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Microwave grading of lumber Leong, Ng Kan 1981

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MICROWAVE GRADING OF LUMBER by NG KAN LEONG B.Sc. (Hons.), University of Strathclyde, Glasgow, 1975 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n THE FACULTY OF GRADUATE STUDIES Department of Electrical Engineering We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA December, 1981 ° Ng Kan Leong, 1981 I n p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r an a d v a n c e d d e g r e e a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e a n d s t u d y . I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by t h e h e a d o f my d e p a r t m e n t o r by h i s o r h e r r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l n o t be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . D e p a r t m e n t o f E l e c t r i c a l Engineering The U n i v e r s i t y o f B r i t i s h C o l u m b i a 2075 W e s b r o o k P l a c e V a n c o u v e r , C a n a d a V6T 1W5 D a t e 0 6 5 0 • 2 8 ' 1 9 8 1 DE-6 (2/79) ABSTRACT Microwave measurements of the e l e c t r i c a l p r o p e r t i e s of wood (Douglas f i r ) at va r i o u s f r e q u e n c i e s , moisture contents and g r a i n o r i e n t a t i o n s were made. Based on these measurements, a frequency of 35 GHz (nominal) was chosen f o r the development of a microwave apparatus f o r s t r e s s grading of lumber as i t gave the best compromise between r e s o l u t i o n and s e n s i t i v i t y . The design and implementation of a homodyne system i n c o r p o r a t i n g a dual balanced mixer i s d e s c r i b e d . The system i s capable of measuring the co-p o l a r , c r o s s - p o l a r and RF phase (of the co-polar) s i g n a l s of a l i n e a r l y p o l a r i z e d electromagnetic wave tran s m i t t e d through wood. The performance of the system i s teste d by measuring samples of Douglas f i r lumber boards which were l a t e r subjected to t e s t s f o r st r e n g t h (modulus of r u p t u r e ) . The r e s u l t s i n d i c a t e e x c e l l e n t q u a l i t a t i v e c o r r e l a t i o n between the microxtfave measurements and the stre n g t h of the lumber boards. i i TABLE OF CONTENTS Page ABSTRACT i i TABLE OF CONTENTS i i i LIST OF ILLUSTRATIONS v i LIST OF TABLES . . . . . . . . . . . . . . . . i x ACKNOWLEDGEMENT x 1. INTRODUCTION . 1 1.1 Stress Grading Systems 1 1.2 Strength P r o p e r t i e s of Lumber 5 1.2.1 Slope of Grain 6 1.2.2 Knots 7 1.2.3 S p e c i f i c G r a v i t y 7 1.2.4 Moisture Content 7 1.3 E l e c t r i c a l P r o p e r t i e s of Wood 7 1.3.1 Wood Density and Moisture Content 8 1.3.2 Degree of D e p o l a r i z a t i o n 9 1.4 Microwave Measurements 14 1.5 Thesis Objective 15 1.6 Thesis O u t l i n e . 15 2. ANALYSIS 17 2.1 C o r r e l a t i o n Between Microwave and P h y s i c a l P r o p e r t i e s of Wood 17 2.2 Choice of Frequency 17 2.3 Methods and Configurations of Measurements 18 2.3.1 Homodyne v s . Heterodyne 18 2.3.2 Modulated Sub-Carrier Method . . . 21 2.3.3 Square-Law or Low Lev e l Detection 21 2.3.4 Li n e a r or High L e v e l Detection . . . . . 27 2.3.5 C a r r i e r Suppression Using Balanced Mixers 27 2.3.6 Homodyne Systems 29 2.3.7 Double Channel System w i t h Balanced Mixers 33 i i i Page 3. DESCRIPTION AND DESIGN OF THE STRESS GRADING SYSTEM 34 3.1 General 34 3.2 The Transmitting Branch . 34 3.2.1 Design of the PIN Diode Amplitude Modulator and 36 Switches 3.2.2 Design of the Pyramidal Horn Lens 41 3.2.3 Design of the Hybrid Ring and Phase S h i f t e r 43 3.3 The Receiving Branch 43 3.4 The Homodyne Detection Bridge . . 45 3.5 The M o d i f i e d System . 46 4. THE ELECTRONICS INTERFACE 50 4.1 General 50 4.2 D r i v e r f o r PIN Diode Amplitude Modulator and Switches . . . . 50 4.3 Balanced Mixer I n t e r f a c e 55 4.3.1 Balancing Network and Instrumentation A m p l i f i e r . . . 58 4.3.2 Band Pass F i l t e r . 59 4.3.3 B u f f e r and AF Phase S h i f t e r . . . . . 62 4.3.4 Summing A m p l i f i e r and Analog Switch 62 4.3.5 Band Pass F i l t e r and I n v e r t i n g A m p l i f i e r 64 4.3.6 RMS-to-DC Converter 66 4.3.7 Phase S e n s i t i v e Detector 66 4.4 The Mo d i f i e d System 68 4.5 C a l i b r a t i o n and Tuning 68 5. EXPERIMENTAL RESULTS 72 5.1 Measurements of Microwave Components . . . . . 72 5.1.1 Pyramidal Horn Lens and C o n i c a l Horn Lens Antennas . . 72 5.1.2 PIN Diode Switches '. 72 5.1.3 Hybrid Rings 72 5.2 Waveguide Measurements of R e l a t i v e P e r m i t t i v i t y and Loss Tangent 78 5.3 Free-Space Measurements at 34.80 GHz 80 5.4 S t a t i c Measurements of Slope of Grain and Knots 85 i v Page 5.5 Re s u l t s from the Double Channel Homodyne System . 85 5.6 Observations 94 6. CONCLUSIONS AND DIRECTIONS FOR FURTHER DEVELOPMENT . 96 6.1 Conclusions 96 6.2 D i r e c t i o n s f o r Further Development . . . . 96 7. REFERENCES . . . . . . . . . . . . . . 98 8. APPENDICES 102 8.1 Wave M a t r i x A n a l y s i s 102 8.2 Computer Program L i s t i n g s of WOOD and FSPACE 106 8.3 Strength (M.O.R.) Results . . 117 8.4 I l l u s t r a t i o n s of the Dual Balanced Mixer Homodyne System . . 137 v LIST OF ILLUSTRATIONS Fig.# Page 1.1 Strength d i s t r i b u t i o n s of four commercial grades based upon 850 2x6 Douglas f i r j o i s t s t e s t e d In bending (from Madsen U . U ] , • • • 3 1.2 Scattergrara of M.O.R. v s . E m £ n (from Madsen [1.1]J 4 1.3 E l e c t r i c f i e l d i n c i d e n t at an oblique angle to d i r e c t i o n of g r a i n 11 1.4 P o l a r i z a t i o n e l l i p s e 11 2.1 Comparison of c r y s t a l n o n - l i n e a r i t i e s f o r DSBWC homodyne and heterodyne a t t e n u a t i o n measurement system (from L i t t l e [2.2]) 20 2.2 Modulated s u b - c a r r i e r method (from Schafer et a l . [2.10]) . . 22 2.3 Phasor diagram of the r e s u l t a n t input s i g n a l . 24 2.4 180° h y b r i d r i n g j u n c t i o n 28 2.5 DSB automated system f o r r e a l - t i m e phase and amplitude measurements (from Cohn et a l . [2.20]) . . . . . . 32 3.1(a) Block diagram of the dual balanced mixer homodyne system. . . 35 3.1(b) Block diagram of the modified dual balanced mixer homodyne system. . 49 3.2 Diode e q u i v a l e n t s c i r c u i t s 36 3.3 S e c t i o n through PIN diode s w i t c h 38 3.4 Pyramidal horn 42 3.5 Pyramidal horn-lens 42 3.6 S e c t i o n through the h y b r i d r i n g 44 3.7 S e c t i o n through the phase s h i f t e r 44 3.8 I n i t i a l adjustment of the phase s h i f t e r , W 2» . . 47 4.1(a) E l e c t r o n i c sub-systems. 51 4.1(b) M o d i f i e d e l e c t r o n i c sub-systems 69 4.2(a) Schematic diagram f o r 1 KHz PIN diode d r i v e r 52 v i Fig.# Page 4.2(b) Schematic diagram f o r 10 KHz PIN diode d r i v e r 56 4.3(a) Schematic diagram f o r balanced mixer i n t e r f a c e I 60 4.3(b) Schematic diagram f o r balanced mixer i n t e r f a c e I I 65 4.4 Schematic diagram f o r a c t i v e f i l t e r AF150 63 4.5 Phase s e n s i t i v e d e t e c t o r 67 5.1(a) R a d i a t i o n p a t t e r n of the pyramidal horn lens antenna (E-plane) . . . . . 73 5.1(b) R a d i a t i o n p a t t e r n of the pyramidal/horn lens antenna (H-plane) 74 5.2 R a d i a t i o n p a t t e r n of the c o n i c a l horn lens antenna (E-plane). 75 5.3 R a d i a t i o n p a t t e r n of the c o n i c a l horn lens antenna (H-plane) 76 5.4 I s o l a t i o n of the microwave switches as a f u n c t i o n of frequency 77 5.5 Waveguide measurement of r e l a t i v e p e r m i t t i v i t y and l o s s tangent of wood 79 5.6 R e l a t i v e p e r m i t t i v i t y of Douglas f i r as f u n c t i o n s of frequency and g r a i n d i r e c t i o n . . . . 81 5.7 Loss tangent of Douglas f i r as f u n c t i o n s of frequency and g r a i n d i r e c t i o n 82 5.8 R e l a t i v e p e r m i t t i v i t y and l o s s tangent of Douglas f i r as f u n c t i o n s of moisture content and g r a i n d i r e c t i o n at a frequency of 34.80 GHz 86 5.9 A t t e n u a t i o n of the co-polar s i g n a l as f u n c t i o n s of moisture content and g r a i n d i r e c t i o n at 34.80 GHz 87 5.10 Cross-polar and co-polar s i g n a l s v s . slope of g r a i n (sample A). 88 5.11 Cross-polar and co-polar s i g n a l s v s . slope of g r a i n (sample B) 89 5.12 Cross-polar and co-polar s i g n a l s v s . slope of g r a i n (sample C) 90 v i i Fig.# Page 5.13 Cross-polar and co-polar s i g n a l s v s . distance (sample D). . . 91 5.14 " " " " (sample E ) . . . 92 5.15 . . . . .. « (sample F ) . . . 93 8.1 R e f l e c t e d and tr a n s m i t t e d waves at a d i s c o n t i n u i t y i n t e r f a c e . 103 8.2 D i e l e c t r i c s l a b d i s c o n t i n u i t y 104 8.3- Homodyne system measurements and the modulus of rupture 8.21 (M.O.R.) t e s t r e s u l t s f o r board samples #01 to #19 8.22 The homodyne system 138 8.23 The t r a n s m i t t i n g branch 138 8.24 The p y r a m i d a l / c o n i c a l horn-lens antennas 139 8.25 The homodyne bridge . 139 8.26 The balanced mixers 140 v i i i LIST OF TABLES Page Table 2.1 Phase and amplitude e r r o r s 26 Table 3.1 Parameters of the PIN diode switches and modulator . . . . 37 Table 5.1 Measurement r e s u l t s of h y b r i d r i n g s Table 5.2 Free-Space measurements of d i e l e c t r i c constant and l o s s tangent (transverse) 84 Table 5.3 Free-Space measurements of d i e l e c t r i c constant and l o s s tangent ( l o n g i t u d i n a l ) 37 i x ACKNOWLEDGEMENT I wish to thank my s u p e r v i s o r , Dr. M.M.Z. Kharadly, f o r h i s g u i d -ance, advice and devoted i n t e r e s t throughout the course of t h i s work. Thanks are due to P r o f . B. Madsen, Dr. T. Enegren, Mr. B. P e t e r s , Mr. E. Lee f o r compiling the programs, WOOD and FSPACE, Mr. A. Buchanan, Mr. A. K i n d s v a t e r , Mr. P. vander Gracht and Mr. J . vander Star f o r numerous h e l p f u l d i s c u s s i o n s , and to Mr. J . Johnston f o r t e s t i n g the e l e c t r o n i c s , Mr. J . Stuber and Mr. T. Stinsen f o r t e c h n i c a l a s s i s t a n c e , and a l s o to Mrs. Kathy Brindamour and Mrs. G a i l Schmidt f o r typing t h i s t h e s i s . The f i n a n c i a l support of the B r i t i s h Columbia Science C o u n c i l i s g r a t e f u l l y acknowledged. F i n a l l y , I would l i k e to thank my w i f e , Kathleen, f o r her patience and understanding throughout the course of t h i s work. 1 CHAPTER I - INTRODUCTION 1.1 Stress Grading Systems One of the many products of wood i s dimension lumber, a term used i n North America f o r a timber product which i s from 1.5 to 3.5 inches i n t h i c k -ness and 3.5 inches or more i n width. I t i s the sawmill's major product s i n c e i t forms about 90% of i t s output [ 1 . 1 ] . At present, there are two methods f o r grading dimension lumber: one uses v i s u a l grading and the other uses a s t r e s s - r a t e d machine whose graded product i s known as machine s t r e s s r a t e d (MSR) lumber. The f i r s t system, v i s u a l grading, i s conducted a c c o r d i n g to the r u l e s of the N a t i o n a l Lumber Grading A u t h o r i t y , which i n t u r n , are based on the standard D245 ASTM (American So c i e t y f o r T e s t i n g and M a t e r i a l s ) f i r s t pub-l i s h e d i n 1926. C e n t r a l to t h i s system i s the concept t h a t the end product i s p r o p o r t i o n a l to the c l e a r s t r e n g t h (obtained by t e s t i n g s m a l l specimens of c l e a r m a t e r i a l ) w i t h subsequent r e d u c t i o n by a s t r e n g t h r a t i o which i s based upon the c h a r a c t e r i s t i c s of the v a r i o u s d e f e c t s , e.g., s i z e and l o c a t i o n of the k n o ts, slope of g r a i n , e t c . With the s t r e n g t h r a t i o s and the s p e c i f i c grading methods e s t a b l i s h e d , the standard then d e f i n e s the a l l o w a b l e s t r e s s e s f o r each grade of lumber. In 1970, the f o l l o w i n g s t r e n g t h r a t i o s f o r v a r i o u s grades were agreed upon by the lumber manufacturers' a s s o c i a t i o n s : S e l e c t S t r u c t u r e s 65% 55% 45% 26% #1 Grade #2 Grade #3 Grade 2 I t has been shown by Madsen [1.1] that the grading r u l e s l e a d to poor u t i l i z a t i o n of the end products. From F i g . 1.1, showing the cumulative s t r e n g t h d i s t r i b u t i o n , i t i s observed that s e l e c t s t r u c t u r a l grade i s d i s -t i n c t l y strongest but there i s l i t t l e d i f f e r e n c e i n s t r e n g t h between #1 Grade and #2 Grade at the low end of the d i s t r i b u t i o n . Moreover, #2 Grade i s stronger than #1 Grade at the high end. The #2 Grade i s only m a r g i n a l l y stronger than the #3 Grade. I t i s apparent, t h e r e f o r e , that the grading r u l e s are not e f f e c t i v e i n c o r r e l a t i n g the v a r i o u s grades w i t h t h e i r s t r e n g t h r a t i o s . Allowable s t r e s s e s are based on the 5th p e r c e n t i l e of the cumulative s t r e n g t h d i s t r i b u t i o n , w i t h a s u i t a b l e s a f e t y f a c t o r . Because v i s u a l g r a d i n g methods are not e f f e c t i v e i n s e p a r a t i n g lumber i n t o grades of d i f f e r e n t s t r e n g t h , each grade e x h i b i t s high v a r i a b i l i t y , and s t r u c t u r a l design methods are much l e s s e f f i c i e n t than would be p o s s i b l e i f a more e f f e c t i v e non-d e s t r u c t i v e grading method were a v a i l a b l e . The other system [1 . 2 ] , machine s t r e s s r a t i n g process, takes measure-ments of the bending modulus of e l a s t i c i t y (MOE), or s t i f f n e s s of each p i e c e of lumber and a s s i g n a corresponding predetermined s t r e n g t h value to the measurements. I t has been found that the system performs b e t t e r [1.2] i f a v i s u a l o v e r r i d e , such as excluding pieces w i t h edge knots and cosmetic d e f e c t s from machine grading, i s a p p l i e d by the o p e r a t o r . Thus"visual g r a d -i n g i s i n v o l v e d . This system does not seem to be e f f e c t i v e i n determining the s t r e n g t h r a t i o from each set of measurements. From F i g . 1.2, i t can be seen that f o r a given l o c a l s t i f f n e s s v a l u e , say E j , the boards i n d i c a t e s t r e n g t h values ranging from about 20 MPa to about 70 MPa, a s t r e n g t h v a r i a -t i o n f a c t o r of about 3.5. Moreover, the s t r e n g t h of about h a l f the boards 3 Fig. 1.1. S t r e n g t h d i s t r i b u t i o n s o f f o u r commercial grades based upon 850 2x6 D o u g l a s - f i r j o i s t s t e s t e d i n bending (from r ^ a d s e n j l . l ] ) . !20n 100" o or 60 o 2 40H 20H N= '685 LEAST SQURRES LINE fl= -8.82 BMOOOJ = 5.467 R= .0.82 BOARDS WITH UNIDENTIFIED STRENGTH 1 BOARDS CORRECTLY GRADED + + + + +' ^ i + ++ + + + + + ++++* BOARDS f V CORRECTLY GRADED 20 40 — i — 60 1 E t 80 100 120 Emln* I0 2 tMPa) 140 160 —T 180 Fig,1.2, Scattergram of M.O.R v s v E . (from Madsen[l«l]). 5 has not been recognized [ 1 . 1 ] , i n other words, the boards are not e f f i c i e n t l y u t i l i z e d . Hence, there i s a great need f o r a r e l i a b l e grading system i n the lumber i n d u s t r y to r e a l i z e the f u l l p o t e n t i a l of s t r u c t u r a l lumber. The f a i l u r e mode of c l e a r m a t e r i a l i s d i f f e r e n t from that of commercial lumber ( i . e . , lumber w i t h the usual occurence of knots and other d e f e c t s ) as noted by Madsen [1.1]. The c l e a r m a t e r i a l , under bending s t r e s s , g e n e r a l l y breaks i n a d u c t i l e mode where compression w r i n k l e s can be seen on the com-p r e s s i o n s i d e before the m a t e r i a l f i n a l l y breaks down. On the o t h e r hand, commercial lumber g e n e r a l l y breaks i n a b r i t t l e f a s h i o n o f t e n caused by cracks s t a r t i n g i n the steep d e v i a t i o n of g r a i n l o c a l i z e d near knots on the t e n s i o n s i d e . Hence, a grading system that i s based on a c t u a l data from the commercial end products r a t h e r than p r e d i c t i o n curves based on s m a l l c l e a r samples and v i s u a l grading, i s l i k e l y to be much more accurate and r e l i a b l e . 