, economic dictated the use of smaller diameter antennas.  The clear weather  crosspolar signal l e v e l was also estimated to be about 40 dB below the copolar signal l e v e l using these antennas.  For these reasons considerably  more front-end s e n s i t i v i t y was required to provide an acceptable p o l a r i z a t i o n measurement  dual-  range.  S c i e n t i f i c Atlanta had produced a superior V-band mixer c a l l e d 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 l o s s .  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 local oscillator  The modified model 17-50-45 mixer has a 7-8 the model 13A-50.  power a m p l i f i e r .  dB increase i n s e n s i t i v i t y over  Modifications and test results of this mixer  documented i n [ 2 . 4 ] .  are  Preliminary d u a l - p o l a r i z a t i o n measurements with t h i s  mixer showed that i t s s e n s i t i v i t y was not adequate.  For these reasons the  decision was made to design a completely new two-channel front-end. The front-end c i r c u i t configuration evolved from design constraints imposed by cost and the available r e c e i v e r .  In the frequency range of  i n t e r e s t , low noise signal a m p l i f i c a t i o n requires p r o h i b i t i v e l y expensive maser or parametric a m p l i f i e r s .  For t h i s reason the incoming RF s i g n a l from  the antenna i s d i r e c t l y converted down to the 45 MHz IF frequency. f e a s i b i l i t y of employing fundamental mixers i n the front-end was because conversion losses of under 10 dB are achievable.  The investigated  Three possible  schemes for generating the fundamental l o c a l o s c i l l a t o r 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 s i g n a l to an IF i n the low GHz range. be  After a m p l i f i c a t i o n , this IF s i g n a l would  mixed with the receiver phase-locked LO to produce a second IF s i g n a l  compatible with the receiver.  (With this scheme the receiver phase locked  loop would have to track frequency changes i n both k l y s t r o n s , r e s u l t i n g 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 m u l t i p l i c a t i o n of the receiver BWO.  53  Unfortunately  none of these a l t e r n a t i v e s came c l o s e to being  the budgetary c o n s t r a i n t s of t h i s p r o j e c t . front-end  2.3.3.2  was  within  two-channel  d e s i g n e d around harmonic m i x e r s .  Front-End C i r c u i t The  As a r e s u l t , the  possible  two-channel 73.5  s e n s i t i v e as e c o n o m i c a l l y  Description GHz  receiver front-end  p o s s i b l e , provide  was  d e s i g n e d to be  as  identical signal transfer  c h a r a c t e r i s t i c s on each c h a n n e l , have h i g h c h a n n e l - t o - c h a n n e l i s o l a t i o n w i t h the S c i e n t i f i c A t l a n t a 1751  operate i n conjunction the  i d e n t i c a l front-end  receiver.  -Each of  channels c o n s i s t s b a s i c a l l y of a harmonic m i x e r ,  i s o l a t o r , mixer b i a s c i r c u i t , l o c a l o s c i l l a t o r c h a i n , IF p r e a m p l i f i e r , d i p l e x e r and  d i g i t a l l y programmable IF  2.10.  A more d e t a i l e d drawing of one  p o r t impedances and a m p l i f i e r and  harmonic-number and and  LO  noise  i s incorporated  hence c o n v e r s i o n  loss.  The  optimum mixer performance i s s u p p l i e d two-channel f r o n t - e n d and  An  s i g n a l s t o t h e i r common c o a x i a l c a b l e . IF p r e a m p l i f i e r i s i n c l u d e d .  and  power supply  i s mounted i n c l o s e p r o x i m i t y  signal attenuation.  i s shown In  channel which shows p a r t  s i g n a l l e v e l s Is shown i n F i g . 2.11.  frequency t r i p l e r  IF  attenuator.  A b l o c k diagram of the complete two-channel f r o n t - e n d Fig.  and  A local  to reduce the  numbers,  oscillator  mixing  IF d i p l e x e r i n t e r f a c e s the  IF  To improve s e n s i t i v i t y , a  low-  mixer b i a s c u r r e n t  required  by the mixer b i a s c i r c u i t s . i s enclosed  for The  entire  i n a waterproof housing  to the r e c e i v i n g antenna to minimize the  A photograph of the IF/LO d i p l e x e r s , LO  f r e q u e n c y m u l t i p l i e r s i s shown i n F i g . 2.12.  amplifiers  A photograph of the  RF  and  two-channel  2-4 OHZ  5.3 GHZ  BANDPASS FILTER  POWER AMPLIFIER  MULTIPLIER  LF.  ponxi or  INJECTION AND MATCHINO  L  45 MHZ  DIGITALLY PROGRAMMABLE I.F. ATTENUATOR  IF. PREAMPLIFIER  0  .Fi  ISOLATOR  MIXER I  nil  k«-  «TTCtlU»TOl CONTROL  >4-< k<—>H RX2 PORT  1.3 OHZ  2-4 GHZ  XJ  BANDPASS FILTER  POWER AMPLIFIER  MULTIPLIER  IF. INJECTION A NO MATCHING  LO _ MIXER 2*^1  DIGITALLY PROGRAMMABLE I.F. ATTENUATOR  I.F. PREAMPLIFIER  >f-«-  « « M MONITOR  COAXIAL CONNECTORS ARE TVPE-tN 8ULKHEA0 JACKS  117 VAC  POWER SUPPLY  IZO VAC OUTDOOR BULKHEAD  MIXER I  MIXER 2  SEALED ENCLOSURE  Fig; 2.10. Complete front-end diagram.  J 1  ISOLATOR  rt  50 n 3.5 GHz 50 A 4 5 MHz  a  3.5 GHz BANDPASS FILTER 3 % BANDWIDTH (MICROSTRIP ON TEFLON)  IF INJECTION AND MATCHING NETWORK (MICROSTRIP ON TEFLON)  AVANTEK APT-4013 THIN FILM 2 - 4 GHz POWER AMPLIFIER  AIG CUSTOM VARACTOR X3 FREQUENCY MULTIPLIER  ^ 50 <<? 10.5 GHz  JTL  un  10 MW 10.5 GHz  (a>  TRQ 922 v HARMONIC MIXER  PORT  so a  PROGRAMMABLE IF ATTENUATOR TEXSCAN PA-51  YIF  ANZAC AM 107 LOW NOISE 1-100 MHz AMPLIFIER  f5> 45 MHz BIAS  28vDC BIAS CONTROL CIRCUIT ATTENUATOR POWER SUPPLY  ALL  CONNECTORS SMA  T  ATTENUATOR CONTROL SIGNAL  MIXER BIAS MONITOR /IN. SIGNAL '  F i g . 2 . 1 1 . D e t a i l e d b l o c k diagram o f one c h a n n e l .  f  1  UG 385/U FLANGE  ANT. PORT  56  F i g . 2.12.  IF/LO d i p 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.  2.3.3.3  The complete front end i s shown i n F i g . 2.14.  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 mixers were: mixing.  The required characteristics  of  V-band RF signal range, 45 MHz IF frequency and harmonic  The two mixers which were seriously considered for this system were  the TRG 922-V and the Hughes 47434H-1000. conversion loss s p e c i f i c a t i o n s .  These two mixers have very s i m i l a r  The Hughes mixer, however, requires  s i g n i f i c a n t l y higher LO power for lowest conversion l o s s .  The Hughes mixer  incorporates a s i l i c o n Schottky b a r r i e r diode which i s not normallyreplaceable i n the f i e l d .  The TRG mixer uses a gallium-arsenide diode  mounted i n a f i e l d - r e p l a c e a b l e Sharpless wafer mount. satisfactory  IF frequency ranges.  Both mixers have  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  2.3.3.4  expensive.  Mixer Specifications  The s p e c i f i c a t i o n s 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 p r e a m p l i f i e r s and  attenuators.  59  F i g . 2.14.  Complete front-end.  60  TABLE 2.4  TRG-922-V Harmonic Mixer Specifications;  Conversion loss Harmonic number  21 10 9 8 7 6  Conversion loss  39-42 dB 28 dB 26 dB 24 dB 22-23 dB 18 dB  LO frequency LO power LO port Impedance LO/IF Isolation IF Bandwidth IF Port Impedance RF VSWR Bias Requirements Max. diode current  2.3.3.5  8.2-12.4 GHz 10 mw Typ. 50 fi 25 dB Min. 10 MHz to 500 MHz 50 fi 2:1 Typ. -0.7 V @ 2 mA Typ. 4 mA  IF/LO Diplexer IF/LO diplexers are required to interface the S c i e n t 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 i n j e c t i o n and to remove the IF s i g n a l . are constructed ports.  The TRG 922V mixers  i n the more common configuration employing separate LO and IF  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 o f r e c e i v i n g system and mixer c o n f i g u r a t i o n i s v e r y u s e f u l and t h i s type o f d i p l e x e r 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 n o t , to our knowledge, been d e s c r i b e d  elsewhere.  The d e s i g n o b j e c t i v e f o r the d i p l e x e r was a well-matched, l o w - l o s s c o n n e c t i o n between c o r r e s p o n d i n g p o r t s a t the I F and LO f r e q u e n c i e s . important  It i s  t o have a well-matched, l o w - l o s s c o n n e c t i o n between the I F  p r e a m p l i f i e r output p o r t and t h e r e c e i v e r LO/IF c a b l e because a mismatch o r l o s s a s s o c i a t e d w i t h t h i s c o n n e c t i o n w i l l reduce sensitivity.  A well-matched  the r e c e i v i n g  system  c o n n e c t i o n a t the LO f r e q u e n c y i s a l s o r e q u i r e d  t o ensure r e l i a b l e o p e r a t i o n of the r e c e i v e r l o c a l o s c i l l a t o r source and t o minimize  LO l o s s through  The  the c o a x i a l c o n n e c t i o n from  the r e c e i v e r .  l o c a l o s c i l l a t o r i n the r e c e i v e r i s o p e r a t e d a t approximately t h e  V-band s i g n a l f r e q u e n c y d i v i d e d by twenty-one, which, i n t h i s c a s e , i s 3.5 GHz.  Other  components of the system do not a l l o w o p e r a t i o n except  in a  narrow two o r t h r e e p e r c e n t bandwidth around the c e n t e r frequency of 73.5 GHz.  T h e r e f o r e , the IF/LO d i p l e x e r c i r c u i t f o r t h i s system i s r e q u i r e d t o  o p e r a t e o n l y over a s i m i l a r percentage the s p e c i f i c requirements (a)  bandwidth.  R e f e r r i n g t o F i g . 2.11,  o f the IF/LO d i p l e x e r a r e :  t o p r o v i d e a matched c o n n e c t i o n w i t h minimum l o s s from the r e c e i v e r p o r t to the LO m u l t i p l i e r c h a i n i n p u t over a bandwidth o f a few percent c e n t e r e d a t 3.5  GHz.  and (b)  t o p r o v i d e a minimum-loss, matched c o n n e c t i o n from the r e c e i v e r p o r t a t 45 MHz.  the I F s i g n a l p o r t to  62  The of  requirement  f o r minimum-loss c o n n e c t i o n s  a d i r e c t i o n a l c o u p l e r type network f o r LO  o f t e n employed i n IF/LO d i p l e x e r s . d i f f e r e n c e between the LO and  precludes  F o r t u n a t e l y , s i n c e the  IF i s l a r g e and  meet the network r e q u i r e m e n t s .  and i t s o p e r a t i o n v e r i f i e d The and  designed  heuristically  circuit  both r e a l i z e d i n m i c r o s t r i p . The  The  IF i n j e c t i o n  and  to p r o v i d e a l o w - l o s s , matched c o n n e c t i o n f o r  The LO bandpass f i l t e r  t h a t o n l y the d e s i r e d 3.5  GHz  s i g n i f i c a n t l o s s or mismatch to the  prevents  LO  l o s s to the IF s i g n a l and  LO  ensures  s i g n a l i s a p p l i e d to the power a m p l i f i e r .  o p e r a t i o n 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 .  can be e x p l a i n e d u s i n g c o n v e n t i o n a l t r a n s m i s s i o n l i n e a n a l y s i s .  i n p u t admittance at planes A-A  of the 25 fi open c i r c u i t  The  shunt s t u b s i s g i v e n  •  1  Y  A  "  TT  assuming n e g l i g i b l e  -jzLtg*  =  =  JVan * 3  w  h  e  r  e  - 25 0 ,  t r a n s m i s s i o n l i n e a t t e n u a t i o n and  from the o p e n - c i r c u i t t e r m i n a t i o n s . effectively in parallel. given  designed  analytically.  the IF s i g n a l to the r e c e i v e r w i t h o u t  by;  designed  components i s shown i n F i g . 2.11.  matching c i r c u i t was  2.15  c o u l d be  IF/LO d i p l e x e r c o n s i s t s of an IF i n j e c t i o n and matching  c o n n e c t i o n of these  The  frequency  because narrowband o p e r a t i o n i s  T h i s c i r c u i t was  a l o c a l o s c i l l a t o r bandpass f i l t e r  signal.  possibility  i n j e c t i o n o r IF removal, as i s  a c c e p t a b l e , a simple m i c r o s t r i p t r a n s m i s s i o n l i n e c i r c u i t to  the  The  negligible  At each node t h e r e are two  (2.1) radiation shunt  stubs,  combined admittance a t each node i s t h e r e f o r e  by Y  g  = 2Y  A  = j2Yj tan  U  (2.2)  r RX PORT TO RECEIVER  2.08  | | HH LO PORT TO 3.5 GHZ BANDPASS FILTER  (50 A)  t n  D  15.02  r 2I NODE 2  (25  n!  T 2.72  1  I A  ALL DIMENSIONS IN MILLIMETRES  r  CONNECTORS ARE SUA  (25 n)  T" 2.72  IF PORT TO MIXER IF PORT  F i g . 2.15. I F i n j e c t i o n and matching  circuit, LO  64  Each s t u b i s a q u a r t e r wavelength t r a n s m i s s i o n l i n e wavelength  l o n g a t the LO f r e q u e n c y .  a t 3.5 GHz Is d e s i g n a t e d  admittance YB a t a f r e q u e n c y , f , o r wavelength,  Ag o*  I f the  the  L  Xg, can be r e w r i t t e n  as:  = j . 0 8 t a n (-J  •  - ~ )  LO T h i s admittance appears i n p a r a l l e l w i t h the admittance l o o k i n g i n t o p l a n e CC, which w i l l be r e f e r r e d  to as Yt>  The t o t a l admittance a t node 1 i s  therefore: Y =  Y  3  c  Y  +  f  (2.4)  i  T h i s a d m i t t a n c e , Y3, w i l l be t r a n s f o r m e d 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 a l s o one q u a r t e r wavelength ^L0»  long a t  The admittance a t node 2 now becomes: Y_ + j .02 t a n ( J  I ) LO  J  = Y  Y  n  +  (2.5)  jr-  .02 .02 + j Y  4  tan (J |  ) LO  Finally,  l o o k i n g i n t o plane D-D  Y  A  the admittance i s :  + j.02 t a n {-} f T 2  f  Y  = .02 .02 + j  One of the problems admittance  A  ) (2.6)  J^J L  Y  4  tan  0  [j j ) LO  i n d e s i g n i n g the matching network i s t h a t Y  J F  ,  the  l o o k i n g i n t o the output p o r t of the I F a t t e n u a t o r , i s unknown i n  65  the v i c i n i t y of f ^ . LO T  J  Even i f the admittance Y , were known, the admittance IF TT  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 i n j e c t i o n and matching network must have  a very low s e n s i t i v i t y to the value of Y o  This i s accomplished i n part  by using low Impedance l i n e s for the shunt quarter-wave stubs. cies around f^o,  t  n  e  At frequen-  admittance YB w i l l be very large and thus w i l l  reduce the e f f e c t of Yc which appears i n 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 i s that,  regardless  of Yc, the admittance at node 2 i s l a r g e , ensuring the admittance at plane D-D i s s m a l l .  The very low admittance at plane D-D w i l l cause almost  no r e f l e c t i o n on the LO l i n e to the LO port at 3.5 GHz. To v e r i f y the operation of the IF Injection and matching c i r c u i t t h e o r e t i c a l l y , a computer program was written i n the BASIC language.  The  program was used to predict the VSWR on the l o c a l o s c i l l a t o r l i n e over the l o c a l o s c i l l a t o r frequency range of the r e c e i v e r . graphically i n F i g . ilO  2 5  The results are shown  2 . 1 6 . Different values of Yc between + j l 0  2 5  and -  mhos produced no s i g n i f i c a n t change i n 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 I F i n j e c t i o n and matching c i r c u i t on the 45 MHz IF signal can be analyzed i n the same manner up to plane D-D. In this case Y T F i s known to be approximately 50 ft at 45 MHz.  The difference i n the  67  a n a l y s i s a r i s e s when the e f f e c t of the impedance l o o k i n g to plane E-E a t 4 5 MHz  i s considered.  prevent  T h i s admittance,  I F s i g n a l mismatch.  bandpass f i l t e r  Y E , must be v e r y low a t 45 MHz  To ensure t h a t YR i s s m a l l , the 3.5  i s p l a c e d a t the output  of the LO  port.  t o p o l o g y d e s c r i b e d by Cohn [ 2 . 1 1 ] chosen because i t was zero a t dc, and  p r e s e n t s almost  tance i s transformed  an open c i r c u i t  The  GHz  bandpass  filter  a transfer function  a t 4 5 MHz.  T h i s s m a l l admit-  by the l e n g t h of 5 0 fi l i n e from the bandpass f i l t e r  p l a n e E-E r e s u l t i n g i n a s m a l l c a p a c i t i v e susceptance  a t plane E-E.  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 s m a l l c a p a c i t i v e susceptance The  to  a t nodes 1 and  p r e d i c t e d e f f e c t of these shunt  VSWR on the I F l i n e .  The  d i s t a n c e from the f i l t e r  i s just  2 and a t p l a n e susceptances  i n c r e a s e s o n l y t o VSWR = 1.6  Thus the  to add  a  E-E.  i s t o produce a s m a l l  r e s u l t a n t VSWR on the I F l i n e w i l l be t o plane E-E i s a p p r o x i m a t e l y  to  1.4  15 cm.  i f the d i s t a n c e i n c r e a s e s to 2 5  i f the  This value cm.  The m i c r o s t r i p s u b s t r a t e 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 fibreglass material. machinable and has  T h i s m a t e r i a l was  a comparatively  by the d i e l e c t r i c  dielectric  constant  relatively  large radiation  The circuit  reduces  inhomogeneity.  a l s o r e s u l t s i n decreased  =  2.55).  the e f f e c t s  (resulting of  U n f o r t u n a t e l y , the  open c i r c u i t  lower  r e s o n a t o r Q due  to  losses.  c h o i c e of the s u b s t r a t e t h i c k n e s s was  r e s o n a t o r 0.  (Er  elements p h y s i c a l l y l a r g e r  l e s s s t r i n g e n t f a b r i c a t i o n t o l e r a n c e s ) , and  d i s p e r s i o n caused  teflon  chosen because i t i s e a s i l y  low d i e l e c t r i c c o n s t a n t  A low d i e l e c t r i c c o n s t a n t makes c i r c u i t in  i s a copper-clad  Both c i r c u i t s  determined  by the open-  i n c l u d e o p e n - c i r c u i t q u a r t e r wave o r h a l f  68  wave microstrip l i n e s - which are referred to as open c i r c u i t  resonators.  Microstrip resonator 0 i s determined by conductor l o s s , d i e l e c t r i c loss and radiation l o s s .  These losses have been calculated f o r the copper and t e f l o n -  f i b r e g l a s s laminate over the frequency range of i n t e r e s t 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 l o s s e s .  The  open-circuit resonator Os were found to be comparable f o r the a v a i l a b l e substrate thicknesses of 10 and 30 mils i n the frequency and impedance ranges required.  The 30 m i l substrate thickness was chosen because i t would r e s u l t  i n larger c i r c u i t dimension and correspondingly lower f a b r i c a t i o n  tolerances.  The laminate used was GX-6098-22-030-55 by 3M Company. Single microstrip c h a r a c t e r i s t i c Hammerstad's synthesis equations [ 2 . 7 ] .  impedances were calculated using The l i n e geometries were  corrected  for conductor thickness i n the IF i n j e c t i o n 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 e f f e c t i v e  dielectric  constant of approximately 1% f o r 25 ft l i n e s and 0.5% f o r 50 ft l i n e s . A correction for the T-junction discontinuity using Hammerstad's method [2.7] resulted i n only a 300 ym increase i n the T-shunt arm length. The stub-length correction due to the open c i r c u i t d i s c o n t i n u i t y capacitance was determined from [2.10] and [2.5],  The f i n a l dimensions f o r the IF i n j e c -  tion and matching c i r c u i t on the s p e c i f i e d laminate are given i n F i g .  2.15.  Cohn's bandpass f i l t e r topology was chosen f o r the L0 f i l t e r to s a t i s f y 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 i p widths and spacings i t e r a t i v e l y from the mode impedances.  To correct f o r the unequal  phase v e l o c i t i e s 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 f o r the 3.5 GHz bandpass f i l t e r are shown i n Fig.  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 i n F i g . 2.17 to account f o r the capacitance between the v e r t i c a l edges of adjacent conductors.  In a d d i t i o n , under-etching problems were also anticipated with  this conductor thickness i n 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 a p p l i e d . The etched microstrip c i r c u i t s 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 l i n e s by threading SMA bulkhead jacks i n t o the boxes so the center conductors of the connectors aligned exactly with the copper  III! I  50 A OUTPUT  • 2.115  50A  INPUT  ALL DIMENSIONS IN MILLIMETRES CONNECTORS ARE SMA  Fig. 2.17. 3.5 GHz microstrip bandpass f i l t e r .  o  71  conductors.  The dimensions of the boxes were chosen by using the r u l e - o f -  thurab that the case walls should be more than three times the conductor width and more than f i v e times the substrate thickness from the microstrip conductors [2.14],  [2.5].  The completed IF i n j e c t i o n 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 i n j e c t i o n and matching c i r c u i t assemblies were tested by measuring the VSWR looking to the receiver p o r t .  Measurements were made with the  LO port terminated with 50 ft and the IF port o p e n - c i r c u i t e d , s h o r t - c i r c u i t e d and terminated i n 50 ft. A 50 ft slotted coaxial l i n e 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 e f f e c t on the receiver port VSWR. F i g . 2.16 shows the measured VSWR for each of the two IF i n j e c t i o n and matching units together with the calculated VSWR. higher than those c a l c u l a t e d .  The measured values are s l i g h t l y  This i s attributed to the e f f e c t s of the  c o a x i a l - t o - m i c r o s t r i p d i s c o n t i n u i t i e s and to the r e s i d u a l VSWR of the measurement system.  This r e s i d u a l VSWR i s 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 i n j e c t i o n and matching c i r c u i t performed very well and had much greater than the required bandwidth.  The i n s e r t i o n loss of  the IF i n j e c t i o n and matching c i r c u i 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 i n s e r t i o n loss between 3.2 and 3.8 GHz. The r e s u l t s , which again did not require p o s t - f a b r i c a t i o n tuning, are shown In F i g . 2.20  72  Fig.  2.19.  3.5  GHz  bandpass  filter  photograph.  Frequency  (GHz)  F i g . 2 . 2 0 . 3.5 GHz bandpass f i 1 t e r performance .  74  along with the t h e o r e t i c a l , lossless response.  Microstrip l o s s e s , which  produce f i n i t e resonator Q ' s , account for the 2 dB f i l t e r i n s e r t i o n l o s s . Agreement between calculated and measured results i s considered to be extremely good.  Some difference between the two units was observed and can be  a t t r i b u t r e d to f a b r i c a t i o n tolerances ( i . e . underetching, copper thickness) and d i e l e c t r i c p e r m i t t i v i t y v a r i a t i o n . It was noticed that when the bandpass f i l t e r enclosure l i d was i n 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 i n v e s t i g a t e d .  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:  (_L_) + ( H - ) + ( 5 _ ) 2  2  f  2  „ " • 4d 2b 2a nm £ f o r e i t h eresonant r TE or TM modes. By exhaustive search, the nm£ =110 c  ;  V  ;  K  J  (2.7) 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 lid.  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 The receiver front-end incorporates 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 c i r c u i t s to reduce harmonic mixing conversion l o s s .  The harmonic  75  mixing  process  r e l i e s on the n o n l i n e a r mixer d i o d e j u n c t i o n to produce h a r -  monics of the l o c a l o s c i l l a t o r s i g n a l . chosen so t h a t one  The  l o c a l o s c i l l a t o r frequency i s  of i t s harmonics mixes w i t h the s i g n a l f r e q u e n c y  produce a s i g n a l a t the IF f r e q u e n c y . the mixer diode decreases  to  The harmonic g e n e r a t i o n e f f i c i e n c y o f  m o n o t o n i c a l l y as the harmonic number I n c r e a s e s .  T h i s r e s u l t s i n i n c r e a s i n g mixer c o n v e r s i o n l o s s w i t h I n c r e a s i n g l o c a l l a t o r harmonic number ( r e f . S e c t i o n 2.3.3.4). i n t o the o p e r a t i o n of the TRG tably high conversion l o s s .  oscil-  A preliminary investigation  mixers a t h i g h harmonic numbers showed unaccepThe  TRG  mixers were m o d i f i e d s l i g h t l y a t  f a c t o r y by i n c r e a s i n g the s i z e of the l o c a l o s c i l l a t o r  the  coupling capacitors to  t e s t the f e a s i b i l i t y of mixing u s i n g the t w e n t y - f i r s t harmonic o f a 3.5 local oscillator.  The  r e s u l t i n g c o n v e r s i o n l o s s was  T h i s c o n v e r s i o n l o s s was quired  unacceptable  to a c c u r a t e l y measure c r o s s p o l a r s i g n a l  the s e l e c t i o n of a times  circuit  realizability  dB can  be  w i t h the 6th to 9 t h  An i n v e s t i g a t i o n of these harmonic numbers showed t h a t the most  f e a s i b l e mixer harmonic number was m u l t i p l i e r , and may  i n X-band, and m i x i n g  resulted  R e f e r r i n g to the  mixer s p e c i f i c a t i o n s , S e c t i o n 2.3.3.4, a c o n v e r s i o n l o s s of 18-26  harmonic.  dB.  levels.  three frequency m u l t i p l i e r .  achieved using a l o c a l o s c i l l a t o r  42  because of the h i g h s e n s i t i v i t y r e -  A t r a d e o f f between c o n v e r s i o n l o s s and in  between 39 and  GHz  the 7 t h , r e q u i r i n g a times  three  r e s u l t i n g i n a p r e d i c t e d 22-23 dB c o n v e r s i o n l o s s .  have been p o s s i b l e to s e l e c t a times f o u r m u l t i p l i e r and mix  f i f t h harmonic.  frequency It also  with  the  T h i s would have r e s u l t e d i n a f u r t h e r 5 dB r e d u c t i o n i n  c o n v e r s i o n l o s s , but was  d e c i d e d a g a i n s t 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 u s a b l e because i t would have r e q u i r e d  o p e r a t i n g the r e c e i v e r l o c a l o s c i l l a t o r a t 4.08 GHz, near the a b s o l u t e upper limit  o f i t s range  C i r c u i t s to u t i l i z e  (4.1 GHz), where r e l i a b l e p h a s e - l o c k i n g i s n o t p o s s i b l e . the e i g h t h o r n i n t h harmonic were r e a l i z a b l e but these  harmonics would r e s u l t i n h i g h e r c o n v e r s i o n l o s s e s than the s e v e n t h . The f r e q u e n c y m u l t i p l i e r c i r c u i t s a c c e p t a 3.5 GHz i n p u t and produce 10.5  GHz output a t a l e v e l o f 13 dBm f o r each mixer.  