1.2 Strength P r o p e r t i e s of Lumber When a s t r u c t u r a l member i s loaded i n bending, bending s t r e s s e s r e s u l t , which c o n s i s t of a combination of a l l three primary s t r e s s e s - compressive, t e n s i l e and shear s t r e s s . They cause f l e x u r e or bending i n the lumber. The r e s i s t a n c e of the lumber to the a p p l i e d s t r e s s i s the s t r e n g t h of the m a t e r i a l . Stresses a c t i n g on the lumber produce a d i s t o r t i o n and i t s measure i s the s t r a i n . In bending, the magnitude of the load r e q u i r e d to cause f a i l u r e i s expressed by the modulus of rupture (M.O.R.). The s t r e n g t h of a piece of lumber i s g e n e r a l l y reduced by the presence of n a t u r a l defects such as slope of g r a i n , s i z e of knots and t h e i r l o c a t i o n . Moisture content and s p e c i f i c g r a v i t y of the m a t e r i a l are a l s o s t r e n g t h determining f a c t o r s f o r small c l e a r specimens, but are of l e s s importance i n commercial lumber where d e f e c t s tend to d i c t a t e the s t r e n g t h . 1.2.1 Slope of Grai n The s t r e n g t h of lumber i s s e r i o u s l y a f f e c t e d by any g r a i n d e v i a t i o n , i . e . , the presence of g r a i n s l o p e s . The s t r e n g t h of wood i n t e n s i o n perpen-d i c u l a r to the g r a i n i s very much l e s s than the s t r e n g t h i n t e n s i o n p a r a l l e l t o the g r a i n , so l o c a l g r a i n d e v i a t i o n can cause s e r i o u s reductions i n s t r e n g t h . Sloping g r a i n may be g e n e r a l i z e d across a piece of lumber due t o s p i r a l g r a i n i n the t r e e or the method of sawing. I t may a l s o e x i s t i n a l o c a l area near a knot. In e i t h e r case i t w i l l a f f e c t the s t r e n g t h s i g n i f i c a n t l y . The g r a i n slope i s taken to be a u n i t d e v i a t i o n from a reference edge f o r n u n i t s of l e n g t h along that edge [ 1 . 5 ] . From the data i n [ 1 . 4 ] , the modulus of rupture i s decreased by 4% when the slope of g r a i n i s 1 i n 25 and the l o s s i n s t r e n g t h i s grea t e r f o r l a r g e r slopes reaching a 45% l o s s f o r a slope of g r a i n of 1 i n 5. Cross g r a i n has the g r e a t e s t e f f e c t on impact bending but the l e a s t e f f e c t f o r compression s t r e n g t h p a r a l l e l to the g r a i n . 1.2.2 Knots As compared to the surrounding t i s s u e , knots are harder, denser and more r e s i n o u s . For sound t i g h t k nots, compression s t r e n g t h , hardness and shear p r o p e r t i e s are i n c r e a s e d . The presence of knots near the edge of a lumber board (subjected to bending s t r e s s ) w i l l produce l o c a l cross g r a i n near the edge and t h i s l o c a l i z e d g r a i n d e v i a t i o n near the knots i s a major cause of s t r e n g t h r e d u c t i o n i n lumber [ 1 . 1 ] , [ 1 . 5 ] . 7 1.2.3 S p e c i f i c G r a v i t y The s p e c i f i c g r a v i t y of lumber i n d i c a t e s the r e l a t i v e amount of s o l i d c e l l w a l l m a t e r i a l and i s g e n e r a l l y r e l a t e d to s t r e n g t h . The compression perp e n d i c u l a r to the g r a i n i s most s e n s i t i v e to s p e c i f i c g r a v i t y w i t h a general increase of about 4 times f o r a doubling i n s p e c i f i c g r a v i t y . The modulus of rupture and the compressive stre n g t h p a r a l l e l to the g r a i n are correspondingly l e s s s e n s i t i v e . 1.2.4 Moisture Content Below f i b r e s a t u r a t i o n p o i n t , there i s an in v e r s e r e l a t i o n s h i p between most of the s t r e n g t h p r o p e r t i e s and moisture content. From the data i n "Wood Handbook" [1.4] the compression p a r a l l e l to g r a i n shows the g r e a t e s t r a t e of decrease i n st r e n g t h w i t h moisture w h i l e that f o r modulus of rupture and s t a t i c bending e l a s t i c i t y are l e s s . 1.3 E l e c t r i c a l P r o p e r t i e s of Wood Wood i s a n i s o t r o p i c i n nature both i n i t s p h y s i c a l and e l e c t r i c a l p r o -p e r t i e s [1.5], i . e . , i t e x h i b i t s d i f f e r e n t p r o p e r t i e s when te s t e d along i t s three major d i r e c t i o n a l axes — tr a n v e r s e , r a d i a l and t a n g e n t i a l . This behaviour a r i s e s from the s t r u c t u r e and o r g a n i s a t i o n of c e l l u l o s e I n the c e l l w a l l s , the elongated shape of the wood c e l l s , and t h e i r l o n g i t u d i n a l - r a d i a l arrangement r e s u l t i n g from the r a d i a l symmetry of the tr e e trunk. The complex d i e l e c t r i c constant of wood e, (e = e' - j e " ) i s l a r g e r and more l o s s y when the e l e c t r i c f i e l d i s p a r a l l e l to the d i r e c t i o n of the g r a i n . Besides being complex, e i s a l s o dependent on the d i r e c t i o n of the e l e c t r i c f i e l d , hence i t i s a tensor f u n c t i o n . As such, when a l i n e a r l y p o l a r i z e d 8 electromagnetic wave i l l u m i n a t e s a lumber board, the transmitted wave i s i n general e l l i p t i c a l l y p o l a r i z e d , besides being attenuated [1.6J. The e i s a l s o a strong f u n c t i o n of the d e n s i t y , moisture content of the wood, and the frequency of operation but the r e l a t i o n s h i p i s n o n - l i n e a r . Wood i s semitransparent to microwave f r e q u e n c i e s , hence i t i s p o s s i b l e to measure but i n a n o n - l i n e a r f a s h i o n . 1.3.1 Wood Density and Moisture Content < Steady-state propagation of a plane wave through a medium depends on the a t t e n u a t i o n , phase change, and degree of d e p o l a r i z a t i o n of the microwave s i g n a l t r a n s m i t t e d through moving boards. The above parameters w i l l determine the moisture content, d e n s i t y , and slope of g r a i n , r e s p e c t i v e l y , where y i s the complex propagation constant and d i s the di s t a n c e from some reference p o i n t . Y = a + j 3 = j 3 n[ e ' ( l - j t a n 6 ) ] 1/2 where a a t t e n u a t i o n constant (Np/m) 3 phase constant (rad/m) 3 0 phase constant of free-space = 2ir/ A 0 free-space wavelength and 9 tan 6 = E"/e' = l o s s tangent Expanding, Y = j 3 0 ( e ' ) 1 / 2 { l - j ( t a n 6)/2 + ( t a n * 6)/8 + ...} i . e . , a = { 0 o ( e ' ) 1 / 2 t a n 5}/2 and 3 = 3 0( e ' ) 1 / 2 { l + ( t a n 2 6)/8}, f o r tan 6 « 1. For low moisture content, the r e s u l t s of James & H a m i l l [1.7] showed that e' i s r e l a t i v e l y constant and c h i e f l y depends on wood d e n s i t y ; i . e . , gd« wood d e n s i t y . A l s o from the data [1 . 7 ] , tan 5 i n c r e a s e s r a p i d l y w i t h mois-tur e content, hence od« moisture content. For higher moisture content, the r e l a t i o n s h i p i s n o n - l i n e a r . 1.3.2 Degree of D e p o l a r i z a t i o n The p h y s i c a l s t r e n g t h and e l e c t r i c p r o p e r t i e s of wood are h i g h l y dependent on the d i r e c t i o n of the g r a i n s i n c e wood i s s t r o n g l y a n i s o t r o p i c . T e n s i l e and compressive strengths are g r e a t e s t when the g r a i n i s i n the l o n g i t u d i n a l d i r e c t i o n of the board. Both the d i e l e c t r i c c onstant, e', and l o s s tangent, tan 6, depend on the g r a i n d i r e c t i o n too, both being g r e a t e s t when the d i r e c t i o n of e l e c t r i c f i e l d , i s l o n g i t u d i n a l to the g r a i n . The a n i s o t r o p y property of wood causes d e p o l a r i z a t i o n of the e l e c t r o -magnetic f i e l d . This d e p o l a r i z a t i o n gives a measure of the slope of g r a i n . When an electromagnetic wave, w i t h i t s e l e c t r i c f i e l d p o l a r i z e d i n the y-d i r e c t i o n , as shown i n F i g . 1.3, i l l u m i n a t e s a piece of lumber board whose g r a i n d i r e c t i o n i s at an a r b i t r a r y angle, y to the x - d i r e c t i o n , both x- and y- component of the e l e c t r i c f i e l d are obtained. This a r i s e s because both the r e l a t i v e p e r m i t t i v i t y , e', and l o s s tangent, tan 6, are d i f f e r e n t i n the x- and y - d i r e c t i o n . There i s no d e p o l a r i z a t i o n i f the i n c i d e n t e l e c t r i c 10 f i e l d i s p a r a l l e l or perpendicular to the g r a i n d i r e c t i o n . A f t e r passing through the lumber board, the x-component, E^, and the y-component, E^, w i l l have d i f f e r e n t magnitudes and phases depending on the t h i c k n e s s of the board, The two components combine to give an e l l i p t i c a l l y p o l a r i z e d wave w i t h i t s major a x i s i n c l i n e d at an angle, t , as shown i n F i g . 1.4. Let E and E represent the instantaneous e l e c t r i c f i e l d of the h o r i z o n -x y t a l l y and v e r t i c a l l y p o l a r i z e d waves, r e s p e c t i v e l y ( F i g . 1.3). Then, as a f u n c t i o n of time, t , and d i s t a n c e , z, E x and E^ can be expressed as E x = E j s i n (wt-gz) 1.1 and E y = E 2 s i n (wt-gz+a) 1.2 where Ej^ = amplitude of h o r i z o n t a l l y p o l a r i z e d wave, E 2 = amplitude of v e r t i c a l l y p o l a r i z e d wave, a = time-phase by which E leads E y j In complex form, . .(ftjt-0z) E x - e J 1.3 . ( lot- 0z+ a) •*v " E 2 e J 1.4 and E E, ' e J - 1.5 E E l x I t can be shown [1.8] that eqns. 1.1 and 1.2 are the parametric equations of Fig.1.4. Polarization ellipse. 12 an e l l i p s e , i . e . , or E 2 2 E E cos a E 2 * _ Z + _Z_ - s i n 2 a 1.6 E l 2 E 1 E 2 E 2 2 a E 2 - b E E + c E 2 = l 1.7 x x y y where a = l / E j 2 s i n 2 a b = 2 cos a / E j E 2 s i n 2 a c = 1/E 2 2 s i n 2 a Equation 1.7 i s the general form of an e l l i p s e , the axes of the p o l a r i z a t i o n e l l i p s e , i n g e n e r a l , do not c o i n c i d e w i t h the x and y axes ( F i g . 1.4). The sense of r o t a t i o n of the e l e c t r i c v e c t o r depends on whether E leads y or lags E^ i n time-phase. Case 1: When E and E are i n phase, a = 0, eqn. 1.5 reduces to y x E = + =— E 1.8 y E i x When E and E are 180° out of phase, a = TV, eqn. (1.5) becomes y x E = =- E 1.9 y E i x The r e s u l t a n t i s l i n e a r l y p o l a r i z e d i n both s i t u a t i o n s as both eqns. 1.7 and 1.8 are equations of s t r a i g h t l i n e s . Case 2: When E leads E by 90° or a = + TT/2, eqn. (1.5) reduces to y x . 13 E 2 „ H = + j ^ r - Ex 1.10 y e x This i n d i c a t e s clockwise e l l i p t i c a l p o l a r i z a t i o n (wave approaching) and f u r t h e r i f E 2 = E p then E = + j 1.11 E x and clockwise c i r c u l a r p o l a r i z a t i o n (wave approaching) i s o b t a i n e d . Case 3: When E lags E by 90°, a = - -? y b x J ' 2 E E 2 "~ ~ ~3 p - 1.12 E 1 x and counter clockwise e l l i p t i c a l p o l a r i z a t i o n (wave approaching) i s obtained. F u r t h e r , i f E 2 = E j , E E -T- = - j 1.13 x g i v i n g counter clockwise c i r c u l a r p o l a r i z a t i o n (wave approaching). Measurement of E^, E 2 and a should be s u f f i c i e n t to determine the t i l t angle, t of the p o l a r i z a t i o n e l l i p s e and hence the slope of g r a i n , y. The t i l t angle, t i s given by [1.8] 14 1.4 Microwave Measurements Since wood i s semi-transparent to electromagnetic waves, i t i s p r a c t i c a l to measure the va r i o u s e l e c t r i c a l p r o p e r t i e s of wood i n order to i n v e s t i g a t e a p o s s i b l e c o r r e l a t i o n between the e l e c t r i c a l and p h y s i c a l s t r e n g t h proper-t i e s . The microwave range of frequencies provides an a t t r a c t i v e and e f f e c -t i v e method to measure the amplitudes and phases of the E x and E^ components and the degree of d e p o l a r i z a t i o n . From these measurements, i t i s p o s s i b l e to deduce the strength-determining f a c t o r s of wood such as slope of g r a i n , s i z e of k n o t s , moisture content and d e n s i t y . When the i n c i d e n t wave i s p o l a r i z e d i n the y - d i r e c t i o n , the re c e i v e d component, E^, which i s p a r a l l e l to the y - d i r e c t i o n i s termed the co-polar s i g n a l and the other component, E x , which i s orthogonal to the co-polar s i g n a l i s c a l l e d the c r o s s - p o l a r s i g n a l . 1.5 Thesis O b j e c t i v e The main o b j e c t i v e of t h i s work i s to attempt to develop a microwave system f o r automatic s t r e s s grading of lumber through c o r r e l a t i n g microwave and p h y s i c a l s t r e n g t h p r o p e r t i e s . Various steps are necessary to achieve t h i s o b j e c t i v e : a) Determination of the r e l a t i v e p e r m i t t i v i t y , e', and l o s s tangent, tan 6, of wood (Douglas F i r ) at orthogonal o r i e n t a t i o n s of slope of g r a i n and at v a r i o u s moisture contents and f r e q u e n c i e s . b) Determination of the a t t e n u a t i o n p r o p e r t i e s of the co- p o l a r and c r o s s -p o l a r s i g n a l s at v a r i o u s o r i e n t a t i o n s of slope of g r a i n . 15 c) The design and implementation of the double channel homodyne system; the components to be designed, f a b r i c a t e d and te s t e d are the pyramidal horn, the microwave switches and amplitude modulator, the h y b r i d r i n g s f o r the balanced mixers and power d i v i d e r s , and the phase s h i f t e r s f o r bridge b a l a n c i n g . d) The design and implementation of the e l e c t r o n i c i n t e r f a c e f o r s w i t c h i n g , processing and p r e s e n t a t i o n of the microwave measurements. e) I n v e s t i g a t i o n of the c o r r e l a t i o n f a c t o r s between the microwave measure-ments and the s t r e n g t h p r o p e r t i e s of Douglas f i r v i a extensive measure-ments and d e s t r u c t i v e t e s t i n g of lumber boards. 1.6 Thesis O u t l i n e The b a s i s of c o r r e l a t i o n , choice of optimum frequency, system comparison of homodyne and heterodyne, the homodyne d e t e c t i o n system at low and h i g h s i g n a l l e v e l and the b a s i s of s e l e c t i o n of the double channel homodyne system are d e s c r i b e d i n Chapter 2. Chapter 3 presents the o v e r a l l f e a t u r e s of the double channel homodyne system i n c l u d i n g d e t a i l s of the design f o r the PIN diode modulator and switches, pyramidal horn, h y b r i d r i n g s and phase s h i f t e r s . The e l e c t r o n i c i n t e r f a c e and i t s f u n c t i o n are presented i n Chapter 4 w i t h d e t a i l s on the inst r u m e n t a t i o n a m p l i f i e r , bandpass f i l t e r , analog s w i t c h , rms-to-dc converters and phase s e n s i t i v e d e t e c t o r s . The experimental r e s u l t s of measurements of r e l a t i v e p e r m i t t i v i t y and l o s s tangent at v a r i o u s o r i e n t a t i o n s of slopes of g r a i n , moisture contents and f r e q u e n c i e s , measurements of the pyramidal horn-lens antenna, microwave 16 switches, and h y b r i d r i n g s , measurements of a t t e n u a t i o n p r o p e r t i e s of co-p o l a r and c r o s s - p o l a r s i g n a l s and the cha r t recordings of the homodyne system are presented i n Chapter 5. Chapter 6 give s the conclusions drawn from t h i s p r o j e c t on the s u i t a -b i l i t y of the double channel homodyne system f o r measurement and c o n t r o l and on the c o r r e l a t i o n s between microwave and the s t r e n g t h p r o p e r t i e s of wood. Proposals and d i r e c t i o n s f o r f u t u r e development are a l s o g i v e n . 17 CHAPTER 2 - ANALYSIS 2.1 C o r r e l a t i o n Between Microwave and P h y s i c a l P r o p e r t i e s of Wood From i n i t i a l experimental r e s u l t s (see Chapter 5) and the r e s u l t s of James and H a m i l l [ 1 . 7 ] , and King [ 1 . 6 ] , there i s evidence of c o r r e l a t i o n between the degree of d e p o l a r i z a t i o n and the g r a i n s l o p e , the a t t e n u a t i o n and the moisture content and t h i r d l y the phase of the r e c e i v e d s i g n a l and the s i z e of the d e f e c t i v e area. The degree of d e p o l a r i z a t i o n i s obtained from the a n i s o t r o p y r a t i o ( l o n g i t u d i n a l to transverse component of the e l e c t r i c f i e l d or co-polar t o c r o s s - p o l a r component of the received s i g n a l ) . The co-polar s i g n a l g i v e s the a t t e n u a t i o n s u f f e r e d by the t r a n s m i t t e d s i g n a l a f t e r p e n e t r a t i n g through the wood. The phase i n f o r m a t i o n i s derived by comparing the phase of the co-p o l a r s i g n a l w i t h that of the reference s i g n a l . These microwave parameters can be obtained by v a r i o u s methods and con-f i g u r a t i o n s and t h e i r m e r i t s and demerits are discussed i n subsequent sec-t i o n s . 2.2 Choice of Frequency The microwave frequency range i s from 1 GHz to 300 GHz. However a s u i t -able range f o r waveguide measurements of these parameters extends from about 10 GHz to about 75 GHz. Measurements of r e l a t i v e p e r m i t t i v i t y , e', and l o s s tangent, tan <5, were taken at frequencies of 10, 26.5, 35, 55 and 75 GHz. From the r e s u l t s (see Section 5.2), i t can be seen that the r e l a t i v e permit-t i v i t y and l o s s tangent are r e l a t i v e l y constant. 18 At 10 GHz, I f an optimum pyramidal horn serves as the t r a n s m i t t i n g antenna, the r e s o l u t i o n i s not good enough to be of p r a c t i c a l use i n measur-in g the d i e l e c t r i c p r o p e r t i e s . With a focused horn lens antenna as the t r a n s m i t t i n g element, the r e s o l u t i o n improves w i t h i n c r e a s i n g frequency. However, at the high end of 75 GHz, the transmitted wave i s s e v e r l y attenu-ated. The frequency of 35 GHz was found to be near optimum (as the spot diameter i s of the magnitude of XQ [2.1]) and i f the wood i s below f i b r e s a t u r a t i o n p o i n t ( f s b ) , the tr a n s m i t t e d s i g n a l i s only f a i r l y attenuated. As t h i s p r o j e c t i s being developed w i t h a view to i n d u s t r i a l a p p l i c a t i o n , a v a i l -a b i l i t y and c o s t - e f f e c t i v e n e s s of commercial microwave components are a l s o important c r i t e r i a . Therefore, 35 GHz (nominal) was chosen to be the operat-i n g frequency. 2.3 Methods and C o n f i g u r a t i o n s of Measurements 2.3.1 Homodyne v s . Heterodyne In the present scheme, determination of the d i e l e c t r i c p r o p e r t i e s of wood i n v o l v e s measuring the amplitudes of the co-polar and c r o s s - p o l a r s i g -n a l s and the phase of the co-polar s i g n a l . Two choices of systems are a v a i l -able - heterodyne and homodyne. The homodyne system i s con s i d e r a b l y more l i n e a r than a heterodyne system f o r n e a r l y equal l o c a l o s c i l l a t o r and RF t e s t s i g n a l l e v e l s as shown by L i t t l e [ 2 . 2 ] . From the e a r l i e r work of Weinschel et a l . [ 2 . 3 ] , L i t t l e e x plained thus: assuming an i d e a l l i n e a r mixer, the IF output i s E_„ = 2b/ IT [ l + ( b / A ) 2 ] 1 / 2 { l / 2 + 3B 2/64 + 7.15BV256.24 + } lb1 2.1 19 where B = 2(b/A)/{l+(b/A)} I t i s observed that when b/A approaches u n i t y , E i s not l i n e a r l y propor-IF t i o n a l to the RF s i g n a l b. For the homodyne output, L i t t l e gave co (k b/A) q P » e = n.b[m cos $ - s i n (j> Y —° . . q G ,(m) lcos w t 2.2 out h L r T q(q+l) q+1,1 J m dP (cos 6) where P ' = — q .. and G ,, , (m) are f a c t o r s as g i v e n by L i t t l e [ 2 . 2 ] . q de q+i»i Eqn. 2.2 shows that the homodyne mixer output i s d i r e c t l y p r o p o r t i o n a l to the in f o r m a t i o n s i g n a l b f o r a l l b > A, provided s i n <j> = 0. E v i d e n t l y , the homodyne system i s i n h e r e n t l y more l i n e a r , e s p e c i a l l y a t hi g h l e v e l s of i n f o r m a t i o n s i g n a l . Experimental comparison of the l i n e a r i t y of the two systems using the same c r y s t a l diodes and d e t e c t o r mounts I s shown i n F i g . 2.1. From the curves, i t can be seen that f o r conversion g a i n l i n e a r i t i e s which are l e s s than 0.1 dB i n a heterodyne system, b/A should be < -15 dB. Thus, the dynamic range of the homodyne system i s g r e a t e r at the upper end. Besides, a great advantage i n using the homodyne system i s that the phase i n f o r m a t i o n i s preserved because the system i s coherent whereas i t i s l o s t i n the heterodyne system. For the present a p p l i c a t i o n of a s t r e s s grading system, the homodyne system was s e l e c t e d a l s o f o r i t s s i m p l i c i t y i n implementation (on l y one l o c a l o s c i l l a t o r and no IF a m p l i f i e r and second d e t e c t o r ) besides g r e a t e r dynamic 20 Fig.2.1. Comparison of crystal nonlinearities for DSBWZ hoirodyne and heterodyne attenuation measurement systems (from L i t t l e C 2 . 2 I )„ 21 range and l i n e a r i t y . A l a r g e r dynamic range means t h i c k e r lumber boards could be stress-graded. I t i s of i n t e r e s t to note that the homodyne system i s f i n d i n g i n c r e a s i n g a p p l i c a t i o n s i n i n d u s t r i a l measurement and c o n t r o l systems [2.4], [2.5] and [2.6]. 2.3.2 Modulated Sub-Carrier Method A method capable of good accuracy i n measuring the amplitude and phase of the co-polar s i g n a l i s given by Shafter and Bowman [2.10] and the arrange-ment i s shown i n F i g . 2.2. . The above method i n v o l v e s mixing an unmodulated c a r r i e r s i g n a l of f r e -quency, 0), w i t h the modulated s u b - c a r r i e r s i g n a l (of the same frequency, a> but w i t h sidebands) and this'sum i s envelope-detected g i v i n g an output at the modulation frequency, ta^. Since the mixing i s coherent, the output i s of zero IF ( i n t e r m e d i a t e frequency) and contains the amplitude and phase i n f o r -mation of the s u b - c a r r i e r or i n f o r m a t i o n channel. The c a r r i e r channel i s a l s o known as the reference channel. Besides the fundamental frequency, the mixer output contains harmonics due to higher order sidebands, e.g., w ± 2co , m e t c . , produced as a r e s u l t of amplitude modulation. But the harmonics can be f i l t e r e d out by using a narrowband a m p l i f i e r . The output i s detected u s i n g e i t h e r square-law or l i n e a r d e t e c t i o n . 2.3.3 Square-Law or Low L e v e l D e t e c t i o n I f the c a r r i e r or reference s i g n a l i s represented by e - A e j W t 2.3 r from modulation theory, the modulated s u b - c a r r i e r or i n f o r m a t i o n s i g n a l I s given by 22 microwave source phase detector attenuator amplitude detector vXl directional coupler carrier channel aitplitude device under test rrodulator © sub-carrier channel modulating source, GO in Fig.2.2. .Modulated sub-carrier method. 23 (wt+<(,) e. .= b f l + m cos a t)e 2.4 i v m ' where A and b are the amplitudes of the reference and i n f o r m a t i o n s i g n a l s , r e s p e c t i v e l y , m, the amplitude modulation index and <|>, the RF phase s h i f t between the reference and i n f o r m a t i o n s i g n a l s . I f the detector i s operated on the square-law region of i t s c h a r a c t e r i s t i c curve, the output at the modu-l a t i o n frequency i s p r o p o r t i o n a l to the envelope of the input s i g n a l squared, i . e . , e Q « e i n 2 * ^ n e p h a s o r diagram of the r e s u l t a n t input s i g n a l to the det e c t o r i s shown i n F i g . 2.3 From the law of c o s i n e s , E , 2 = A 2 + b 2 ( l + m cos u t ) 2 + 2Abfl + m cos u t ) cos <J> 2.5 a v m ' v m ' T The detected output i s p r o p o r t i o n a l to E ^ 2 s i n c e E^ represents the envelope of the r e s u l t a n t input s i g n a l and the det e c t o r i s square-law. Since the output w i l l be narrowband f i l t e r e d , only the wm terms w i l l be con-s i d e r e d , e = rub2!!! cos u t + nAbm cos A cos w t 2.6 o x , m T m = ri„Abmfb/A + cos *lcos to t 2.7 where i s the conversion e f f i c i e n c y of the d e t e c t o r . n should remain constant over the dynamic range of b. This i s p o s s i b l e I f the operation i s w i t h i n the square-law region.or b i s very much l e s s than A, thereby l i m i t i n g the dynamic range of b at i t s upper end. This r e s t r i c t i o n can be removed as shown i n the f o l l o w i n g d i s c u s s i o n . From eqn. 2.7, i t can be seen that the zeros i n the response always Fig.2.3.. Phasor diagram of the resultant input signal. 25 occur when cos <|> = -k Qb/A f o r square law d e t e c t i o n . For k Q = 1, the zeros occur when [2.6] <J> - ± [(2n+l) TT/2 + ( - l ) n e p ] n = 0,1,2,... 2.8 where e = s i n - 1 k b/A 2.9 P o i s the phase e r r o r from some odd m u l t i p l e of ± TT/2. Table 2.1 shows the phase and amplitude e r r o r s . Thus, i t i s evident that the upper end of the dynamic range of b i s l i m i t e d by the t o l e r a b l e phase e r r o r . For a phase e r r o r of l e s s than 2°, k Qb/A should be l e s s than about -30 dB. Therefore, i f the r e s t r i c t i o n b « A can be r e l a x e d , the dynamic operating range f o r both amplitude and phase measurements would be improved 20-30 dB [ 2 . 9 ] , For double sideband suppressed c a r r i e r (DSBSC) amplitude modulation, as before from eqn. 2.5, E , 2 = A 2 + b 2 fk + m cos o> t ) 2 + 2Abfk + m cos to t ] c o s * 2.10 d o m J v o m - ' Y and the detected output i s e = n Abm (Kob/A + cos <b]cos a) t 2.11 o i v T J m where k Q i s the c a r r i e r suppression f a c t o r . I f the non l i n e a r term k b/A i n eqn. 2.11 can be made n e g l i g i b l e by suppress 26 TABLE 2.1 Phase and amplitude e r r o r s f o r various r a t i o s of c a r r i e r amplitude i n the in f o r m a t i o n channel to c a r r i e r amplitude of the reference channel (from King [ 2 . 9 ] ) . e a = k Qb/A e p = s i n - l ( k 0 b / A ) -dB % degrees 0 100 90 3 70.79 45.07 5 56.23 34.22 8 39.81 23.46 10 31.62 18.43 15 17.78 10.24 20 10.00 5.739 25 5.63 3.24 30 3.12 1.82 35 1.778 1.019 40 1.000 0.573 45 0.562 0.322 50 0.316 0.181 55 0.178 0.102 60 0.100 0.057 70 0.031 0.018 80 0.010 0.006 90 0.003 0.002 in g the c a r r i e r , the output i s p r o p o r t i o n a l to b cos (j>, w i t h the requirement that b « A. Therefore, suppressing the c a r r i e r , which can be accomplished e i t h e r by using a balanced modulator [2.7] or a balanced mixer [ 2 . 8 ] , has the great advantage of extending the upper end of dynamic range of b by k Q when measuring amplitude or phase using square-law d e t e c t i o n . 27 2.3.4 L i n e a r or High L e v e l Detection For l i n e a r or high l e v e l d e t e c t i o n [2.9], the envelope of the r e s u l t a n t input s i g n a l i s E, = A + bfk + m cos CD t ) c o s * 2.12 d K o ra J Y which i s obtained from eqn. 2.10 by m u l t i p l y i n g the n e g l i g i b l y s m a l l second term by c o s 2 <{> and completing the square. Considering only the term, the output i s e = n,bm cos <b cos tot 2.13 o h r m which i s d i r e c t l y p r o p o r t i o n a l to b cos <j> but not A. This i n d i c a t e s that o high l e v e l d e t e c t i o n i s l i n e a r f o r amplitude measurements even i f b » A [2.10], However, f o r phase measurements at high l e v e l s , the requirement k b o « A i s s t i l l needed f o r double sideband modulation [ 2 . 9 ] . This r e s t r i c t i o n can be removed by suppressing the c a r r i e r i n the i n f o r m a t i o n channel as shown i n S e c t i o n 2.3.5. 2.3.5 C a r r i e r Suppression Using Balanced Mixers C a r r i e r suppression can be accomplished us i n g e i t h e r a balanced modula-t o r or balanced mixer or both. Two of the most common forms of the 180° h y b r i d j u n c t i o n s used are the magic T and the h y b r i d r i n g and the use of the l a t t e r i n the balanced mixer arrangement w i l l be d e s c r i b e d . Balanced mixing i n v o l v e s the f a c t that port 1 ( F i g . 2.4) d i v i d e s i t s input so that the f i e l d s i n ports 2 and 4 are of opposite phase at phanes spaced symmetrically about the j u n c t i o n while the f i e l d s i n p o r t s 2 and 4 obtained from port 3 are of the same phase. The output from port 4 i s of the form s i m i l a r to eqn. 2.7; i . e . 28 Fig.2.4. 180° hybrid ring junction. 29 e u = nAbm(b/A + cos (h)cos o> t 2.14 4 m and from port 2, e 0 = -r)Abm(-b/A + cos <b)cos a) t 2.15 ^ m The above two s i g n a l s are then fed i n t o an audio transformer to be sub t r a c t e d g i v i n g an output ( f o r a turns r a t i o of u n i t y ) , e bm _ 2nAbm cos <b cos w t 2.16 o m where A and b are the input s i g n a l s e n t e r i n g ports 1 and 3 r e s p e c t i v e l y . Thus the output eqn. 2.16 i s s i m i l a r to eqn. 2.7 f o r a s i n g l e mixer w i t h the exception that the r e s t r i c t i o n b « A has been removed due to the suppression a c t i o n of the balanced mixer. Therefore, w i t h balanced mixing, the high end of the dynamic range i s extended by about 20-30 dB as the i n f o r m a t i o n s i g n a l , b, can now be as l a r g e as the reference s i g n a l , A [2 . 9 ] . In a d d i t i o n , balanced mixing a l s o suppressed the noise that i s present i n the reference channel [2.9]. 2.3.6 Homodyne Systems Before d i s c u s s i n g the s e l e c t i o n of the f i n a l system to be implemented i n the p r o j e c t , a review of the developments of the va r i o u s systems and con-f i g u r a t i o n s would be a p r o p r i a t e . As e a r l y as 1955, C u l l e n and Parr [2.11] described homodyne or coherent d e t e c t i o n w i t h a modulated s c a t t e r e r to meas-ure the f i n e s t r u c t u r e of the f i e l d s i n f r e e space. A disadvantage of t h i s system i s that high i s o l a t i o n i s r e q u i r e d between the source and d e t e c t o r . In the same year, Richmond [2.12] a l s o proposed a modulated s c a t t e r e r w i t h homodyne d e t e c t i o n and a balanced d e t e c t o r . 30 A c o a x i a l a m p l i t u d e - i n s e n s i t i v e phase-detection system using a balanced mixer and a balancing network at i t s output was given by Burton [2.12]. King [2.14] gave a d e s c r i p t i o n w i t h e r r o r a n a l y s i s of a modulated s c a t t e r e r w i t h homodyne d e t e c t i o n and a s i n g l e mixer to measure amplitude and phase. The above methods s u f f e r from the common disadvantage of having to make point-by-point measurements of amplitude and phase. When continuous data i s r e q u i r e d as i n an i n d u s t r i a l process, automatic measurements of amplitude and phase are necessary. Vernon [2.15] was, perhaps, among the f i r s t to r e a l i z e that the homodyne output of a DSB-amplitude modulated arrangement could be used to c o n t r o l the p o s i t i o n of a c a l i b r a t e d phase s h i f t e r f o r phase measure-ment. L a t e r , E l l e r b r u c h [2.16] described an automated DSB homodyne system f o r measuring phase. For DSB (double sideband) modulation, the homodyne detected s i g n a l which i s p r o p o r t i o n a l to b cos <j> cos w t i s compared w i t h the m modulating s i g n a l cos w^t i n a phase s e n s i t i v e d e t e c t o r , g i v i n g a DC output e r r o r s i g n a l p r o p o r t i o n a l to b cos <j>. As b cos $ i s p o s i t i v e or negative depending on the value of <j>, t h i s e r r o r voltage s i g n a l can be employed to c o n t r o l a servo motor which i s mechanically coupled to the c a l i b r a t e d phase s h i f t e r i n the reference channel. The servo motor seeks a p o s i t i o n f o r which the e r r o r s i g n a l , b cos <|>, i s zero or <j> = ±(2n+l)Tr/2. To achieve automatic phase and i n t e n s i t y measurements of microwave f i e l d s , Howard [2.17] used homodyne d e t e c t i o n to generate e r r o r s i g n a l s f o r servo mechanisms which balance the a t t e n u a t i o n and phase secondary standards. Mathews [2.18] f o r h i s v i b r a t i n g d i p o l e technique, used a phase modulated wave f o r simultaneous determination of amplitude and phase d i s t r i b u t i o n of electromagnetic f i e l d s . He too i n c l u d e d a servo loop to make h i s measurements automatic. 