a  The 13 dBm output  i n c l u d e s a maximum 3 dB budget f o r c a b l e l o s s and mismatch t o r e s u l t i n 10 dBm minimum a t each mixer LO p o r t .  A frequency m u l t i p l i e r i n t h i s  frequency  range uses the n o n l i n e a r j u n c t i o n c a p a c i t a n c e of a s i l i c o n v a r a c t o r o r s t e p r e c o v e r y diode t o produce  t h e harmonic s i g n a l .  The m u l t i p l i e r i n p u t , output  and b i a s c i r c u i t s have t o be c a r e f u l l y matched to the d i o d e c h a r a c t e r i t i c s t o result and  i n stable, 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 o f e f f i c i e n t  s t a b l e harmonic m u l t i p l i e r s i n t h i s frequency range  requires test  ment which was not a v a i l a b l e i n the E l e c t r i c a l E n g i n e e r i n g Department. t h i s r e a s o n c o m m e r i c a l l y b u i l t m u l t i p l i e r c i r c u i t s were Due  t o the many p o s s i b l e combinations  equipFor  purchased.  o f m u l t i p l i e r f r e q u e n c i e s and  power l e v e l s and t h e i r i n h e r e n t 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  i n v o l v e d i n t h i s o r d e r made i t v e r y d i f f i c u l t Grayzel, Inc.  and s m a l l q u a n t i t i e s  to f i n d a s u p p l i e r .  The A . I .  Company which s p e c i a l i z e s i n f r e q u e n c y m u l t i p l i e r s was a b l e to  s u p p l y a d e v i c e t o our s p e c i f i c a t i o n s a t a good p r i c e and w i t h an a c c e p t a b l e d e l i v e r y time.  D e s i g n t r a d e o f f s i n v o l v i n g e f f i c i e n c y and bandwidth were  n e g o t i a t e d d i r e c t l y w i t h the company's c i r c u i t d e s i g n e r s .  77  2.3.3.7  Frequency M u l t i p l i e r Specifications and Testing The manufacturer's  s p e c i f i c a t i o n s for the A . I . Grayzel model OX-3.5  frequency m u l t i p l i e r s are given i n Table  TABLE 2.5  2.5.  A . I . Grayzel OX-3.5 Frequency M u l t i p l i e r Specifications  3.5 GHz  Input frequency  10.5 GHz  Output frequency  135 mW  Input power required f o r 20 mW output  2%  Bandwidth  The three frequency m u l t i p l i e r s (one i s a spare) were tested by supplying an input power of 150 mW at frequencies between 3.45 and measuring the X-band power output. F i g . 2.21.  and 3.55 GHz  Results of t h i s test are plotted i n  The results of a second test with d i f f e r e n t 3.5 GHz input powers  i s shown i n F i g . 2.22.  These tests showed that none of the three m u l t i p l i e r s  met the manufacturers s p e c i f i e d 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 r c u i t s was not matched or that the generator produced an unexpected output waveform.  Subsequent tests including  attenuator pads (to ensure matched impedances) and d i f f e r e n t s i g n a l sources did not improve the m u l t i p l i e r performance.  78  003 '  •  3.^8  i  i  3.50  3.52  Frequency  F i g . 2.21.  ,  i . .  1  3.5A  3.56  (GHz)  Frequency m u l t i p l i e r f r e q u e n c y  response.  F i g . 2.22.  Frequency m u l t i p l i e r  conversion  loss.  80  Because the m u l t i p l i e r s were sealed and time constraints  did not  ini-  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 supplying a higher input power to the m u l t i p l i e r s 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 m u l t i p l i e r s , did have enough extra gain and power output c a p a b i l i t y to make this solution p o s s i b l e . 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 i n mid 1981. also shown i n F i g s . 2.21  2.3.3.8  and  Its subsequent performance i s  2.22.  Local O s c i l l a t o r Power Amplifier Power amplifiers are included In the front-end to supply the 3.5 GHz  drive l e v e l for the frequency m u l t i p l i e r s .  The two-channel front-end i s  mounted adjacent to the receiving antenna and i s connected to the v i a two 35 metre long coaxial cables.  Low-loss 7/8  cable i s used to minimize signal attenuation. attenuation of 4 dB at the LO frequency. receiver,  inch,  receiver  air-dielectric  These cables have a measured  With the maximum LO output from the  16 mW of LO drive i s available at the input to the f r o n t - e n d .  The  expected i n s e r t i o n loss of the IF 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 about 1 dB and 3 dB r e s p e c t i v e l y . maximum Input to the LO power a m p l i f i e r .  This r e s u l t s i n an 8 dBm  To provide the design 135 raW m u l t i -  p l i e r input l e v e l , the power amplifier required a minimum gain of 14 dB.  The  Avantek APT-4013 t h i n - f i l m power a m p l i f i e r met these s p e c i f i c a t i o n s with best economy.  These devices have a minimum gain of 18 dB and a power output at  81  s a t u r a t i o n o f 25  dBm  o v e r a f r e q u e n c y range of 2-4  output c a p a c i t y made i t p o s s i b l e to use not LO  perform a c c o r d i n g  to t h e i r design  s p e c i f i c a t i o n s , i n one  LO Frequency M u l t i p l i e r C i r c u i t  Three c i r c u i t f o r the LO  frequency m u l t i p l i e r chain.  o n l y one  LO  of the  possible  section.  The  were i n v e s t i g a t e d  receiver provides  A f r o n t panel adjustable  connection  and  Configurations  t o s e t the output l e v e l at each c o n n e c t o r .  o f F i g . 2.23 and  i n the next  c o n f i g u r a t i o n s , shown i n F i g . 2.23,  c o n n e c t o r s as shown i n F i g . 2.9. included  This extra gain  the f r e q u e n c y m u l t i p l i e r s , which d i d  c h a i n c o n f i g u r a t i o n s which are d i s c u s s e d  2.3.3.9  GHz.  two  LO  output  attenuator  In c i r c u i t s  is  (a) and  (b)  i s used w i t h the m u l t i p l i e r s , a m p l i f i e r s  a two-way power d i v i d e r to p r o v i d e  LO  s i g n a l s f o r both mixers.  These  c o n f i g u r a t i o n s 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. Circuit a m p l i f i e r and o n l y 35  dB  (a) which uses a 10.5  power d i v i d e r , r e q u i r e s  m u l t i p l i e r but when t h i s c i r c u i t was  i s o l a t i o n between c h a n n e l s .  of the mixers ( S e c t i o n first  GHz  I F s i g n a l was  even though no 45  low  one  t e s t e d , however, t h e r e  was  IF/LO i s o l a t i o n s p e c i f i c a t i o n  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  being  MHz  The  only  coupled between mixers t h r o u g h the LO  s i g n a l c o u l d be observed on the LO  connections  cables.  A test  was  performed by  adding s e c t i o n s of X-band waveguide between the power d i v i d e r  and  ports.  mixer LO  T h i s waveguide would not a l l o w any  propagate out  from the mixer LO  not  As a r e s u l t the presence o f 45  improve.  s i g n a l was  suspected.  No  ports.  The  spectrum a n a l y z e r  45  MHz  s i g n a l s to  i s o l a t i o n between c h a n n e l s d i d MHz was  s i d e b a n d s on  the  10.5  a v a i l a b l e to v e r i f y  GHz  this  LO  i g . 2.23.  LO  frequency m u l t i p l i e r chain c i r c u i t  configurations.  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. channel of the r e c e i v e r .  The mixer IF port was connected to the second IF This resulted i n an indicated signal l e v e l i n the  second channel which was 40 dB below that i n the channel with the harmonic mixer and  V-band input, thus v e r i f y i n g the presence of 45 MHz sidebands on  the LO s i g n a l .  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 a l l e v i a t e d by including i s o l a t o r s the power d i v i d e r , but this would not have been cost C i r c u i t (b) uses a 3.5 quency m u l t i p l i e r s .  after  effective.  GHz power d i v i d e r , one amplifier and two f r e -  This c i r c u i t would be less susceptable to 45 MHz modula-  t i o n of the LO signal because of the reverse Isolation of the m u l t i p l i e r s . It was not usable however, because the unexpectedly high conversion loss of the m u l t i p l i e r s meant there was i n s u f f i c i e n t amplifier output to drive two multipliers.  (The previous c i r c u i t had a s i m i l a r disadvantage.)  The i n -  creased cost of an amplifier with s u f f i c i e n t gain and output negated any advantage of this c i r c u i t over c i r c u i t In comparison with c i r c u i t s (a)  (c). and (b),  circuit (c),  which employs  two amplifiers and two m u l t i p l i e r s , has extremely high channel-to-channel i s o l a t i o n and the added advantage of being able to use the front panel attenuators to set the individual mixer LO levels (and thus e a s i l y for the differences i n m u l t i p l i e r e f f i c i e n c y . )  compensate  To provide 10 mW at the mixer  LO port i n this configuration, the amplifier driving m u l t i p l i e r 002  (before  84  repair) must supply close to 25 dBm ( m u l t i p l i e r 003 was not used).  For these  reasons c i r c u i t (c) was chosen f o r the f i n a l front-end design.  2.3.3.10  Mixer Bias C i r c u i t s  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 c h a r a c t e r i s t i c  f o r minimum conversion l o s s .  These c i r c u i t s supply a dc output voltage which i s 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 proba b i l i t y of diode damage even i f a component i n the mixer bias c i r c u i t  fails.  Reverse voltage protection diodes are included to protect the mixer diodes against reverse voltage damage i n the event of a f a i l u r e of the p o s i t i v e power supply.  Voltage and current meters are included i n each bias current  as an a i d i n mixer bias adjustment.  The mixer diode voltage i s coupled  through an i s o l a t i o n r e s i s t o r to an external jack on the bias c i r c u i t e n c l o sure.  These signals are applied to analog input ports on the data a c q u i s i -  tion system.  By monitoring the mixer diode voltage, any changes i n either  the bias or LO s i g n a l applied to the mixer can e a s i l y be detected.  A  schematic of one mixer bias c i r c u i t i s shown i n 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 i n each IF signal  10  K  Fig. 2.24. Mixer bias c i r c u i t schematic.  co  86  path.  In any receiving system, dynamic range i s limited at high signal  l e v e l s by saturation or n o n - l i n e a r i t y and at low signal l e v e l s by the noise level.  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 f o r maximum s e n s i t i v i t y (with the programmable attenuator minimum) f o r best crosspolar measurement s e n s i t i v i t y . measurement the programmable attenuator prevent receiver  set at  During copolar s i g n a l  reduces the IF s i g n a l l e v e l to  saturation.  The model PA-51 attenuator steps and switches i n 6 ms.  i s programmable from 0 to 63 dB i n 1 dB  Switch contacts i n the p o l a r i z a t i o n 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 f o r the reduced receiver copolar gain.  2.3.3.12  IF Preamplifier  Low noise IF preamplifiers are included i n the front end to improve s e n s i t i v i t y and thus increase s i g n a l - t o - n o i s e r a t i o during crosspolar signal measurements.  The front end single-sideband noise figure i s given by  [2.15]: F  F.E.  = L (F , + t C IF m V  T T  1)  (  where: L ?  c  IF  t  m  = mixer conversion loss (power ratio) = t o t a l IF noise figure (power ratio) = mixer noise temperature  ratio  2  *  8  )  The t o t a l IF noise figure i s that of the IF amplifier cascade and can be approximated by F  2n  F  IF ~ l s t JF F  G  +  1  AMF (  2  '  9  )  The mixer noise temperature r a t i o i s related to the mixer noise figure by:  F  M= C *m L  C  (2  ' > 10  The expression f o r the front end noise figure cannot be evaluated d i r e c t l y because manufacturers do not quote mixer noise figures f o r harmonic mixers i n this frequency range.  An estimate of the mixer noise temperature  r a t i o can be derived from equations appearing i n [2.16] and [2.17], The single sideband mixer noise figure f o r the case of a r e s i s t i v i t y terminated image i s given by [2.16]:  M =r  F  - t  c  m  ^  (  L  . L  c -  >  2  +  2  * c L  (2.11)  c  where T  D  = diode noise temperature  TQ = ambient temperature  (°K)  (°K)  This expression i s derived from the equations i n [2.16] and does not agree with the equation f o r mixer noise f i g u r e In [2.17].  The authors of both  references discuss the discrepancies i n these mixer noise figure equations and i t i s not obvious which i s precisely c o r r e c t .  However, the differences  88  i n the two expressions w i l l not produce a s i g n i f i c a n t error i n the following analysis. Solving f o r t  yields: T = i [ - £ ( L _ - l ) + 2] C o  t m  References  L  T  (2.12)  c  [2.16], [2.17] and [2.18] state that f o r an i d e a l Schottky  diode: T  0  D ~ T~ °  T  (  K)  ( 2 , 1 3 )  This value i s probably very optimistic f o r this type of application [2.19]. [2.20] but w i l l be used i n an attempt to ascertain the r e l a t i v e contribution of the IF preamplifier to the front-end noise f i g u r e .  Using t h i s expression  f o r T „ , t can be rewritten as: D' m !_ t m = 0.5 + I, This expression f o r t  (2.14)  can now be substituted into the expression  m  for the front-end noise f i g u r e , (2.8), to y i e l d , F  FE  =  1 +  V  F  I F  The equation i l l u s t r a t e s  ~ °'  5 )  ( 2  *  1 5 )  the r e l a t i v e e f f e c t of the IF preamplifier  noise f i g u r e . The f i r s t stage of IF gain i n the S c i e n t i f i c Atlanta receiver uses a 40235 t r a n s i s t o r .  This device i s not characterized f o r noise f i g u r e at the  IF frequency but extrapolation of i t s s p e c i f i c a t i o n s indicates i t s noise figure i s i n 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 a m p l i f i e r selected to be used as an IF  preamplifier i s 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. dB, an approximate improvement of 1.5  The t o t a l IF noise figure i s then dB.  1.8  This improvement i n IF noise  figure results i n a 2.0 dB improvement i n front-end noise figure at a very low c o s t .  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 i s exactly twenty-one times the receiver LO frequency plus or minus the 45 MHz IF frequency. klystron was free-running, changes i n i t s supply voltages, and cavity tuning a l l affect i t s operating frequency.  Because the  case temperature  Changes i n the m i l l i -  metre frequency can result i n changes i n the received signal levels due to the frequency sensitive behaviour of many components i n 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 peri o d s , seven BCD d i g i t s 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 S e n s i t i v i t y The noise figure of the receiving system front-end i s given by: F  = 1 + L (F  p E  c  I p  - 0.5)  (2.15)  From Section 2.3.3.12 the t o t a l IF noise figure i s : F „ = 1.5 = 1.8 dB Ir  (2.16)  T  The mixer conversion loss with the l o c a l o s c i l l a t o r chain described i n Section 2.3.3.6 dB.  was estimated from the manufacturer's  catalogue, to be 22-23  However, the measured mixer conversion loss i n 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 c a l c u l a t i o n of a receiving system s e n s i t i v i t y i f this front-end were used i n a s i n g l e conversion non-radiometer [2.15].  type receiver with no image band noise  rejection  However, with the S c i e n t i f i c Atlanta model 1751 receiver, an  additional s e n s i t i v i t y degradation r e s u l t s because there Is also no secondconversion image-noise r e j e c t i o n . frequency domain representation  This problem w i l l be i l l u s t r a t e d using the  i n F i g . 2.25.  In the single conversion case,  the RF and I F signal spectrum are shown i n F i g . 2.25(a) and 2.25(b) respectively.  I f the IF signal i n 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 73.50 GHz  LO  e 1 eve 1  image  73.5*»5 GHz 73.590 GHz  (a) RF signal  spectrum  Noise level  45 MHz 1st IF BW (= 7 MHz) (b) First IF spectrum t 1 '1 1 IF 45 MHz  LO  Noise level »«  image  45.001 MHz ^5.002 MHz  (c) Second conversion spectrum Noise level  1 KHz2nd 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 r e j e c t the image band noise the IF s i g n a l - t o - n o i s e r a t i o 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 t y p i c a l double-conversion receiving system, the noise f i g u r e 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 n o i s e .  In the model 1751 receiver no  such f i l t e r i s included because the 1 kHz second IF frequency i s too low to make such f i l t e r i n g p r a c t i c a l .  (This second IF frequency was chosen because  1 kHz i s a widely used standard frequency and thus makes the receiver compatible with d i f f e r e n t detection systems.)  The f i r s t and second IF  spectrum diagrams i n F i g s . 2.25(c) and 2.25(d) show how In this case an a d d i t i o n a l doubling of noise power occurs before s i g n a l 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 f o r by using an " e f f e c t i v e " receiving system noise figure of 29 dB. The noise contribution of the receiver,  referred to i t s i n p u t , can  also be expressed as an e f f e c t i v e input noise temperature, T using [2.15]: (2.17) T = T (F-1) e o g  where T = 290°K. o 2.3 • 1 0 K .  From (2.17) this receiver has a noise temperature of T  £  -  5o  The equivalent input noise power of the receiver can be calculated using this noise temperature and the receiver predetection noise bandwidth. The predetection bandwidth i s determined by the second order f i l t e r s i n the  93  d i g i t a l amplitude measurement u n i t s .  The 30 Hz - 3 dB bandwidth of these  f i l t e r s corresponds to a noise equivalent bandwidth of approximately: B = 44 Hz [2.22]. P , n  Equation 2.18 relates the equivalent input noise power,  to these q u a n t i t i e s : P  n  = kT B e n  where k = Boltzman's constant - 1.38 • 10~ P  n  n  - 1.4 • 1 0 ~  2.3.5.2  16  (2.18) 23  J/°K.  Thus, f o r this  receiver  W = -129 dBm.  Measured Receiving System S e n s i t i v i t y 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 a f t e r the receiver IF a m p l i f i e r .  Because of the high gain of the receiver IF  a m p l i f i e r , there i s no s e n s i t i v i t y reduction due to noise contributions of the following stages.  A resolution bandwidth of 30 Hz was used f o r 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 approximately 1.2 times their 3 dB bandwidths [2.23], necessitating a noise l e v e l measurement correction of -0.7 dB. An a d d i t i o n a l correction of +2.5 dB i s required when observing random noise to correct f o r the spectrum analyzers average l e v e l i n d i c a t i o n and logarithmic compression [2.23].  Thus the " i n d i c a t e d " s i g n a l - t o - n o i s e  ratio  on the spectrum analyzer was 1.8 dB higher than that f o r the complete r e ceiving system with the same input s i g n a l .  94  Figure 2.26  i s a photograph of the spectrum analyzer d i s p l a y f o r a  -100 dBm Input s i g n a l at 73.5 GHz.  When measuring noise l e v e l s on a spectrum  analyzer, the average noise l e v e l i s u s u a l l y displayed by adjusting the video f i l t e r bandwidth to be one-hundredth or l e s s of the r e s o l u t i o n bandwidth [2.23].  This procedure could not be followed f o r t h i s measurement because  the minimum video f i l t e r bandwidth was 10 Hz. l e v e l can only be estimated.  As a r e s u l t , the average noise  From s e v e r a l observations s i m i l a r to F i g . 2.26,  the approximate s i g n a l - t o - n o i s e r a t i o i s 24 dB ± 3  dB.  After Including the  c o r r e c t i o n f a c t o r s , t h i s corresponds to an equivalent input noise power f o r the r e c e i v i n g system of -122 dBm.  With the uncertainty i n the measured  conversion l o s s and noise l e v e l and the estimates i n the c a l c u l a t e d noise f i g u r e , and because of the numerous p o s s i b l e impedance mismatches, t h i s value was considered to be i n reasonable agreement. Another p o s s i b l e cause f o r the discrepancy between the c a l c u l a t e d and measured r e c e i v i n g 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 r e s u l t i n an unexpectedly higher noise  l e v e l i n the p r e v i o u s l y described t e s t .  Due to the very high s e n s i t i v i t y of  t h i s r e c e i v e r , even i f a spectrum analyzer could be used to monitor the 73.545 GHz m u l t i p l i e d LO s i g n a l at the mixer diode, these noise sidebands would probably not be observable.  The p o t e n t i a l f o r t h i s 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 R e s o l u t i o n bandwidth = 30 Video f i l t e r = 10  Hz/div. Hz KHz  Scan time = 10 s V e r t i c a l s c a l e = 10 dB/div.  Signal  F i g . 2.26  i n t o r e c e i v e r i s 73.5  GHz  § -100  dBm.  Spectrum a n a l y z e r d i s p l a y of 1st IF s i g n a l .  96  2.3.5.3  Receiving-System Small-Signal Performance At low i n p u t - s i g n a l l e v e l s , the measurement accuracy of the receiving  system i s corrupted by noise.  The complete receiving system was tested by  applying a known signal l e v e l to the mixer i n p u t s .  F i g . 2.27 shows the i n -  dicated d i g i t a l signal levels f o r 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 f o r 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 s i g n a l leakage into the f r o n t - e n d . i n [2.24].  This problem was also observed during s i m i l a r tests  Radiation from the klystron and waveguide flanges resulted i n a  s i g n i f i c a n t 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 f l u c t u a t i o n s .  peak-to-  To reduce the ambient l e v e l and front-end ingress, the  front-end was shielded and moved as f a r away from the klystron as p r a c t i c a l . In a d d i t i o n , a l l waveguide junctions were v i s u a l l y Inspected a f t e r connection and then wrapped i n metal f o i l .  These measures reduced the undesired signal  l e v e l 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 r o o f .  For this reason the  actual receiving system performance i s actually 5 to 6 dB better than i n d i c a ted i n F i g .  2.27.  The results from tests performed on the bench  ( F i g . 2.27)  indicate  that average indicated levels of the receiving system are l i n e a r to with ± 0.3 dB for input levels down to -95 dBm. noise fluctuations are 1.0 dB or l e s s .  At this input l e v e l ,  peak-to-peak  (When the system was i n s t a l l e d on the  roof, s i m i l a r performance was obtained f o r -100 dBm.) The e f f e c t of these  cc H H A B  INDICATION 73.5 GHz  .27. R e c e i v i n g  Signal  level  (dBm)  •  system s m a l l s i g n a l performance on the bench.  98  fluctuations i n Indicated signal l e v e l can be reduced by averaging during data a n a l y s i s .  The nonlinearity at low signal l e v e l s was l i k e l y due to  signal ingrees. This front end i s approximately 30 dB more sensitive than the S c i e n t i f i c Atlanta model 13-50A mixer, but an exact comparison has not been made.  2.3.5.4  Receiving System I s o l a t i o n and Frequency Response The measured channel-to-channel i s o l a t i o n of the complete receiving  system was greater than 75 dB. This i s the measurement l i m i t imposed by saturation i n the channel with the signal applied (without IF attenuation) and noise l e v e l i n the other channel. Fig.  2.28 shows a t y p i c a l response of the complete receiving system to  input frequencies between 73.0 and 73.5 GHz. The frequency response of the receiving system i s mainly determined by the frequency m u l t i p l i e r s and mixers.  Changing the p o s i t i o n of the mixer backshort tuning adjustment w i l l  s i g n i f i c a n t l y a l t e r the receiving system frequency response.  2.3.5.5  Front-end Alignment The following procedure i s followed to a l i g n the front end for a new  receiver frequency. 1.  Adjust the LO l e v e l for 10 mW at the mixer LO p o r t .  CAUTION:  exceed 20 mW LO l e v e l or the mixer diode may be damaged.  Do not  LO l e v e l i s  adjusted by the receiver front panel LO attenuator or by placing a fixed pad with SMA connectors on the LO a m p l i f i e r i n p u t .  F i g . 2.29 shows a  t y p i c a l v a r i a t i o n i n mixer conversion loss for various LO l e v e l s .  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 c o n v e r s i o n l o s s .  101  2.  Adjust the mixer bias l e v e l for maximum signal i n d i c a t i o n . not exceed 4 mA diode current.  F i g . 2.30  CAUTION:  shows a t y p i c a l v a r i a t i o n i n  signal and noise l e v e l for various mixer bias conditions.  (These  would be changed for d i f f e r e n t LO l e v e l s and tuning p o s i t i o n s . ) the noise l e v e l i s r e l a t i v e l y constant, maximum signal l e v e l o n l y .  Do  results Because  i t i s permissible to adjust f o r  The optimum bias s e t t i n g i s very dependent on  LO drive l e v e l . 3.  Adjust the mixer waveguide backshort for maximum signal i n d i c a t i o n . maxima for the backshort closest  The  to the diode w i l l give the widest  frequency response. 4.  2.4  Repeat steps 2 and 3.  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 b u i l d i n g . The antennas are separated by a horizontal distance of 20 metres to prevent any stray coupling.  