31 One drawback of using servo mechanisms i s i t s response time which can introduce appreciable e r r o r s due to i t s sluggishness [2,15]. The response i s s l u g g i s h because the servo motors and the recorder cannot f o l l o w r a p i d changes. To avoid automatic c o n t r o l l o o p s , Garbacz and Eberle [2.25] described a m o d i f i c a t i o n which outputs the r e a l and imaginery components of the t e s t s i g n a l i n r e a l - t i m e . This technique has s i n c e been used i n s e v e r a l systems - K a i s e r et a l . [2.19], Cohn and Weinhouse [2.20] and O'Brien [2.21]. F i g u r e 2.5 shows the DSB automated system used by Cohn and Weinhouse [2.20]. The reference and i n f o r m a t i o n s i g n a l s are fed i n t o a phase d i s c r i m i n a t o r which c o n s i s t s of two homodyne mixers. Power d i v i s i o n f o r the reference s i g n a l i s done v i a the 180° h y b r i d j u n c t i o n while that f o r the i n f o r m a t i o n s i g n a l i s v i a the 90° or quadrature-type 3 dB c o u p l e r . The out-puts at the e A and e^ ports are as f o l l o w s : where n^A and are the conversion e f f i c i e n c i e s f o r square-law and l i n e a r d e t e c t i o n r e s p e c t i v e l y . Various c o n f i g u r a t i o n s are a v a i l a b l e to process the output s i g n a l s e and e , A B the c o n f i g u r a t i o n to be s e l e c t e d depends on how the output data i s to be d i s p l a y e d . Cohn and Weinhouse [2.20] used a r a t i o meter to compute the r a t i o of e A and e R g i v i n g tan <j> or cot <J). Phase s e n s i t i v e d e t e c t o r s , employed i n COS <i> COS U) t m 2.17 and s i n i> cos tj t T m 2.18 ', 9 information channel F i g . 2.5. DSB automated system for real-time phase and amplitude measurements (from Cohn et a l Q 2 . 2 0 3 ) • 33 O'Brien's set-up [2.21], coherently detect e. and e g i v i n g DC v o l t a g e s V A. i> X and V . They were d i s p l a y e d on an o s c i l l o s c o p e or X-Y recorder g i v i n g a p o l a r p l o t be ^. and V^ can be converted to d i g i t a l form by A/D con-v e r t e r s and processed to give b ( t ) and <j>(t). K o e l l e et a l . [2.22] used a quadrature method f o r d i r e c t d i s p l a y of b ( t ) and <Ji(t). 2.3.7 Double Channel System w i t h Balanced Mixers The above outputs e^ and e^ were obtained by u s i n g a phase d i s c r i m i n a t o r and s i n g l e mixers. Balanced mixers have the great advantage of reducing both amplitude and phase e r r o r s due to an unsuppressed c a r r i e r A and an unwanted CW s i g n a l A^ [ 2 . 9 ] , besides extending the upper end of the dynamic range of b, as discussed i n S e c t i o n 2.3.5. Very p r e c i s e a t t e n u a t i o n measurements on short lengths of waveguide have been obtained by Warner et a l . [2.23] u s i n g a phase d i s c r i m i n a t o r and homodyne balanced mixers. K i n g [2.24] used a me-c h a n i c a l l y spun modulated s c a t t e r e r to measure the amplitude, phase and de-p o l a r i z a t i o n of the electromagnetic wave that was t r a n s m i t t e d through wood. 34 CHAPTER 3 - DESCRIPTION AND DESIGN OF THE STRESS GRADING SYSTEM 3.1 General From the d e l i b e r a t i o n s i n Secti o n 2.2 through S e c t i o n 2.3.6, the double channel homodyne system w i t h balanced mixers at 34.8 GHz was considered to be the most s u i t a b l e f o r implementing t h i s p r o j e c t . The o v e r a l l system c o n s i s t s of the t r a n s m i t t i n g branch, r e c e i v i n g branch, homodyne d e t e c t i o n b r i d g e and the e l e c t r o n i c i n t e r f a c e . The d e s c r i p t i o n and design of various p a r t s of the system are d e t a i l e d below. 3.2 The Tra n s m i t t i n g Branch The schematic diagram of the o v e r a l l system i s shown i n F i g . 3.1(a). The microwave source, A, i s a Gunn diode o s c i l l a t o r tuned to the o p e r a t i n g frequency of 34.80 GHz. As discussed i n Secti o n 2.2, the frequency of about 35 GHz was chosen p r i m a r i l y because of near optimum r e s o l u t i o n of the probed a r e a . Since the microwave PIN diode switches, Pj^, P 2 and modulator, F, e x h i b i t v a r i a t i o n i n i s o l a t i o n and i n s e r t i o n l o s s w i t h frequency, 34.80 GHz was f i n a l l y s e l e c t e d as a compromise. D i r e c t i o n a l c o u p l e r , B, couples -10 dB of power i n t o the homodyne bridge v i a the phase s h i f t e r , Z, which i s employed f o r i n i t i a l tuning of the b r i d g e . I s o l a t o r s , C, and D are i n s e r t e d i n order to prevent the leakage of the modu-l a t e d s i g n a l i n t o the reference channel. The t o t a l i s o l a t i o n i s about 45 dB w h i l e the t o t a l i n s e r t i o n l o s s i s about 2.5 dB. The E-H tuner, E, i s used to match the amplitude modulator to the microwave source w h i l e the placement of E-H tuner, J , i s meant to tune out r e f l e c t i o n s from the pyramidal horn/ microwave cw source 8 S cf) CD ^ J amplitude modulator E-H tuner hybrid rina depolari-zation detector SG-tp-EC co.-iverter (X-polar) K-5-to-DC converter (co-pslar) modulating source,u upper balanced mixer of co-polar output cross-polar output phase sensitive detector (Y) phnso sensitive detector(Z) MIX 10 KHz hybrid ring junction Fig.3.1(a). ElccX diagram of tho dual balanced mixer hxodyne system 36 c o n i c a l horn arrangement. The tuning out of the r e f l e c t i o n s i s monitored by the coupler/wavemeter/detector combination, I . The amplitude modulator, F, i s d r i v e n by the PIN diode d r i v e r , G. The pyramidal horn-lens, K, was designed using geometrical o p t i c s to have a focused spot of Xq which i s 0.339 inches f o r the operating frequency of 34.80 GHz. The d e t a i l s of the design of the amplitude modulator and the pyramidal horn-lens are given below. 3.2.1 Design of the PIN Diode Amplitude Modulator and Switches The PIN diode switch operates i n the a t y p i c a l mode [3.1] i n which low l o s s i s obtained when the diode i s under forward b i a s and h i g h i s o l a t i o n under reverse b i a s . The equivalent c i r c u i t s f o r the diode under forward and reverse b i a s are shown i n F i g . 3.2(a) and ( b ) , r e s p e c t i v e l y . (a) Reverse Bias (b) Forward B i a s F i g . 3.2 Equivalent C i r c u i t s 37 In F i g . 3.2, Lp = package inductance Cp = package capacitance R g = s e r i e s r e s i s t a n c e R. = i u n c t i o n r e s i s t a n c e Cj = j u n c t i o n capacitance Rj = RF r e s i s t a n c e of the I - l a y e r Cj. = capacitance of the I - l a y e r Under forward b i a s , the package capacitance of a p a r t i c u l a r diode can be s e l e c t e d to resonate ( i n p a r a l l e l resonance) w i t h the package inductance, whereby the switch i s i n the ON s t a t e . Under reverse b i a s , the package capacitance i s s e l e c t e d to s e r i e s resonate w i t h the I - l a y e r capacitance; i n t h i s case, the switch i s i n the OFF s t a t e . With t h i s i n mind, the diodes (VSD-213A11) w i t h the f o l l o w i n g parameters (see Table 3.1) were s e l e c t e d to give an i s o l a t i o n b e t t e r than 40 dB and an i n s e r t i o n l o s s of l e s s than 2 dB at the operating frequency of 34.80 GHz. Each switch or modulator c o n s i s t s of a p a i r of diodes, the s e p a r a t i o n of the diodes being 3X /4 from each other, as shown i n F i g . 3.3. TABLE 3.1 Parameters of the PIN diode switches and modulator. Switch #1 Switch #2 Amplitude Modulator L P C P R s R. 3 R I C I I s o l a t i o n <46 dB <45 dB <56 dB I n s e r t i o n < 1 dB < 1 dB < 1 dB Loss Under reverse b i a s , from F i g . 3.2(a), the impedance f u n c t i o n [3.2] i s (nH) 0.22 0.22 0.22 0.22 0.22 0.22 (pF) 0.10 0.10 0.10 0.10 0.10 0.10 (n) 0.84 0.84 0.84 0.84 0.20 0.20 (a) =0 =0 =0 =0 =0 =0 (pF) =0 =0 =0 =0 =0 =0 (£2) 101* 101* 101* 10'» l O 4 10^ (pF) 0.109 0.096 0.120 0.111 0.100 0.120 A l l dimensions in inches Fig.3,3; Section through PIN diode switch. s i n c e w C « 112 o p At resonance, the reactance i s zero, and and The i s o l a t i o n i s given by [3.3] Under forward b i a s , from F i g . 3.2(b), the admittance f u n c t i o n i s and 39 Z(u) R, R + s (l+RjZc 2o>2) + j R j 2 ^ (I+RjZCj.2*)2) 3.1 (0 R 2 C T - L L R 2 C 2 p I I 3.2 R, Z(f ) = R + 1 + R T 2 C j 2 a)2 3.3 G Z 2 e o - ^  °H = 1 0 l o g 1 0 -C1 + - ^ 2 £ ) 3.4 R Y( a)) = s R 2 + u 2 L 2 s p + j K -R 2 + w2 L 2 s p 3.5 At resonance, the susceptance i s zero o r , 0)C P R 2 + U)2 L 2 S p = 0 3.6 R Y(f ) = G o e R 2 + o>2 L 2 s p 3.7 40 and the i n s e r t i o n l o s s i s [3.3] \ = 1 0 l o S l O (1 + G e Z o/2)2 3.8 The c a l c u l a t e d values of the i s o l a t i o n and i n s e r t i o n l o s s of the switches and modulator using eqns. 3.4 and 3.8 are shown i n Table 3.1. The experimental values of the i s o l a t i o n and i n s e r t i o n l o s s f o r each of the devices w i l l be given i n S e c t i o n 5.1.2. For each PIN diode switch or modulator, a p a i r of PIN diodes are used. The two packaged diodes are mounted between the top w a l l of the waveguide and a waveguide s e c t i o n , whose Impedance i s matched to the waveguide Impedance by a 3-step Tchebyshev transformer at each end, as shown i n F i g . 3.3. The wave-guide s e c t i o n i s DC i s o l a t e d from the base of the waveguide by a t h i n c o a t i n g of low l o s s expoxy and i s h e l d i n place by two nylon screws. The 3-step Tchebyshev transformer (see F i g . 3.3) i s designed as f o l l o w s [3.4]: Impedance r a t i o , R = _ = = 2.6411 (take R = 3.00) and bandwidth, toq = 20% was s e l e c t e d . From Table (6.02-3), r e f . [ 3 . 4 ] , 2 s e c t i o n s w i l l be s u f f i c i e n t . From Table (6.04-1), r e f . [ 3 . 4 ] , Z = 1.278 2.6411 1.278 = 2.067 Since f o r a waveguide, [3.5] 41 c h a r a c t e r i s t i c impedance, Z = / — — -c 6 a /T^TTfyz c i . e . Z = b c .'. Z1 « b j = 1.278 x 0.053 = 0.0677 inches Z 2 = b 2 = 2.067 x 0.053 = 0.1095 inches The completed design i s as shown i n F i g . 3.3. 3.2.2 Design of the Pyramidal Horn Lens The t r a n s m i t t i n g pyramidal horn i s equipped w i t h a convex l e n s made of polystyrene ( d i e l e c t r i c constant = 2.56). Figure 3.5 shows the v a r i o u s parameters f o r the l e n s . The parameters are r e l a t e d by the equation [3.6] ( n 2 - l ) d 2 + 2 ( n - l ) f d - a 2 = 0 3.9 In C a r t e s i a n co-ordinates w i t h the o r i g i n as shown i n F i g . 3. x 2 - (n 2-!) z 2 - 2 f z ( n - l ) = 0 3.10 The convex lens was designed w i t h an aperture of 3.00 i n c h e s , f o c a l lengths of 7.50 inches and 5.00 inches f o r the back and f r o n t curved s u r f a c e of the l e n s , r e s p e c t i v e l y . For f a b r i c a t i o n of the l e n s , a computer program, LENS was w r i t t e n using equation 3.10 to generate the corresponding t h i c k n e s s of the lens f o r each step of x. The beamwidths of the pyramidal horn [3.7] are obtained from the f o l l o w -i n g equations f o r a = 3.5 inc h e s , b = 2.5 Inches and A = 0.339 inches (see o F i g . 3.4). E-plane: beam width, <}> (3 dB) = 51 ^  ° = 6.9° 3.13 H-plane: beam width, <}> (3 dB) = 80 ^  ° = 7.7° 3.14 42 Fig.3.4. Pyramidal hom. x z Fig. 3.5. Pyramidal horn lens. 2a = aperture f = focal length d = iraximum thickness of the lens n = refractive index = / e 7 £ - dielectric constant of the lens 4 3 3.2.3 Design of the Hybrid Ring and Phase S h i f t e r The design of the h y b r i d r i n g i s s t r a i g h t f o r w a r d and i s shown i n F i g . 3 . 6 . The frequency of operation i s 3 4 . 8 0 GHz g i v i n g a guide wavelength, X of 0.423 i n c h e s , using the equation below. X X „ — ° 3 . 1 5 o where X Q , X c i s the free-space wavelength, c u t - o f f wavelength r e s p e c t i v e l y . The design parameters are shown i n F i g . 2.4 and F i g . 3 . 6 . The phase s h i f t e r i s of the squeeze-section type, whose c u t - o f f f r e -quency, f c , i s v a r i e d by squeezing or s t r e t c h i n g the dimension of the broad w a l l , a, t h e r e f o r e changing i t s e l e c t r i c a l l e n g t h . The completed design i s shown i n F i g . 3 . 7. 3.3 The Rec e i v i n g Branch The c o n i c a l horn (see F i g . 3 . 1 ( a ) ) w i t h i t s f o c u s i n g lens r e c e i v e s the two p o l a r i z a t i o n s of the tra n s m i t t e d s i g n a l , the co- p o l a r s i g n a l which i s p a r a l l e l to the l i n e a r l y p o l a r i z e d i n c i d e n t wave and the c r o s s - p o l a r s i g n a l which i s orthogonal to the co-polar s i g n a l . The TRG A857-6C c o n i c a l horn i s provided w i t h an orthomode transducer, M, and a c i r c u l a r - t o - r e c t a n g u l a r wave-guide t r a n s i t i o n , N. The r e s u l t of the t e s t s on the c o n i c a l horn/orthomode transducer/ waveguide t r a n s i t i o n combination w i l l be g i v e n i n Chapter 5. The co-polar and c r o s s - p o l a r s i g n a l s are fed i n t o the PIN diode switches P j and P 2 r e s p e c t i v e l y v i a i s o l a t o r s 0^ and 0 2 « The co-polar and c r o s s - p o l a r s i g -flange mounting Fig.3.6. Section through hybrid ring. Fio.3.7. Section throufh phase shifter. 45 n a l s are a l t e r n a t e l y switched at a r a t e of 10 KHz by the PIN diode d r i v e r s , R. Each s i g n a l i s a l t e r n a t e l y fed i n t o the homodyne bridge v i a the h y b r i d r i n g j u n c t i o n , Q. 3.4 The Homodyne Det e c t i o n Bridge The reference and i n f o r m a t i o n s i g n a l s enter the homodyne bridge v i a the h y b r i d r i n g s , X, and S, r e s p e c t i v e l y (see F i g . 3 . 1 ( a ) ) . The balanced mixer (uj^ or u 2 ) c o n s i s t s of a h y b r i d r i n g (as shown i n F i g . 2.4) and two detectors at the ports 2 and 4. The output s i g n a l from the balanced mixer a f t e r pass-i n g through a balancing network i s given by eqn. 2.16. Hence, from the upper balanced mixer, U p the output i s £ubm _ 2n„Abm cos <b cos a> t 3.16 o I y m and t h a t from the lower balanced mixer, u 2 , i s ( w i t h 90° phase s h i f t a t the lower branch of the b r i d g e ) , e&bm = 2TI Abm s i n <f> cos u t 3.17 o £ T m There must be adequate i s o l a t i o n between the reference and i n f o r m a t i o n chan-n e l s and the input r e f l e c t i o n c o e f f i c i e n t of a l l components must be s m a l l . These requirements are assured by using h y b r i d r i n g s , X, and S f o r power d i v i d i n g , h y b r i d r i n g s , U p and U 2 f o r power combining and i s o l a t o r s , T p T 2, and V 2 f o r channel i s o l a t i o n . V a r i a b l e a t t e n u a t o r , Y, i s i n s e r t e d to set the power l e v e l of the reference channel f o r square-law or l i n e a r d e t e c t i o n w h i l e the phase s h i f t e r s , Wp W2 and Z are used f o r i n i t i a l tuning and c a l i -b r a t i o n . 46 For the i n i t i a l set-up of the homodyne b r i d g e , the s h i f t e r , W2 must be adjusted so that the e l e c t r i c a l lengths from the h y b r i d r i n g , S, to both the balanced mixers are equal w i t h respect to the i n f o r m a t i o n s i g n a l , b. This i s accomplished (see F i g . 3.8) by connecting a f l e x i b l e waveguide, A, to port 2 of U 2 and one port of the s l o t t e d l i n e . The detected output of the s l o t t e d l i n e i s adjusted f o r a voltage minimum and l e f t untouched. F l e x i b l e wave-guide, A, i s then removed from U 2 and connected to p o r t 2 of U^. The phase s h i f t e r , W2, i s adjusted u n t i l the detected output of the s l o t t e d l i n e again shows a voltage minimum, thus completing the tuning f o r W2. 3.5 The M o d i f i e d System The PIN diode switches that were designed d i d not meet the mechanical t o l e r a n c e s , robustness and the s t r i n g e n t alignment requirements f o r t h i s purpose and thus t h e i r i s o l a t i o n c h a r a c t e r i s t i c s changed e r r a t i c a l l y . No funds were a v a i l a b l e to purchase s u b s t i t u t e s and i t was necessary at t h i s stage to bypass the switches at the expense of o b t a i n i n g l e s s i n f o r m a t i o n . As a r e s u l t of t h i s m o d i f i c a t i o n , the three s i g n a l s a v a i l a b l e as d i a g -n o s t i c i n d i c a t o r s of the p h y s i c a l s t r e n g t h p r o p e r t i e s of wood are the co-p o l a r s i g n a l , the c r o s s - p o l a r s i g n a l and the phase change between the co-p o l a r s i g n a l and the modulating s i g n a l . The co-polar s i g n a l i s fed d i r e c t l y i n t o the homodyne bridge while the c r o s s - p o l a r s i g n a l i s envelope detected and fed i n t o the l o c k - i n a m p l i f i e r . The l o c k - i n a m p l i f i e r i s a s e n s i t i v e narrowband DC a m p l i f i e r . The modified system i s shown i n F i g . 3.1(b). f l e x i b l e /waveguide, A phase shifter,W 2 hybrid ring,U^ hybrid ring,U 2 * detector s i g n a l input s l o t t e d l i n e F i g . 3.8. I n i t i a l adjustment of the phase s h i f t e r , W 2 48 Extensive experimentation has shown that the c r o s s - p o l a r s i g n a l g i v e s a r e l i a b l e i n d i c a t i o n of slope of g r a i n and hence t h i s s i g n a l i s used i n s t e a d of the expression of eqn. 1.14. The magnitude of the co-polar s i g n a l at the DC l e v e l r e l a t e s to the moisture content of wood w h i l e i t s phase which I n d i -cates a change i n d e n s i t y gives a measure of the d e f e c t i v e area surrounding a knot, as i n d i c a t e d by the theory given i n Section 1.3.1 and S e c t i o n 1.3.2. These three s i g n a l s may prove to be s u f f i c i e n t f o r t h i s a p p l i c a t i o n of a s t r e s s grading system. microwave cw source —> amplitude modulator X E-H tuner modulating G (~) . X» E-H tuner I r\ a H Q W pyramidal ? wavemeter/ ' l*>rn-lcns detector a n t c n n a lumber board i n 'A L M orthcrnode transducer conical hom-lens antenna upper balanced mixer hybrid ring upper balanced mixer I in "8 phase sensitive detector (if) leck-in amplifier RMS-to-DC converter (co-polar) narrowband amplifier co-polar output cross-polar output detector 6 Fig. 3.1(b). Bloc* diagram of the modified dual balanced mixer homodyne system. 50 CHAPTER. 4 - THE ELECTRONICS INTERFACE 4.1 General E l e c t r o n i c c i r c u i t s are required to i n t e r f a c e w i t h the microwave system f o r s w i t c h i n g , processing and p r e s e n t a t i o n of microwave measurements as shown i n F i g . 4.1(a). The amplitude modulator i s d r i v e n by a 1 KHz modulating s i g n a l provided by the PIN diode d r i v e r . One KHz was s e l e c t e d to be the modulating s i g n a l , p r i m a r i l y f o r two reasons: one was the commerical a v a i l -a b i l i t y of components and t e s t equipment at t h i s frequency; the other was that 1 KHz d i s p e r s i v e e f f e c t s on r e l a t i v e a t t e n u a t i o n should be small so that the modulator could precede the m a t e r i a l to be t e s t e d . One KHz i s adequate f o r a l a b o r a t o r y prototype w i t h a board speed of 1 metre/sec. The PIN diode switches are d r i v e n at 10 KHz, 10 times the modulating frequency, which i s adequate f o r sampling. The output s i g n a l s from the microwave balanced mixers are fed i n t o e l e c t r o n i c c i r c u i t s f o r f u r t h e r pro-c e s s i n g and p r e s e n t a t i o n . 4.2 D r i v e r f o r PIN Diode Amplitude Modulator and Switches The schematic f o r the d r i v e r i s shown i n F i g . 4.2(a). From the data sheet [ 4 . 1 ] , the I n t e r s i l 8038, IC7 i s connected as a waveform generator which outputs a square wave at p i n 9 i n t o the b u f f e r , IC8 A. The waveform generator i s TTL compatible, has low frequency d r i f t w i t h temperature (50 ppm/°C) and high l i n e a r i t y (0.1%) and can be operated from a dual power supply (±5 to ±15 v o l t s ) or a s i n g l e power-supply (10 to 30 v o l t s ) . I t i s set at 10 v o l t s f o r t h i s a p p l i c a t i o n . The frequency of the waveform genera-IS Fig.4.2(a). Schematic diagram for 1 kHz .PIN diode d r i v o r . 53 to r i s a d i r e c t f u n c t i o n of the DC voltage at p i n 8, and f o r the connection shown, i t i s v a r i a b l e from 20 Hz to 20 KHz. I t i s set at 1 KHz. The duty c y c l e which can be adjusted w i t h R 2 and P 2 i s set at 50% f o r t h i s a p p l i -c a t i o n . IC9 (1/2 DS 8830) i s a d i f f e r e n t i a l l i n e d r i v e r [4.2] that i n t e r f a c e s w i t h IC10 (DH 0035) which i s a TTL compatible, DC coupled, h i g h speed PIN diode d r i v e r . In PIN diode s w i t c h i n g , there are two important c o n s i d e r a t i o n s i n the "ON" c o n d i t i o n [ 4 . 3 ] . The f i r s t c o n s i d e r a t i o n i s that the "ON" con-t r o l c urrent must be s u f f i c i e n t such that RF s i g n a l c u r r e n t w i l l not s i g n i f i -c a n t l y modulate the "ON" impedance of the diode. Secondly, i t i s necessary to minimize the time required to achieve the "ON" c o n d i t i o n . The conductance of the diode when "ON" i s p r o p o r t i o n a l to the t o t a l c u r r e n t , I , which i s the sum of IJ-JQJ the steady s t a t e "ON" current and Igj.> the RF s i g n a l c u r r e n t . I n order to minimize modulation due to RF s i g n a l , I , » I ™ . I, can be v a r i e d dc RF dc from 50 mA to 200 mA depending on diode type. The time r e q u i r e d f o r the diode to achieve the "ON" s t a t e could be shortened by a p p l y i n g a c u r r e n t s p i k e , I , to the diode and then dropping the current t o the steady s t a t e p K v a l u e , I n r > . To achieve optimum response, where T i s the mean l i f e time of the m i n o r i t y c a r r i e r s . In the "ON" c o n d i t i o n , a charge I^Q*? was stored i n the diode and t h i s charge must be removed r a p i d l y from the diode to achieve the "OFF" c o n d i t i o n . This can be done by applying a la r g e reverse current to the diode: 4.1 DC - I » 0/T 4.2 p k 54 where 0 i s the stored charge due to the excess m i n o r i t y c a r r i e r s . The PIN diode d r i v e r DH 0035 i s capable of p r o v i d i n g both the c u r r e n t l e v e l s and timing i n t e r v a l s r e q u i r e d to d r i v e the PIN diode modulator o p t i m a l l y . Owing to the f a b r i c a t i o n geometry of the microwave modulator, the grounded cathode arrangement was s e l e c t e d , as shown i n F i g . 3.3. The peak turn-on current i s : ( V + - V " ) ( h + 1 ) I , s 4.3 pk R 3 = 800 mA, f o r h f g = 20 and i n t e r n a l r e s i s t a n c e R g = 500 il. The steady s t a t e c u r r e n t , I ^ i s set by R 1 5 and i s given by: V + - 2V T - BE , . DC = 4 ' 4 h 7 T T + R i 5 fe or ( h f e + l ) ( v + - 2 V B E ) - I D C R 3 = 62.2 a f o r I„_ = 100 mA and V D r, = 0.7 v o l t s . The value of C^g i s given by: X»c T C 1 8 = — — 4 ' 6 V = 0.00476 uF, f o r x = 200 nS ( V a r i a n diode VSD-213AN11). The peak t u r n - o f f current i s given by: - I , = h, x 50 mA 4.7 pk fe = 1000 mA 55 The c i r c u i t r y f o r the PIN diode d r i v e r s at 10 KHz i s s i m i l a r to that at 1 KHz except f o r the l i n e d r i v e r IC3a which provides a l t e r n a t e s w i t c h i n g at 10 KHz f o r the diode d r i v e r s (see F i g . 4.2(b)). 4.3 Balanced Mixer I n t e r f a c e As shown i n F i g . 4.1(a), the s i g n a l outputs from the upper balanced mixer are f e d , i n sequence to a balancing network, an i n s t r u m e n t a t i o n a m p l i -f i e r , an a c t i v e band-pass f i l t e r and a voltage f o l l o w e r , i n t o the summing a m p l i f i e r . From the lower balanced mixer, the s i g n a l outputs f o l l o w a separ-ate but s i m i l a r sequence w i t h the exception of the 90° audio frequency phase S h i f t e r . The output of the summing a m p l i f i e r i s fed i n t o an analog switch where i t i s synchronously switched at 10 KHz by the PIN diode d r i v e r , R, i n c o n j u n c t i o n w i t h the two PIN diode switches at the output of the c o n i c a l horn, g i v i n g two outputs v i z . , the co-polar and c r o s s - p o l a r . The co-polar and c r o s s - p o l a r s i g n a l s are each band-pass f i l t e r e d , a m p l i f i e d and d i r e c t e d to be converted i n t o a DC s i g n a l l e v e l . The phase s e n s i t i v e d e t e c t o r (Y) senses the phase angle, a between the co-polar and c r o s s - p o l a r s i g n a l s w h i l e the phase s e n s i t i v e detector' (Z) detects the RF phase angle, <{> between the co-polar and the modulating s i g n a l s . The inputs to the d e p o l a r i z a t i o n angle d e t e c t o r are the magnitude of the co-polar and c r o s s - p o l a r s i g n a l s and the phase angle, a, between them. I t outputs the d e p o l a r i z a t i o n angle which gives a measure of slope of g r a i n of lumber. The magnitudes of the co-polar and c r o s s - p o l a r s i g n a l s , the RF phase angle, <j>, and the d e p o l a r i z a t i o n angle, x, are being sampled at v a r i o u s predetermined i n t e r v a l s by the data a c q u i s i -t i o n sub-system. CI PI < 10K O.luF R3 > 15K IC1 8038 P3 20K 10 M ^20K R 5 ^ ISM -5*0.0047ui 11 C2 12 R6 S 100K -O +iov C5 +5VQ °-luF 10,11 13 IC2A 12 12 13 V6 74IS04 IC3 V2 D68830 C7 AO.luF C6 + 5 V Q°.luF H t L 14 10,11 12 13 1/6 74I£04 IC4A 1/2 DS8830 14 1,2,3 IC2C V6 74I£04 IC4B V2 DS8830 C8 200pF +10V R13' 62 <• CIO 0.0047uP IC2D V6 74LS04 F i g , 4,2(b). Schematic diagram for 10 kHz PIN diode driver C9 20r;F -^-3 ICS DH0035 i i 12 OH +5V O.luF OP2 I L W4 > C14 62 > 0.0047uF C12 r-i [[. f : j i . v . 5 B IU L 0 PI'— !0 20OpF -E~6 C13 20pF -3r-IC 6 DH0035 a . 12 O.luF i n 15 — i — -1.07 -in-. OH tirr. OH 12 13 14 15 16 17 IS 15 20 21 22 to INI, CONMETOR {2, Fig.4.3(b) ON 57 The microprocessor system could c o n t r o l the op e r a t i o n of the whole s y s -tem and determine the rev e l a n t data to be gathered and process them and the req u i r e d i n f o r m a t i o n could be di s p l a y e d on the video monitor console or any other s u i t a b l e I/O p e r i p h e r a l . The implementation of the microprocessor system i s not w i t h i n the scope of t h i s l a b o r a t o r y prototype p r o j e c t which p r i m a r i l y i n v e s t i g a t e s the f e a s i b i l i t y of using the microwave homodyne measurements to c o r r e l a t e to the p h y s i c a l strengths of lumber boards. Instead, p o s i t i o n - c o n t r o l l e d chart recordings of the c o - p o l a r , c r o s s - p o l a r ( r e l a t e d to d e p o l a r i z a t i o n ) and RF phase change s i g n a l s are d i s p l a y e d . For square-law d e t e c t i o n , the equations of the s i g n a l s at v a r i o u s p o i n t s of the balanced mixer i n t e r f a c e (see F i g . 4.1(a)) are as f o l l o w s : a l Point a j i e Q = ^Ji c 1 A D m ( k / A + cos <j>)cos uM: (from eqn. 2.14) 4.8 a2 P o i n t a 2 : e Q " = - n ^ c 2 Abm(-b/A + cos <ji)cos uM: (from eqn. 2.15) 4.9 where c^, c 2 are the a t t e n u a t i o n f a c t o r s of the c u r r e n t shunting p o t e n t i o -meter ( b a l a n c i n g network); the potentiometer i s i n i t i a l l y adjusted such that Point b: e U ^ m = 2Gn„Abra cos <j> cos cj t 4.10 o £ r ra where G i s the voltage g a i n of each i n s t r u m e n t a t i o n a m p l i f i e r , s e t equal t o each other. a3 Point a,:' e = n„ c„Abm(b/A + s i n A)cos u> t 4.11 J o £g -3 m 58 a4 Point a,,: e = -r\„ c^AbinC-h/A + s i n (fc)cos ui t 4.12 4 o \ * m Poin t f : e ^ m = 2Gn„Abm s i n 6 cos u t 4.13a o £ y m Point g: e = -2Gn„Abm s i n d> s i n w t 4.13b b o £ r m Combining the s i g n a l s from p o i n t s b and g, the output a t p o i n t h i s : e = 2Gn„Abm cos( to t + d>) 4.14 out £ m Y 4.3.1 Balancing Network and Instrumentation A m p l i f i e r The b a l a n c i n g network [4.4], c o n s i s t i n g of a 50 Kft current shunting potentiometer and two 10 uF c a p a c i t o r s , removes the DC components a s s o c i a t e d w i t h the outputs from the balanced mixer detectors and balances the c o e f f i -a l a2 c i e n t s of e and e such that n„ c, = n„ c„ = n„ {see eqns. 4.8 and 4.9}. o o &j * ^ • * The IF impedance of a p o i n t contact d e t e c t o r diode i s about 100 to 500 fi [4.5] and the nominal impedance of the premium AF transformer (Hammond 101D) used i s about 300 £2 which, together w i t h the balancing network, matches the IF impedance of the diode. The i n s t r u m e n t a t i o n a m p l i f i e r , LH0038 [4.6] i s a p r e c i s i o n a m p l i f i e r w i t h very low o f f s e t voltage (25 uV t y p i c a l ) and very low input noise (0.2 uV p-p). I t i s capable of measuring input s i g n a l s i n the mV range. I t s c l o s e d loop g a i n can be changed w i t h jumpered gain pins and f o r t h i s a p p l i c a t i o n , the g a i n i s set at 100. The output of the premium AF transformer i s fed i n t o the h i g h common input impedance (1 GQ) of t h i s a m p l i f i e r and i t s low imped-ance (1 mft) output i s connected to the bandpass f i l t e r (see F i g . 4 . 3 ( a ) ) . 59 4.3.2 Band Pass F i l t e r The f i l t e r , f o l l o w i n g the instrumentation a m p l i f i e r , i s a 4-pole Butter-worth band pass f i l t e r w i t h Q B p = 30 and centre frequency, f £ = 1 KHz u s i n g two AF150 [4.7] modules. The AF150 i s a wide band, second order a c t i v e f i l -t e r w i t h a 0 frequency product of 2 x l 0 5 . t r a n s f e r f u n c t i o n i s : For the band pass output, the T(S) = a 2 s u) s 2 + —-- S + 0) 2 0 c 4.15 where w = r a d i a n centre frequency and 0 = f /bandwidth, c c The design (see F i g . 4.4) of the a c t i v e band pass f i l t e r i s as f o l l o w s : 4-pole Butterworth Band Pass F i l t e r QBP " 3 0 f = 1 KHz c From eqn. 33 [ 4 . 7 ] , band pass centre frequency g a i n , From eqn. 6 [4 .7 ], 'Bp i n 2 x l 0 3 ^ + 10*^ R IN (JOFU) 1 b 1 +2x103 R I N 4.16 1 0 l 3.160(1.1 -1 IN Using the computer program, BNPASS (LP to BP t r a n s f o r m a t i o n ) : Input data: f = 1.0, 0 = 0.70711, Q B p = 30 4.17 +15V o I W v -14 i n o—VW R AF 150 1st section 12 0 •15V 13 +15V o 14 R. i n R AF 150 2nd section 12 6 >15V 13 60 F i g . 4.4. Schematic diagram for active f i l t e r AF 150. 61 Output data: f = 1.011854, Q = 42.44294 f = 0.98828, Q = 42.43196 n 1st Section f = f x f = 1 KHz x 1.0118 = 1.0118 KHz o c n Q = 42.443 For frequency from 1 KHz to 100 KHz, using eqn. 1 [ 4 . 7 ] , D 228.8 x 1 0 6 . 1 f t = - j 4.18 o = 226.1 Kfl S o l v i n g eqns. 4.16 and 4.17 f o r u n i t y gain and Q = 42.443, R. = 270 Kft xn R Q - 67.3Q 2nd Sec t i o n f = f x f = 1 KHz x 0.98828 = 0.9883 KHz o c n 0 = 42.432 Using eqn. 1 [ 4 . 7 ] , R f = 2 2 8 - * X 1 0 6 = 231.5 Ki l o Sol v i n g eqns. 4.16 and 4.17 f o r u n i t y g a i n and Q = 42.432, R. = 270 KQ i n R„ = 67.3 a 6 2 4.3.3 B u f f e r and AF Phase S h i f t e r The output of the band pass f i l t e r i s connected t o the inp u t of the summing a m p l i f i e r v i a the high impedance b u f f e r , IC7. In the B channel (see F i g . 4 . 