The r e f l e c t o r  building 880 metres away. Fig 2.31,  i s mounted on the roof of the Gage Towers  This provides a t o t a l path length of 1.76 km.  from [2.1], shows the path d e t a i l s .  showing the path looking from the r e f l e c t o r  2.5  F i g . 2.32  i s a photograph  toward the antennas.  Antennas and Orthomode Transducers TRG model V822 Cassegrain parabolic antennas are used for both  transmitting and r e c e i v i n g .  These antennas are 61 cm i n diameter and have  Mixer diode current  (mA)  i g . 2 . 3 0 . E f f e c t o f m i x e r b i a s c u r r e n t on f r o n t - e n d p e r f o r m a n c e .  ANTENNAS  F i g . 2.31.  Propagation path d e t a i l s .  F i g . 2.32. Propagation path photogra  105  machined aluminum r e f l e c t o r s .  Corrugated, c o n i c a l , scalar feed horns are  incorporated f o r p o l a r i z a t i o n i n s e n s i t i v e c h a r a c t e r i s t i c s , e f f i c i e n c y and low sidelobe l e v e l s [2.25].  high aperture  D u a l - l i n e a r p o l a r i z a t i o n cap-  a b i l i t y i s r e a l i z e d by including orthomode transducers which interface to the c i r c u l a r waveguide ports on the feedhorns.  The orthomode transducers for  these antennas were s p e c i a l l y manufactured to y i e l d the highest possible polarization i s o l a t i o n .  The manufacturers s p e c i f i c a t i o n s for the two anten-  nas assemblies are included i n Table 2.6.  Crosspolar i s o l a t i o n performance,  measured by the manufacturer, f o r the complete antennas i s shown i n F i g . 2.33. TABLE 2.6  TRG V822 Antenna Specifications at 73.5 GHz.  S e r i a l no.  S e r i a l no. 23  22 On axis gain through port cross port  50.6 dB 50.6 dB  50.9 dB 50.9 dB  VSWR through port cross port  1.07 1.09  1.12 1.11  3 dB Beam Width through port cross port  0.45 0.A6  Sidelobe l e v e l s (max.) through port cross port  -23 dB -22 dB  c  C  0.45 0.45  c c  21 dB 21 dB  Additional tests were made on the orthomode transducers to supplement  the manufacturer's p  o l a r i z a t i o n i s o l a t i o n data.  This was accomplished by  Fig.  2.33.  Antenna  crosspolar  isolation  performance.  107  connecting  the two  orthomode t r a n s d u c e r s  "back-to-back" through t h e i r  c u l a r waveguide p o r t s as shown i n F i g . 2.34.  cir-  I s o l a t i o n between the two  per-  p e n d i c u l a r p a i r s of r e c t a n g u l a r waveguide p o r t s were measured u s i n g a power meter w i t h The  the unused p o r t s of the t r a n s d u c e r s  terminated  t e s t r e s u l t s , (which are c o r r e c t e d f o r the source  quency r e s p o n s e ) f o r f r e q u e n c i e s between 73.0  and  73.6  w i t h matched  and  loads.  power meter  GHz,  fre-  a r e shown i n F i g .  2.35. The  c o p o l a r i n s e r t i o n l o s s e s of the two  found to be s l i g h t l y d i f f e r e n t . arm  - s t r a i g h t arm  arm  connection.  connection  was  The 0.8  This f a c t introduced  orthomode t r a n s d u c e r s  average i n s e r t i o n l o s s f o r the dB  some u n c e r t a i n t y i n t o the manufacturers  c r o s s p o l a r i s o l a t i o n between p o r t s was  T h i s i s l i k e l y due  - an u n l i k e l y  ences between the two  through arras.  i s o l a t i o n s i s p a r t l y due  p o l a r i z a t i o n s may  to a s l i g h t  f o r one  differ-  of the p o l a r i z a t i o n s , This  could  l o c a t i n g p i n s which  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 t r a n s d u c e r s  in this  was  polariztion  not be e x a c t l y p e r p e n d i c u l a r .  i n v e s t i g a t e d because the c i r c u l a r f l a n g e s had  prevented  different.  I t i s a l s o p o s s i b l e t h a t the  o r i e n t a t i o n mismatch between the t r a n s d u c e r s i . e . the output  a l s o found to be  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  r e a l i z e d i n the c r o s s and  varied  - cross  In v i e w 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  not be  straight  l e s s than f o r the c r o s s arm  antenna g a i n 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 f o r each arm result  were  from  being  test configuration.  When a s i m i l a r t e s t of c r o s s p o l a r i s o l a t i o n f o r the orthomode t r a n s d u c e r s  was  two  back-to-back  made u s i n g the r e c e i v i n g system i n s t e a d of  power meter, a v e r y d i f f e r e n t  frequency  response was  observed.  This  the  THROUGH ARM  TRANSMIT ORTHOMODE TRANSDUCER  TEST SIGNAL  RECEIVE ORTHOMODE TRANSDUCER  CROSS ARM  Fig. 2.34.  Orthomode transducer test configuration.  MATCHED TERMINATION  109  28  46 I  r  I 73.05  I 73.15  I  I  1  73.25  73.35  73.^5  Frequency  Fig.  —1 73.55  (GHz)  2 . 3 5 . Orthomode t r a n s d u c e r 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 d i f f e r e n t 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  d e l i b e r a t e l y 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 i s o l a t o r ahead of the second mixer as shown i n F i g . 2.37.  The crosspolar  i s o l a t i o n without the i s o l a t o r and with no attenuation shows a s i m i l a r r e s u l t to F i g . 2.36.  The improvements which result with the addition of the  i s o l a t o r 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 s l i g h t mismatches i s the reason a l l ports of both orthomode transducers are connected through isolators.  The t h e o r e t i c a l 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 i n v e s t i g a t i o n of methods to improve the crosspolar  measurement range at 73 GHz resulted from several 1.  factors:  Theoretically predicted levels of XPD near 73 GHz are very h i g h . Published calculations predict XPD values around 40 - 50 dB for 20 dB  Ill  28  r  73.05  73.15  73.25  Frequency  73.35  73.'.5  73.55  (GHz)  F i g . 2.36. Orthomode t r a n s d u c e r t e s t r e s u l t s w i t h one p o r t mismatched.  112  TEST SIGNAL  MATCHED TERMINATION ORTHOMODE TRANSDUCERS  VARIABLE ATTENUATOR  i  FRONT END  TO RECEIVER  F i g , 2.37-..'-Orthomode t r a n s d u c e r t e s t w i t h t h e r e c e i v i n g  system f r o n t - e n d .  113  73.05  73.15  73.25  Frequency  73.35  (GHz)  F i g . 2.33. Test r e s u l t s f o r F i g . 2.37.  73.^5  114  copolar fades.  The p r o b a b i l i t y of a 20 dB or greater copolar fade on the  UBC path i s very low (approximately 10 min/year). 2.  Even with the excellent transducers  performance of the s p e c i a l l y fabricated orthomode  (OMT), careful alignment could not y i e l d simultaneous i s o l a -  tions on both channels of greater than approximately 34 dB and 36 dB. These i s o l a t i o n s i n this frequency range are extremely high but s t i l l do not result i n e a s i l y interpreted XPD data for most r a i n f a l l  events.  Measurements taken without the crosspolar cancellation network have confirmed 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 i s possible with certain combinations of OMT port terminations and antenna and feed alignments to have clear weather,  system i s o l a t i o n s  higher than 34-36 dB f o r one p o l a r i z a t i o n over narrow frequency ranges. Unfortunately this appears to be accompanied by very poor i s o l a t i o n i n the other channel.  Simultaneous improvement i s not possible because  adjusting port terminations and alignments does not provide s u f f i c i e n t degrees of freedom.  A complete explanation of the effects of OMT port  terminations and alignment are found i n Section 5.5.2 and 2.5.3  respec-  tively.  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 i n the l i t e r a t u r e as orthogonalization and c a n c e l l a t i o n . (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 dualpolarized l i n k .  Orthogonalization uses a rotatable d i f f e r e n t i a l phase  s h i f t e r and a rotatable d i f f e r e n t i a l attenuator i n a c i r c u l a r waveguide. XPD improvement i s accomplished i n e s s e n t i a l l y the same way i n which a d e p o l a r i zing medium, ( i . e . rain) decreases XPD.  Cancellation techniques  incorporate  two d i r e c t i o n a l couplers, an attenuator and a phase s h i f t e r f o r 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 t a t i c a l l y or adaptively.  Static  XPD improvement i s . u s e d to increase clear-weather XPD by compensating f o r the crosspolar signals due to the f i n i t e i s o l a t i o n of the system's orthomode transducers  and antennas and i s usually employed to improve the XPD measure-  ment range i n propagation experiments.  In an adaptive a p p l i c a t i o n , an e l e c -  tronic control system - usually including a microprocessor - varies the four XPD - improvement - network parameters to continually correct f o r d e p o l a r i z a tion r e s u l t i n g 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  links.  The orthogonalization method f o r 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 s h i f t e r  and d i f f e r e n t i a l attenuator which can be oriented at any desired angle ween horizontal and v e r t i c a l . transforms  The rotatable d i f f e r e n t i a l phase  bet-  shifter  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 i n e a r l y polarized non-  116  orthogonal waves.  These l i n e a r l y 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 c i r c u l a r waveguide and, therefore,  must be  i n s t a l l e d 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 f a b r i c a t i n g and adjusting the network and the fact that the network must precede the receiver front-end and therefore w i l l reduce s e n s i t i v i t y [2.31], [2.26].  The advantage of this  method, however, i s that i t w i l l probably produce the widest operating bandwidth because the entire c i r c u i t i s fabricated within a s i n g l e , short section of waveguide [2.27]. Kannowade [2.32] has further analyzed the Chu type orthogonalization network f o r adaptive correction on s a t e l l i t e  links.  He has also proposed a  method of r e a l i z i n g a Chu type orthogonalization i n a rectangular waveguide network i n s t a l l e d a f t e r the orthomode transducer.  This i s accomplished by  incorporating two networks for coordinate rotation each of which i s constructed from two 3-dB couplers and a phase s h i f t e r .  D i f f e r e n t i a l phase  s h i f t and attenuation are accomplished by applying different amounts of phase s h i f t and attenuation to signals i n each separate signal path. No example of an actual a p p l i c a t i o n of the Chu method could be found i n the l i t e r a t u r e .  This i s because at lower microwave frequencies - where  almost a l l e x i s t i n g systems operate - a s i m p l i f i c a t i o n of this technique i s practical.  Depolarization at lower frequencies i s mainly due to d i f f e r e n t i a l  phase s h i f 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 i r c u i t can be realized  117  w i t h o n l y two c o n t r o l l a b l e p a r a m e t e r s .  T h i s t h e o r y 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 e n t i a l phase c o r r e c t i v e n e t w o r k ) , ducer [ 2 . 3 3 ] .  (which a c t as a d i f f e r -  t h r e e r o t a r y j o i n t s and an orthomode t r a n s -  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 . 3 4 ] showed t h a t t h i s a d a p t i v e system was c a p a b l e of m a i n t a i n i n g a system XPD of b e t t e r t h a n 25 dB f o r r a i n r a t e s as h i g h as 130 mm/hr.  Uncorrected,  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 t o e n t i a l attenuation [2.26].  In t h i s c a s e , the s u b o p t i m a l network would  require a rotatable d i f f e r e n t i a l attenuation. XPD improvement c o u l d be found i n the  differonly  No examples of t h i s type of  literature.  Evans and Thompson [ 2 . 3 5 ] were p r o b a b l y 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 s y s t e m .  The  b a s i c - c a n c e l l a t i o n t e c h n ^ u e , w h i c h has been used i n v a r i o u s a p p l i c a t i o n s ,  is  a c c o m p l i s h e d 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 t e n u a t e d and p h a s e s h i f t e d sample of the u n d e s i r e d s i g n a l f r o m the c h a n n e l p r e v i o u s l y b o t h the d e s i r e d and u n d e s i r e d s i g n a l s .  containing  In microwave c a n c e l l a t i o n n e t w o r k s ,  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 t o sample the u n d e s i r e d s i g n a l and t o inject  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 .  T h i s t e c h n i q u e can be a p p l i e d a t R F ,  IF and i n some s y s t e m s , even at b a s e b a n d . The advantages of c a n c e l l a t i o n o v e r o r t h o g o n a l i z a t i o n a r e cancellation:  that  i s e a s i e r t o i m p l e m e n t , uses r e a d i l y a v a i l a b l e components,  e a s i e r t o a d j u s t m a n u a l l y or e l e c t r o n i c a l l y and can be implemented a f t e r  is  118  amplification i n systems where the coupler i n s e r t i o n loss would be objectionable [2.26].  Cancellation techniques can also be r e a d i l y applied to  single or d u a l - p o l a r i z a t i o n systems. Evans and Thompson [2.35] i n s t a l l e d a single-channel cancellation network on an 11.6 GHz, 1.6 km experimental l i n k at the University of Essex, England.  The network was used to improve the clear weather system i s o l a t i o n  from around 40 dB to 55-60 dB. No d e t a i l s of the c i r c u i t r e a l i z a t i o n were given.  Results were shown for an " a r t i f i c i a l " p r e c i p i t a t i o n event and the  authors note that "the v a r i a t i o n of the crosspolar s i g n a l f o r the cancelled l i n k are consistent,  whereas, for the uncancelled l i n k ,  the addition of the  system and atmospheric phasors y i e l d s a s i g n a l which fluctuates around the clear weather v a l u e . " the clear-weather  The published results also seem to show some d r i f t i n  crosspolar signal l e v e l s , e s p e c i a l l y on the cancelled  link. Sobieski [2.36] has described a switched p o l a r i z a t i o n experiment at 12 GHz over a 2 km l i n k at the Universite Catholique de Leuvain, Belgium. The construction of this experiment was not complete when [2.36] was w r i t t e n , but the authors intended to incorporate a two-channel cancellation network to improve the XPD measurement range. use at IF frequencies was proposed.  An alternative  c i r c u i t r e a l i z a t i o n for  This cancellation network used four 3 dB  hybrid junctions and four attenuators but no phase s h i f t e r . Dilworth [2.26] has reported a single-channel adaptive c a n c e l l a t i o n network i n s t a l l e d on the 11.6 GHz l i n k 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 m i c r o s t r i p .  This c i r c u i t  increased  the clear weather l i n e a r XPD from 40 dB to 60 dB, which was the system noise  119  floor.  Dilworth and Evans [2.37] have recently published results where t h i s  cancellation network was used adaptively to correct c i r c u l a r p o l a r i z a t i o n on the same experimental l i n k .  A microcomputer was used to control the c a n c e l -  l a t i o n network by searching f o r 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'Neill  [2.38] has described a receiving system including a single  channel cancellation network designed f o r propagation measurements using the European O r b i t a l Test S a t e l l i t e .  This 11.7 GHz c i r c u i t used the standard  configuration of two d i r e c t i o n a l 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 o r i g i n a l l y presented by Evans and Thompson [2.35]. Dintelmann [2.39] has published a description of a 12 GHz cancellation network i n an O r b i t a l Test S a t e l l i t e propagation experiment underway at the Research Institute  of the Deutsche Bundesport, Darmstadt, F . R . G .  Single  channel cancellation networks for l i n e a r and c i r c u l a r cancellation networks are described.  In this experiment cancellation i s used s t a t i c a l l y to improve  the XPD measurement  range.  Murphy, i n this t h e s i s ,  [2.40] has reported a single channel c a n c e l l a -  tion network i n a fixed p o l a r i z a t i o n 30 GHz propagation experiment on a 1.02 km l i n k 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 l e v e l d r i f t e d over a considerable range.  120  2.5.1.2  XPD Improvement i n this Experiment A single channel crosspolar cancellation network was chosen f o r XPD  improvement i n 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 s h i f t e r s 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 i g n ment could be used to improve the XPD l e v e l on the other channel.  This would  allow comparison to be made between the XPD response of cancelled and uncanc e l l e d systems.  No information i s l o s t by not cancelling both channels  because the o f f diagonal elements i n the dual-polarized transmission matrix are equal (See Chapter 4 ) .  In a d d i t i o n , i f only one cancellation network was  i n s t a l l e d , i t would be possible to s i g n i f i c a n t l y reduce the length of waveguide required to interconnect shifter.  the d i r e c t i o n a l couplers, attenuator and phase  Short interconnections are desirable to increase the operating  bandwidth, as discussed i n 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 a c t u a l l y i n s t a l l e d i n working systems, formed at the propagating-signal frequency.  cancellation was per-  T h e o r e t i c a l l y , cancellation  could also be applied i n the IF sections of a receiver which had two separate IF channels. The advantages  of IF cancellation are that:  - there would be no reduction i n receiving system s e n s i t i v i t y .  121  - necessary  components such as c o u p l e r s , a t t e n u a t o r s  be f a r l e s s expensive,  at the lower  and  phase s h i f t e r s would  frequency.  - f l e x i b l e - c o a x i a l r a t h e r than waveguide i n t e r c o n n e c t i o n s can be used, -  and  the e l e c t r i c a l l e n g t h of i n t e r c o n n e c t i o n s i n terms of the c a n c e l l a t i o n frequency  would be much s h o r t e r , r e s u l t i n g i n a l a r g e r o p e r a t i n g  as d i s c u s s e d The  i n S e c t i o n 5.6.2.  o n l y disadvantage of IF c a n c e l l a t i o n i s t h a t phase or g a i n  i n e i t h e r c h a n n e l of the r e c e i v i n g system p r e c e d i n g will  bandwidth,  the c a n c e l l a t i o n network  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 e r r o r [2.27],  of the c a n c e l l a t i o n e r r o r due  to phase and  drift  An a n a l y s i s  g a i n e r r o r s or d r i f t s  i s given i n  S e c t i o n 5.6.1. The g a i n and  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 i n t o the  phase s t a b i l i t y of the r e c e i v i n g system f r o n t - e n d .  operating experience system and  on  with  Considerable  the f r o n t - e n d , both i n s t a l l e d i n the  the bench, has  shown t h a t the g a i n s t a b i l i t y was  experimental v e r y good.  T y p i c a l g a i n v a r i a t i o n s on the bench, a f t e r a warm up p e r i o d , are one tenths is  of a dB f o r p e r i o d s over an hour.  installed  tions  and  i n the system are s l i g h t l y l a r g e r , presumably due  ( f o r s h o r t term v a r i a t i o n s ) and  variations) . may  The  to  two  front-end scintilla-  temperature changes ( f o r l o n g  g a i n v a r i a t i o n s are n e g l i g i b l e f o r p r o p a g a t i o n  term  measurements  even have been t o 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  FM  Gain v a r i a t i o n s when the  or  conversion  factor.  discovered A 0.1  t h a t the f r o n t - e n d had  dB change i n the f r o n t - e n d  s m a l l adjustment i n the r e c e i v e r LO  output  approximate 10 to 15 degree phase s h i f t  was  an unacceptable g a i n induced  found to r e s u l t  i n that channel.  AM-  by a  i n an  T h i s phase  shift  122  appeared to be due  to the l o c a l o s c i l l a t o r f r e q u e n c y m u l t i p l i e r s , but  harmonic mixers may believed  to be due  a l s o have been p a r t i a l l y r e s p o n s i b l e .  t e d , however, because both d e v i c e s conditions.  AM-PM c o n v e r s i o n I n an  Crosspolar  For  largest obtainable  decided  to perform  millimetre-wave crosspolar c a n c e l l a t i o n c i r c u i t  the g r e a t e s t operating  p o s s i b l e degree of t u n a b i l i t y and  bandwidth.  t u n a b i l i t y i s n e c e s s a r y to be a b l e  These d e s i g n  to a d j u s t  c l e a r weather c r o s s p o l a r s i g n a l c a n c e l l a t i o n .  changes.  crosspolar  limited  by  the  c r o s s p o l a r and  and  phase s h i f t e r .  (The  c a n c e l l a t i o n i s discussed  the  the u n a v o i d a b l e  the c i r c u i t  fre-  A h i g h degree of f o r almost  total  Large c a n c e l l a t i o n c i r c u i t  and  ambient  C a n c e l l a t i o n network t u n a b i l i t y i s determined by  of the a t t e n u a t o r on  to source f r e q u e n c y d r i f t  was  c o n s t r a i n t s were  bandwidth i s d e s i r a b l e to reduce the changes i n the c l e a r - w e a t h e r due  the  Description  of the f r e e r u n n i n g m i l l i m e t r e - w a v e s o u r c e .  signal baseline  drift  GHz.  the d e s i r e f o r maximum measurement range and  quency: d r i f t  unexpec-  i t i s obvious t h a t t h i s degree o f  t h i s reason i t was  Cancellation Circuit  single-channel  d e s i g n e d to p r o v i d e  imposed by  T h i s i s not e n t i r e l y  would r e s u l t i n u n a c c e p t a b l e c r o s s p o l a r s i g n a l l e v e l  c r o s s p o l a r c a n c e l l a t i o n at 73  The  is  are designed to o p e r a t e under maximally  From S e c t i o n 5.1.6  IF c a n c e l l e d system.  2.5.1.4  phase s h i f t  to a change i n the m u l t i p l i e r or mixer d i o d e impedance  r e s u l t i n g from the s m a l l amplitude v a r i a t i o n .  non-linear  The  the.  crosspolar-  temperature the a d j u s t a b i l i t y  e f f e c t s of s m a l l adjustment  i n Section  5.6.1).  Bandwidth i s  t o t a l phase v a r i a t i o n w i t h f r e q u e n c y between the c a n c e l l a t i o n s i g n a l s at the j u n c t i o n of  errors  undersired-  the combining  coupler.  123  The most s i g n i f i c a n t source  of t h 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  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 ports.  length  coupler  ( T h i s i s d e s c r i b e d i n d e t a i l i n S e c t i o n 5.6.2). The  d i r e c t i o n a l c o u p l e r s i n c o r p o r a t e d i n the c r o s s p o l a r 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 b a s i s o f the u n c o r r e c t e d polar i s o l a t i o n .  I f the e n t i r e e x p e r i m e n t a l  c l e a r weather c r o s s -  system was a l i g n e d f o r b e s t  c r o s s p o l a r i s o l a t i o n f o r o n l y 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 t h e o t h e r 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. a worst case e s t i m a t e  Using  25 dB as  and c o n s i d e r i n g the i n s e r t i o n l o s s o f the a t t e n u a t o r ,  phase s h i f t e r and the waveguide i n t e r c o n n e c t i o n s , r e s u l t e d i n t h e s e l e c t i o n of 10 dB c o u p l e r s  f o r both the sampling and combining d i r e c t i o n a l  " I d e n t i c a l " c o u p l e r s a r e used t o e q u a l i z e the v e r t i c a l t i o n l o s s of t h e c a n c e l l a t i o n network. A s s o c i a t e s MA-655.  and h o r i z o n t a l i n s e r -  The c o u p l e r s used a r e Microwave  These c o u p l e r s have an i n s e r t i o n l o s s o f  0.8 dB, which w i l l r e s u l t  couplers.  i n a corresponding  approximately  r e d u c t i o n i n r e c e i v i n g system  sensitivity. 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 a p p l i e d i n the s e l e c t i o n o f the a t t e n u a t o r and phase s h i f t e r . 410  Devices  and DBB-910, r e s p e c t i v e l y .  mechanically  dB w i t h  These components a r e a l m o s t  DBB-  identical  and i n c o r p o r a t e micrometer d r i v e t u n i n g which w i l l  maximum degree o f a d j u s t a b i l i t y . 40  chosen were the Demornay B o n a r d i  p r o v i d e the  The a t t e n u a t o r i s a d j u s t a b l e from 0 t o  a 0.5 dB I n s e r t i o n l o s s .  The phase s h i f t e r  i s adjustable over a  range g r e a t e r than 360° and has a maximum i n s e r t i o n l o s s o f 1.25 dB a t 360° phase s h i f t . these  The p h y s i c a l l e n g t h between the waveguide f l a n g e s on each o f  components i s 14.6 cm.  124-  The  m e c h a n i c a l l a y o u t of the c r o s s p o l a r c a n c e l l a t i o n network  d e s i g n e d to m i n i m i z e the l e n g t h of the waveguide c o n n e c t i o n s circuit  elements and  attaching  the c o u p l e r s  the a t t e n u a t o r possible* two  and  The  d i r e c t l y to the f r o n t - e n d  T h i s was  between  arms and F i g . 2.39  i n p u t p o r t s and  as  t o t a l p h y s i c a l l e n g t h of the waveguide c i r c u i t between  i n t e r c o n n e c t i o n s , i s a p p r o x i m a t e l y 93  by  by mounting  phase s h i f t e r as p h y s i c a l l y c l o s e to the c o u p l e r s  the  phase s h i f t e r ,  cm.  i s a schematic o f the c r o s s p o l a r c a n c e l l a t i o n network.  Antenna Mounting and F i g . 