3 ( a ) ) , the output from the band pass f i l t e r i s phase s h i f t e d by 90° using IC9. With R 1 5 = R 1 6 = 10 KQ, the t r a n s f e r f u n c t i o n of the phase s h i f t e r , IC9, i s given by: /„ 2 . v 2 . -1 r X 1 5 >, / P 9 + X 1 5 tan ( — J T - - - L _ (4.19-} / 2 . v 2 . - l r 15 >, / p g + X 1 5 tan t — p — J 9 i where X 15 coC 1 5 For f = 1 KHz, C = 0.01 uF and to o b t a i n 90° phase s h i f t , c P g = 2.65 Kft 4.3.4 Summing A m p l i f i e r and Analog Switch The summing a m p l i f i e r sums the output s i g n a l s from channels A and B to giv e a s i g n a l as represented by eqn. 4.14 which i s the d e s i r e d s i g n a l , g i v i n g amplitude, 2Gn^Abm, and phase, <j>, i n f o r m a t i o n . In s y n c h r o n i z a t i o n w i t h the PIN diode switches o p e r a t i n g at 10 KHz, the analog s w i t c h , IC2 (see F i g . 4.3(b)) switches the co-polar and c r o s s - p o l a r s i g n a l s a l t e r n a t e l y between channels E and F which are i d e n t i c a l i n c o n f i g u r -a t i o n and design. The analog s w i t c h , DG189 [4.81 has low ON r e s i s t a n c e (<10 n) and i t s t u r n - o f f speed i s f a s t e r than turn-on speed r e s u l t i n g i n break-before-make a c t i o n . 64 4.3.5 Band Pass F i l t e r and I n v e r t i n g A m p l i f i e r At the output of the analog switch (see F i g . 4.3(b)), a band pass f i l t e r w i t h centre frequency of 1 KHz i s re q u i r e d to e x t r a c t the 1 KHz i n f o r m a t i o n s i g n a l from the switched waveform of 10 KHz. A s t a t e - v a r i a b l e c o n f i g u r a t i o n i s used which fe a t u r e s e x c e l l e n t s e n s i t i v i t y p r o p e r t i e s and the c a p a b i l i t y to c o n t r o l resonant frequency and 0 independently. The t r a n s f e r f u n c t i o n i s given by (see IC3, F i g . 4.3(b)) s/CRg T ( s ) „ 4.20 s 2 + s/C(R 1 Q+P 1) + 1 / R 1 3 ( R U + P 2 ) C 2 where C j = C 2 = C and the centre frequency, f and 3 dB bandwidth can be expressed as f = _ 1 4.21 c 2TrC/R 1 3(R 1 1+P 2J BW •= —T -T 4*22 3-dR 2 u ( R 1 0 + P 1 J f ° - 4.23 B W3-dB Using eqns. 4.21, 4.22 and 4.23, f o r f = 1 KHz, 0 = 20 and u n i t y g a i n , and l e t C x = C 2 = C = 0.1 uF, R 1 3 = R n + P 2 = R = 2^TC = i'59 K Q ( R ^ + P j = QR = 31.8 VLSI R10 314K fpTI, 4—Wv-TT-Wv-t R11 1.3K P2 500 B1 +15 P5 10K -|5 o-VvV-o •15 P4 10K -15 R22<3M CONNECTOR til T IM1 "15 , O—I OH LA/K B1 OH . E GNO 10 11 12 JJL 15  16  1 7  1S  19  20 21 O-H 22 -A//V ,„ i I R4016K F i g . 4.3(b). Schematic diagram for balanced mixer interface I I . 66 1 = 31.8 Kft The centre or resonant frequency, f £ , and the Q can be adjusted by a d j u s t i n g P 2 and P x r e s p e c t i v e l y . The i n v e r t i n g a m p l i f i e r i s used f o r f i n a l adjustment of the s i g n a l l e v e l before i t enters the RMS-to-DC con v e r t e r . 4.3.6 RMS-to-DC Converter The AC i n f o r m a t i o n s i g n a l at 1 KHz i s converted i n t o a DC s i g n a l , s u i t -able to be chart recorded or to be converted f u r t h e r i n t o a d i g i t a l s i g n a l f o r p r o c e s s i n g . The t r a n s f e r f u n c t i o n of the rms-to-dc converter LH009 [4.9] i s given by w i t h a conversion accuracy of 0.1% of reading using an e x t e r n a l t r i m procedure. 4.3.7 Phase S e n s i t i v e Detector This d e t e c t o r uses c i r c u i t elements that respond to the sequence i n which the two input waves a r r i v e and i t can measure phase d i f f e r e n c e s of up to 360° [4.10]. As shown i n F i g . 4.5, the CD4013 i s configured f o r 360° phase d e t e c t i o n by the f o l l o w i n g connections: 0-^ output of F F j connected to the r e s e t ( R 2 ) input of F F 2 and 0 2 output of F F 2 to the r e s e t (R^) i n p u t of F F X ; the set i n p u t s " ( S j , S 2 ) are e f f e c t i v e l y removed by grounding them; the "D" inputs ( D p D p are pulled-up high v i a a 47 Kft r e s i s t o r to +V; i n p u t s to the detector are v i a c l o c k i n p u t s ( C L ^ C L ^ ) . 4.24 f i g , 4,5, Phase sensitive detector, 68 The p o s i t i v e t r a n s i t i o n of the comparator, IC1, output s i g n a l t r a n s f e r s Dj's hard-wired 1 to the output, which causes Qj to go high and Oj to go low. With 0^ low, the re s e t l e v e l i s removed from R 2« 0^ remains h i g h u n t i l , as i n F F p the p o s i t i v e t r a n s i t i o n of the comparator, IC2, output causes Q 2 to go h i g h , which r e s e t s FF ^  and forc e s low. The Qj^ output pulse has a width d i r e c t l y p r o p o r t i o n a l to the phase d i f f e r e n c e between the inp u t s i g n a l s to the two comparators, w i t h the maximum pulse width corresponding t o 360°. IC4 i s an i n v e r t i n g a m p l i f i e r w i t h a l e v e l s h i f t e r . In t h i s a p p l i c a t i o n , the adjustment i s made f o r 4 v o l t s to correspond to 360° w i t h a l i n e a r s c a l e down to 0 v o l t s f o r 0°. the pulse width i s i n t e g r a t e d by IC5, w i t h i t s time con-s t a n t set at 2.2 m i l l i s e c o n d s , to give a DC output. 4.4 The Mod i f i e d System Since the 10 KHz sw i t c h i n g i s not i n o p e r a t i o n , the analog s w i t c h and channel F are d i s a b l e d , and the modified e l e c t r o n i c i n t e r f a c e Is shown i n F i g . 4.1(b). 4.5 C a l i b r a t i o n and Tuning Before the system i s ready f o r o p e r a t i o n , the f o l l o w i n g tuning and c a l i -b r a t i o n procedures are r e q u i r e d , a f t e r a warm-up period of about one-half hour: (a) With the at t e n u a t o r , Y, set at maximum a t t e n u a t i o n , i . e . w i t h reference s i g n a l reduced to a n e g l i g i b l e l e v e l , the E-H tuner i s tuned f o r maximum output as i n d i c a t e d by any one of the balanced mixer d e t e c t o r s (see F i g . 3.1(b)). •4 o a a H o 3 C l video monitor console microprocessor controlled system data acquisition sub-system M. < o o a n> rr H» n * n & s O rt K W 3-D O r - f f O Hi til rr V* > a o *=i H 69 70 The E-H tuner i s adjusted next f o r minimum r e f l e c t i o n s from the horn-lens antennas as i n d i c a t e d by the detector attached to the waveraeter, which i s a l s o used to monitor the frequency of operation of the Gunn diode o s c i l l a t o r . Frequency t u n i n g , i f necessary, i s achieved by ad-j u s t i n g the screw attached to the top of the o s c i l l a t o r . The d e t e c t o r s of each balanced mixer are next checked f o r balance, i . e . , equal output from each d e t e c t o r . I f they are not, the de t e c t o r s are tuned and/or the attenuators are adjusted f o r balance. The upper and lower balanced mixers are then balanced against each o t h e r . With the a t t e n u a t o r , Y, set at 6 dB (square-law d e t e c t i o n ) , the outputs of the balanced mixers are connected to the i n p u t s of the bala n c i n g networks. The current shunting potentiometers, and P , f o r the upper and lower balanced mixer, r e s p e c t i v e l y , are i n d i v i d u a l l y adjusted f o r a d i s p l a y of a symmetrical waveform as monitored at the output of each i n s t r u m e n t a t i o n a m p l i f i e r (see F i g . 4.1(b)). A h i g h input impedance (say 1 HQ, 30 pF) o s c i l l o s c o p e , commonly a v a i l a b l e i n the l a b o r a t o r y , i s used. The i n s t r u m e n t a t i o n a m p l i f i e r output of the upper balanced mixer i s monitored f o r maximum output by a d j u s t i n g the phase, s h i f t e r , Z {see F i g . 3.1(b)}, while that f o r the lower balanced mixer i s monitored f o r m i n i -mum output by a d j u s t i n g the phase s h i f t e r , W^ . The band pass f i l t e r s f o l l o w i n g the i n s t r u m e n t a t i o n a m p l i f i e r and the summing a m p l i f i e r s are tuned f o r u n i t y g a i n and zero phase s h i f t f o l l o w -i n g the standard procedure of observing L i s s a j o u s f i g u r e s . 71 Normally, the above c a l i b r a t i o n and tuning procedures are not necessary f o r short-term o p e r a t i o n . 72 CHAPTER 5 - EXPERIMENTAL RESULTS 5.1 Measurements of Microwave Components 5.1.1 Pyramidal Horns Lens and C o n i c a l Horn Lens Antennas The beam widths of the pyramidal horn lens and c o n i c a l horn l e n s anten-nas were measured using a pyramidal horn w i t h plano-convex lens and a d i p o l e probe r e s p e c t i v e l y . The r a d i a t i o n patterns obtained are i l l u s t r a t e d I n F i g . 5.1 through 5.3. 5.1.2 PIN Diode Switches Measurements, centred around 34.80 GHz, were taken to determine the i s o -l a t i o n of the three PIN diode switches; one of them was used as the a m p l i -tude modulator. The r e s u l t s are shown i n F i g . 5.4. 5.1.3 Hybrid Rings The measurement r e s u l t s of the f a b r i c a t e d h y b r i d r i n g s are shown i n Table 5.1. Table 5.1. Measurement r e s u l t s of the h y b r i d r i n g s . Ring # •V.S.W.R. Port 1 Power (d) Port 3 0 Unbalance I s o l a t i o n (dB) 1 2 1.35 (Port 2) 1.27 (P o r t 4) 1.41 (Port 2) 1.27 (Port 4) 27.00 26.80 42.50 42.40 27.35 26.60 42.10 42.20 0.35 0.20 0.40 0.20 35.4 (P o r t 1-3) 33.50 (Port 1-3) Port 2 Port 4 3 4 1.07 (Port 1) 1.16 (Port 3) 1.10 (Port 1) 1.28 (Port 3) 27.00 27.30 41.40 41.70 27.40 26.80 41.70 41.20 0.40 0.50 0.30 0.50 27.30 ( P o r t 2-4) 40.6 (P o r t 2-4) 40 r 8 a I -P (T3 rH 35 h 30 h 25 2 0 r 15 0 73 20 8 pyramidal horn (with planoconvex lens) 40 pyramidal horn (with focused lens) — H i i " \ separation 60 80 angle (deg.) Fig.5.1(a). Padiation pattern of the pyramidal horn-lens antenna (E-plane) 60 I ! t • ! _ _ l 0 20 40 60 80 a n g l e (deg.) Fig.5.1(b) . R a d i a t i o n p a t t e r n o f t h e pyramidal h o r n - l e n s antenna (H-plane). 7" s e p a r a t i o n d i p o l e probe 0.24" c o n i c a l horn-lens antenna s e p a r a t i o n bearrwidth (inches) ( 3 dB ) 6 0.28" 7 0.24" 8 0.26" 1 1 - 2 3 d i s t a n c e ( i n c h . ) 5.2. R a d i a t i o n p a t t e r n o f the c o n i c a l h o r n - l e n s antenna (E-plane) 6" s e p a r a t i o n 76 ( d i p o l e probe c o n i c a l horn-lens antenna 40 r s e p a r a t i o n beamwidth (inches) ( 3 dB ) . 6.00 0.28" 7.50 0.26" 8.75 0.28" 2 4 6 d i s t a n c e (inches) F i g . 5 , 3 . R a d i a t i o n p a t t e r n o f the c o n i c a l . h o r n - l e n s antenna (K-plane) T3 C O •H •P ri o •H 30 25 20 15 10 34.2 Device Insertion loss at 34.8 GHz switch #1 2.4 dB switch #2 2.5 dB amplitude 3.0 dB modulator switch #2 amplitude modulator 34.4 34.6 34.8 35,0 frequency (GHz) Fig.5.4. Isolation of the microwave switches as function of frequency. 78 5.2 Waveguide Measurements of R e l a t i v e P e r m i t t i v i t y and Loss Tangent Measurements of r e l a t i v e p e r m i t t i v i t y and l o s s tangent were made us i n g the method described by S. Roberts and A. von H i p p e l [ 5 . 1 ] . The r e l e v a n t equations are: 2nx 1 • - ° — - l tan — - — tanh Y,d - j X, S X, . _ — = _ _ . = C e J 5 5.1 Y 2d 2ird ^ 2irx c where (see a l s o F i g . 5.5). Y 2 = propagation constant i n the d i e l e c t r i c , i . e . , wood, d = l e n g t h of d i e l e c t r i c i n the waveguide, Xj = free-space wavelength S = voltage standing wave r a t i o (V.S.W.R.) E max E . min x o distance of the f i r s t v o l t age minimum, i n a i r , from the surface of the d i e l e c t r i c . X c = c u t - o f f wavelength of waveguide to = r a d i a n frequency e = complex p e r m i t t i v i t y of the d i e l e c t r i c = e'-j e" u = p e r m e a b i l i t y of the d i e l e c t r i c = u 0 P r « Eqn. 5.1 and eqn. 5.2 are solved f o r various samples of wood usin g a computer program, WOOD, as documented i n the S e c t i o n 8.2 The i n p u t data to the pro-field intensity minxmum i n a i r position of f i r s t voltage waveguide short-circuiting •plate dielectric (wood) Fig.5.5. Waveguide measurement of relative permittivity and loss tangent of wood, ^ 80 gram a r e , d, the length of wood, S, the voltage standing wave r a t i o , x , the d i s t a n c e of the f i r s t voltage minimum, i n a i r , from the surface of the d i e l e c t r i c and f , the frequency of o p e r a t i o n . The computer output gives the complex r e l a t i v e p e r m i t t i v i t y , e = e' - j e " , and the graphs of the r e l a t i v e p e r m i t t i v i t y , e', and l o s s tangent, tan 6, against frequency and g r a i n d i r e c t i o n are shown i n F i g . 5.6 F i g . 5.7. 5.3 Free-Space Measurements at 34.80 GHz The r e l a t i v e p e r m i t t i v i t y , e', and l o s s tangent, t a n 6, of Douglas f i r at various moisture contents were determined by making free-space measure-ments of the r e f l e c t i o n c o e f f i c i e n t (R^) and t r a n s m i s s i o n ( T 1 2 ) c o e f f i c i e n t and using a computer program FSPACE to solve the r e l e v a n t wave m a t r i x equa-t i o n s 5.6 and 5.7 i n c o n j u n c t i o n w i t h the f o l l o w i n g e q u a t i o n s . 6 = 3ft 5.3 0 = (2u/X ) ( e - s i n 2 Q,)l/2 5.4 o i where cos 0^  ( e - s i n 2 6 . ) 1 / ? 8 = e l e c t r i c a l l e n g t h of the d i e l e c t r i c = g = phase constant i n d i e l e c t r i c ft = thi c k n e s s of d i e l e c t r i c 6^  = angle of incidence at the a i r - d i e l e c t r i c i n t e r f a c e = 0° f o r t h i s experiment 5.5 o.io r § 0.09 w V) O 0.08 0.07 0.06 0,05 0,04 0,03 10 l o n g i t u d i n a l transverse 20 30 40 50 60 7Q frequency (GHz) 80 Fig.5,7, Loss tangent of Douglas-fir as functions of frequency and grain d i r e c t i o n . oo (S3 83 X Q = free-space wavelength z = normalized impedance e = complex p e r m i t t i v i t y . As shown i n Section 8.1, 1/T 12 -R 2/T 1 2 R l / T 1 2 5.6 T 2 1 ~ R l R 2 y ' T 1 2 where c p b 2 and b p c 2 are the i n c i d e n t and r e f l e c t e d waves r e s p e c t i v e l y ; R and T are the r e f l e c t i o n and tr a n s m i s s i o n c o e f f i c i e n t s r e s p e c t i v e l y . j _ s i n 0 ( z 2 + l ) + c o s . 2z - j s i n 0 ( z 2 - l ) 2z j s i n 0 ( z 2 - l ) - j s i n 0 (z2+l) + cos0 5 2z 2z where 0 = gJl = e l e c t r i c a l l e n g t h of d i e l e c t r i c , z = normalized impedance. The r e s u l t s are tabulated i n Table 5.2 and 5.3. Figure 5.8 shows the graphs of r e l a t i v e p e r m i t t i v i t y , e', and l o s s tangent, tan 5, f o r the l o n g i t u d i n a l and and transverse d i r e c t i o n s as a f u n c t i o n of moisture content. The a t t e n u a t i o n of the co-polar s i g n a l i n the l o n g i t u d i n a l and t r a n s -verse d i r e c t i o n s as a f u n c t i o n of moisture content i s shown i n F i g . 5.9. 84 Table 5.2 - Free-space measurement of d i e l e c t r i c constant and l o s s tangent. Frequency = 34.80 GHz E f i e l d t ransverse to g r a i n Thickness Moisture R e f l e c t i o n Transmission Complex P e r m i t t i v i t y Loss Tangent - C* of Wood Content C o e f f i c i e n t C o e f f i c i e n t e' tan6 = -§,-(cm) (%) 1.90 2.3 0.200 0.733 2.10 •0.043 0.020 1.93 6.2 0.153 0.589 2.20 0.260 0.118 1.93 10.7 0.253 0.391 2.50 0.172 0.069 1.94 12.4 0.207 0.372 2.70 0.243 0.090 1.95 16.9 0.211 0.285 2.99 0.375 0.125 1.95 18.6 0.202 0.262 3.04 0.410 0.135 1.97 23.2 0.359 0.175 3.80 0.443 0.116 1.97 26.0 0.476 0.132 3.97 0.450 0.113 Table 5.3 - Free-space measurement of d i e l e c t r i c constant and l o s s tangent. Frequency = 34.80 GHz ->• E f i e l d p a r a l l e l to g r a i n Thickness Moisture R e f l e c t i o n Transmission Complex Permi 1 1 i v i t y Loss Tangent of Wood Content C o e f f i c i e n t C o e f f i c i e n t e' - j e tan6 = fr (cm) (%) 1.91 2.3 0.221 0.519 2.50 0.162 0.065 1.93 6.2 0.221 0.343 2.67 0.310 0.116 1.97 10.7 0.287 0.152 2.80 0.420 0.150 1.98 12.4 0.248 0.130 3.60 0.610 0.169 2.00 16.9 0.211 0.085 3.80 0.800 0.211 2.00 18.6 0.243 0.062 3.98 0.860 0.216 2.10 23.2 0.566 0.018 4.20 0.960 0.228 2.10 26.0 0.653 0.012 3.47 0.920 0.265 85 5.4 S t a t i c Measurements of Slope of Grain and Knots The rec e i v e d co-polar and cross s i g n a l s were measured f o r a f u l l 360° r o t a t i o n of slope of g r a i n of Douglas F i r board us i n g a pyramidal horn lens and a c o n i c a l horn lens antennas, arranged f o r near f i e l d measurements ( w i t h the s e p a r a t i o n of the lenses at about 12 1/2 i n c h e s ) . The r e s u l t s are shown i n F i g . 