2.40  the  accomplished  c o u p l e r j u n c t i o n s , i n c l u d i n g the l e n g t h of the a t t e n u a t o r ,  coupler  2.5.2  thus maximize the bandwidth.  was  Rain  Shields  i s a photograph o f the t r a n s m i t t i n g 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 . mounts are f a b r i c a t e d from heavy gauge m i l d s t e e l and mounts are a t t a c h e d  to the c o n c r e t e  The  antenna  angle i r o n s t o c k .  r a i l i n g around the b u i l d i n g r o o f .  The The  extreme r i g i d i t y of these mounts i n s u r e s t h e r e w i l l be no antenna d e f l e c t i o n even d u r i n g  1  severe wind c o n d i t i o n s .  The s h o r t e s t p o s s i b l e c o i n - s i l v e r XtfR-15 waveguide i n t e r c o n n e c t i o n s were f a b r i c a t e d by f i l l i n g the waveguide s e c t i o n s w i t h a low m e l t i n g temperature m e t a l a l l o y b e f o r e bending. F i l l i n g the waveguide w i t h s o l i d metal b e f o r e 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 r a d i u s and t h e r e f o r e the t o t a l l e n g t h of the i n t e r c o n n e c t i o n . The metal a l l o y i s removed a f t e r bending by h e a t i n g the waveguide s e c t i o n and then f l u s h i n g i t w i t h v e r y hot water.  RECEIVING ANTENNA  '  ORTHOMODE TRANSDUCER  PHASE COMPENSATION 10 d B  W v  DIRECTIONAL COUPLER (SAMPLE)  VARIABLE  10 d B DIRECTIONAL  ATTENUATOR  COUPLER (INSERTION)  FRONT  END  ENCLOSUREN  r  1  I I  I  CROSSPOLAR  COPOLAR  MIXER  F i g . 2.39. C r o s s p o l a r c a n c e l l a t i o n  MIXER  network.  F i g . 2.42. Reflector photograph.  127  A p o l y - v i n y l - c h l o r i d e (PVC) r a i n s h i e l d covers the top half of each antenna to prevent r a i n accumulation on the antenna components.  The mounting  stress of the PVC shield i s d i s t r i b u t e d by connecting i t to an aluminum r i n g with numerous small fasteners. durability.  PVC was chosen f o r i t s toughness and  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 e r r o r . It i s important not to allow r a i n to accumulate on the antenna reflector, isolation.  subreflector or feedhorn to prevent a reduction i n crosspolar Several experimenters have reported crosspolar i s o l a t i o n  reduction due to r a i n accumulation [2.41],  2.5.3  [2.42],  [1.80],  [1.85].  Antenna Alignment The antennas are f i r s t aligned f o r maximum copolar signal l e v e l and  then f o r minimum crosspolar signal l e v e l . antennas and the r e f l e c t o r ,  After a coarse alignment of both  the copolar signal was maximized by i t e r a t i v e l y  adjusting the antenna azimuth and e l e v a t i o n .  The p o l a r i z a t i o n angle of the  antennas Is most e a s i l y adjusted by loosening the set screws i n the c o l l a r 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 v e r t i c a l 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 r e f l e c t o r .  The  maximum gain of the copolar lobe nominally corresponds to the n u l l i n the crosspolar lobe and crosspolar levels t y p i c a l l y increase at pointing angles deviating from this n u l 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 d i f f e r e n t from the pointing angle for maximum copolar gain [2.45]. [2.47],  [2.48].  [2.46],  In this case, the most desirable alignment i s f o r minimum  crosspolar l e v e l .  F i g . 2.33 shows that the best i s o l a t i o n does occur f o r  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 f o r best system XPD, i t i s necessary to examine the XPD through a range of frequencies.  The t h e o r e t i c a l  explanation f o r the reason why i t i s not s u f f i c i e n t to examine system XPD at one frequency i s given i n Chapter 5.  F i g . 2.41 shows the system XPD's  measurer! f o r three s l i g h t l y d i f f e r e n t transmit-antenna azimuth adjustments. The f i n a l antenna alignment involved a tradeoff between copolar and crosspolar signal levels to y i e l d the maximum system XPD.  2.6  Reflector The one metre square, f l a t r e f l e c t o r used as the radar path target i s  shown i n F i g . 2.42.  It i s constructed from a sheet of 9.5 mm thick plate  glass supported by an angle-iron frame.  A coating of " S c o t c h t i n t " , a p l a s t i c  loaded with m e t a l l i c p a r t i c l e s , was used to make the surface [2.1].  reflective  A PVC r a i n shield with an aluminum frame was i n s t a l l e d on the  130  r e f l e c t o r to prevent water accumulation which may cause depolarization (as discussed i n Section 2 . 5 . 2 ) . The calculated 3 dB beamwidth of the r e f l e c t o r radiation pattern i s approximately 0 . 2 1 ° [2.50],  This angular displacement corresponds to an  approximate d e f l e c t i o n of only 3.7 mm at the top of the r e f l e c t o r . prevent wind d e f l e c t i o n of the r e f l e c t o r , i n s t a l l e d on the upper r e f l e c t o r  To  two s t a b i l i z i n g struts were  corners.  These tubular struts are  adjustable to allow proper strut tensioning a f t e r r e f l e c t o r alignment. A test was performed to v e r i f y that the received signal l e v e l s were from the r e f l e c t o r and not due to r e f l e c t i o n s from the building on which the r e f l e c t o r was mounted or antenna coupling.  This was accomplished by  comparing received signal l e v e l s f o r the r e f l e c t o r aligned and misaligned. The copolar levels were 34-38 dB lower f o r various misaligned r e f l e c t o r positions.  Cross-polar l e v e l s were observed to be at l e a s t 30 dB lower f o r  r e f l e c t o r misalignment.  A more accurate measurement could not be made f o r  the crosspolar l e v e l s because of l i m i t a t i o n s imposed by the receiver sensitivity.  Some of the measured signal when the r e f l e c t o r was misaligned  may have been from a minor lobe on the r e f l e c t o r r a d i a t i o n pattern.  This i s  l i k e l y because the r e f l e c t o r mount only allowed r e f l e c t o r misalignments of a few degrees.  This was not investigated further because the minimum 30 dB  change i n l e v e l was s u f f i c i e n t to ensure accurate r e s u l t s even during deep fades.  131  2.7  Transmission  Loss  A f t e r t h e antennas and r e f l e c t o r s were a l i g n e d , a comparison was made between the c a l c u l a t e d and measured t r a n s m i s s i o n l o s s between t h e t r a n s m i t t i n g and r e c e i v i n g antenna p o r t s . antenna and r e f l e c t o r alignments significant  T h i s was done to v e r i f y t h e  and t o be sure t h a t t h e r e were no  a n t e n n a - f e e d l i n e mismatches.  A p r e r e q u i s i t e f o r t h e c a l c u l a t i o n of the t r a n s m i s s i o n l o s s i s the v e r i f i c a t i o n of o p e r a t i o n i n the f a r f i e l d The  boundary between t h e near f i e l d  o f the antennas and r e f l e c t o r .  r e g i o n and the f a r f i e l d  region f o r a  2D r a d i a t i n g a p e r t u r e i s commonly e s t i m a t e d where D = a p e r t u r e  diameter  operating frequency, approximately  o r square  the f a r f i e l d  to o c c u r a t a d i s t a n c e R = — — [2.49].  side-dimension  of the antennas b e g i n s  1 8 0 m and t h e f a r f i e l d  2  A t the  at a d i s t a n c e of  o f the r e f l e c t o r b e g i n s a t about 5 0 0  m. When c o n s i d e r i n g t h e antenna and r e f l e c t o r necessary  t o have them s e p a r a t e d by the sum of t h e i r near f i e l d d i s t a n c e s .  I n s t e a d , t o ensure approximations.  t h e two a p e r t u r e systems can be d e s c r i b e d by f a r f i e l d  Jasik d  >  where A i = a p e r t u r e  [2.50]  X  A /l A  suggests 2  2  separation i s d = 3 7 0 meters. f o r this  x+ a6Aj  the a p p r o x i m a t i o n :  •A A  x+ A A  (2.19)  2  area.  F o r one antenna ( A j = 0 . 2 9 2 m )  be used  together i t i s not  system.  and the r e f l e c t o r  (A = 1 m )  Therefore, f a r f i e l d  2  2  the required  approximations  can s a f e l y  132  The  angle between the normal t o the r e f l e c t o r and e i t h e r o f the  antennas i s o n l y 0.651°. along  For t h i s a n g l e ,  the p r o j e c t e d a r e a of the r e f l e c t o r  the antenna a x i s i s i n s i g n i f i c a n t l y s m a l l e r than the r e f l e c t o r p h y s i c a l  area.  Therefore  perpendicular The  the antenna w i l l be assumed t o occupy the same l o c a t i o n  t o the r e f l e c t o r .  two way path  l o s s or "basic transmission  loss"  [2.51] a t 73.5 GHz  i s g i v e n by: 4Tt(2r)  L^ =  10 l o g  H  The  1 ( )  [  2  ~ ]  (2.20)  e n t i r e r e f l e c t o r s u r f a c e i s w e l l w i t h i n the f i r s t  F r e s n e l zone a t  t h i s d i s t a n c e because the v a r i a t i o n i n path l e n g t h from the c e n t e r o f the r e f l e c t o r t o one o f i t s c o r n e r s wavelength [ 2 . 5 2 ] .  Therefore,  i s approximately  one s i x t e e n t h o f a  the r e f l e c t o r g a i n can be c a l c u l a t e d from  [2.50]: 2  G  REF -  1  0  l o  «10  [  A  RFF  -Xr-  2  ]  (  2  '  2  1  )  = -5.1 dB The  atmospheric l o s s due t o m o l e c u l a r  dB/km a t t h i s f r e q u e n c y  absorption  i s nominally  0.3  ( s e e F i g . 1.2 and [2.53]) o r about 0.5 dB f o r the  t o t a l p a t h , but t h i s v a l u e w i l l depend on the atomospheric water vapour content,  which i s q u i t e v a r i a b l e .  The  s p e c i f i e d antenna p o r t  transmission  VSWR a r e l e s s than 1.12. T h i s produces a  l o s s o f 0.014 dB which i s n e g l i b l e .  Thus the t o t a l t r a n s m i s s i o n  loss i s :  133  L  TOT  ^^  L  E  G  r  X  ~  G r E F  +  (2.22)  L a t m o s  = 134.7 - 50.6 - 50.9 - (- 5.1) + 0.5 = 38.8 dB The attenuator  t r a n s m i s s i o n l o s s was measured by c o n n e c t i n g between the model  a calibrated  13-50A mixer and the f e e d l i n e p o r t n o r m a l l y  connected t o the t r a n s m i t t i n g antenna.  T h i s i s p o s s i b l e because t h i s mixer  was connected to the r e c e i v e r v i a a l o n g f l e x i b l e c o a x i a l c a b l e . has  T h i s method  the advantage t h a t the l o s s and mismatch i n the t r a n s m i t t i n g antenna  f e e d l i n e and mixer c o a x i a l c a b l e a r e a u t o m a t i c a l l y i n c l u d e d i n the measurement. When 43 dB of a t t e n u a t i o n was i n s e r t e d , the r e c e i v e r i n d i c a t e d the same s i g n a l l e v e l as when t h i s mixer was connected d i r e c t l y t o the r e c e i v i n g antenna.  There i s an e s t i m a t e d  attenuator The value. The  accuracy  t 2 dB u n c e r t a i n t y i n t h i s measurement due t o  and p o s s i b l e impedance mismatch.  c a l c u l a t e d t r a n s m i s s i o n l o s s i s 4.2 dB l e s s than the measured  Experimental  u n c e r t a i n t y cannot account f o r the t o t a l d i f f e r e n c e .  extra l o s s i s probably  due t o a combination o f r e f l e c t o r  imperfections,  r e f l e c t o r m i s a l i g n m e n t , waveguide f l a n g e mismatch, mixer mismatch, e r r o r i n the s p e c i f i e d antenna g a i n s , and u n c e r t a i n t y i n t h e a t m o s p h e r i c water vapour content.  2.8  Fade M a r g i n Using  -100  the measured path  dBm, the c o p o l a r  l o s s and a u s a b l e  r e c e i v e r s e n s i t i v i t y of  s i g n a l fade margin i s a p p r o x i m a t e l y  65 dB.  T h i s can  -  134  be extended to approximately 70 dB i f averaging times of ten seconds or over are used during data a n a l y s i s .  It i s more d i f f i c u l t to estimate a crosspolar  measurement fade margin because of the uncertainty i n the crosspolar baseline and because the crosspolar l e v e l increases with respect to the copolar l e v e l during deep fades.  If a crosspolar baseline 40 dB below the copolar baseline  i s assumed and depolarization i s 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. extension of the one described i n [ 2 . 1 ] . ran  This system i s an  The o r i g i n a l data acqusition system  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 a c q u i s i t i o n system can be operated on either the NOVA 840 or a smaller, more a v a i l a b l e , SUPERNOVA system.  After preprocessing, the data i s recorded  on one h a l f i n c h , 9-track magnetic tape.  Data analysis i s then performed on  the main u n i v e r s i t y computing f a c i l i t i e s . The following data i s recorded from peripheral instruments i n d i g i t a l form once per second: -  channel A and B received signal levels  -  l o c a l o s c i l l a t o r frequency  -  r e a l time A s i x t e e n channel A/D  converter  i s used t o sample the f o l l o w i n g  parameters once per second: -  t h r e e wind v e l o c i t y v e c t o r s temperature  -  polarization state  -  mixer d i o d e  -  k l y s t r o n power output  voltages  The s t a t u s of the f i v e r a i n g a u g e s are sampled Hardware and software p r o v i s i o n s size categories  once per second.  16 times per s e c o n d .  a l s o e x i s t to record  sixteen  drop  136  3.  3.1 3.1.1  METEOROLOGICAL INSTRUMENTATION  Raingauge Network 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 s u f f i c i e n t s p a t i a l and temporal r e s o l u t i o n .  In two  reviews by Crane [3.1],  between  [3.2] he concludes that the lack of agreement  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 f o r a s i m i l a r 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 i n propagation experiments. High s p a t i a l and temporal resolution i s required f o r path rainrate measurements because r a i n f a l l i s not uniform, but instead, occurs i n " c e l l s " of f i n i t e horizontal extent.  Rain c e l l s vary i n extent from a few kilometers  up to approximately twenty kilometres.  Within a r a i n c e l l , rainrates may only  be uniform over distances of a few hundreds of metres.  Rain c e l l s can also  change morphologically over periods of a few seconds and t r a v e l h o r i z o n t a l l y at speeds approaching the wind v e l o c i t y .  F i g . 3.1 from [3.6], gives two  examples of r a i n c e l l structure and temporal change.  Small r a i n c e l l s and  r a p i d l y changing point r a i n f a l l rates are c h a r a c t e r i s t i c thundershower a c t i v i t y .  of heavy r a i n f a l l or  Medium and l i g h t r a i n f a l l i s t y p i c a l l y much more  137  : Cf-  °  !  _J  I  km  Z  I  3  (Top) Plot of rainfall-rate contours (in millimeters per hour), showing two rain cells on the Bedfordshire raingauge network; (bottom) contours 2 minutes 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.  F i g . 3.1. Rain c e l l examples, from [3.6].  138  u n i f o r m h o r i z o n t a l l y and changes much more s l o w l y .  F u r t h e r d a t a on  rain  c e l l s i s a v a i l a b l e i n [3.9]. To be a b l e to c h a r a c t e r i z e the r a i n r a t e along a path w i t h a c c u r a c y i t i s n e c e s s a r y 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. s p a c i n g s of " s e v e r a l hundred metres".  reasonable  Crane  [3.1]  F e d i and M a n d a r i n i  suggests  [3.4] have e s t i m a -  t e d the spread of a t t e n u a t i o n v a l u e s which they expected  f o r a propagation  experiment  collecting  spaced  at 30 GHz  u s i n g raingauges w i t h a 730 sq.cm.  at 100 m and 1 km and w i t h i n t e g r a t i o n times of 10 sec and  T h e i r r e s u l t s are shown i n F i g .  3.1.2  area  60 s e c .  3.2.  R a i n Gauge Types The  two  b a s i c types of non-disdrometer  used i n p r o p a g a t i o n experiments  r a i n gauges which have been  are the t i p p i n g - b u c k e t and c a p a c i t i v e .  A  t i p p i n g - b u c k e t r a i n gauge c o l l e c t s water i n a f u n n e l and d i r e c t s i t t o a s m a l l two  chambered bucket.  " t i p - s i z e " has accumulated  When a q u a n t i t y of water e q u a l to the gauge the weight  and empty, a l l o w i n g the second s i g n a l i s generated  of the water causes  chamber to s t a r t f i l l i n g .  as the bucket  tips.  An  to t i p  electrical  A c a p a c i t i v e 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 f u n n e l between two which form the e l e c t r o d e s of a c a p a c i t o r . c a p a c i t a n c e i s u s u a l l y monitored  the bucket  p a r a l l e l plates  The r e s u l t i n g change i n  as a s h i f t  i n the f r e q u e n c y of an  oscillator  c i r c u i t i n c o r p o r a t i n g the c a p a c i t o r . C a p a c i t i v e r a i n gauges have been used Laboratories  [3.-10], [3.11],  [3.12] and  by s e v e r a l i n v e s t i g a t o r s at B e l l  by F e d i and h i s coworkers  [3.13],  139  40  f = 30  GHz  10  sec theoretical  .*=100 m  20  h  13  o  g  200  100 R a i n r a t e (mm/h)  F i g . 3.2.  A t t e n u a t i o n spread f o r d i f f e r e n t s p a c i n g and i n t e g r a t i o n t i m e s .  raingauge  140  [3.3].  The basic advantage of these r a i n gauges i s t h e i r quasi-instantaneous  response and t h e i r a b i l i t y to measure extremely high r a i n r a t e s .  Fedi and  Merlo [3.13] have shown the superior response of capacitance gauges compared to tipping-bucket r a i n gauges f o r 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 r a i n r a t e s . [3.11] report s a t i s f a c t o r y readings only above 10 mm/hr.  Freeny and Gabbe  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 i n accuracy.  Capacitive r a i n gauges were t r i e d i n an  e a r l i e r study at UBC but were abandoned because of t h e i r poor performance at low r a i n rates  [2.1].  The tipping-bucket r a i n gauge i s "simple, r e l i a b l e 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], B l e v i s , Dohoo and McCormick [3.15]., Fedi [3.3], Skerjanec and Samson [3.16] and Ippolito [3.17], size of the gauges used i n these experiments were: 0.25 mm [3.15], [3.17] and 0.2 mm [3.3].  The t i p  [3.16],  This results i n an integration time at 50 mm/hr of  18 and 14.4 seconds r e s p e c t i v e l y .  These periods are compatible with the  l i m i t s described i n 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 i p p i n g bucket raingauges at various r a i n r a t e s .  The analysis showed that the gauges  he used had very s i m i l a r accuracies f o r higher rainrates and that the tipping bucket gauges were more accurate for lower r a i n r a t e s .  Segal [3.9]  also  141  includes a d i s c u s s i o n of raingauge accuracy.  F i g . 3.3 from [ 3 . 9 ] shows the  e f f e c t of h o r i z o n t a l windspeed on gauge catch e f f i c i e n c y .  The reduction i n  c o 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 c a r r y i n g 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  p r o b a b i l i t y of intense r a i n f a l l i n Vancouver (see F i g . 3.4 from [3.9]) l e d to the s e l e c t i o n of t i p p i n g bucket r a i n gauges f o r t h i s experiment.  To reduce  the problems of integration-time averaging, r a i n gauges with a very small t i p s i z e (0.05 mm of r a i n ) were constructed.  The f i r s t v e r s i o n of these 920 cm  c o l l e c t i n g area r a i n gauges i s described i n [2.1].  2  These r a i n gauges had a  t i p s i z e which was adjustable to a minimum of 0.05 mm.  However, a t t h i s t i p  s i z e these gauges suffered some inaccuracy due to water r e t e n t i o n i n the bucket.  This problem was a l l e v i a t e d by i n c o r p o r a t i n g a new bucket geometry  and by the i n c l u s i o n of several small b a l l bearings i n a c a v i t y i n the lower p o r t i o n 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 r e s u l t s i n a r a p i d and f o r c e f u l t i p ,  g r e a t l y reducing the water retained i n the bucket.  This extremely small t i p  s i z e r e s u l t s i n an i n t e g r a t i o n time of only 3.6 seconds a t 50 mm/hr. acceptable i n t e g r a t i o n times down to a few mm/hr.  and :  ( I t i s not p o s s i b l e to put  an exact lower l i m i t on the acceptable i n t e g r a t i o n time because at low r a i n rates the rate-of-change  of point r a i n r a t e i s also g r e a t l y 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 c a t c h e f f i c i e n c y as a f u n c t i o n  of h o r i z o n t a l  windspeed,  from [3.9.]  143  Fig.  3.4. P r o b a b i l i t y of e x c e e d i n g 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 r a i n gauges to the data a c q u i s i t i o n system i s described i n  [2.1]. The accuracy of the r a i n gauges i s determined b y the t i p size accuracy and the t i p i n t e r v a l sampling p e r i o d .  The average t i p size accuracy  -  measured by allowing a l a r g e , known volume of water to pass through the gauge and recording the number of tips - i s better than ± 1% for a l l gauges. Sampling of the r a i n gauge t i p i n t e r v a l i s done sixteen times a second by the data a c q u i s i t i o n system.  At low r a i n rates the t o t a l measurement•error  almost e n t i r e l y due to the t i p size accuracy.  is  At higher r a i n rates the  sampling i n t e r v a l i s the larger source of e r r o r .  At 50 mm/hr rainrate  the  t o t a l error i s below ± 2.7%.  A photograph of one r a i n gauge with i t s cover  removed i s included as F i g .  3.5.  3.1.4  Raingauge Locations Rainrate i n this experiment i s measured by a network of f i v e r a i n  gauges spaced along the propagation path.  These r a i n 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 s p a t i a l r e s o l u t i o n f o r v i r t u a l l y a l l rainstorms i n this climatic region.  The r a i n gauge signals are  transmitted to the data a c q u i s i t i o n system on dedicated half-duplex telephone lines.  3.2  Raindrop Size Measurement To be able to accurately correlate observed 73 GHz attenuation and  meteorological conditions, the r a i n drop size d i s t r i b u t i o n must also be measured.  Most propagation studies have compared attenuation observations to  1 4 5  F i g . 3.5.  Raingauge with c o v e r removed.  146  calculated values based on the "standard" rain-drop size d i s t r i b u t i o n s referred to as the Laws and Parsons, Marshall and Palmer and Joss et a l distributions.  These d i s t r i b u t i o n s seem to provide reasonable agreement for  most observations on an average b a s i s , e s p e c i a l l y at the lower frequencies. However, some experimenters have made attenuation observations, e s p e c i a l l y i n the millimetre frequency range, which do not appear to f a l l within the l i m i t s calculated from these d i s t r i b u t i o n s [3.18],  [3.19],  [3.20],  [3.4].  Some of the discrepancies between measured and calculated  attenuation  are undoubtably due to the n a t u r a l , wide v a r i a t i o n i n r a i n drop size distribution.  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 d i s t r i b u t i o n s . Simultaneous measurement of the drop size d i s t r i b u t i o n , e s p e c i a l l y including the smaller drops, i s f a r more important i n the upper millimetre range than at the lower millimetre and microwave frequencies.  For shorter  wavelengths, the e f f e c t 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 d i s t r i b u t i o n has only a small effect on the attenuation [3.24],  [3.25],  [3.4].  However, i n the range between 50 and 100 GHz the  s e n s i t i v i t y of attenuation to drop size d i s t r i b u t i o n i s very high [3.21], [3.24],  [3.2],  [1.58],  [1.85].  For these reasons,  the measurement of drop  size d i s t r i b u t i o n has been given careful consideration i n the design of t h i s experiment.  147  3.3  Raindrop s i z e t r a n s d u c e r methods The  three basic  t r a n s d u c e r mechanisms c o n s i d e r e d f o r  measurement of r a i n d r o p s i z e s were: static.  A c a r e f u l s e a r c h of the  o p t i c a l , e l e c t r o m e c h a n i c a l and  the  d i f f e r e n t methods has  method was  3.3.1  chosen f o r f u r t h e r  two  comprehensive A r e v i e w of  here to show why  the  the  electrostatic  investigation.  O p t i c a l Methods O p t i c a l methods r e l y on e i t h e r :  scanning, a r r a y s of sensors,  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 w i t h the e x c e p t i o n of the the  No  been p u b l i s h e d .  d i s d r o m e t e r t r a n s d u c e r methods i s i n c l u d e d  two  of o p t i c a l schemes and  language r e f e r e n c e s to e l e c t r o s t a t i c methods.  comparison of  electro-  l i t e r a t u r e uncovered r e f e r e n c e s to  modern e l e c t r o m e c h a n i c a l methods, a wide v a r i e t y english  real-time  or s c a t t e r i n g .  or assumptions about the drop v e l o c i t y or d i r e c t i o n of s c a n n i n g and orientation  a r r a y methods may  degrade the  require  ( i . e . canting angle).  methods, w i t h the  o p e r a t i o n of the  s c a n n i n g , a r r a y and overheads a s s o c i a t e d  to the  correction  An a d d i t i o n a l  e x c e p t i o n of the  o p e r a t i n g problems due  O p t i c a l methods,  l a s e r c o r r e l a t i o n method, have the  drop s i z e i s measured d i r e c t l y , without r e l y i n g on  that  simultaneous knowledge travel.  However,  f o r drop geometry advantage of  the  the  and  optical not  A l l o p t i c a l methods s u f f e r some  large variations  i n ambient l i g h t l e v e l .  l a s e r methods a l s o have h i g h e l e c t r o n i c with s i g n a l  advantage  l a s e r method, i s t h a t wind w i l l  transducer.  laser  processing.  hardware  The  148  3.3.1.1  O p t i c a l 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 s c a n n e r s .  Conventional  s u i t a b l e because scanning  r a t e s were not  its  terminal v e l o c i t y .  (even i n one real-time  with  F l y i n g - s p o t scanner type equipment c o u l d p r o b a b l y  be  t h e i r use.  No  high  examples of  disdro-  literature.  O p t i c a l A r r a y Methods  Methods u s i n g a r r a y s f e a s i b l e o p t i c a l methods.  of p h o t o d e t e c t o r s The  are the most p r o m i s i n g  basic operation  depends on the drop  the l i g h t from a source which would n o r m a l l y  s t r u c t e d on the elements of a p h o t o d e t e c t o r  array.  method i s f a b r i c a t i n g the a r r a y of d e t e c t o r s . the e f f e c t i v e s p a c i n g  The  This precludes  crete photodetectors  of  the  partially  have f a l l e n unobd i f f i c u l t y with  this  To have the r e q u i r e d r e s o l u -  between a r r a y elements would need to be  the minimum measurable drop diameter ( i . e . p r e f e r r a b l y l e s s than microns).  constructed  the p r a c t i c a l problems a s s o c i a t e d w i t h  meters u s i n g e i t h e r of these approaches were found i n the  tion,  enough  image p r o c e s s i n g would be p r o h i b i t i v e f o r t h i s  l e v e l s of ambient l i g h t seem to p r e c l u d e  occluding  at  d i m e n s i o n ) , the hardware requirements f o r u l t r a - h i g h speed,  adequate scan r a t e s but  3.3.1.2  not  adequate to r e c o r d a drop f a l l i n g  Even i f an imaging tube c o u l d be scanned f a s t  d i g i t i z a t i o n and  experiment.  t e l e v i s i o n cameras were c o n s i d e r e d  l e s s than  250  the p o s s i b i l i t y of an a r r a y f a b r i c a t e d from d i s -  unless  a l e n s or f i b r e o p t i c system was  also incor-  porated.  A p r e l i m i n a r y i n v e s t i g a t i o n showed the l e n s system would be  quite  l a r g e and  probably  the  require special f a b r i c a t i o n .  The  d i s a d v a n t a g e s of  149  f i b r e o p t i c system a r e the d i f f i c u l t y of c o n s t r u c t i o n f o r l a r g e a r r a y s large individual fibre  beamwidths.  E x c e l l e n t monolithic photodetector available. limited.  and  a r r a y s w i t h good r e s o l u t i o n are  The major problem i s t h a t the l i n e a r s i z e of the a r r a y s i s T h i s w i l l mean t h a t the c o l l e c t i n g a r e a u s i n g a s i n g l e a r r a y  u s u a l l y be  too s m a l l to o b t a i n a s t a t i s t i c a l l y v a l i d  distribution  [3.26].  The  a r r a y s cannot be l i n e a r l y concatenated  l a r g e r a r r a y because of the i n t e g r a t e d c i r c u i t s e v e r a l a r r a y s c o u l d be staggered be a c c e p t a b l e  packages used.  to form a l a r g e r a r r a y , but  i f the drops f e l l v e r t i c a l l y .  f e a s i b l e t o use  sample of the  raindrop  to form a Conceivably,  t h i s would  I t i s however, p r o b a b l y  a l a r g e number of a r r a y s i n r e a s o n a b l y  will  still  close proximity  and  combine t h e i r measured r a i n d r o p h i s t o g r a m s to improve the r e l i a b i l i t y of statistical  only  the  sample.  A s m a l l i n t e g r a t e d o p t i c a l a r r a y has been used by Cunningham [3.27] t o make measurements on a v a r i e t y of hydroraeteors. sample s i z e was and  The  problem of the  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 a r r a y  a f f i x i n g i t t o the e x t e r i o r of a j e t a i r c r a f t ,  small  vertically,  thus c o n s i d e r a b l y i n c r e a s -  i n g the number of drops sampled per u n i t t i m e . Knollenberg  [3.28] has c o n s t r u c t e d an o p t i c a l a r r a y f o r hydrometeor  s i z e measurement u s i n g o p t i c a l f i b e r s and method, one o t h e r end  end  d i s c r e t e photodetectors.  o f each o p t i c a l f i b e r i s p l a c e d i n a l i n e a r a r r a y and  i s connected to a p h o t o m u l t i p l i e r t u b e .  associated with  In  this the  There a r e o b v i o u s problems  the f a b r i c a t i o n of l a r g e a r r a y s u s i n g t h i s method, even i f  smaller photodetectors  c o u l d be employed.  T h i s type of a r r a y was  used f o r  150  sampling from a i r c r a f t where the small l i n e a r array extent i s 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 d i s t r i b u t i o n over a path of up to 200 meters i n length. A medium power cw laser i s o p t i c a l l y expanded to a 20 cm beam diameter and oriented h o r i z o n t a l l y along the path. t a l l i n e a r photodetectors  The receiver consists of two horizon-  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 i n an analog c i r c u i t .  The correlator  output  for d i f f e r e n t correlation delays i s then proportional to the number of drops which t r a v e l l e d the v e r t i c a l distance between the sensors i n the correlation delay time. Unfortunately this technique r e l i e s on the assumption of a timeinvariant monotonic relationship between drop-size and v e r t i c a l v e l o c i t y . a result,  As  changes i n drop v e r t i c a l v e l o c i t y due either to v e r t i c a l wind  v e l o c i t i e s or turbulence w i l l produce a distorted raindrop size histogram. The error i n calculated drop size due to a change i n drop v e r t i c a l velocity can be determined from the known drop size terminal v e l o c i t y relationships [3.31].  As an example a 1 m/s updraft would produce an approximate error i n  diameter of 23% for a 3 mm drop and 40% f o r a 5 mm drop.  151  V e r t i c a l wind v e l o c i t i e s w i l l also produce v e r t i c a l l y correlated o p t i c a l 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 i s 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-  e l e c t r i c raindrop spectrometer  constructed by Mason and Ramanadham [3.32],  This disdrometer measured the l i g h t scattered by a drop as i t f e l l near an intense source.  The scattered l i g h t at an angle of 20 degrees o f f - a x i s was  collected i n a telescope-type lens system and directed to a photomultiplier tube.  The drops were then e l e c t r o n i c a l l y sorted into eight size  categories.  Dingle and Shulte [3.33] constructed a disdrometer s i m i l a r to the one described by Mason and Ramanadham.  In this reference the theory f o r an optimum  scattering type instrument i s presented. drops from 0.72 mm to 3.13 mm i n diameter.  The instrument was calibrated with The r e s u l t i n g c a l i b r a t i o n curve  shows that the output pulse height i s proportional to the drop diameter squared. Very recently, Klaus [3.34] has reported a s i m i l a r photoelectric drometer.  dis-  In this case the degree of extinction of a beam i s used to deter-  mine the drop s i z e .  This system uses s o l i d - s t a t e diode sources and detectors  and a microprocessor to sort the drops into eight  categories.  A serious l i m i t a t i o n of both these analog o p t i c a l systems i s the change i n the small-signal s e n s i t i v i t y of the photodetectors with changes i n ambient l i g h t l e v e l .  This i s p a r t i c u l a r l y troublesome during periods of r a i n  152  when the ambient l i g h t l e v e l can be quite variable [3.31].  This type of  system could conceivably be improved by using narrow bandwidth o p t i c a l ters and higher i n t e n s i t y l i g h t sources.  fil-  Dingle and Shulte [3.33] have also  designed a " l i g h t s h i e l d " which improved the operation of, their scattered l i g h t disdrometer to some extent.  3.3.2  Electromechanical Methods The disdrometers most commonly used i n 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  signal.  The mechanical to e l e c t r i c  energy con-  version i s accomplished using either a moving c o i l In a s t a t i c magnetic f i e l d , piezoelectic  3.3.2.1  transducers  or a conventional audio microphone.  Moving C o i l i n Magnetic F i e l d Method The disdrometer using a moving c o i l i n 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 i n studies by Waldvogel [3.38], Joss, Thams and Waldvogel [3.39], Brewer and Kreuels [3.40] and K e i z e r , Snieder, and Haan [3.41]. The construction of the coil-magnet transducer conventional acoustic loudspeaker. connected to the moving c o i l .  A c o l l e c t i n g surface, usually 50 c m , i s 2  The c o l l e c t i n g surface i s designed to have a  low mass f o r maximum signal output. permanent magnet.  i s very s i m i l a r to a  The c o i l i s situated i n the a i r gap of a  The momentum of the drop causes a displacement of the c o i l  thus producing an e l e c t r i c  signal at the c o i l terminals.  153  In some models, a second coil-magnet assembly i s 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  P i e z o e l e c t r i c Method The p i e z o e l e c t r i c 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 p i e z o e l e c t r i c disdrometer uses a s o l i d a c r y l i c clyinder with a beveled top. a brass block.  The cylinder and a p i e z o e l e c t r i c transducer are then bonded to The Impact of the drop on the top of the cylinder causes an  acoustic wave to t r a v e l through the cylinder to the transducer.  Rowland  instead cast the transducer i n a s o l i d block of epoxy and thus eliminated the brass block.  The p i e z o e l e c t r i c disdrometer has been used by Goldhirsh  [3.22], [3.43] and Rowland, Bennett and M i l l e r  3.3.2.3  [3.44].  Other electromechanical Disdrometers Other electromechanical disdrometers have been constructed using con-  ventional audio microphones.  K i n n e l l [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 microphone using a i r or a f l u i d .  None of these instruments were s a t i s f a c t o r y but  they d i d lead to the design of the other electromechanical transducers cribed p r e v i o u s l y .  des-  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 p i e z o e l e c t r i c proportional to D^*-*.  The range of measurable drop sizes i s 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 f o r electromechanical transducers  than  for transducers with a pulse proportional to a lower power of the drop diameter (assuming s i m i l a r noise l e v e l s ) . The major disadvantage of electromechanical transducers i s t h e i r s e n s i t i v i t y to drop v e r t i c a l v e l o c i t y .  Rowland also investigated the r e s -  ponse of these sensors to drops f a l l i n g below terminal v e l o c i t y .  He found  the response of the transducers was reasonably well predicted by the quant i t y : mv /Djwhere ra = drop mass, v = v e l o c i t y and D = drop diameter. 2  This,  i s 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 f o r drops f a l l i n g at v e r t i c a l speeds other than their a i r terminal v e l o c i t y .  However, to be able to use this c o r r e c t i o n ,  drop v e r t i c a l v e l o c i t y must be known.  still  actual  This requires simultaneous knowledge  of the v e r t i c a l wind speed and the drop d i r e c t i o n of t r a v e l with respect to the sensor. K i n n e l l [3.48] has examined the effects of drop shape, drop v e l o c i t y and impact l o c a t i o n on the Joss-Waldvogel disdrometer.  This i n v e s t i g a t i o n  found a discontinuity i n the response of the transducer associated with drop  155  velocity.  No d e f i n i t e conclusions regarding the cause or e f f e c t of this  d i s c o n t i n u i t y were g i v e n .  Variations i n the p o s i t i o n of the drop impact on  the target were observed to cause a change i n transducer output which was described as "quite l a r g e " .  The drop shape was also found to introduce a  s i g n i f i c a n t uncertainty i n transducer reponse. "variations i n factors  K i n n e l l concludes that  such as r a i n drop v e l o c i t y and raindrop shape genera-  ted by a i r movements might produce unacceptable errors i n the measurement of raindrop size by the disdrometer under some r a i n f a l l c o n d i t i o n s " . . . A further disadvantage of the coil-magnet transducers i s t h e i r s u s c e p t a b i l i t y to wind-produced acoustic n o i s e .  This problem i s accentuated  by the requirement of a low mass, large area c o l l e c t i n g surface.  Wind  shielding i s only p a r t i a l l y e f f e c t i v e i n reducing t h i s 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  E l e c t r o s t a t i c Methods E l e c t r o s t a t i c methods work by f i r s t arranging f o r a drop to a r t i f i -  c i a l l y accumulate a charge which i s related to the drop size and then measuring this charge as the drop impacts on a conductor at ground p o t e n t i a l . The only detailed english language reference to e l e c t r o s t a t i c  measurement of  rain-drop sizes which could be located was a paper by Lammers [3.49]. An e a r l i e r paper by Keiley and M i l l e n [3.50] described a s i m i l a r technique to measure cloud-drop s i z e s . and used by Sander [1.84], [3.51]. by Humpleman and Watson -[1.85].  electrostatic  A Lamraers-type disdrometer was b u i l t  A unit developed by Sander was also used  156  The instrument described by Lammers b a s i c a l l y consisted of two fine horizontal wire grids separated h o r i z o n t a l l y by a small distance.  The top  g r i d was connected to a 300 V positive dc supply.  A high impedance a m p l i f i e r  was connected between the bottom g r i d and ground.  The grids were constructed  from p a r a l l e l strands of 0.05  mm tungsten wire spaced 0.75 mm apart.  This  instrument had a 25 cm c o l l e c t i n g area. 2  Lammers found that this instrument produced a pulse amplitude propor2.32 t i o n a l 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 grid.  This i s important to ensure that the pulse amplitude i s 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 t h i s did not cause "much v a r i a t i o n " i n the output s i g n a l . The explanation given by Lammers as to how the transducer functioned was b a s i c a l l y 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 a m p l i f i e r . The e l e c t r o s t a t i c instrument described by Keiley and M i l l e r [3.50] was designed for measurements  of cloud-drop size d i s t r i b u t i o n s .  Drops sampled by  this instrument were directed through a small conducting o r i f i c e by a high v e l o c i t y a i r stream.  They then impacted on a s o l i d conducting target which  was connected to an a m p l i f i e r .  A potential difference of 400 V was main-  tained between the o r i f i c e and target p l a t e .  The 200 micron diameter  157  sampling o r i f i c e o f t h i s 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 v o l t a g e p u l s e produced  by t h i s instrument was a p p r o x i m a t e l y  p r o p o r t i o n a l t o the drop diameter squared.  I n t h i s i n s t r u m e n t t h e sampled  drop does not c o n t a c t the c o n d u c t i n g o r i f i c e .  K e i l e y and M i l l e r  believed  t h a t the p u l s e was due t o a h e m i s p h e r i c a l induced charge a c q u i r e d by the drop as i t c r o s s e d the a i r gap.  The a c t u a l p u l s e was b e l i e v e d t o r e s u l t from t h e  c a n c e l l a t i o n of the charge on one s i d e of the drop as i t s t r u c k t h e t a r g e t . T h i s i n s t r u m e n t was s e n s i t i v e enough to measure drop s i z e s down t o 4 microns.  3.3.4  Comparison o f Methods An exact q u a n t i t a t i v e comparison  i s not p o s s i b l e because methods.  between drop s i z e measurement methods  comparable d a t a are not a v a i l a b l e f o r d i f f e r e n t  A summary of the major advantages  and d i s a d v a n t a g e s a r e g i v e n  below: - O p t i c a l s c a n n i n g methods a r e e i t h e r too slow o r p r o h i b i t i v e l y e x p e n s i v e and s u f f e r from ambient l i g h t  problems.  - O p t i c a l a r r a y methods have the advantage have inadequate  o f d i r e c t s i z e measurement but  sampling s i z e s and r e q u i r e c o r r e c t i o n f o r drop  orientation  and c a n t i n g a n g l e . - L a s e r 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 s u f f e r s from the disadvantage t h a t drop v e l o c i t y i s a c t u a l l y b e i n g observed.  T h i s method i s a l s o v e r y e x p e n s i v e .  158  - L i n e a r o p t i c a l methods ( i . e . s c a t t e r i n g and i n e x p e n s i v e but have s e n s i t i v i t y and - The  two  e x t i n c t i o n ) are simple  ambient l i g h t  level  p r o p o r t i o n a l to D^*^  to D^*^  r e s u l t s i n a low s e n s i t i v i t y e r r o r s due  and drop v e l o c i t y squared. to s m a l l d r o p s .  impact  r e l a t i v e l y easy  not w e l l documented.  I t produces a p u l s e a p p r o x i m a t e l y  drop diameter  and  No data was  a v a i l a b l e on the e r r o r s due location.  a l s o have  location. to c o n s t r u c t but i s p r o p o r t i o n a l to  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  angle of i n c i d e n c e or impact  to  This  These i n s t r u m e n t s  to drop shape, angle of i n c i d e n c e and  squared  are easy  t h a t the t r a n s d u c e r p u l s e i s  - The e l e c t r o s t a t i c method i s s i m p l e and  drops.  problems.  e l e c t r o m e c h a n i c a l methods are v e r y w e l l documented and  implement but have the disadvantage  and  to s m a l l  to drop v e l o c i t y ,  shape,  I n t u i t i v e l y , these s o u r c e s of e r r o r  should be l e s s s e r i o u s than f o r the e l e c t r o m e c h a n i c a l methods. These c o n s i d e r a t i o n s l e d 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 f o r f u r t h e r i n v e s t i g a t i o n i n t h i s experiment. s e n s i t i v i t y was s t u d i e d and  The  p o t e n t i a l f o r improved  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 s h o r t wavelength b e i n g  the r e c e n t s p e c u l a t i o n s i n the l i t e r a t u r e t h a t h i g h e r than  d i c t e d a t t e n u a t i o n s i n the h i g h e r m i l l i m e t r e range ( i . e . above 40 GHz) p a r t l y due  to u n d e r - e s t i m a t i n g  S e c t i o n 3.2.  I t was  a l s o hoped t h a t the e l e c t r o s t a t i c method would be  transducers.  were  the number of s m a l l drops^ as d i s c u s s e d i n  prone to the types of e r r o r s which degrade the a c c u r a c y of the mechanical  pre-  electro-  less  159  3.4  Disdrometer Transducer The e l e c t r o s t a t i c disdrometer transducers  constructed f o r this e x p e r i -  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 s i m i l a r 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 i n s t r u ment resulted i n several improvements to the basic design. ments were incorporated i n a second generation  These improve-  transducer.  The f i r s t transducer b u i l t had a 25 cm sampling area and grids formed 2  from double layers of horizontal wires with 0.45 mm horizontal spacing.  This  double layer g r i d system was also used by Lammers and results from the method used to form the g r i d s .  Because of the small spacing between the wires, the  most f e a s i b l e way to construct the grids i s by winding the wire on a frame s i m i l a r to the one shown i n F i g . 3.6, producing a double layer  structure.  The g r i d spacing was reduced from the 0.75 mm used by Lammers to 0.45 mm to improve the minimum measurable drop s i z e .  The diameter of the Individual  g r i d 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 r e a d i l y available and  corrosion r e s i s t a n t . The basic operating l i m i t a t i o n s of this transducer were found to r e s u l t from movement of the grid wires and the double g r i d 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 p r e a m p l i f i e r .  S i g n i f i c a n t motion of the g r i d wires resulted from:  the passage of the drop through the g r i d s , high wind v e l o c i t i e s and b u i l d i n g  Polycarbonate Frame  Tungsten Wi re Copper Bar  F i g . 3.6. Disdrometer t r a n s d u c e r g r i d .  o  161  vibration.  Passage of the drop through the g r i d s r e s u l t e d i n a d e c a y i n g  s i n u s o i d a l output from the t r a n s d u c e r a f t e r seem to s e r i o u s l y a f f e c t c r e a s e the t o t a l  the main p u l s e .  the main p u l s e a c c u r c y but d i d s i g n i f i c a n t l y i n -  p e r i o d of the p u l s e due  to a s i n g l e drop and hence the  minimum p e r i o d between drops f o r a c c u r a t e r e s u l t s . was  not u s u a l l y as d e t r i m e n t a l as g r i d motion due  b u i l d i n g v i b r a t i o n was  T h i s d i d not  G r i d motion due to wind to b u i l d i n g v i b r a t i o n .  The  a p p a r e n t l y caused by the movement o f l a r g e numbers of  s t u d e n t s between c l a s s e s and a l a r g e v e n t i l a t i o n f a n motor on the r o o f . These u n d e s i r e d s i g n a l s c o u l d not be reduced by f i l t e r i n g because r e l a t i v e l y broadband  and o c c u p i e d f r e q u e n c i e s s i m i l a r t o the major  components of the d e s i r e d  they were spectral  pulse.  The double g r i d s t r u c t u r e was  a d i s a d v a n t a g e because i t r e s u l t e d i n  g r e a t e r drop breakup and i n c r e a s e d water r e t e n t i o n .  I t was  observed  that  a f t e r a p e r i o d o f o p e r a t i o n i n a c t u a l r a i n t h e r e were s m a l l d r o p l e t s o f water a t t a c h e d to the g r i d w i r e s . the  lower g r i d s l a y e r s .  The amount of water was  T h i s was  considerably larger  on  b e l i e v e d t o be due t o the i n 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 s u c c e s s i v e grid layer.  R e t a i n e d water on the upper g r i d r e s u l t s i n reduced d i s d r o m e t e r  a c c u r a c y because a p a r t of the drop c a p t u r e d by the upper g r i d w i l l not charge on the lower g r i d r e s u l t i n g i n a reduced o u t p u t f o r t h a t d r o p . 5  a d d i t i o n , i f t h i s water i s d i s l o d g e d by a subsequent t h a t drop w i l l be l a r g e r . be  disIn  drop, the I n d i c a t i o n f o r  Water r e t a i n e d on the lower g r i d i s not thought t o  detrimental. Another problem w i t h the f i r s t  between the upper and lower g r i d s .  d i s d r o m e t e r was  leakage c u r r e n t s  A f t e r l o n g p e r i o d s of o p e r a t i o n t h e 5  162  b a s e l i n e o r dc o u t p u t l e v e l of the t r a n s d u c e r p r e a m p l i f i e r o f t e n  drifted.  When the t r a n s d u c e r was c l e a n e d i n a l c o h o l and d r i e d , t h i s problem ed.  disappear-  T h i s seemed t o i n d i c a t e t h a t a h i g h r e s i s t a n c e leakage path had'been  e s t a b l i s h e d a l o n g the s u r f a c e o f the g r i d contaminants  frame, and was p r o b a b l y due t o  e n t e r i n g the t r a n s d u c e r w i t h t h e r a i n and a b u i l d u p of  moisture. The  d e s i g n o f t h e second d i s d r o m e t e r t r a n s d u c e r a l l e v i a t e d t h e  problems d i s c u s s e d p r e v i o u s l y , i n c r e a s e d the sampling s i z e and f u r t h e r r e duced  the g r i d c o n d u c t o r s p a c i n g .  i n c r e a s e d t o 50 c m statistically  2  The sampling a r e a o f the t r a n s d u c e r was  i n o r d e r t o reduce  the p e r i o d o f time r e q u i r e d f o r a  v a l i d drop d i s t r i b u t i o n sample.  (A 50 c m  2  sampling a r e a i s  a l s o used on almost a l l e l e c t r o m e c h a n i c a l d i s d r o m e t e r s . ) The major improvement i n c o r p o r a t e d i n the second d i s d r o m e t e r was an improved  grid structure.  These g r i d s used a s i n g l e l a y e r of more  spaced wire w i t h f a r g r e a t e r w i r e t e n s i o n . reduced t o 0.234 mm t o f a c i l i t a t e  closely  G r i d wire s p a c i n g was f u r t h e r  the measurement o f s m a l l e r d r o p s .  This  g r i d s p a c i n g i s b e l i e v e d t o be v e r y c l o s e t o the minimum p r a c t i c a l s p a c i n g f o r g r i d s of t h i s a r e a .  A s i n g l e g r i d l a y e r was used  t o reduce  breakup,  splatter  and water r e t e n t i o n .  minimize  the g r i d movement and t o i n c r e a s e t h e n a t u r a l o s c i l l a t i n g  of t h e g r i d v i b r a t i o n s .  The maximum p o s s i b l e w i r e t e n s i o n was used t o frequency  Maximum w i r e t e n s i o n i s a l s o n e c e s s a r y f o r b e s t w i r e  spacing u n i f o r m i t y . The wire chosen f o r the g r i d was 0.038 mm t u n g s t e n .  This choice  i n v o l v e d a t r a d e o f f between t h e s m a l l e s t p o s s i b l e d i a m e t e r - t o reduce and the h i g h e s t p o s s i b l e t e n s i l e s t r e n g t h - t o a l l o w maximum w i r e  breakup-  tension.  163  Tungsten was  chosen over o t h e r metals because  v e r y h i g h t e n s i l e s t r e n g t h and was Fig.  3.6  shows the g r i d  P o l y c a r b o n a t e was  a v a i l a b l e i n the diameter range  frame and the method of winding  chosen f o r the frame because  s t r o n g and e a s i l y machinable. important because  i t i s corrosion resistant,  found to be  required.  the w i r e .  i t is insulating,  Frame r i g i d i t y was  has  extremely  extremely  the combined f o r c e s of the a p p r o x i m a t e l y f o u r hundred  wires  - each o f which i s under a t e n s i o n c l o s e to the b r e a k i n g p o i n t of the w i r e tends to deform  the g r i d near the c e n t e r .  