5.10 through F i g . 5.12. The above experiment was repeated w i t h boards having knots. Instead of r o t a t i o n , the boards were moved h o r i z o n t a l l y . The r e s u l t s are shown i n F i g . 5.13 through F i g . 5.15. 5.5 R e s u l t s from the Double Channel Homodyne System The c r o s s - p o l a r and RF phase change s i g n a l s were obtained v i a cha r t r e c o r d i n g s , which gave i n f o r m a t i o n of the slope of g r a i n and d e f e c t i v e area surrounding the knot r e s p e c t i v e l y . The co-polar s i g n a l which giv e s informa-t i o n on the moisture content of the wood w i l l be used when necessary. Nine-teen boards were scanned on the t e s t j i g and the chart recordings are shown i n F i g . 8.3 through F i g . 8.21. They were then t e s t e d i n the C i v i l Engineer-in g Laboratory to determine the l o c a t i o n of f a i l u r e and the modulus of rup-ture (M.O.R.) and the r e s u l t s are shown on the same c h a r t s . 01 1 1 I I I U I I t - ' ' _ l I 2 4 6 8 10 12 14 16 18 20 22 24 moisture content (% o f dry weight) Fi g . 5 . 8 , R e l a t i v e p e r m i t t i v i t y and l o s s tangent of D o u g l a s ^ f i r as f u n c t i o n s o f moisture content and g r a i n d i r e c t i o n a t a frequency of 34.80GHz. CO ON 0 I I I I I I I _1 1 1 1 ; 1 1 2 4 6 8 10 12 14 16 18 .20 2 2 24 iroisture content (% of dry weight) Fig.5.9. Attenuation of the co-polar signal as functions of •; moisture content and grain direction at 34.80 GHz. 91 40-1 T 1 , , 1 1 r 0 2 4 6 B 10 12 14 distance ( inches ) Fig.S.14. Cross-polar and co-polar signals vs. distance (-sample E ) 93 40-j 0 -4 0 2 4 6 8 10 12 14 distance ( inches ) Pig.5.15. Cross-polar and co-polar signals vs. distance ( sample F ) 94 5.6 Observations The t e s t r e s u l t s of the microwave components ( s e c t i o n 5.1.1 through s e c t i o n 5.1.3), i . e . , the horn lens antennas, PIN diode switches and h y b r i d r i n g s , show that s p e c i f i c a t i o n s are met except the switches. However, any one of the switches was good enough to be used as the modulator si n c e i t s s p e c i -f i c a t i o n was l e s s s t r i n g e n t . The r e l a t i v e p e r m i t t i v i t y , e', and l o s s tangent, tan 6, ( s e c t i o n 5.2) do not seem to vary s i g n i f i c a n t l y w i t h frequency ( F i g . 5.6 and 5.7). The f r e e -space measurements ( F i g . 5.8) a t 34.80 GHz i n d i c a t e t h a t the r e l a t i v e permit-t i v i t y , e', f o r both the l o n g i t u d i n a l and transverse d i r e c t i o n s increases w i t h moisture content. The l o s s tangent, tan 6, f o r both o r i e n t a t i o n s i n -creases at a more r a p i d r a t e than the r e l a t i v e p e r m i t t i v i t y but drops o f f at higher moisture contents. These r e s u l t s agree w i t h those of James and H a m i l l [ 1 . 7 ] , although the operating frequency i s d i f f e r e n t . The a t t e n u a t i o n of the co-polar s i g n a l f o r the l o n g i t u d i n a l and transverse d i r e c t i o n s i n c r e a s e s w i t h moisture content ( F i g . 5.9). The graphs of the c r o s s - p o l a r s i g n a l ( F i g . 5.10 through 5.12) v s . angle of r o t a t i o n of g r a i n show that i n v a r i a b l y , the curves are p e r i o d i c w i t h maxi-mum s i g n a l magnitude at 45°, 135°, 225° and 315°, as p r e d i c t e d from the anisotrophy property of wood. This suggests that the c r o s s - p o l a r s i g n a l i s a r e l i a b l e i n d i c a t o r of the slope of g r a i n . There i s a r a p i d change of s i g n a l l e v e l f o r small change i n slope angle near 0°, 90° and m u l t i p l e of 90° but the change i s more gradual around 45°, 135°, 225° and 315°. I t i s f o r t h i s reason that both the t r a n s m i t t i n g and r e c e i v i n g antennas are mechanically r o t a t e d through 45° r e l a t i v e to the nominal d i r e c t i o n of the g r a i n . 95 The graphs i n F i g . 5.13 through F i g . 5.15 show that there are g r a i n d e v i a t i o n s l o c a l i z e d near the knots as i n d i c a t e d by the c r o s s - p o l a r s i g n a l . From the graphs showing the v a r i a t i o n of the co-polar s i g n a l near the knot, i t may be deduced that the co-polar s i g n a l i s a f u n c t i o n of both d e n s i t y and moisture content. The measurement r e s u l t s from the homodyne system and the s t r e n g t h (M.O.R) values are shown i n Section 8.3 ( F i g . 8.3 through F i g . 8.21). From the observations on the 19 boards, there appears to be a very c l o s e q u a l i t a -t i v e c o r r e l a t i o n between the measured s t r e n g t h and the width of the d e f e c t i v e r e g i o n (as i n d i c a t e d by the phase s i g n a l ) , and the slope of g r a i n (as i n d i -cated by the s i z e of the c r o s s - p o l a r s i g n a l ) . Of the 19 boards, o n l y one gave a negative r e s u l t and the others gave a r e s u l t that i s not d e f i n i t e but probable. Board #15 was not completely t e s t e d . These r e s u l t s were decided mainly by l o o k i n g at the upper scan (about 3/4 inches from the top edge) but were confirmed through s c r u t i n i z i n g the lower scan (about 1 1/2 inches from the top edge). The lower scan appears to give a d e c i s i v e i n d i c a t i o n i n cases of u n c e r t a i n t y . Any q u a n t i t i v e c o r r e l a t i o n w i l l r e q u i r e the use of p r o p e r l y matched det e c t o r s and knowledge of the exact range of t h e i r o p e r a t i o n . These detec-t o r s were, however, u n a v a i l a b l e at the time these measurements were made. E v e n t u a l l y , f u r t h e r e l e c t r o n i c c i r c u i t r y w i l l have to be designed t o imple-ment the q u a n t i t a t i v e c o r r e l a t i o n c r i t e r i a between s t r e n g t h and microwave measurements. 96 CHAPTER 6 - CONCLUSIONS AND DIRECTIONS FOR FURTHER DEVELOPMENT 6.1 Conclusions The s u i t a b i l i t y of the designed homodyne system, i n c o r p o r a t i n g balanced mixers and focused lens antennas to measure the e l e c t r i c a l p r o p e r t i e s of Douglas F i r f o r c o r r e l a t i o n w i t h i t s s t r e n g t h p r o p e r t i e s , i s e s t a b l i s h e d . From the r e s u l t s of the microwave and s t r e n g t h measurements, there appears to be a very c l o s e c o r r e l a t i o n between the measured s t r e n g t h and the width of the d e f e c t i v e r e g i o n (as i n d i c a t e d by the phase s i g n a l ) , and the slope of g r a i n (as i n d i c a t e d by the s i z e of the c r o s s - p o l a r s i g n a l ) . The o p e r a t i o n of the system i s simple and once the I n i t i a l c a l i b r a t i o n and tuning i s completed, f u r t h e r adjustment i s minimal. This microwave s y s -tem f o r s t r e s s grading i s capable of being a c c u r a t e , r e l i a b l e , compact and p o r t a b l e , besides being almost maintenance-free. In i t s present form, i t may prove to be a s u i t a b l e replacement f o r v i s u a l grading.. 6.2 D i r e c t i o n s f o r f u r t h e r development At t h i s time, i t i s hoped that f u r t h e r work w i l l continue on t h i s s y s -tem. The areas r e q u i r i n g f u r t h e r development a r e : (1) Determination of the appropriate weighting f u n c t i o n s of the co-p o l a r and phase change s i g n a l s i n co n j u n c t i o n w i t h the c r o s s - p o l a r to g i v e a quan-t i t i v e measure of the stren g t h of the lumber board. (2) Determination of an optimum r e s o l u t i o n ( i . e . , the s i z e of the focused spot of the lens antennas) and the d i s t a n c e from the top edge f o r which the board i s to be scanned. 97 (3) Automation of the e n t i r e system by using a microprocessor c o n t r o l l e d subsystem f o r tuning and c a l i b r a t i o n of the system before each board i s graded, t e s t i n g of the board, processing of the acquired data, stamping the grading r e s u l t on the board and p r e s e n t a t i o n of the r e q u i r e d i n f o r m a t i o n on the video monitor or any appropriate I/O p e r p h e r a l . (4) Development of the system i n t o a compact and mechanically sound u n i t , s u i t a b l e f o r i n d u s t r i a l a p p l i c a t i o n . (5) Adaptation of the system to grade other species of lumber of v a r i o u s s i z e s and moisture contents. (6) Gathering of s t a t i s t i c s using a microcomputer f o r planning and con-t r o l and research i n t o b e t t e r management and u t i l i z a t i o n of s t r u c t u r a l lumber resources. 98 CHAPTER 7 - REFERENCES [1.1] Madsen, B., "North American Grading P r a c t i c e and In-grade T e s t i n g , " P r o c , Wood Engineering Group, I n t e r n a t i o n a l Union of F o r e s t r y Research Organizations, Japan, August 1981. [1.2] Madsen, B., "Parameters A f f e c t i n g the E f f i c i e n c y of Mechanical Grad-i n g , " Proc., Wood Engineering Group, I n t e r n a t i o n a l Union of F o r e s t r y Research O r g a n i z a t i o n s , Oxford, United Kingdom, A p r i l 1980, pp. 175-192. 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[2.24] K i n g , R.J., "Microwave Electromagnetic Nondestructive T e s t i n g o f Wood," Proc. 4th Nondestructive T e s t i n g of Wood Symposium, Vancouver, Washington, August, 1978. [3.1] Nyss, M.L., " M i l l i m e t r e PIN Diode C o n t r o l Devices," Agard Conf. Proc. No. 245, NATO, Feb., 1979. [3.2] Norman, C.B., "High Frequency Microwave Switch," Systems Lab. Report, A p r i l 1980, Dept. of E l e c t r i c a l E ngineering, U n i v e r s i t y of B r i t i s h Columbia. [3.3] C h a f f i n , R.J., "Microwave Semiconductor Devices: Fundamentals and Ra d i a t i o n E f f e c t s , " pp. 190-192, John Wiley & Sons. 1973. [3.4] M a t t h a e i , G.L., Young, L and Jones, E.M.T.: Microwave F i l t e r s , Impedance Matching Networks and Coupling S t r u c t u r e s , " McGraw H i l l , New York, 1964. Ch. 6. [3.5] R e i c h , R.J., Ordung, P.F., Krauss, H.L., and S k a l n i k , J.G.: Microwave Theory and P r a c t i c e , pp. 285-287, D. Van Nostrand, New York, 1953. f3.6] Brown, J . , and Jones, S.S.D., "Microwave Lenses," E l e c t r o n i c Engineering, A p r i l , 1950, pp. 127-131. [3.7] Schelkunoff, S.A., and F r i i s , H.T.: Antennas Theory and P r a c t i c e , John Wiley and Sons, New York, 1952. [4.1] I n t e r s i l 8038 P r e c i s i o n Waveforraer Generator/Voltage C o n t r o l l e r O s c i l l a t o r Data Sheet, I n t e r s i l , I n c . , Cupertino, C a l i f . [4.2] DS7830/DS8830 Dual D i f f e r e n t i a l L ine D r i v e r Data Sheet, N a t i o n a l Semiconductor Corp., Santa C l a r a , C a l i f . [4.3] A p p l i c a t i o n Note: AN-49 PIN Diode D r i v e r s N a t i o n a l Semiconductor Corp., Santa C l a r a , C a l i f . [4.4] Burton, R.W., "A C o a x i a l A m p l i t u d e - I n s e n s i t i v e Phase-Detection System," Microwave J . , A p r i l , 1964, pp. 51-53. 101 [4.5] Jaggard, D.L., and K i n g , R.J.: " S e n s i t i v i t y and Dynamic Range Considerations f o r Homodyne Detection Systems," IEEE Trans., 1973, IM-22, ( 4 ) , pp. 331-338. [4.6] LH0038/LJ0038C True Instrumentation A m p l i f i e r Data Sheet, N a t i o n a l Semiconductor Corp., Santa C l a r a , C a l i f . [4.7] AF150 U n i v e r s a l Wideband A c t i v e F i l t e r Data Sheet, N a t i o n a l Semiconductor Corp., Santa C l a r a , C a l i f . [4.8] DG180-DG191 High Speed D r i v e r w i t h JFET Switches, I n t e r s i l , I n c . , Cupertino, C a l i f . [4.9] LH0091 True RMS to DC Converter Data Sheet, N a t i o n a l Semiconductor Corp., Santa C l a r a , C a l i f . [5.1] Roberts, S., and von H i p p e l , A., "A New Method f o r Measuring, D i e l e c t r i c Constant and Loss i n the Range of Centimeter Waves," Jo u r n a l of Applied P h y s i c s , v o l . 17, J u l y 1946, pp. 610-616. [8.1] C o l l i n , R.E.: F i e l d Theory of Guided Waves, McGraw-Hill, New York, 1960, Ch. 3. 102 CHAPTER 8 - APPENDICES 8.1 Wave M a t r i x A n a l y s i s The wave matrix [8.1] i s given by (see F i g . 8.1) " l / T 1 2 -R 2/T 1 2 c 2 [A] c 2 I _b2 . b2 where C j , b 2 and b j , c 2 are the i n c i d e n t and r e f l e c t e d waves r e s p e c t i v e l y ; R and T are the r e f l e c t i o n and tr a n s m i s s i o n c o e f f i c i e n t s r e s p e c t i v e l y . From F i g . 8.1, [A] i s given by (8.2) [A] ( z - l ) / 2 z (z+l)/2z (z+l)/2z ( z - l ) / 2 z For the case of a s l a b of d i e l e c t r i c i n free-space ( F i g . 8.2), l / T 1 9 -R 2/T 1 2 12 R x / T 1 2 T 2 r R l R 2 ^ T 1 2 . (z+l)/2z ( z - l ) / ( 2 z ) ( z - l ) / 2 z ( z + l ) / ( 2 z ) ~ e j G 0 0 - j e (z+l)/2 - ( z - l ) / 2 - ( z - l ) / 2 (z+l)/2 where 6= 3£ = e l e c t r i c l e n g t h of d i e l e c t r i c , 7, = normalized impedance of d i e l e c t r i c . (z+1) -(z-1) 1_ 4z ( z + l ) e j G ( z - l ) e - j G ( z - l ) e j G ( z + l ) e ~ i G -(z-1) (z+1) 1_ 4z ( z + l ) 2 e j 0 - ( z - l ) 2 e _ ; j Q ( z 2 - l ) e j 0 - ( z 2 - l ) e - j G - ( Z 2 - l ) j G + ( z 2 - l ) e j G ' - ( z 2 - l ) e j 0 + ( z + l ) 2 e ~ j G F i g . 8 . 1 . R e f l e c t e d a n d t r a n s m i t t e d w a v e s a t a d i s c o n u i t y i n t e r f a c e . 104 F i g . 8.2. D i e l e c t r i c s l a b d i s c o n u i t y . using ( e j 0 + e ~ j 0 ) = 2cosQ and ( e J 0 - e ~ j 0 ) = 2 j s i n 0 " ( z ^ D t e ^ - e - ^ ^ z t e J 0 ^ 0 ] ( 2 2 - l ) [ e - i 0 - e ^ 0 ] _ ( z 2 + 1 ) [ e 3 0_e-3 0 ] + 2 z [ e J e ^ - j G ] j sinQ(z 2KL)+cosQ 2z j s i n G ( z 2 - l ) 2z - j s i n G ( z 2 - l ) 2z - j s i n G ( z ^ l ) 2z +cosG 8.3 106 8.2 Computer program l i s t i n g s of WOOD and FSPACE 1 c 2 C T H I S PROGRAM I S WRITTEN BY EDWIN K . L . L E E SUMMER 8 0 * * * * * * * * * * * * * * * * * * * * 3 C * * * * • * * • * + * + * * • * * * » * + + * * • • * * • + » * * * * » * + * * * * * • * * * * * • * * 4 C * * s c $ WOOD * 6 C T H I S PROGRAM I S D E S I G N E D FOR F I N D I N G THE COMPLEX R E L A T I V E * ft 7 C P E R M I T T I V I T I E S OF S U 3 S T A N C E S . * * * * * * * * * * * * * * * * * * * * 8 C THE ALGORITHM OF T H I S PROGRAM I S AS FOLLOWS: 9 C 1 ) I T S T A R T S WITH AN I N I T I A L E S T I M A T E OF THE ROOT(COMPLEX 10 C R E L A T I V E P E R M I T T I V I T Y ) . 11 C 2 ) F 0 U R P O I N T S ARE GENERATED AROUNO T H I S BASE P O I N T . 12 C 3 ) T H E ABSOLUTE F U N C T I O N VALUE I S EVALUATED AT THESE F I V E 13 C P O I N T S 5 THE POINT WITH MINIMUM ABSOLUTE F U N C T I O N VALUE 14 C BECOMES THE NEXT BASE POINT U N T I L ONE OF THE T E R M I N A T I O N 15 C R U L E S I S S A T I S F I E D . 16 C 4 )BEFORE T E R M I N A T I O N . O N E .OR MORE S T E P S ARE T A K E N P L A C E . E A C H 17 C STEP I N C R E A S E S THE ACCURACY BY 10 T I M E S U N T I L REQUIRED• 18 C TOLERANCE I S S A T I S F I E D . 19 C T E R M I N A T I O N R U L E S : 2 0 C A )THE R E O U I R E D T O L E R A N C E . I S S A T I S F I E D . 21 C B ) A B A S E POINT AT A C E R T A I N STAGE BECOMES A B A S E P O I N T P E R -2 2 C M A N E N T L Y . 2 3 C C ) T H E NUMBER OF I T E R A T I O N S EXCEEDS THAT S P E C I F I E D BY M A X I T . 2 4 C 2 5 C I N P U T : 2 6 C D N U M B E R OF ROOTS WANTEDt » < 2 0 ; I F > 2 0 . RESET D I M E N S I O N 2 7 C OF A L L THE A R R A Y S IN THE MAIN P R O G R A M . ) 28 C 2 ) P A R A M E T E R S : F R E Q U E N C Y ( F ) , S T A N D I N G - W A V E - R A T I 0 ( S ) , 2 9 C L M I N ( A L M I N ) , L E N G T H - O F - S U B S T A N C E ( T ) . 3 0 C 3 ) A R R A Y OF I N I T I A L E S T I M A T E S OF THE R O O T S . T H E NUMBER OF 31 C ELEMENTS OF T H I S ARRAY MUST BE >= NUMBER OF ROOTS. 32 C 4 ) T H E BREADTH OF THE W/G ' A ' I S TO BE SET I N THE PROGRAM. 