T h i s d e f o r m a t i o n would, then  result  i n a r e d u c t i o n i n the w i r e t e n s i o n and s p a c i n g u n i f o r m i t y i n the middle of the g r i d .  A copper bar i s bonded i n t o a s l o t  p r o v i d e an e l e c t r i c a l  on each s i d e of the frame t o  c o n t a c t between the w i r e s and a c o n n e c t i o n to the  grid.  S l o t s f o r each w i r e were machined i n t o the p o l y c a r b i n a t e and copper b a r u s i n g t h e t h r e a d c u t t i n g f a c i l i t i e s on a l a t h e . cm x 9.4  cm a r e a was  A f t e r the t h r e a d s were c u t , a  m i l l e d through the frame.  The g r i d a r e a i s l a r g e r  9.4 than  the sampling a p e r t u r e t o ensure t h a t drops e n t e r i n g the a p e r t u r e a t an a n g l e pass  through both g r i d s .  The d i s t a n c e s from the g r i d w i r e s t o the g r i d  mounting h o l e s were i n c r e a s e d to reduce the p r o b a b i l i t y of s u r f a c e leakage between g r i d s .  In a d d i t i o n , n y l o n , r a t h e r than m e t a l , s u p p o r t s 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 ing  the w i r e onto the frames.  frames  I n i t i a l attempts  by hand were not s a t i s f a c t o r y because  maintaining uniform wire t e n s i o n . was  to wind the w i r e onto  of the extreme d i f f i c u l t y  the of  I f the winding were to be done by hand i t  e s t i m a t e d t h a t each g r i d would p r o b a b l y r e q u i r e two men  one day.  a c t u a l l y wind-  f o r approximately  The method f i n a l l y d e v i s e d to wind the g r i d s used a l a t h e to s l o w l y  164  r o t a t e the frame and an automatic wire t e n s i o n i n g mechanism. the time f o r f a b r i c a t i n g one g r i d A f t e r the g r i d was  T h i s reduces  to l e s s than one man-day.  wound, the w i r e s were bonded w i t h epoxy to the  frame a l o n g the e n t i r e o u t s i d e edge. s h e e t , c u t to the same dimensions  Then another p i e c e of p o l y c a r b o n a t e  as the frame, was  frame t o f u r t h e r secure the w i r e s .  One  bonded t o the top of the  s e t of the two  l a y e r s of w i r e s were  then c u t away t o l e a v e a s i n g l e l a y e r of w i r e s on the frame. method of s e c u r i n g the w i r e s was  This elaborate  found to be n e c e s s a r y to p r e v e n t the h i g h  wire t e n s i o n from c a u s i n g bond f a i l u r e a f t e r the w i r e s were c u t . The two g r i d assemblies and aluminum h o u s i n g shown i n F i g . 3.7 the top opening  s u p p o r t i n g s t r u c t u r e a r e mounted i n t h e and F i g . 3.8.  The g r i d s are l o c a t e d  near  to ensure t h a t drops p a s s i n g through the a p e r t u r e pass  through both g r i d s and t h a t water does not s p l a s h back up t o the g r i d s the d r a i n g r a t i n g on the bottom of the h o u s i n g .  To p r e v e n t water  from  accumula-  t i o n on the h o u s i n g top, the top s l o p e s towards the s i d e s of the u n i t . S p l a s h i n g i n t o the a p e r t u r e i s reduced by a l i p around expanded metal g r i d s l i g h t l y above the housing t o p .  the opening and  an  (The e f f e c t i v e n e s s o f  these s p l a s h r e d u c t i o n methods has not been e x p e r i m e n t a l l y v e r i f i e d . )  A  removable l i d i s p r o v i d e d to p r o t e c t the g r i d s i d e s from dust and h a i l when the d i s d r o m e t e r i s not i n u s e .  Connections  mounted on the s i d e of the h o u s i n g . transducer.  to the g r i d s are v i a type-N j a c k s  F i g . 3.9  shows the complete  disdrometer  7.1  9.4  26.7  A l l measurements i n centimetres  F i g . 3.7. Disdrometer transducer dimensions.  166  167  168 3.5  Disdrometer  Electronics  The interconnection of the disdrometer transducer, detector and microprocessor  i s shown i n F i g . 3.10.  Eveready 493 or Mallory M722 supplies the dc  preamplifier, peak  A 300 V primary battery,  voltage to the upper g r i d .  Batteries are used for the g r i d 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  also tend to induce 60 Hz noise onto the lower transducer  grid.  transducer The 0.005 pF  capacitor connected from the upper g r i d to ground was found to reduce susceptability of the transducer The transducer  to 60 Hz e l e c t r o s t a t i c  preamplifier, shown i n F i g . 3.11,  the  interference. 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 e s s e n t i a l l y equal to R, i n F i g . 3.11. in I  A discrete JFET  i s used as the f i r s t stage i n the preamplifier because this device r e s u l t s i n better low frequency noise performance than can be obtained with monolithic operational a m p l i f i e r s .  Metal f i l m r e s i s t o r s are used i n the f i r s t stages of  the preamplifier to reduce thermal noise contributions.  Capacitor Cj i s  provided for testing the preamplifier using a signal generator. operation this capacitor i s shorted.  In normal  When driven by a signal generator,  voltage gain of the preamplifier i s adjustable from approximately 0.5 At a gain setting of 2.4 Hz to 1.8 MHz.  to  the 15.  the amplifier has a 3 dB frequency response from 0.1  The preamplifier i s mounted i n a gasketed die cast box and  mounted d i r e c t l y on the transducer  housing using a type N plug-plug adapter.  300 V  DISDROMETER TRANSDUCER  PEAK DETECTOR  A/D CONVERTER  MICROPROCESSOR  PEAK DETECTOR RESET  F i g . 3.10. Disdrometer system b l o c k diagram.  r t  0  DATA OUTPUT  INPUT  F i g . 3.11.  Transducer  preamplifier.  o  171  The  peak d e t e c t o r , shown i n F i g . 3.12,  p r e a m p l i f i e r output  pulse.  ponse, low o v e r s h o o t  and h i g h dynamic range.  i s p r o v i d e d f o r the A/D resets  the peak d e t e c t o r a f t e r A/D  processor.  to have a f a s t  the  res-  More than adequate h o l d i n g time  conversion.  The  The  microprocessor  12 b i t A/D  converter  to a d i g i t a l q u a n t i t y f o r i n p u t t o the  micro-  P u l s e s are then s o r t e d i n t o up to s i x t e e n s i z e c a t e g o r i e s .  microprocessor  outputs  the number of drops  t e c t e d d u r i n g the sample Two  designed  c o n v e r s i o n of the s t o r e d p u l s e .  c o n v e r t s the p u l s e amplitude  put.  T h i s c i r c u i t was  s t o r e s the peak v a l u e of  minicomputer.  the microcomputer was The  i n each c a t e g o r y which were  de-  intervals.  d i f f e r e n t schemes were used  At f i r s t ,  The  t o r e c o r d the microcomputer d a t a i n t e r f a c e d to the d a t a  number of drops was  out-  acquisition  t r a n s f e r r e d each second  and  recorded  on the magnetic tape a l o n g w i t h a l l the o t h e r e x p e r i m e n t a l d a t a .  T h i s method  worked w e l l and was  The  used  t o produce the d a t a r e p o r t e d i n [3.53].  advantage of t h i s method was  the h i g h s o f t w a r e and  computing c o s t s a s s o c i a t e d  w i t h p r o c e s s i n g the l a r g e amounts of d a t a r e c o r d e d . p e r i o d s of d i s d r o m e t e r  tically valid meter d a t a . printer.  Because o n l y s h o r t  d a t a were a c t u a l l y a n a l y z e d and because  times of up to one minute (depending  The microcomputer i s now  adopted  t o handle  statis-  the d i s d r o -  i n t e r f a c e d d i r e c t l y t o a hardcopy  A hardware t i m e r , which i s manually  a c q u i s i t i o n system, i s used  integration  on r a i n r a t e ) a r e r e q u i r e d f o r a  sample, a semimanual method was  dis-  s y n c h r o n i z e d to the d a t a  to d e f i n e sample and  print periods.  At the  end  of the sample p e r i o d , the microcomputer p r i n t s out the number of drops i n each s i z e c a t e g o r y . grammable  Drop s i z e d a t a i s then a n a l y z e d w i t h the a i d of a p r o -  calculator.  ALL  DIODES ARE IN458  F i g . 3.12. Peak d e t e c t o r .  ho  173  3.6  Disdrometer The  gated  System T e s t R e s u l t s  e f f e c t s of v a r i o u s d i s d r o m e t e r  circuit  parameters were i n v e s t i -  i n an attempt to e x p e r i m e n t a l l y o p t i m i z e the d i s d r o m e t e r  3.13 shows the peak p u l s e amplitudes grid voltages.  system. F i g .  f o r v a r i o u s drop s i z e s w i t h  different  With p r e a m p l i f i e r v o l t a g e g a i n s of o n l y 1 t o 2 the p r e a m p l i -  f i e r s a t u r a t e d on the l a r g e s t drops when u s i n g a 600 V b a t t e r y .  Because the  s e n s i t i v i t y of the t r a n s d u c e r i s l i m i t e d by the time v a r y i n g c a p a c i t a n c e produced by g r i d movement, a l a r g e r g r i d v o l t a g e d i d not improve t h e t r a n s ducer s i g n a l t o n o i s e r a t i o .  F o r these reasons  no advantage c o u l d be r e a l -  i z e d by u s i n g more than one 300 V b a t t e r y to power the upper g r i d . The  s e l e c t i o n of the p r e a m p l i f i e r i n p u t r e s i s t a n c e , R i , i n v o l v e s n  a t r a d e o f f between the p u l s e amplitude t h a t l a r g e r v a l u e s o f R^ amplitudes.  n  and p u l s e p e r i o d .  F i g . 3.14 shows  a r e d e s i r a b l e because they produce l a r g e p u l s e  However, l a r g e r v a l u e s of R^  p e r i o d s as shown i n F i g . 3.15.  n  also r e s u l t i n longer  The p u l s e p e r i o d i s d e f i n e d here  from the s t a r t o f the p u l s e t o when t h e p r e a m p l i f i e r output noise l e v e l . i s mainly  The p u l s e p e r i o d i s l i n e a r l y r e l a t e d  as the time  s e t t l e s t o the  t o the v a l u e o f R ^ «  This  n  due t o the time c o n s t a n t of the t r a n s d u c e r c a p a c i t a n c e - a m p l i f i e r  input r e s i s t a n c e product.  In a r a i n f a l l o f 50 mm/hr the average  between drop a r r i v a l s i n a 50 c m the v a l u e o f R^ amplitude  pulse  n  2  area i s approximately  35 msec.  interval As a r e s u l t  was chosen t o be 100 Mfi, which p r o v i d e s an a c c e p t a b l e  and a p u l s e p e r i o d o f a p p r o x i m a t e l y  16 msec.  pulse  174  1.4  0  200  400  600 G r i d voltage  800  1000  1200  (Volts)  F i g . 3.13. Peak p u l s e amplitude v s g r i d v o l t a g e f o r d i f f e r e n t  drop  diameters.  120  r-  F i g . 3.15. P u l s e p e r i o d v s R. .  177  3.7  Disdrometer C a l i b r a t i o n The disdrometer was c a l i b r a t e d by measuring the peak pulse amplitude  of drops of known s i z e and v e 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 F i g . 3.16, which d i r e c t e d a v a r i a b l e a i r flow around a v i b r a t i n g hypodermic needle.  By using d i f f e r e n t  combinations of needle diameter, a i r flows, v i b r a t i o n frequency and v i b r a t i o n amplitude, drops as small as 0.5 mm could be formed.  The drop s i z e s were  determined by weighing a number of drops c o l l e c t e d i n a very small container. Drop v e l o c i t i e s were c o n t r o l l e d by varying the distance each drop f e l l . The c a l i b r a t i o n r e s u l t s f o r drops at terminal v e l o c i t y are shown i n F i g . 3.17.  This same data i s shown i n F i g . 3.18 but here the square root of  the pulse amplitude i s p l o t t e d against drop s i z e , r e s u l t i n g i n an almost l i n e a r curve. A l e a s t squares exponential curve f i t to t h i s data r e s u l t s i n the  relationship: V  PEAK - ° '  where V i s i n v o l t s and D i s i n mm.  0 2 7  ° " 2  6 2  ( 3  "  X )  From the r e s u l t s gathered from several  s i 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 r e l a t i o n s h i p between the peak pulse amplitude and drop s i z e  depends on the p r e a m p l i f i e r bandwidth  and time constant. The e f f e c t s of drop v e l o c i t y on the peak pulse amplitude f o r various s i z e drops i s shown i n F i g . 3 . 1 9 . This graph shows that the peak response was l i n e a r l y r e l a t e d to the drop v e l o c i t y .  178  VARIABLE FREQUENCY AMPLIFIER  GENERATOR  VALVE  F i g . 3.16. Apparatus  f o r c r e a t i n g small  drops.  F i g . 3.17.  Disdrometer c a l i b r a t i o n  f o r drops a t t e r m i n a l  velocity.  1.75  o I  ;  0  1  l  1  1  2  3 Drop d i a m e t e r  F i g . 3.18.  1  4  '  5  (mm)  Square r o o t of p u l s e a m p l i t u d e v s drop  diameter.  1  °  F i g . 3.19.  E f f e c t of drop v e l o c i t y on p u l s e  amplitude.  182  T h i s e l e c t r o s t a t i c disdroraeter system has an output p u l s e p r o p o r t i o n a l 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 .  m e c h a n i c a l d i s d r o m e t e r s produce v e l o c i t y squared.  p u l s e s p r o p o r t i o n a l to D  the e l e c t r o 3.7  to D  These d i f f e r e n c e s make the e l e c t r o s t a t i c  advantageous f o r measuring errors.  In comparison, 3.5  and  disdrometer  s m a l l drops and l e s s s u s c e p t i b l e t o wind  An a d d i t i o n a l advantage  velocity  over e l e c t r o m e c h a n i c a l d e v i c e s i s the f a c t  t h a t the output p u l s e i s independent  of impact  l o c a t i o n on the t r a n s d u c e r .  The d i s a d v a n t a g e s of t h i s d i s d r o m e t e r a r i s e from the d e l e t e r i o u s e f f e c t s o f r e s i d u a l water r e t e n t i o n . r a i n , the upper g r i d o f t e n accumulates  A f t e r a p e r i o d of o p e r a t i o n i n a c t u a l s m a l l water d r o p l e t s .  These a r e the  r e s u l t o f e x t r e m e l y s m a l l drops which have inadequate v e l o c i t i e s t o escape the h y d r o s t a t i c a t t r a c t i o n o f the g r i d w i r e s and from l a r g e r drops the edge o f the t r a n s d u c e r h o u s i n g and s p l a s h i n g onto the g r i d . water d r o p l e t s a r e d i s l o d g e d , t h e r e w i l l be an erroneous In  striking  When t h e s e  transducer output.  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 b l o w i n g t h e  upper g r i d d r y .  T h i s c o u l d e a s i l y be accomplished  automatically with a  s e r i e s of s m a l l a i r j e t s i n s i d e the t r a n s d u c e r h o u s i n g .  A second  problem  w i t h t h i s t r a n s d u c e r a r i s e s when the e n t i r e g r i d frame s t r u c t u r e I s s a t u r a t e d w i t h s m a l l water d r o p l e t s .  T h i s o n l y o c c u r s a f t e r s e v e r a l hours o f o p e r a t i o n  but when a leakage path i s e s t a b l i s h e d between the g r i d s , the e n t i r e s a t u r a t e s and the d i s d r o m e t e r must be c o m p l e t e l y d r i e d .  system  I f the disdrometer  was f i t t e d w i t h a i r j e t s , t h i s problem would p r o b a b l y be overcome a l s o . The d i s d r o m e t e r system a c t u a l l y used i n t h i s experiment drops down t o 0.3 t o 0.35 mm i n d i a m e t e r .  would measure  Drops were s o r t e d i n t o the t h i r -  t e e n " s t a n d a r d " drop c a t e g o r i e s used i n most  experiments.  183  3.8  Anemometer Three components of the wind v e l o c i t y vector were continually measured  on the roof of the E l e c t r i c a l Engineering b u i l d i n g .  The anemometer assembly  i s 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 b u i l d i n g .  ted to an analog signal using a three-phase [2.1].  Wind d i r e c t i o n i s conver-  syncro c i r c u i t described i n  Horizontal and 60° elevation wind v e l o c i t y are measured using p r o -  p e l l e r s 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 e f f e c t i v e p i t c h .  Their threshold i s  between 0.1 and 0.2 m/s and they are calibrated at 9.18 m/s h o r i z o n t a l f o r 1800 rpm. The horizontal and 60° elevation wind speed are used to calculate the v e r t i c a l wind speed during data a n a l y s i s .  This method a l l e v i a t e s  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 v e r t i c a l wind v e l o c i t y would be given by: V  VERT  6 0 ° ~ H0RIZ sin 60 V  C  O  S  6  °°  .....  6  The measured angular response of the propellers from the manufacturers s p e c i f i c a t i o n s , i s shown i n F i g . 3.21. actual v e r t i c a l wind i s calculated from:  Using the data from this graph, the  Fig.  3.20.  Anemometer  photograph.  180  240  300  0  Wind a n g l e 9  F i g . 3.21.  60  120  (Deg)  Anemometer p r o p e l l e r a n g u l a r  response.  180  186  V, VERT  3.9  V60° - 0.40 V. HORIZ 0.82  (3.3)  Temperature Measurement A commercial temperature probe, B & K Precision TP-28, was used to  monitor the ambient a i r temperature. per °C or ° F . use.  This unit provides an output of 10 mV  Boiling water and ice were used to c a l i b r a t e the device before  The temperature transducer output was connected to one of the analog  channels on the data a c q u i s i t i o n system for continuous recording.  4.  The  THEORETICALLY PREDICTED PROPAGATION PARAMETERS  purpose  of t h i s c h a p t e r i s t o use e x i s t i n g t h e o r e t i c a l methods t o  p r e d i c t the p r o p a g a t i o n parameters  for different rain conditions.  R e s u l t s of  these c a l c u l a t i o n s w i l l be used as Inputs to the e x p e r i m e n t a l model d e s c r i b e d i n the next c h a p t e r and compared to the measured p r o p a g a t i o n d a t a . p r e d i c t i v e p r o c e d u r e s r e q u i r e t h a t the parameters  of the r a i n medium, i n c l u d -  i n g 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, and drop shape, be s p e c i f i e d .  The  c a n t i n g angle  From the drop shape and temperature,  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 .  the For a  s p e c i f i c drop s i 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 a t t e n u a t i o n and phase s h i f t at d i f f e r e n t r a i n r a t e s f o r waves l i n e a r l y p o l a r i z e d a l o n g the drop major and minor axes ( o r p r i n c i p a l p l a n e s ) . From these i n t e r m e d i a t e r e s u l t s and an assumed c a n t i n g a n g l e , i t i s then p o s s i b l e 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 c o p o l a r a t t e n u a t i o n and p h a s e , s h i f t , d i f f e r e n t i a l a t t e n u a t i o n , d i f f e r e n t i a l phase s h i f t and XPD both  polarizations. I t was  n e c e s s a r y to c a l c u l a t e t h e s e p r o p a g a t i o n parameters  crude a p p r o x i m a t i o n s  following i s a brief [4.1],  because  and i n t e r p o l a t i o n s would have been needed to compare the  d u a l - p o l a r i z e d r e s u l t s of t h i s experiment  Chu  s for  to published propagation data.  survey of the p r e v i o u s l y p u b l i s h e d t h e o r e t i c a l  i n one of the e a r l i e r papers  i n this area, did include  r e s u l t s a p p l i c a b l e i n t h i s f r e q u e n c y range.  The problem  i s that  For example, t h i s r e f e r e n c e i n c l u d e s a graph showing  results.  graphical practical  c o n s t r a i n t s mean t h a t data can o n l y be p r e s e n t e d f o r a few d i f f e r e n t conditions.  The  rain  188  d i f f e r e n t i a l phase s h i f t , but o n l y at r a i n r a t e s of 5, 25 and one  drop s i z e d i s t r i b u t i o n .  Data are a l s o presented  f o r XPD  r a i n r a t e but o n l y f o r a simultaneous 20 dB c o p o l a r f a d e and angle.  R e c e n t l y , Evans [4.2]  showing XPD  and  H o l t and  f o r b o t h p o l a r i z a t i o n s v s . CPA  u n f o r t u n a t e l y , d a t a are o n l y presented one  drop d i s t r i b u t i o n .  100  Evans [4.3]  one  137  amplitudes,  GHz.  The  of 2°  In another r e c e n t paper, Neves and Watson [4.4]  Oguchi [4.5]  has  also published  p r i n c i p a l - p l a n e complex p r o p a g a t i o n  f e r e n t canting angles  results  but,  canting angle  a t d i f f e r e n t c a n t i n g a n g l e s , d i f f e r e n t i a l a t t e n u a t i o n and  phase a t 36.5  canting  GHz  p u b l i s h e d comprehensive c a l c u l a t e d 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 XPD  at 34.8  for  a t the same  have p u b l i s h e d  f o r 57, 94 and  f o r a constant  mra/h and  and  have  amplitudes,  differential  t a b l e s of s c a t t e r i n g  constants  and XPD  for dif-  GHz.  development of t h i s c h a p t e r w i l l f o l l o w the n a t u r a l 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 .  A c c o r d i n g l y , the m e t e r o l o g i c a l i n p u t s to  c a l c u l a t i o n s w i l l be d i s c u s s e d f i r s t . w i l l be p r e s e n t e d .  These two  compute the p r o p a g a t i o n  Then, the s c a t t e r i n g a m p l i t u d e  s e t s of i n f o r m a t i o n w i l l  parameters at the frequency  the data  then be used to  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  M e t e r o l o g i c a l Inputs To p r e d i c t the macroscopic p r o p a g a t i o n  path,  assumed to c o n t a i n s p a t i a l l y u n i f o r m  e f f e c t s of each i n d i v i d u a l drop a l o n g the m i c r o s c o p i c  p r o p e r t i e s of a  transmission  r a i n , i t i s necessary  the p a t h .  to sum  the  T h i s r e q u i r e s a knowledge o f  r a i n p r o p e r t i e s 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  (canting scopic  a n g l e ) and r a i n temperature.  r a i n properties  Lack of i n f o r m a t i o n about t h e s e m i c r o -  i s the l a r g e s t source o f u n c e r t a i n t y  p r o p a g a t i o n parameters.  Because i t i s so d i f f i c u l t  n e c e s s a r y t o r e s o r t t o models o r e s t i m a t e s .  tions.  i n predicting  to accurately  some o f these m i c r o s c o p i c r a i n parameters i n n a t u r a l  predictive  orientation  measure  rain, i t i s often  T h i s u s u a l l y means t h a t t h e  c a l c u l a t i o n s must be performed f o r a range o f assumed r a i n  condi-  The r e s u l t i n g range o f v a l u e s c a n then be compared t o the measured  propagation conditions to a c o n s i s t e n t  4.1.1  w i t h t h e hope o f b e i n g a b l e t o match t h e o b s e r v a t i o n s  s e t o f r a i n parameters.  Rainrate R a i n r a t e i s the most r e a d i l y measured r a i n parameter and t h e r e f o r e i s  c o n v e n i e n t t o use as the prime i n d i c a t o r o f the r a i n medium c o n d i t i o n comparing p r e d i c t i o n s able,  the p r e d i c t i v e  values.  and o b s e r v a t i o n s .  Because r a i n r a t e i s e x t r e m e l y  vari-  c a l c u l a t i o n s must be performed f o r a wide range o f  The upper l i m i t on t h e r a 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 h i g h e s t expected r a i n r a t e i n t h i s l o c a t i o n . parameters were c a l c u l a t e d 6.25,  when  f o r the f o l l o w i n g  rainrates:  1.25, 2.5, 3.75, 5.0,  7.5, 10, 12.5, 15, 17.5, 20, 25, 30, 40 and 50 mm/h.  p r o p a g a t i o n parameters a r e smoothly v a r y i n g  functions  t i o n can be used between these v a l u e s i f n e c e s s a r y .  Propagation  Since a l l o f t h e  of rainrate,  interpola-  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 t u d y r a i n d r o p  size  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 t h a t 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 w h i c h a r e w i d e l y used f o r p r o p a g a t i o n p r e d i c t i o n s a r e t h e : et a l . T h u n d e r s t o r m , Widespread and D r i z z l e and Laws and Parsons [ 4 . 8 ] .  Joss  [ 4 . 6 ] , M a r s h a l l and Palmer [ 4 . 7 ]  A negative exponential d i s t r i b u t i o n Is  usually  used t o 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 b a s i c form of t h e s e d i s t r i b u t i o n s i s g i v e n  the t a b u l a t e d d a t a ) .  by:  N (D,R) = ^ e " ^  (4.1)  D  where: •A = oR"  3  and: :  N(D,R)  i s the number of drops per m i n the s i z e c a t e g o r y between D3  0 . 5 mm and D + 0 . 5 mm at a g i v e n r a i n r a t e , 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 i a m e t e r i n mm.  a, 3  N  q  R.  are c o n s t a n t s  was o r i g i n a l l y c o n s i d e r e d a c o n s t a n t  [4.6],  [ 4 . 7 ] , but H a r d e n ,  Norbury and White [ 4 . 9 ] have p o i n t e d out t h a t the o r i g i n a l J o s s et a l d i s t r i b u t i o n s 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 t h e r w o r d s ,  if  t h e 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 c o n s i d e r e d  191  to be f a l l i n g at t h e i r terminal v e l o c i t y 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 d i s t r i b u t i o n .  Olsen [4.10] proposed that N  q  be renormalized as a  function of R so that the d i s t r i b u t i o n s did s a t i s f y the rainrate i n t e g r a l equation over a certain range of r a i n r a t e s . Olsen indicated that the largest discrepancy with the rainrate equat i o n was f o r the Joss Thunderstorm d i s t r i b u t i o n .  Neves and Watson [4.4] and  Shkarofsky [4.11] have recently used the renormalized Joss Thunderstorm distribution.  Shkarofsky, however, does not use the renormalized versions  for the other d i s t r i b u t i o n s , presumably because Olsen has indicated that the greatest rainrate discrepancy i s for the Joss Thunderstorm d i s t r i b u t i o n .  To  test whether i t was necessary to use the renormalized d i s t r i b u t i o n s In this work, sample calculations  of 74 GHz copolar attenuation were performed using  both normalized and unnormalized d i s t r i b u t i o n s .  The test calculations  showed  that the largest attenuation differences were f o r the thunderstorm d i s t r i b u t i o n but that the two d r i z z l e d i s t r i b u t i o n attenuations were also cantly d i f f e r e n t .  For this reason,  signifi-  i t was decided to use the renormalized  d i s t r i b u t i o n s exclusively f o r the following c a l c u l a t i o n s .  To avoid confusion  with the unnormalized d i s t r i b u t i o n s , these d i s t r i b u t i o n s w i l l be referred to as the Joss/Olsen Thunderstorm, e t c . The renormalized d i s t r i b u t i o n s and their range of greatest v a l i d i t y for the new values of N 1.  q  are given below [4.10]:  Joss/Olsen Thunderstorm:  192  N (D,R) = 1.31 1 0 R * 3  rainrate: 2.  0  exp (-3.0 DR ° "  0 8 4  2 1  )  (4.2)  25-150 mm/hr  M a r s h a l l and Palmer o r J o s s / O l s e n Widespread:  3 0 021 —0 21 N (D,R) = 6.62 1 0 R * ^ exp(-4.1 DR ) J  U  U  U  ,  Z  (4.3)  i  D  rainrate: 3.  1-50 mm/hr  Joss/Olsen  Drizzle:  N (D,R) = 3.38 1 0 R 4  _ 0 , 0 3  D  rainrate: The  exp(-5.75R~  0 , 2 1  )  (4.4)  0.25-5 mm/hr  Laws and Parsons d i s t r i b u t i o n was n o t used because i t cannot be  a c c u r a t e l y d e s c r i b e d by a n e g a t i v e e x p o n e n t i a l d i s t r i b u t i o n . calculations  can o n l y be performed a t the r e l a t i v e l y few r a i n r a t e s  t a b u l a t e d drop d i s t r i b u t i o n s a r e g i v e n distribution closely f i t s sizes  T h i s means t h a t  [4.11].  [4.8].  where t h e  The M a r s h a l l and Palmer  the Laws and Parsons d a t a except  f o r t h e s m a l l drop  C a l c u l a t e d 74 GHz a t t e n u a t i o n v a l u e s f o r t h e Laws and Parsons  d i s t r i b u t i o n s would be between the v a l u e s f o r the Joss Thunderstorm and M a r s h a l l and Palmer d i s t r i b u t i o n s The  drop s i z e diameter  0.5 mm i n t e r v a l s  [4.10].  c a t e g o r i e s used i n these  c e n t e r e d on 0.5, 1, 1.5, ... 6.5 mm.  calculations are These c a t e g o r i e s were  used by Laws and Parsons and appear t o have been adopted as a s t a n d a r d m a j o r i t y of i n v e s t i g a t o r s  since.  o n l y 0.5 mm, i t i s important volume i n these  by the  Because these i n t e r v a l s are s e p a r a t e d by  t o remember t h a t the number o f drops p e r u n i t  c a t e g o r i e s i s one h a l f  the v a l u e o f N , as c o n v e n t i o n a l l y  d e f i n e d , which i s the number i n a 1 mm width  size  category.  193  I m p l i c i t i n the relationship between the standard drop size d i s t r i b u tions and t h e i r corresponding r a i n r a t e s , wind v e l o c i t y .  i s the assumption of zero v e r t i c a l  Nonzero v e r t i c a l wind v e l o c i t i e s can s i g n i f i c a n t l y a l t e r  raindrop size d i s t r i b u t i o n above the ground.  The effects of v e r t i c a l wind  v e l o c i t i e s on copolar attenuation are analyzed i n Section  4.1.3  the  4.4.  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 P i t t e r  [4.12].  A water  drop f a l l i n g i n a i r assumes a shape so that the i n t e r n a l and external at the surface of the drop are i n equilibrium.  The aerodynamic forces  forces are  symmetrical about a v e r t i c a l axis through the center of drop mass for a drop falling in s t i l l air. axis.  As a r e s u l t ,  the drop shape i s symmetrical around this  Pruppacher and P i t t e r accurately determined the drop's asymmetric  oblate spheroidal shape by solving a pressure balance equation at the surface of the drop.  Oguchi [4.5]  P i t t e r to calculate Parsons drop s i z e s .  used the techniques described by Pruppacher and  the deformation (or e c c e n t r i c i t i e s )  for the Laws and  Oguchi concluded that the propagation parameters c a l c u -  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 e a r l i e r for oblate spheroids. The scattering  amplitudes used i n the following calculations are for the  Pruppacher-Pitter drop  eccentricities.  The largest uncertainties  i n the a p p l i c a b i l i t y of the Pruppacher-  P i t t e r drop shape arise from the assumption that the a i r surrounding the drop i s not i n a state of turbulence and the fact that drop c o l l i s i o n s are  194  ignored.  Warner [4.13] has calculated that drops c o l l i d e every few seconds  i n heavy r a i n . seconds.  He also states that drop o s c i l l a t i o n s can persist f o r several  Warner concludes that "raindrops are l i k e l y to take on a v a r i e t y of  shapes and orientations" and that "they are u n l i k e l y to follow c l o s e l y a mean o r i e n t a t i o n or canting angle".  Haworth and McEwen [4.14] have recently used  a 20 GHz b i s t a t i c scatter l i n k to study the Doppler spectrum of the i n coherent forward scattered signal from r a i n , hoping to detect drop vibrations.  They conclude that "suggestive but not conclusive evidence f o r  the detection of drop vibrations has been p r e s e n t e d . . . " .  4.1.4  Canting Angle As a raindrop f a l l s , v e r t i c a l wind gradients cause the o r i e n t a t i o n of  the drops axis of symmetry (or minor axis) to s h i f t from v e r t i c a l .  The angle  between the axis of symmetry and v e r t i c a l i s c a l l e d the canting angle. Brussaard [4.15], explained that this wind gradient i s caused  by f r i c t i o n  with the ground and results i n a decreasing wind speed with decreasing height i n the region below 1 km i n height.  The v e r t i c a 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 r e l a t i o n s h i p between drop s i z e and canting angle.  F i g . 4.1, from [4.15] shows Brussaard's predictions f o r  canting angle as a function of drop size and height above ground f o r a horizontal wind speed of 15 m/s. Maher, Murphy and Sexton [4.16] l a t e r developed a theoretical model to explain the d i s t r i b u t i o n of canting angles based on the effects  of wind  195  0  1.0  2.0  3.0  4.0  DROP DIAMETER Fig.  4.1.  5.0  6.0  (mm)  C a n t i n g a n g l e as a f u n c t i o n o f s i z e and  height.  7.0  1.96  gusting. of  T h e i r model p r o v i d e d an e x p l a n a t i o n o f the simultaneous  observation,  drops w i t h p o s i t i v e and n e g a t i v e c a n t i n g a n g l e s . Very  little  d a t a e x i s t from the d i r e c t measurement o f c a n t i n g a n g l e s .  The most n o t a b l e i n v e s t i g a t i o n o f c a n t i n g angle was c a r r i e d out by Sanders [4.23] u s i n g a " r a i n d r o p camera".  In t h i s study 463 photographs from two  storms were c o l l e c t e d and the c a n t i n g angles were measured u s i n g a protractor. had  R e s u l t s f o r t h e two storms showed t h a t about 40% o f t h e drops  a c a n t i n g angle i n excess  angles  i n excess  of 15° and about 25% had n e g a t i v e c a n t i n g  of - 1 5 ° .  These t h e o r e t i c a l models and l i m i t e d e x p e r i m e n t a l  observations  i n d i c a t e t h a t drops have a d i s t r i b u t i o n o f c a n t i n g a n g l e s i n n a t u r a l r a i n . The t h e o r e t i c a l models t o p r e d i c t c a n t i n g angles i n c l u d e many v a r i a b l e s > some of which a r e almost these reasons  as d i f f i c u l t  t o measure as the c a n t i n g a n g l e i t s e l f .  For  i t i s n o t , a t p r e s e n t , p o s s i b l e t o make m e a n i n g f u l l j r a c c u r a t e  e s t i m a t e s o f c a n t i n g angle d i s t r i b u t i o n s f o r use i n p r o p a g a t i o n p r e d i c t i o n s . . As a r e s u l t , most e x p e r i m e n t a l  i n v e s t i g a t o r s have s i m p l y used a v a r i e t y o f  constant or " e f f e c t i v e " canting angles experimental  i n c a l c u l a t i o n s f o r comparisons  d a t a , even though t h e o r e t i c a l models have now been  which can use more c o m p l i c a t e d  c a n t i n g angle models.  t h i s problem o f r e l a t i n g measurements t o c a n t i n g angle  with  developed  Watson [4.17] d i s c u s s e s statistics.  As a  s o l u t i o n , Watson has d e f i n e d an " e q u i v a l e n t mean, c a n t i n g angle as t h a t v a l u e of  c a n t i n g angle  i n a constant-canting-angle  rainfall  model r e q u i r e d t o g i v e  an e q u i v a l e n t c r o s s p o l a r i z a t i o n t o t h a t measured i n t h e r a i n s t o r m . " definition will  be used i n t h i s experiment.  meters were c a l c u l a t e d  This  In t h i s study, propagation  para-  f o r c o n s t a n t o r e q u i v a l e n t mean c a n t i n g a n g l e s of 1,  197  2,  3 , 4, 6 , 8,  1 0 , 15,  2 0 , 3 0 and  p o l a r i z a t i o n case f o r any  canting  45°  (which i s e q u i v a l e n t  to the  circular  angle.)  Some q u a l i t i t i v e improvement on the assumption of a constant a n g l e can be made by c o n s i d e r i n g the r e s u l t s of Oguchi [4.5] [4.18].  These two  papers show graphs of c r o s s p o l a r i s o l a t i o n  f o r p r a c t i c a l purposes i s equal c a n t i n g angle s t a n d a r d attenuations  to XPD  deviation.  [4.19],  Kobayashi  [XPI]  (which,  [4.18]) as a f u n c t i o n of  Both graphs use  r e s u l t s show t h a t XPI  the p r i n c i p a l plane  s e t s of r e s u l t s d i f f e r by a s m a l l amount.  ( o r XPD)  w i l l improve f o r i n c r e a s i n g standard  Oguchi s t a t e s t h a t "when the s t a n d a r d  to improve as compared w i t h  equioriented raindrops."  He  devia-  those c a l c u l a t e d f o r  a l s o c o n c l u d e s t h a t "the r e s u l t s show t h a t  c a n t i n g a n g l e of the e q u i o r i e n t e d model i s r e p l a c e d by the e f f e c t i v e  factor.  the d i f f e r e n t i a l p r o p a g a t i o n  constant  i s 48%,  and  p o l a r i z a t i o n , c a l c u l a t e d at 34.8 propagation  path of 1 km,  e q u i o r i e n t e d model."  Chu  differential  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 GHz  f o r a r a i n r a t e of 50 mm/h  improves about 7.5 [4.1]  canting  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 constant  the  i s reduced by a m u l t i p l y i n g  An example of the c a l c u l a t i o n s based on the measured  propagation  The  d e v i a t i o n exceeds 3 0 ° , c r o s s -  p o l a r i z a t i o n f a c t o r s tend  a n g l e and  the  c a l c u l a t e d by Oguchi [ 4 . 5 ] , but f o r some reason, which Is not  r e a d i l y a p p a r e n t , the two  tion.  and  canting  dB as compared with  a l s o used a constant  c o r r e c t r e s u l t s c a l c u l a t e d f o r a constant  and  for a  that f o r  m u l t i p l y i n g f a c t o r to  c a n t i n g a n g l e model.  A  recent  r e v i e w by O l s e n [4.20] i n c l u d e s a survey of methods 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 to account f o r c a n t i n g angle d i s t r i b u t i o n s . t h a t the c a l c u l a t i o n s f o r a constant  These r e s u l t s i n d i c a t e  c a n t i n g angle w i l l be a worst-case  condition compared to a d i s t r i b u t i o n with the same mean but they could probably be corrected i f adequate canting angle information were a v a i l a b l e .  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 v e n t i l l a t e d wet bulb thermometer, regardless of drop s i z e .  It turns out, however, that i n the  higher m i l l i m e t r i c range, the effect of drop temperature does not s i g n i f i c a n t l y e f f e c t the calculated attenuations.  Olsen [4.10] has published r e s u l t s  which indicate that the difference i n attenuation f o r r a i n temperatures between 0 and 20°C are n e g l i g i b l e 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 s i g n i f i c a n t effect on the calculated value of A [attenuation],  and even then the effect i s not l a r g e " .  Rogers and Olsen [4.22] have published a graph showing the v a r i a t i o n i n 70 GHz attenuation f o r r a i n temperatures between - 5 ° C and 4 0 ° C .  these  results indicate that attenuation over the approximate range of 3°C to 23°C is,  for a l l p r a c t i c a l purposes, i d e n t i c a l to the attenuation at the 20°C  reference temperature.  For this reason i t appears to be possible to use any  reasonable value f o r drop temperature i n the frequency range used i n this experiment.  The scattering parameters used i n the following calculations  are for a drop temperature of 2 0 ° C .  199  4.1.6  Spatial Uniformity It was shown i n Section 3.1.1 that the rainrate during natural r a i n i s  not uniform h o r i z o n t a l l y .  This w i l l also mean that the drop d i s t r i b u t i o n 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 d i s t r i b u t i o n s of r a i n parameters within i n d i v i d u a l r a i n c e l l s when predicting propagation e f f e c t s , e . g . [1.85],  [4.4],  [4.24].  Fortunately, i s only 900 m.  i n this experiment,  the physical length of the radar path  It i s therefore reasonably accurate to assume, f o r c a l c u l a -  t i o n purposes, that the meteorological conditions along this path are uniform and can be characterized by the path average rainrate calculated from the f i v e raingauges.  When making comparisons to i n d i v i d u a l r a i n events, the  v a l i d i t y of this assumption can e a s i l y be checked by comparing the results from the i n d i v i d u a l raingauges along the path.  4.2  Scattering Amplitudes The forward scattering  amplitudes presented i n this s e c t i o n  2  were  calculated using a f i e l d point-matching program developed by Dissanayake and Watson [4.25] using the following conditions:  2  1.  Frequency = 74 GHz.  2.  Pruppacher-Pitter drop shape  eccentricities.  Provided by D r . P . A . Watson, University of Bradford, U . K .  3.  Drop temperature = 2 0 ° C .  4.  Refractive index = 3.6994 + j2.1824.  5.  Angle of incidence = 90° ( i . e . t e r r e s t r i a l  6.  Laws and Parsons drop s i z e s .  path).  The scattering complex amplitudes under these conditions f o r the drop p r i n c i p l e planes are shown i n Table 4 . 1 .  Table 4.1  Forward Scattering Amplitudes at 74 GHz  Drop Diameter (mm) 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5  4.3  S (o)  1.67648 . 1 0 3.70110 . l O 1.03925 1.68310 2.60981 3.56138 4.71177 5.9625 7 .3685 8.932 10.6 12.4 14.0 ,  - 2  - 1  .  S (o)  T  II  -j5.81169.lO -j3.43414 - l O - j 2.98682*10" -13.79032 .10" ~j4.39117 « 1 0 -j4.89027 » 1 5 -j6.19467 *10 -j7.0845 .10" -j8.49.10~ -19.65 ' l O -jl.06 -jl.l -jl.2  -2 - 1 1 1 1 1  _1  1  1  - 1  1.69305.10" 3.81541 . 1 0 " 1.07658 1.77801 2.80529 3.88261 5.21626 6.6288 8.240 9.953 11.8 13.8 15.9  2 1  -j5.84513.lO - j 3.46684.10" - j 2.74903.10" - j 3.14879 . l O " - j 2.26872.lO" - j 1.05223 .10" +j 9.11839 . l O +J3.5173.10 +J6.571.10 +j 1.013 +11.39 +J1.8 +J2.4  -2 1 1 1 1  1  - 2  -1  -1  Calculated Propagation Parameters In t h i s s e c t i o n , 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, d i f f e r e n 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 i n the procedure i s to calculate the  p r i n c i p a l plane attenuations and phase s h i f t s .  P r i n c i p a l plane complex  a t t e n u a t i o n s ( i . e . magnitude and phase) would be e q u a l to the c o p o l a r a t t e n u a t i o n s f o r v e r t i c a l and h o 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 c a n t i n g angle.  I n t h i s c a s e , when a l l the drops a r e a l i g n e d and  the t r a n s m i t t e d p o l a r i z a t i o n s a r e i n the drop p r i n c i p a l p l a n e s , t h e r e w i l l a l s o be no s i g n a l  depolarization.  F o r nonzero c a n t i n g a n g l e s , the t r a n s m i t t e d p o l a r i z a t i o n i s l i n e a r l y transformed through  t o be p a r a l l e l w i t h the drop p r i n c i p a l p l a n e s .  After  propagation  the a n i s o t r o p i c medium, the v e c t o r s a r e r e t r a n s f o r m e d t o y i e l d the  r e c e i v e d 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 .  T h i s procedure  r e s u l t s i n the  elements o f the medium t r a n s m i s s i o n m a t r i x ( i . e . the p r o p a g a t i o n assuming i d e a l a n t e n n a s ) .  parameters  From these r e s u l t s the d i f f e r e n t i a l a t t e n u a t i o n  and phase s h i f t and t h e XPDs f o r b o t h p o l a r i z a t i o n s can be d i r e c t l y  calcula-  ted.  4.3.1  P r i n c i p a l Plane A t t e n u a t i o n s and Phase  Shifts  v The b a s i c method f o r c a l c u l a t i n g the a t t e n u a t i o n 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 t o the drop major and minor axes i s a t t r i b u t e d to Van de H u l s t [4.26].  A. = 0.434 I, II  e.  i,ii  = -36  TT  From [ 4 . 1 ] , the e q u a t i o n s a r e :  I RefSj Drop sizes  I Drop sxzes  Im{S  where: - S  I,II  are from T a b l e 4.1  T  I X  ( 0 ) }N  D  . AD .. (dB/km)  jj_(0) }N^« AD .. (deg/km)  (4.5)  (4.6)  202  - N are from (4.2) - (4.4) D  -  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 f o r v e r t i c a l and horizontal p o l a r i z a t i o n s ,  respectively.  Hogg and Chu [4.27] note that the relationship between (4.5) and the t r a d i t i o n a l Medhurst [4.28] method for c a l c u l a t i n g copolar attenuation can be shown by the following relationship between the extinction cross section, Q, and the forward scattering f u n c t i o n :  Q = -f- Re {S(0)}  (4.7)  F i g s . 4.2 and 4.3 show the magnitudes and angles of the p r i n c i p a l plane attenuations  vs rainrate f o r the three drop size d i s t r i b u t i o n s 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 f o r a and 3 f o r 74 GHz were obtained  by l i n e a r i n t e r p o l a t i o n 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 d i s t r i b u t i o n s i n Section 4 . 1 . 2 . Olsen's results  by Olsen for each of the drop size  The average value of  and A^j agreed with  to within 3.7%, 6%, and 4.3% (percent of dB difference) f o r  the Joss/Olsen D r i z z l e , M & P or Joss/Olsen Widespread and Joss/Olsen Thunderstorm d i s t r i b u t i o n s , r e s p e c t i v e l y .  The largest differences were a l l  at the largest v a l i d value of rainrate for each d i s t r i b u t i o n , indicating that some of the difference i s l i k e l y due to increasing error i n the regression  203  F i g . 4.2.  Magnitude of p r i n c i p a l p l a n e a t t e n u a t i o n , vs. r a i n r a t e .  204 140  Drop s i z e  distributions:  1. J o s s / O l s e n D r i z z l e 2. J o s s / O l s e n Widespread or M & P 3. J o s s / O l s e n Thunderstorm  A,  120  II  100  80  60  A. II  40  AT  TLT  20  10  20  30  40  _J 50  R a i n r a t e (mm/h)  F i g . 4.3.  Angle of p r i n c i p a l p l a n e a t t e n u a t i o n s v s .  rainrate.  205  performed by O l s e n . considered  4.3.2  to be v e r y good.  Propagation The  constant  The agreement between the two s e t s o f c a l c u l a t i o n s i s  Parameters f o r Canted Raindrops  propagation  parameters f o r a r a i n medium composed o f drops with a  c a n t i n g angle a r e c a l c u l a t e d by t r a n s f o r m i n g  the transmitted p o l a r -  i z a t i o n I n t o t h e drop p r i n c i p a l p l a n e s , a p p l y i n g t h e p r i n c i p a l plane a t t e n u a t i o n s and then r e t r a n s f o r m i n g horizontal  complex  the p o l a r i z a t i o n s back i n t o v e r t i c a l and  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  t r a n s f o r m a t i o n 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 t o t h e  p r i n c i p a l plane d i r e c t i o n s ( I and I I ) i s g i v e n by:  I  _  E _II The  cos <{>  s i n (j) E„ V  s m <J>  cos <j>  (4.8)  _H  r e v e r s e t r a n s f o r m a t i o n , from the p r i n c i p a l p l a n e s  t o v e r t i c a l and  horizontal i s : cos <{> - s i n <J> If  s i n <j>  E_ I  COS  E _II  (J)  (4.9)  the s u b s c r i p t s TX and RX a r e used t o d e s i g n a t e  r e c e i v e d s i g n a l s r e s p e c t i v e l y and T^ and T a t t e n u a t i o n s over  the t r a n s m i s s i o n path,  2  the t r a n s m i t t e d and  a r e used t o d e s c r i b e the complex  then t h e e f f e c t  of the r a i n medium  on waves l i n e a r l y p o l a r i z e d i n the I and I I d i r e c t i o n s c a n be d e s c r i b e d by:  206  F i g . 4.4.  Geometry f o r canted drop  calculations.  0  RX II  0  TX E  RX  II  (4.10)  TX  The o f f - d i a g o n a l elements of this matrix are zero because no depolarization occurs f o r signals l i n e a r l y polarized i n the p r i n c i p a l planes.  Similarly,  the path transmission matrix f o r v e r t i c a l and horizontal polarizations can be written: E.  12  11  RX  21  22  L  RX  TX  (4.11)  H,  L  TX  Using (4.8)-(4.10) to describe equation (4.11) E  cos  v RX  $  -sin  H _ RX E  s i n <j> T  1  <> j cos <j>  0  0 T,  cos s i n (j)  - s i n <J> cos <> j  TX  (4.12)  _ TX H  Solving f o r T ^ y i e l d s :  T  ll  =  T  l  C O S  T  22  =  T  l  S  T  1 2  = T  2 1  l  n  2 ^ 2 *  +  T  2  s  +  T  2  C O S  = (T 2  T l  )  i  n  2 *  (4.13)  2 *  (4.14)  sin2 j) t  These equations f o r T  (4.15)  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  cos <|<j)|>, sin^jc})^ and <sin2<J>> f o r the corresponding terms present i n 2  208  (4.13)-(4.15).  The formal use of the ensemble average i s rigorously correct  but i s not used here to simplify notation and because only constant  canting  angles are a c t u a l l y used i n the following c a l c u l a t i o n s . From (4.15) i t can be seen that the depolarizing contribution of drops with p o s i t i v e and negative canting angles tend to cancel.  This i s the basic  mechanism which explains the results of Oguchi [4.5] and Kobayashi [4.18] which show XPI improvements f o r large canting angle standard deviations ( r e f . 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 ° . ?  It should be pointed out that even though depolarization contributions from p o s i t i v e and negative canting angles cancel, the depolarized signals r e s u l t i n g from the two way propagation of a radar path w i l l not cancel.  This  can be r e a d i l y shown by resolving the signal transmitted into the anisotropic r a i n medium into components p a r a l l e l to the drop axes, which l i e i n the p r i n c i p a l planes of the medium.  The two way propagation of the path, i n the  +Z and - Z d i r e c t i o n s , w i l l y i e l d results i d e n t i c a l to (4.13)-(4.15) f o r the same t o t a l path length, assuming a homogeneous r a i n medium along the path. Using (4.13)-(4.15), the f o l l o w i n g , d i r e c t l y measurable,  propagation  parameters can be defined: D i f f e r e n t i a l attenuation = 20 l o g ( | T „ | - | T . | )  (4.16) (4.17)  (4.18)  209  XPD  R  = 20 l o g  Jl 22  (4.19)  [  I t i s Important t o note t h a t the c o p o l a r a t t e n u a t i o n s are l i n e a r l y r e l a t e d t o the p r o p a g a t i o n  ( T J J and  path l e n g t h , assuming u n i f o r m  T  2 2  )  rain.  I t i s , t h e r e f o r e , a l s o p o s s i b l e t o express d i f f e r e n t i a l a t t e n u a t i o n and d i f f e r e n t i a l phase on a p e r k i l o m e t e r  basis.  However, because T j i s a 2  v e c t o r , r a t h e r than s c a l a r , d i f f e r e n c e , i t i s not p o s s i b l e t o p r e c i s e l y express T ^ , and t h e r e f o r e XPDs, on a per u n i t l e n g t h b a s i s . 2  ( I t should  be  mentioned t h a t t h e r e i s an a p p r o x i m a t i o n f o r XPD which uses a " s m a l l argument a p p r o x i m a t i o n " t h a t r e s u l t s i n an e x p r e s s i o n  f o r XPD t h a t i s l i n e a r l y r e l a t e d  t o path l e n g t h  [4.20].) For t h i s r e a s o n , the f o l l o w i n g r e s u l t s f o r T  XPDs are g i v e n  f o r the 1.8  The  km path l e n g t h used i n t h i s  parameters c a l c u l a t e d at 74 GHz f o r the m e t e o r o l o g i c a l  T  1 0  and  respectively. I t i s very  shown i n F i g . 4.9 T h i s occurs is and  vs r a i n r a t e a r e shown i n F i g s . 4.5,  XPD^ vs CPA^ i s shown i n F i g .  described  4.6,  4.7,  4.8  4.10.  i n t e r e s t i n g t o note t h a t the XPD vs r a i n r a t e r e l a t i o n , i s almost t o t a l l y independent of drop s i z e  because the h i g h e r  CPA f o r the d i s t r i b u t i o n s w i t h  almost p e r f e c t l y compensated by a lower v a l u e o f T  4.7.  conditions  propagation  D i f f e r e n t i a l a t t e n u a t i o n , d i f f e r e n t i a l phase, magnitude o f  , angle o f T „, and XPD 4.9  and  experiment.  f o l l o w i n g graphs show a r e p r e s e n t a t i v e sampling of t h e  i n S e c t i o n 4.1.  1 2  1  2  distribution. smaller  drops  as shown i n F i g s .  4.2  210  1.2 Drop s i z e  distributions:  •1. J o s s / O l s e n D r i z z l e 2. J o s s / O l s e n Widespread or M & P 3. J o s s / O l s e n Thunderstorm  1.0  Canting a n g l e i n b r a c k e t s  0.8 a o  I u u td  0.6  •rf a u <4-l  •H  0.4  0.2  20  30  40  R a i n r a t e (mm/h)  F i g . 4.5.  D i f f e r e n t i a l attenuation vs. rainrate  and c a n t i n g a n g l e .  50  211  Drop s i z e  distributions:  1. J o s s / O l s e n D r i z z l e 2. J o s s / O l s e n Widespread or jM & P 3. J o s s / O l s e n Thunderstorm Canting a n g l e i n b r a c k e t s  DD QJ  •U <+-l -H  1  (20°)  1  (10°)  43 CO  OJ  V \  w  Ji  1 (2°)  X  •H  4J  a  OJ S-J  2  (20°)  3  (20°)  2  (10°)  2  (2°)  3  (10°)  UH •rl  Q  20  30  50  R a i n r a t e (mm/h)  F i g . 4.6.  D i f f e r e n t i a l phase s h i f t v s . r a i n r a t e  and c a n t i n g a n g l e .  3  < °> 2  212  100  Drop s i z e  distributions:  •1. J o s s / O l s e n D r i z z l e 2 . J o s s / O l s e n Widespread o r M & P  90  3. J o s s / O l s e n  Thunderstorm  Canting angle  i n brackets  P a t h l e n g t h = 1.8  1  (2")  3  (6°)  km  80  70  60  50  40  30 10  20  30  Rainrate (mm/h)  Fig.  4.7.  Magnitude of T  vs. 12  rainrate.  40  50  213  100 i -  50  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  U  Path length = 1,8  0  km  r-  to  -50  U  o CD rH 60  -100  -150  -200  10  JL  20  30  R a i n r a t e (mm/h)  F i g . 4.8.  Angle of T  vs.  rainrate..  40  "50  214  Drop s i z e  distributions:  •1. J o s s / O l s e n D r i z z l e 2. J o s s / O l s e n Widespread o r M & P 3. J o s s / O l s e n  Thunderstorm  Canting a n g l e i n b r a c k e t s  Path l e n g t h = 1.8 km  I 0  I 10  ! 20 Rainrate  Fig.  4.9.  I 30  ! 40  (mm/h)  XPD v s . r a i n r a t e for h o r i z o n t a l  polarizations.  I 50  215  Drop s i z e 1.  distributions:  Joss/Olsen  Drizzlt Widespi Thunderstorm  _L  10  20  30  40  Horizontal copolar attenuation  F i g . 4.10  . XPD  v s . CPA  for horizontal  (dB)  p o l a r i z a t ion,  50  1  (2°)  2  (2°)  3 1  (2°) (6°)  2  (6°)  3  (6°)  216  4.4  Effects of V e r t i c a l Wind on Copolar Attenuation V e r t i c a l components of wind v e l o c i t y can s i g n i f i c a n t l y affect  attenua-  t i o n by changing the drop size d i s t r i b u t i o n above the ground [4.28], The d i s t r i b u t i o n i s altered because the v e r t i c a l wind equally affects the d i f ferent f a l l v e l o c i t i e s of drops of d i f f e r e n t s i z e s .  In this section, the  effects of a constant v e r t i c a l wind v e l o c i t y component on CPA w i l l be estimated i n terms of the change i n the attenuation/measured-rainrate  relation.  A l l other propagation parameters w i l l , of course, also be s i m i l a r l y affected by a change i n the drop size d i s t r i b u t i o n . There are at least two known causes f o r v e r t i c a l wind v e l o c i t i e s . Semplak and Turrin [4.29] state that "the c l a s s i c a l picture f o r v e r t i c a 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 r o n t " . second cause of v e r t i c a l wind i s changes i n topography. "...  lee-wave v e r t i c a l v e l o c i t i e s of order 1 m s e c  - 1  The  From Caton [4.30],  may occur over a sub-  s t a n t i a l azimuth sector to at least 20 km downstream of even small h i l l s 100 m high.  The wavelength of such waves i s t y p i c a l l y 5-16 k m . . . " In s t i l l a i r , drops f a l l at a terminal v e l o c i t y at which the forces of  gravity and aerodynamic drag are i n e q u i l i b r i u m .  Terminal v e l o c i t i e s f o r the  standard drop sizes are given i n Table 4.2 from [ 4 . 3 1 ] :  217  T a b l e 4.2  Drop T e r m i n a l V e l o c i t i e s  Drop Diameter  (mm)  Terminal  in Still Air  Velocities  2.06 4.03 5.40 6.49 7.41 8.06 8.53 8.83 9.00 9.09 9.13 9.14 9.14  0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5  For cases where t h e r e i s a c o n s t a n t v e r t i c a l wind v e l o c i t y , vertical  f a l l velocity  V  = V  w  -V  I ^ E L  To e s t i m a t e  (4.20)  m  the e f f e c t s  a r e d e f i n e d t o be upward.  of a v e r t i c a l wind v e l o c i t y ,  assumed t h a t the v e r t i c a l wind o n l y o c c u r s  These a r e r e a s o n a b l e  assumptions when the v e r t i c a l wind i s  v e r t i c a l winds a s s o c i a t e d with weather f r o n t s .  measured  distribution  c e l l and  to h e i g h t s w e l l above the  c r e a t e d by t o p o g r a p h i c a l changes but a r e of course  the drop s i z e  i t w i l l be  a t h e i g h t s below the r a i n  t h a t the v e r t i c a l wind has a c o n s t a n t v e l o c i t y path.  the s t e a d y - s t a t e  i s g i v e n by:  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  microwave  (m/s)  not s t r i c t l y v a l i d f o r  For t h i s v e r t i c a l wind model,  l e a v i n g the r a i n c e l l i s the same as would be  on the ground i n the absence of v e r t i c a l wind.  I t w i l l a l s o be  assumed t h a t the: depth of the v e r t i c a l wind r e g i o n 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 s i z e d i s t r i b u t i o n i n the v e r t i c a 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 v e r t i c a l wind i s to change the rainrate measured on the ground.  This approach i s 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 v e r t i c a l v e l o c i t i e s f o r drops of d i f f e r e n t s i z e s . Because the drop size d i s t r i b u t i o n i s inversely proportional to the drop v e l o c i t y , the value of  f o r each drop size i n the presence of v e r t i c a l  wind i s now given by: DRQP (D) ' I V  N  (D) = N  ( A  *?  D  )  (4.21)  This c a l c u l a t i o n may only be v a l i d for v e r t i c a l wind v e l o c i t i e s up to the smallest s t i l l a i r drop v e l o c i t y considered ( i . e . 2.06 m / s ) . At higher upward 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 v e r t i c a l wind region. Horizontal CPAs for d i s t r i b u t i o n s calculated from (4.21) at several wind v e l o c i t i e s are shown i n F i g . 4.11.  For this analysis, i t has been  assumed that the drop size d i s t r i b u t i o n above the v e r t i c a l wind region i s described by the Joss/Olsen Widespread or Marshall and Palmer d i s t r i b u t i o n . Even though the v e r t i c a l wind model used here i s probably a s i m p l i f i c a t i o n of  219  F i g . 4.11.  H o r i z o n t a l CPA  vs.  rainrate for different  v e r t i c a l wind  velocities.  the actual conditions during natural r a i n , the results i n F i g . 4.11  are  considered to be s u f f i c i e n t l y accurate for v e r t i c a l v e l o c i t i e s below 2 m/s for comparison to experimental r e s u l t s .  These results i l l u s t r a t e the Import-  ance of measuring v e r t i c a l wind v e l o c i t i e s i n propagation experiments.  4.5  Backscatter Calculation Because a radar path i s used i n this experiment, a component of the  received s i g n a l w i l l result from backward scattering from the r a i n volume common to both antenna beams. red to as r a i n c l u t t e r ,  The r a i n backscattered copolar s i g n a l , r e f e r -  Is a l i m i t i n g factor i n radar systems and accordingly  has been studied t h e o r e t i c a l l y and experimentally by several i n v e s t i g a t o r s . A c a l c u l a t i o n of the r a i n backscatter  for this path w i l l be made to estimate  the r e l a t i v e l e v e l of this undesired s i g n a l compared to the signal returned from the r e f l e c t o r at the end of the path. The type of radar configuration used i n this experiment i s referred to as a b i s t a t i c radar because the transmitting and receiving antennas are not collocated.  Rain backscatter  for a b i s t a t i c radar can be calculated from  [4.33]:  3 V o ( 6) e 4TTX  where:  P , P  2  R  2  R  -aR, - aR. (4.22)  2 2  are the received and transmitted powers.  A ^ , A^, are the antennas' e f f e c t i v e areas R , R„ are the ranges to the r a i n volume common to the antenna beams 3 i s the scattering cross section per unit volume  V i s t h e s c a t t e r i n g volume of. 0) g i v e s t h e a n g u l a r p r o p e r t i e s of the s c a t t e r i n g p r o c e s s and  e  -oR  i s t h e atmospheric a t t e n u a t i o n  In t h i s experiment, the ranges and antenna e f f e c t i v e a r e a s a r e e q u a l .  The  s c 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 i g n o r e d i f the b a c k s c a t t e r c r o s s s e c t i o n i s used f o r g. T h e r e f o r e , i g n o r i n g a t t e n u a t i o n , t h i s e q u a t i o n can be r e w r i t t e n f o r t h i s experiment a s :  6V  (4.23)  The volume common t o t h e 3 dB beamwidths o f t h e two antennas c u l t t o c a l c u l a t e e x a c t l y because o f the c o m p l i c a t e d geometry and because changes  is diffi-  o f the volume  s m a l l e r r o r s I n the assumed p o i n t i n g a n g l e s w i l l r e s u l t i n l a r g e  i n t h i s volume.  An a d d i t i o n a l c o m p l i c a t i o n a r i s e s i n t h i s  experiment  because o f t h e p r o x i m i t y o f the b u i l d i n g on which t h e r e f l e c t o r i s mounted. On t o p o f t h i s b u i l d i n g , a penthouse  s h i e l d s t h e r a i n volume b e h i n d 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 s h i e l d e d by the t o p f l o o r o f the b u i l d i n g .  T h e r e f o r e , o n l y the  common r a i n volume i n f r o n t o f the r e f l e c t o r can b a c k s c a t t e r a s i g n a l . first  p o i n t common t o both antenna 3 dB beamwidths i s a p p r o x i m a t e l y 660 m  from the antennas. would  The  ( I f the b u i l d i n g were not t h e r e , t h e f a r t h e r common p o i n t  be about 1300 m. from the a n t e n n a s ) .  about 6.8 m i n diameter a t the r e f l e c t o r .  The antenna This r e s u l t s  3 dB beamwidths a r e i n a common volume i n  222  front of the r e f l e c t o r or approximately 3000 m . 3  (Without the building this  would have been approximately 11000 m ) . 3  Calculated backscatter  cross sections f o r 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 C u r r i e , Dyer and Hayes [4.35] and Dyer and Currie [4.36]. backscatter 10"  3  m  - 1  Crane's calculated  cross sections per unit volume at 73 GHz are appoximately 1.0 •  and 1.1 • 1 0  - 3  m * f o r the Laws and Parsons and Marshall and Palmer -  drop size d i s t r i b u t i o n s , respectively, at a rainrate of 50 mm/hr. Using these results the l i n e a r l y p o l a r i z e d , copolar backscatter calculated using (4.23).  can be  The results f o r this c a l c u l a t i o n , which ignores  attenuation, predicts a received, r a i n backscattered signal approximately 92 dB below the transmitted s i g n a l at the antenna ports f o r a rainrate of 50 mm/h. Attenuation was ignored i n this c a l c u l a t i o n to allow a s i m p l i f i e d comparison to be made between the received r a i n backscatter signals.  and r e f l e c t o r  Because of the geometry of the antenna beams' common volume, the  major portion of the r a i n backscatter w i l l originate within a short distance of the r e f l e c t o r .  As a result the r a i n backscatter  experience very s i m i l a r attenuations.  This allows a d i r e c t comparison to be  made between the calculated r a i n backscatter culation i n Section 2.7.  and r e f l e c t o r signal w i l l  and the transmission loss c a l -  The calculated transmission loss including the  r e f l e c t o r was approximately 39 dB, or 53 dB higher than the r a i n backscattered s i g n a l at a rainrate of 50 mm/h.  223  Another way to compare the signals from the r a i n and r e f l e c t o r i s to compare the two scattering cross sections. ing cross section i s about 3 m at 50 mm/h. 2  For the r a i n volume, the s c a t t e r The scattering cross section f o r  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 f o r the r e f l e c t o r of 7 . 5 * 1 0 m , or about 54 dB larger than the 50 mm/h r a i n cross s e c t i o n . 5  2  It i s not possible to accurately estimate the magnitude of the depolarized backscatter t h i s phenomena.  at this frequency because very l i t t l e i s known about  Shimabukuro [4.33] states that "The scattered wave i s nearly  completely polarized over the entire range of scattering angles.  There i s a  s l i g h t depolarization at angles away from the forward and backscatter t i o n s , with the maximum depolarization occuring near 6 = 9 0 ° . "  direc-  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 . 3 9 ] .  The f i r s t two of these references  discuss aspects of the  theory and do not contain any results which are d i r e c t l y applicable to this problem.  However, the results i n Tsang and Kong [4.37] do i n d i c a t e that the  depolarization cross section i s much smaller than the copolar cross section for general random media. depolarized backscattered scattered s i g n a l .  Results i n [4.39] indicate t h a t , i n general, the signal i s at least  30 dB below the copolar back-  224  The  r e s u l t s i n t h i s s e c t i o n show c o n c l u s i v e l y t h a t c o p o l a r  from r a i n i s not a source ment.  of e r r o r f o r the radar path used i n t h i s e x p e r i -  While the s i t u a t i o n f o r d e p o l a r i z e d b a c k s c a t t e r i s f a r l e s s  the a v a i l a b l e evidence  i n d i c a t e s that t h i s e f f e c t  data.  certain,  i s much s m a l l e r than t h e  c o p o l a r b a c k s c a t t e r and t h e r e f o r e w i l l not be a source experimental  backscatter  of u n c e r t a i n t y i n the  225  5.  DUAL-POLARIZED EXPERIMENTAL MODEL  This chapter describes a general theory and an experimental model developed to analyze the performance of a p r a c t i c a l dual-polarized atomospheric propagation l i n k including a crosspolar cancellation network.  The  major functions of this experimental model are to predict the dual-polarized l i n k XPD performance and to separate, as far as possible, the depolarized signals r e s u l t i n g from the f i n i t e antenna/OMT i s o l a t i o n s and the atmospheric propagation path.  This type of analysis i s e s p e c i a l l y important when  comparing measured and predicted XPDs i n this frequency range because the l e v e l of the r a i n depolarized signal i s usually lower than the signal due to the uncancelled clear weather system i s o l a t i o n . The basic idea of analyzing the XPD performance of a dual-polarized l i n k by vector addition of a l l of the depolarized signals i s 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 ports.  This model also incorporates  of mismatches on the OMT  a number of s i m p l i f i c a t i o n s , approxima-  tions and a more descriptive notation which makes i t easier to apply i n a practical situation. effects  Since they are not important i n this experiment,  the  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 i s shown i n F i g . 5.1.  A number of s i m p l i f i c a t i o n s ,  approximations and assumptions which were used to arrive at this system  FIG. 5.1  EXPERIMENTAL SYSTEM SIGNAL FLOW DIAGRAM  227  diagram are discussed i n Section 5.2. are defined i n Section 5.3.  The symbols and notation i n F i g . 5.1  The equations describing the signals throughout  the experimental system are discussed i n Section 5.4.  The rest of this  chapter i s devoted to the results and p r a c t i c a l implications of the e x p e r i mental model.  5.1  Previous Work Several investigations have previously discussed some aspects of the  problem of separating the antenna and path depolarized s i g n a l s .  Shkarofsky  [5.1] and Shkarofsky and Moody [5.2] have included the effects of hydrometeors,  antenna i s o l a t i o n s , antenna misalignment and Faraday rotation i n the  XPD analysis of s a t e l l i t e  links.  Nowland and Olsen [5.3] have developed a  s i m p l i f i e d analysis of XPD including the same effects previous references.  as discussed i n the two  Dintelmann [2.39] has investigated some aspects of the  performance of dual-polarized l i n k s including crosspolar cancellation networks.  Evans and Thompson [2.35] and Delogne and Sobieski [5.4] have pre-  sented graphs showing the error bounds on XPD measurements f o r conventional, uncancelled dual-polarized experimental  5.2  systems.  S i m p l i f i c a t i o n s , Approximations and Assumptions In order to reduce the complexity of the algebraic manipulations, only  a s i n g l e , f i x e d , transmitted p o l a r i z a t i o n i s included i n the model. To facilitate  the reading of the following equations, the two polarizations w i l l  be referred to as the copolar and crosspolar, zontal as Is usually the case.  rather than v e r t i c a l or h o r i -  These s i m p l i f i c a t i o n s can be made without  228  l o s s of g e n e r a l i t y up to the p o i n t where the a c t u a l m e t e o r o l o g i c a l  parameters  are s u b s t i t u t e d i n t o the e q u a t i o n s . To make the f o l l o w i n g a n a l y s i s f e a s i b l e , i t i s n e c e s s a r y t o make some assumptions.and  approximations.  l o s s e s , phase s h i f t s  Most o f these s i m p l i f i c a t i o n s  and r e f l e c t i o n s  t o be i g n o r e d .  cause  small  Where i t i s f e l t  t o be  n e c e s s a r y , a s h o r t e x p l a n a t i o n i s i n c l u d e d w i t h the reasons why t h e s e approximations  are j u s t i f i a b l e .  Assumptions and a p p r o x i m a t i o n s : 1.  - the magnitude of the r e f l e c t e d network can be i g n o r e d . a r e connected  s i g n a l s throughout  the c a n c e l l a t i o n  T h i s i s reasonable because the c o u p l e r p o r t s  t o e i t h e r the w e l l matched antenna  ports or the i s o l a t o r s  p r e c e d i n g the m i x e r s . 2.  - t h e e f f e c t s of s i g n a l s due t o 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 . t h i s assumption  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 ,  i s v a l i d e i t h e r because o f the f i r s t  assumption o r  because the u n d e s i r e d coupled s i g n a l i s v e r y much s m a l l e r than t h e desired 3.  signal.  - a l l s i g n a l s are t o t a l l y i d e a l coherency multiple  4.  coherent.  Only v e r y s m a l l v a r i a t i o n s  occur due e i t h e r t o atmospheric  from  turbulence or to  scattering.  - the p l a n e s A-A and B-B of F i g . 5.1 a r e the 3-port  d i r e c t i o n a l coupler  r e f e r e n c e p l a n e s 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.  I t i s a l s o assumed t h a t no  229  s i g n i f i c a n t phase v a r i a t i o n w i t h frequency c o u p l i n g at these r e f e r e n c e 5.  - the phase s h i f t  over the bandwidth  between the  dB p o r t s can be c o n s i d e r e d as a s e c t i o n of  waveguide i n c l u d i n g the a t t e n u a t o r l o s s and 7.  - the XPD  - the c l e a r weather a t t e n u a t i o n and XPD assumed to be  9.  directional uniform  phase s h i f t e r  angle.  of the antennas a r e independent of the atmospheric c o n d i t i o n s  i . e . near f i e l d antenna e f f e c t s can be 8.  varia-  considered.  - the t o t a l l e n g t h of the waveguide c i r c u i t c o u p l e r -10  the  planes.  i n t r o d u c e d by the phase s h i f t e r has n e g l i g i b l e  t i o n w i t h frequency 6.  occurs as a r e s u l t of  zero and  ignored. of the p r o p a g a t i o n  path  are  infinite,respectively.  - the waveguide l o s s e s b e f o r e the d i r e c t i o n a l c o u p l e r s and  the  through-  l i n e l o s s e s of the c o u p l e r s can be modelled as a r e d u c t i o n i n r e c e i v i n g system s e n s i t i v i t y and 10. - the amplitude  N o t a t i o n and The  ignored.  of the c r o s s p o l a r s i g n a l d e p o l a r i z e d to the  p o l a r i z a t i o n can be  5.3  otherwise  ignored.  Units  n o t a t i o n used i n the f o l l o w i n g s e c t i o n was  number of times accomplished  designed  to reduce  the symbol d e f i n i t i o n s would have to be c o n s u l t e d .  definitions: - c o p o l a r s i g n a l , i . e . s i g n a l of the same l i n e a r polarization originally  ( v e r t i c a l or h o r i z o n t a l ) as  transmitted.  the  This i s  i n p a r t by i n c l u d i n g the f o l l o w i n g d e s c r i p t i v e s u b s c r i p t s .  Subscript CP  copolar  was  230  XP  -crosspolar  signal, i.e. linear  polarization  o r t h o g o n a l t o CP. CN  -cancellation the  s i g n a l , r e f e r r i n g to the signal i n  a t t e n u a t o r - phase s h i f t e r l i n e o f the  cancellation CW  circuit.  - c l e a r weather, v a l u e o f a s i g n a l o r q u a n t i t y under c l e a r weather  TX,RX  conditions.  - T r a n s m i t t i n g and R e c e i v i n g .  When r e f e r r i n g t o  s i g n a l s , designates signals  p r o p a g a t i n g on t h e  path a t the "output" o f t h e t r a n s m i t t i n g and  a t the " i n p u t "  respectively.  t o the r e c e i v i n g  antenna  antenna  When r e f e r r i n g t o antenna p a r a -  meters TX and RX r e f e r t o t h e i n d i v i d u a l antennas. PATH  - v a l u e o f a t t e n u a t i o n , phase s h i f t o r XPD r e s u l t i n g from t h e s i g n a l p r o p a g a t i o n o v e r t h e p a t h .  FE  -front-end refers receiving  system.  to s i g n a l a t the input to the These q u a n t i t i e s  r e c o r d e d by the d a t a a c q u i s i t i o n The usually are  u n i t s used i n the f o l l o w i n g  associated  are,  w i t h the i n d i v i d u a l q u a n t i t i e s .  system.  whenever p o s s i b l e ,  those  F o r example: a t t e n u a t i o n s  i n dB, a n g l e s a r e i n degrees and s i g n a l l e v e l s a r e i n dB r e l a t i v e t o t h e  c l e a r weather l e v e l o f t h e r e c e i v e d c o n v e n t i o n s a r e used when d i s c u s s i n g the  analysis  a r e those  most n a t u r a l  association  copolar s i g n a l .  These f a m i l i a r u n i t s and  d a t a and a n a l y s i s  r e s u l t s and p r o v i d e  w i t h t h e a c t u a l measurement system.  However, i n  231  the a c t u a l e q u a t i o n s , where complex v o l t a g e s a r e used, s i g n a l r e p r e s e n t a t i o n i n dB i s n o t c o n v e n i e n t .  To s o l v e t h i s problem, a s u p e r s c r i p t V i s used,  when n e c e s s a r y , on the a t t e n u a t i o n s and XPD s to d e s i g n a t e a v o l t a g e  ratio.  For example, i n the case of X P D : XPD i n d i c a t e s  the v a l u e i n dB and XPD^ i s the same v a l u e as a v o l t a g e  ratio, i.e.  .Hl/2  -XPD XPD  10  =  V  A  1 0  -XPD  10  2 0  J i 6  A s i m i l a r s i t u a t i o n a r i s e s when a n g l e s a r e w r i t t e n i n the form e t h i s case The  "  and i n  t  the a n g l e i s assumed t o be i n r a d i a n s . symbol E i s used t o d e s i g n a t e s i g n a l s which a r e complex v o l t a g e s ,  i . e . s i g n a l s h a v i n g a magnitude and a n g l e . Symbol  definitions:  Tf'CPCW  -refers  to t h e c l e a r - w e a t h e r  complex v o l t a g e o f the  c o p o l a r r e c e i v e d s i g n a l a t the i n p u t t o the r e f e r e n c e p l a n e D-D  of F i g . 5 . 1 .  dB r e f e r e n c e throughout E  E  rjpcw  *  s  t l i e  ^  the f o l l o w i n g a n a l y s i s .  -the general received copolar signal at D-D,  i.e.  D d u r i n g anomolous p r o p a g a t i o n c o n d i t i o n s . E  CP,  -refers  t o the n o r m a l i z e d  s i g n a l generated  by the  s m i l l i m e t r e source.  T h i s s i g n a l I s n o r m a l i z e d to  i n c l u d e the c l e a r weather t r a n s m i s s i o n l o s s , antenna g a i n s and d i s p e r s i v e path  loss.  i.e.  refers  t o t h e c o p o l a r s i g n a l a t the "output" o f  the t r a n s m i t t i n g antenna, i . e . a t the path "input". -refers  t o the c o p o l a r s i g n a l a t the " i n p u t " t o t h e  r e c e i v i n g antenna a f t e r p r o p a g a t i n g -the  c o p o l a r s i g n a l a t the o u t p u t  the path,  of r e f e r e n c e  j u n c t i o n s A-A, i . e . the c o p o l a r s i g n a l a t the front-end -refers  input,  t o the c l e a r weather c r o s s p o l a r r e c e i v e d  s i g n a l a t the i n p u t o f the r e f e r e n c e j u n c t i o n B-B. - r e f e r s t o t h e same c r o s s p o l a r s i g n a l under anamolous atmospheric c o n d i t i o n s , -refers  t o the c r o s s p o l a r s i g n a l a t the "output" o f  the t r a n s m i t t i n g antenna. to  T h i s s i g n a l i s due o n l y  XPD . TX  -refers  t o the c r o s s p o l a r s i g n a l a t the r e c e i v i n g  antenna i n p u t , -the  s i g n a l a t the output  of reference j u n c t i o n  B-B, i . e . the t o t a l s i g n a l i n t o t h e c r o s s p o l a r c h a n n e l o f the f r o n t - e n d .  T h i s w i l l be the  measured s i g n a l l e v e l o f t h e c r o s s p o l a r -refers  t o the c o p o l a r s i g n a l  channel,  a t the r e f e r e n c e  233  plane A-A  which i s coupled through the  c o u p l e r - 10  dB  output, i . e . the  sampling  cancellation  s i g n a l b e f o r e a t t e n u a t i o n or phase s h i f t i n g a f t e r the  - 10  - r e f e r to the  dB  but  coupling,  cancellation  s i g n a l at the  input  to  B the  coupled port  i s the E„ , A  a t t e n u a t e d and  and  x  at r e f e r e n c e j u n c t i o n  includes  the  B-B.  This  phased s h i f t e d v e r s i o n  of  e f f e c t of both d i r e c t i o n a l  C N  couplers. XPD^.XPD^ V  -refers  to the  crosspolar  discrimination  ,XPD  transmitting  and  receiving  antennas ( i n c l u d i n g  orthomode t r a n s d u c e r ) i n dB ratio. ,6  Y t m  XPD  the  V  XPD_  8  of  T X  XPD^  These are  considered. - r e f e r s t o the the by  angle of  crosspolarized the  antennas.  c o p o l a r s i g n a l and differences  f o r the  and  as a v o l t a g e  transmitted  the  the  polarization  phase s h i f t  added  to  signal after It i s depolarized The  a n g l e i s r e l a t i v e to  includes  through the  any  path  the  length  antenna f o r the  two  polarizations. AG>VDR  -refers  to the  difference  between  XPD A0  -refers  x p u  = ©  X P D  ~ °XPD  and  .  VT)T  XPD i.e.  AIQ  Q  T X  0 XPD^  '  to the path l e n g t h d i f f e r e n c e which  causes  refers  to the magnitude r a t i o of the  d e p o l a r i z e d s i g n a l a t the r e s p e c t to the antenna. the  receiving  path antenna w i t h  c