3 3 C N . B . READ THE PROGRAM FOR THE INPUT FORMAT. 34 C 3 5 C OUTPUT : 3 6 C D P R I N T S OUT P A R A M E T E R S READ & SET I N THE PROGRAM. 3 7 C 2 ) E C H 0 E S THE I N I T I A L E S T I M A T E . 3 8 C 3 ) P R I N T S THE ROOT FOUND. 3 9 C 4 ) ' S 0 L N ' SHOWS WHETHER THE ROOT FOUND S A T I S F I E D THE T O L -4 0 C ERANCE R E Q U I R E D . 4 1 C 5 ) T H E FUNCT ION I S EVALUATED AT THE ROOT FOUNO WHICH G I V E S 4 2 C THE ERROR D I F F E R E D FROM THE VALUE ZERO WHICH SHOULD BE 4 3 C THE C A S E IF THE FUNCT ION I S EVALUATED AT TRUE ROOT. 44 C G ) ' A O O ' S H O W S THE A P P R O X I M A T E AVERAGE RATE OF CHANGE OF THE 4 5 C ABSOLUTE F U N C T I O N VALUE W . R . T . THE ARGUMENT AND I S USEO 4 6 C TO MODIFY THE T E R M I N A T I O N C O N D I T I O N ACCORDING TO THE 4 7 C F U N C T I O N B E H A V I O R AROUND THE BASE P O I N T , 4 8 C 4 9 C COMMENTS ON THE P O S S I B L E O U T P U T S : 5 0 C D ' S O L N " I S T BUT MAX IT NOT EXCEEDED MEANS F I N E R E S U L T , 51 C EXCEPT WHEN THE IMAGINARY PART OF ROOT FOUND I S P O S I - . 52 ' C T I V E ( R E M E D Y : T R Y I N I T I A L E S T I M A T E WITH IMAGINARY PART 5 3 C MAGNITUDE B I G G E R THAN A N B H ) . 54 C 2 ) ' S 0 L N ' I S F GUT M A X I T NOT E X C E E D E D . I T P R 0 8 A B L Y MEANS 5 5 C THE BASE POINT ENDS UP I N A B A S I N OR P L E A T E A U ABOVE 5 6 C Z E R O . B U T S O M E T I M E S I F THE ERROR I S S M A L L . I T MAY MEAN 5 7 C THERE E X I S T S AN UNDETECTED ROOT N E A R B Y . 5 8 C R E M E D Y : B I G ERROR > 1 0 0 « E P . U S E BETTER E S T I M A T E 5 9 C SMALL ERROR < 1 0 0 « E P . U S E THE POINT ROOT FOUND 6 0 C AS I N I T I A L E S T I M A T E & REDUCE ' E P ' BY 1 0 - 1 0 0 5 1 C T I M E S . 6 2 C 3 ) M A X I T EXCEEDED WITH ' S O L N ' T MEANS TOLERANCE I S S A T -6 3 c I S F I E D IN THE P R E C E E D I N G S T E P , B U T BECAUSE THE S L O P E 6 4 c I S SO GENTLE THAT I N THE CURRENT S T E P , T H O U G H MAXIT 6 5 c I T F R A T I O N S ARE T A K E N , T H E B A S E POINT CANNOT REACH THE 6 S c ROOT. 67 c R E M E D Y : U S E THE POINT ROOT FOUND AS I N I T I A L E S T I M A T E . 6 8 c 4 ) M A X I T EXCEEDED WITH ' S O L N ' F MEANS THE BASE POINT WAS 6 9 c T R A P P E D IN A ' B A S I N ' IN THE P R E C E E D I N G S T E P BUT I N 7 0 c THE CURRENT S T E P , I T COMES OUT THROUGH A P A T H . B U T IT 71 c CANNOT REACH THE ROOT WITHIN MAXIT I T E R A T I O N S . 7 2 c R E M E D Y : B E T T E R I N I T I A L E S T I M A T E . 7 3 c 5 ) M A X I T EXCEEDED WITH ' S O L N ' U MEANS THE I N I T I A L E S T I -74 c MATE I S SO FAR AWAY FROM THE ROOT THAT EVEN IN THE 7 5 c F I R S T S T E P THE MAX IT I S E X C E E D E D . 7 6 c R E M E D Y : B E T T E R I N I T I A L E S T I M A T E . 77 c ' A D J ' S ' E R R O R ' A L W A Y S G I V E U S E F U L INFORMATION TO MAKE WISE C H O I C E . 7 8 c IF ' E R R O R ' HAS A B I G V A L U E , T H E N IT I S BETTER TO CHANGE THE I N I T I A L 7 9 c E S T I M A T E . B I G ' A D J ' MEANS R A P I D CHANGE OF BEHAVIOR AROUND THE POINT 8 0 c R O O T ' F O U N D ( I E . T H E SLOPE NEARBY I S S T E E P : T H E R E F O R E SOMETIMES EVEN 8 1 c WHEN THE ERROR > E P . T H E R E S U L T I S S T I L L GOOD IF IT I S OUTPUT C A S E 8 2 c 1) WITH B I G ' A D J ' ) . 8 3 c 8 4 c 8 5 c PROGRAM P A R A M E T E R S : 8 6 c 1 ) E P - T O L E R A N C E REQUIRED 8 7 c 2 ) A N B H - T H E D I S T A N C E BETWEEN THE BASE POINT AND THE GENERA TED 8 8 c P O I N T S I N THE F I R S T S T E P . ( S E T A N B H » 0 . 5 N O R M A L L Y ) 8 9 c 3 ) M A X I T - M A X I M U M NUMBER OF I T E R A T I O N S ALLOWED I N E A C H S T E P 9 0 c (NORMALLY SET IT TO 10O) 9 1 c 9 2 c 9 3 c 9 4 c M A I N PROGRAM STARTS H E R E . 9 5 c 9 6 I M P L I C I T R E A L * 8 ( A - H , 0 - Z ) 9 7 E X T E R N A L FN 9 8 C O M P L E X ' 1 6 Z I ( 2 O ) , Z 0 ( 2 O ) , W , F N , O C M P L X 9 9 COMMON F , S , A L M I N . T , A , B S P A C E , W , P I 1 0 0 L O G I C A L S O L N ( 2 0 ) , M X I T ( 2 0 ) 101 R E A L * 8 E R R O R ( J O ) , A D ( 2 0 ) 102 c 103 ' c READ & SET INPUT PARAMETERS 104 c 105 c READ NUMBER OF ROOTS 106 c 107 R E A D ( 5 . 5 ) NR 108 5 FORMAT( I X , I 2 1 109 • c 1 10 c ' F ' I S THE FREQUENCY 1 1 1 c ' S ' I S THE STANDING WAVE R A T I O 1 12 c ' A L M I N ' I S THE MINIMUM I N A I R N E A R E S T TO THE WOOD 1 13 c *T' I S THE LENGTH OF THE WOOD 1 14 . c ' A ' I S THE BREADTH OF THE RECTANGULAR W/G 1"15 c 1 1 6 R E A D ( 5 , G ) F , S , A L M I N , T 117 6 F O R M A T ( 4 ( 1 X , D 1 1 . 4 ) ) 118 c 1 1 9 c 1 2 0 A - 7 . 1 1 2 D - 3 121 PI=3.141592654 122 BSPACE=2*PI -F/3 .0D8 123 Bl=OSQRT(BSPACE**2-(PI/A)**2) 124 W"DCMPLX(-S'DTAN(B1«ALMIN).-1.D0)/(B1*T)/DCMPLX(S,-DTAN(B1*ALMIN)) 125 C 12G C READ INITIAL ESTIMATES OF COMPLEX RELATIVE PERMITTIVITY 127 C 128 DO 200 IN=1 ,NR 129 READ(5 ,7 ) Z I ( IN) 130 ZO(IN)=ZI( IN) 131 7 F 0 R M A T ( 2 ( 1 X . F G . 2 ) ) 132 200 CONTINUE 133 C 134 C SET PROGRAM PARAMETERS 135 C 136 ANBH=0.1 137 E P " 1 . D - 7 138 MAXIT=100 139 C 140 C DCMFCN IS CALLED 14 1 C 142 CALL DCMFCN(FN,NR,ZO ,ANBH,EP ,SOLN,ERROR,MAXIT,MX IT,AD) 143 C 144 C RESULTS ARE PRINTED 145 C 146 W R I T E(6 . 6 7 ; F,S,ALMIN,T 147 67 FORMAT('F«',D10.4,3X.'S"'.010.4,3X,'ALMIN"',010.4.3X.'T«*.010.4) 148 WRITE(G,69) A 149 69 F O R M A T ( ' A = ' , 0 1 0 . 4 ) 150 WRITE(6.60) ANBH.EP,MAX IT -151 68 FORMATf'ANBH'',08.2.3X.'EP»',08.2,3X.'MAXIT"',14) 152 WRITE(6 ,2) 153 2 F0RMAT(4X . ' IN IT IAL GUESS'.11X.'ROOT FOUND'.7X,'SOLN ERROR AOd') 154 DO 300 10 -1 ,NR 155 IF ( .NOT. MXIT(IO)) GOTO 310 156 WRITE(6 .51) MAXIT 157 51 FORMAT('NUMBER OF ITERATIONS EXCEEDS MAXIT*',15) 158 310 WRITE(6 ,4) ZI(10),ZO(10),SOLN(10),ERROR(10).AD(10) 159 4 F0RMAT(2D11.3 .2D12.4,1X.L1 ,209.2) 160 300 CONTINUE 161 STOP 1C2 END 163 C 164 C 165 C MAIN PROGRAM ENDS HERE. 1C6 C 167 C 168 SUBROUTINE DCMFCN(FN.NR,Z.ANBH,EP,SOLN.ERROR,MAXIT,MXIT,AD) 169 IMPLICIT REAL*8(A -H,0 - Z ) 170 C0MPLEX'16 Z(NR).ZB.FCN1,FCN2,DCMPLX.FN.FCNX(2),FCNY(2) 171 R E A L ' 8 ERROR(NR),AD(NR) 172 R E A L M SNGL, AL0G1O.G 173 LOGICAL S0l.N( NR ), MXIT(NR ) , ACC. FLAOIT 174 C 175 C BEGIN 176 C fc" 177 G»SNGL(ANBH/(EP*1.00100)) ' ' S 178 N » I N T ( A L 0 G 1 0(G))+2 179 00 11 M-1.NR 180 ZB*Z(M) 181 F C N 1 « F N ( Z 3 ) 182 F C N 2 = F N ( Z B + D C M P L X (1 . D O .1 . D O ) ) 183 A D J = C O A B S ( F C N 1 - F C N 2 ) / 0 S Q R T(2 . 0 O ) 184 DO 10 I = 1 , N 185 T O L = ( A N B H / 1 0 . * * ( I - 1 ) ) 186 TCLP=TOL*ADU 187 C A L L S O L V E ( F N . Z B , T O L , T O L P , A C C , E M I N , F C N X , F C N Y . M A X I T , F L A G I T ) 188 I F ( F L A G I T ) GOTO 12 189 A O J M C D A B S ( F C N X ( 1 ) - F C N X(2 ) ) + C D A B S ( F C N Y ( 1 ) - F C N Y (2) ) )/(4 . *TOL) 1 9 0 10 CONTINUE 191 12 S O L N ( M ) = A C C 192 E R R O R ( M ) » E M I N 193 Z ( M ) = Z B 194 M X I T ( M ) * F L A G I T 195 A D ( M ) - A D J 196 11 CONTINUE 197 RETURN 198 END 199 C 2 0 0 C 2 0 1 C 2 0 2 SUBROUTINE S O L V E ( F N , Z B , T O L , T O L P , A C C . E M I N , F C N X , F C N Y . M A X I T . F L A G I T ) 2 0 3 I M P L I C I T R E A L * 8 ( A - H , 0 - Z ) 2 0 4 C 0 M P L E X * 1 6 Z B . F N , 0 C M P L X , F C N X ( 2 ) , F C N Y ( 2 ) , Z B X ( 2 ) . Z B Y ( 2 ) 2 0 5 L O G I C A L A C C , F L A G I T 2 0 6 C 2 0 7 C 2 0 8 F L A G I T - . F A L S E . 20D E M I N = C D A B S ( F N ( Z B ) ) 2 1 0 ' I F ( E M I N . L E . T O L P ) GOTO 101 2 1 1 X = D R E A L ( Z B ) 2 1 2 Y = D I M A G ( Z B ) 2 13 M A X I T P ' M A X I T 2 1 4 1 4 0 XP = X 2 1 5 YP = Y 2 1 6 M A X I T P = M A X I T P -1 2 1 7 IF ( M A X I T P . L T . 0 ) GOTO 130 2 18 O X = X P - T O L 2 1 9 O Y = Y P - T O L 2 2 0 DO 1 1 0 I X - 1 , 2 2 2 1 D X X = D X + T 0 L*2.* D F L 0 A T ( J X-1) 2 2 2 Z B X ( I X ) * D C M P L X ( O X X , Y P ) 2 2 3 F C N X ( I X ) « F N ( Z B X ( I X ) ) 2 2 4 E R R = C D A B S ( F C N X ( I X ) ) 2 2 5 IF (ERR . G E . E M I N ) GOTO 110 2 2 6 EMIN=ERH 2 2 7 X=DXX 2 2 8 Y = YP 2 2 9 110 CONTINUE 2 3 0 DO 1 6 0 IY>1,2 2 3 1 D Y Y = D Y + T 0 L*2 . * 0 F L 0 A T ( I Y-1) 2 3 2 Z B Y ( I Y ) » D C M P L X ( X P , D Y Y ) 2 3 3 F C N Y ( I Y ) = F N ( Z B Y ( I Y ) ) 2 3 4 E R R - C D A B S ( F C N Y ( I Y ) ) 2 3 5 IF (ERR . G E . E M I N ) GOTO 1 6 0 2 3 6 EMIN=ERR 2 3 7 X=XP 2 3 8 Y C D Y Y 2 3 9 160 CONTINUE 2 4 0 I F ( ( X . E O . X P ) . A N D . ( Y . E O . Y P ) ) GOTO 1 2 0 241 IF (EMIN .GT . TOLP) GOTO 140 242 ACC = .TRUE. 243 ZB*DCKPLX(X,Y) 244 GOTO 100 245 120 A C C ' . F A L S E . 246 GOTO 100 247 101 ACC* .TRUE. 248 GOTO 100 249 130 FLAGIT* .TRUE. 250 ZB=DCMPLX(X.Y) 251 100 CONTINUE 252 RETURN 253 ENO 254 C 255 C 256 C 257 FUNCTION FN(Z) 258 IMPLICIT R E A L * 8 ( A - H , 0 - Z ) 259 C0MPLEXM6 Z , TZ , CDCOS .DCMPLX. W, COSIN, FN. GAMMAT 2G0 COMMON F . S . A L M I N , T , A , B S P A C E , W . P I 261 G A M M A T « T * ( C D S 0 R T ( ( P I / A ) * » 2 - B S P A C E * * 2 * Z ) ) 262 TZ 3 DCMPLX(O.DO,1.DO)*GAMMAT 263 F N » ( ( C 0 C 0 S ( T Z ) / C D S I N ( T Z ) ) * D C M P L X ( O .00.-1 . D O ) / G A M M A T ) - W 264 RETURN 265 END End of F i l e 1 C THIS PROGRAM HELPS FIND THE PEL . COMPLEX PERMITTIVITY OF * * * * * * * * * * * * * * * * * * * * 2 C DIELECTRIC SLAB IN FREE SPACE BY INPUTTING FREQUENCY,TRANS- £ £ 3 C MISSION/REFLEXION C O E F F . , I N C . A N G L E & TWCKNESS OF DIELECTRIC. 5 - p C D A r ' T ? 2 4 C * FS P A C E £ 5 C * , , , , , , , * S C THE ALGORITHM OF THIS ROUTINE IS AS FOLLOWS: * * * * * * * * * * * * * * * * * * * * 7 C 1)IT STARTS WITH AN INITIAL ESTIMATE OF THE ROOT. 8 C 2)rOUR POINTS ARE GENERATED AROUND THIS BASE POINT. 9 C 3)THE FUNCTION VALUE IS EVALUATED AT THESE FIVE POINTS 8 THE 10 C POINT WITH MINIMUM VALUE IS SOUGHT WHICH BECOMES THE NEXT 11 C BASE POINT UNTIL ONE OF THE TERMINATION RULES IS SAT ISF IED. 12 C 4 JBEFORE TERMINATION,ONE OR MORE STEPS ARE TAKEN PLACE.EACH 13 C STEP INCREASES THE ACCURACY BY 10 TIMES UNTIL REQUIRED 14 C TOLERANCE IS SATISFIED. 15 C TERMINATION RULES: 1G C A)THE REQUIRED TOLERANCE IS SATISFIED. 17 C B)THE NUMBER OF ITERATIONS EXCEEDS THAT SPECIFIED BY MAXIT. 18 C 19 C INPUT: 20 C O)T0LP(7.):'/. DEVIATION OF RM/RC OR TM/TC FROM 1 21 C 1 )FREQ(GHZ) 22 C 2)TXN:AMPL.0F TX COEFF. 23 C 3)RXN:AMPL.0F RX COEFF. 24 C 4)THI (0 -90DEG) : INCIDENT ANGLE 25 C 5)D(CM):TH1CKNES5 OF DIELECTRIC 2G C 6)NUM3ER OF ROOTS WANTED(=<20;IF >20,RESET DIMENSION 27 C OF ALL THE ARRAYS IN THE MAIN PROGRAM.) 28 C 7)ARRAY OF INITIAL ESTIMATES OF THE ROOTS.THE NUMBER OF 29 C ELEMENTS OF THIS ARRAY MUST BE > » NUMBER OF ROOTS. 30 C INPUT FORMAT: 3 1 C [ 0 . 1 0 0 (TOLP 32 C [ 0 3 4 . 8 0 (FREQ ^ 33 C 1 0.119D+00 0.2G3D+00 0 0 . 0 0 01.30 (TXN.RXN.THI,D 34 C [ 1 0 (NR 35 C [ +02.54 - 0 0 . 0 0 {EPC ESTIMATE 3G C 37 C OUTPUT: 38 C 1(WRITE INPUT » SET PARAMETERS 39 C 2)ECHOES THE INITIAL ESTIMATE. 40 C 3)PRINTS THE ROOT FOUND. 41 C 4)THE FUNCTION IS EVALUATED AT THE ROOT FOUND WHICH GIVES 42 C THE ERROR DIFFERED FROM THE VALUE ZERO WHICH SHOULD BE 43 C THE CASE IF THE FUNCTION IS EVALUATED AT TRUE ROOT. 44 C 45 C COMMENTS ON THE POSSIBLE OUTPUTS: 46 C IF ERROR DOES NOT HAVE THE MAGNITUDE OF THE ORDER COM-47 C PARABLE TO THAT OF THE TOLERANCE EP, THEN THE RESULT 48 C 'SHOULO NOT BE TRUSTED. 49 C 50 C 51 C PROGRAM PARAMETERS: 52 C 1 )EP-TOLERANCE REOUIREO [I.OD-i**] 53 C 2 JANBH-THE DISTANCE BETWEEN THE BASE POINT AND THE GENERATED 54 C POINTS IN THE FIRST STEP.<SET ANBH»1.0 NORMALLY) 55 C 3)MAXIT-MAXIMUM NUMBER OF ITERATIONS ALLOWED IN EACH STEP 56 C (NORMALLY SET IT TO 100) 57 C l_i 58 C ' M 59 C N> 60 C MAIN PROGRAM STARTS HERE, 61 C 62 IMPLICIT REAL*B(A-H.O-Z) 63 EXTERNAL FN,DABS 64 COMPLEX*16 Z I ( 2 0 ) , Z O ( 2 0 ) 65 COMMON TXRCP.RXRCP.COSTH.SINQTH.D.KO 66 LOGICAL S0LN(2O),MXIT(20) 67 REAL '8 ERROR(20),FN,TXN,RXN 68 C 69 C READ INPUTS (FREO,TNX,RNX,THI,D) 70 C 71 READ(5 ,50) TOLP 72 50 FORMAT(1X .F5.3) 73 READ(5 ,51) FREO 74 51 FORMAT(1X,F6 .2) 75 . READ(5 .6 ) TXN,RXN,THI ,D . 76 6 F0RMAT(2(1X.09.3) ,2(1X.FB.2)) 77 C 78 C ECHO THE ABOVE INPUTS 79 C 80 WRITE(6,49) TOLP 81 49 FORMAT( ' TOLPC/.)*' ,F5.3) 82 WRITE(6,52) FREO 83 52 FORMAT( ' FRE0(GHZ)*>' , 1X.F6.2) 84 WRITE(6,67) TXN,RXN,THI,D 85 C7 FORMAT(' T X N ' ' , 0 9 . 3 , ' RXN"'.09.3,' THI(DEG)•'.F5.2. 86 D ( C M ) * ' , F 5 . 2 ) 87 C 88 c CONSTANT CALCULATION 89 c 90 T0LP=T0LP*0.01 91 PI=3.141592653GDO 92 K0= 2 4 PI * FREO/30.0 93 TXRCP=1.0/1XN 94 RXRCP=1.O/RXN 95 T H I " T H I « P I / 1 B 0 96 COSTH'0COS(THI) 97 SIN0TH=(0SIN(THI))""2 98 c 99 c INPUT # OF ESTIMATES & ESTIMATES OF EPC 100 c 101 READ(5 ,5) NR 102 5 FORMAT(1X,I 2) 103 DO 200 !N=1,NR 104 READ(5 ,7 ) Z I ( IN) 105 ZO(IN)=ZI( IN) 106 7 FORMAT(2(1X.F6.2)) 107 200 CONTINUE 103 C 109 C SET & WRITE PROGRAM PARAMETERS 1 10 C 1 1 1 ANBH=0.2 1 12 EP-1.0-7 1 113 MAXIT=200 1 14 WRITE(6,68) ANBH,EP,MAXIT 115 68 FORMATC ANBH"',D8.2.2X.'EP»'.08.2.2X.'MAXIT"',14) 1 16 C 117 C DCMFCN IS CALLED 118 c CALL DCMFCN(FN,NR,ZO,ANBH,EP,SOLN,ERROR,MAX IT,MXIT,TOLP) 1 19 120 c 121 C R E S U L T S ARE P R I N T E D 122 C 123 W R I T E ( 6 , 2 ) 12-1 2 F 0 R M A T ( 4 X . ' I N I T I A L GUESS',11X,'ROOT FOUND',7X,'SOLN ERROR') 125 DO 3 0 0 10=1,NR 12G IF ( . N O T . M X I T ( I O ) ) GOTO 310 127 W R I T E ( 6 , 5 5 ) MAXIT 128 5 5 F O R M A T ( ' N U M B E R OF I T E R A T I O N S EXCEEDS MAXIT"',15) 129 3 1 0 W R I T E ( 6 , 4 ) Z I ( I0) ,Z0( I0),SOLN(IO),ERR0R(IO) 1 3 0 4 F O R M A T ( 2 D 1 1 . 3 , 2 D 12.4,1X.L1.D9.2) 13 1 3 0 0 CONTINUE 132 STOP 133 END 134 C 135 C 136 C M A I N PROGRAM ENDS H E R E . 137 C 13B C SUBROUTINE DCMFCN(FN.NR.Z,ANBH,EP,SOLN,ERROR.MAXIT.MXIT.TOLP) 139 1 4 0 I M P L I C I T R E A L * 8(A - H,0 - Z ) 141 C 0 M P L E X * 1 6 Z ( N R ) . Z B . D C M P L X 142 R E A L * 8 E R R O R ( N R ) 143 R E A L * 4 S N G L , A L O G 1 0 ,G 144 L O G I C A L SOLN(NR),MXIT(NR).ACC.FLAGIT 145 C 146 C SET UP U OF S T A G E S 147 C 148 G = S N G L ( A N B H / ( E P * 1 . 0 0 1 D O ) ) 149 N = I N T ( A L 0 G 1 0 ( G ) ) + 2 1 5 0 DO 11 M=1,NR 151 Z B * Z ( M ) 152 c 153 c I N C . OF STAGE WITH EACH INC. OF I 154 • c 155 DO 10 1 - 1 .N 106 T U L - ( A N B H / 1 0 . * * ( I - O ) 157 C A L L SOLVE(FN.ZB.TOL,TOLP.ACC.EMIN,MAXIT.FLAGIT) 158 IF ( F L A G I T . O R .ACC) GOTO 12 159 10 CONTINUE 1 6 0 c 161 c T E R M I N A T I O N 1G2 c 163 12 SOLN(M)=ACC 164 E R R O R ( M ) = E M I N 165 Z ( M ) « Z B 166 M X I T ( M ) " F L A G I T 167 11 CONTINUE 160 RETURN 169 END 1 7 0 C 171 C 172 173 c S U B R O U T I N E SOLVE(FN,ZB.TOL.TOLP.ACC.EMIN,MAXIT,FLAGIT) 174 I M P L I C I T REAL'B(A-H.O-Z) 175 C O M P L E X M G Z B . D C M P L X , ZBX(2) ,ZBY(2) 176 REAL*8 FN,FCNX(2),FCNY(2) 177 L O G I C A L ACC,FLAGIT 178 c 1 7 9 c 180 FLAGIT" .FALSE. 181 EMIN*DABS(FN(Z6)) 182 IF (EMIN .LE .TOLP) GOTO 101 183 X=DREAL(ZB) 184 Y*DIMAG(ZB) 185 MAXITP'MAXIT 18S 140 XP = X 187 YP"Y 188 C 189 C CHECK MAXIT 190 C 191 MAXITP=MAXITP-1 192 IF (MAXITP . L T . 0) GOTO 130 193 DX-XP-TOL 194 DY=YP-TOL 195 C 19S C GENERATE 2 NEIGHBOURING POINTS ALONG X OIRECTION 197 C 198 00 110 IX=1,2 199 0XX*0X+T0L '2 .*DFL0AT( IX -1 ) 200 ZBX(IX)=DCMPLX(DXX,YP) 201 F C N X ( I X ) ' F N ( Z B X ( I X ) ) 202 ERR*DABS(FCNX(IX)) 203 IF !ERR . G E . EMIN) GOTO 110 204 EMIN'ERR 205 X*DXX 20S Y = YP 207 110 CONTINUE 208 C 209 C GENERATE 2 NEIGHBOURING POINTS ALONG Y OIRECTION 210 C 211 DO 160 I Y » 1 , 2 . 212 D Y Y = D Y + T 0 L » 2 . * D F L 0 A T ( I Y - 1 ) 213 ZBY( IY) -OCMPLX(XP.DYY) 214 FCNY(1Y)=FN(ZBY( IY) ) 215 ERR=OABS(FCNY(IY)) 216 IF (ERR . G E . EMIN) GOTO 160 217 EMIN=ERR 218 X 'XP 2 19 Y = DYY 220 160 CONTINUE 22 1 C 222 C IF THE BASE POINT IS STUCK FOR THE CURRENT TOL 223 C THEN PROCEED TO THE NEXT STAGE. 224 C ELSE REPEAT THE PROCESS WITH THE NEW BASE POINT. 225 C 226 IF ((X .EO . XP ) .AND. (Y .EQ . YP) ) GOTO 120 227 IF (EMIN.GT.TOLP) GOTO 140 228 A C C . TRUE. 229 ZB*DCMPLX(X.Y) 230 GOTO 100 231 120 A C C * . F A L S E . 232 GOTO 100 233 101 ACC*.TRUE. 234 GOTO 100 235 130 FLAGIT* .TRUE. 236 ZB*DCMPLX(X.Y) 237 100 CONTINUE H" 238 RETURN H 1 239 END ^ 241 C 242 C 243 FUNCTION FN(EPC) 244 IMPLICIT R E A L * 8 ( A - H , 0 - Z ) 245 COMPLEX*16 Z .CDCOS.DCMPLX.CDSIN,EPC,TMSTR1,Z2 24S COMPLEX*16 BETA,BETO,UT,VT,WWT,UR,VR.WWR 247 COMMON TXRCP.RXRCP.COSTH.SINQTH.D.KO 248 TMSTR1-CDSQRT(EPC-SINQTH) 249 BETA=K0'TMSTR1 250 Z=C0STH/TMSTR1 251 BETD=BETA*D 252 • UT=C0C0S(BET0) 253 V T M ( 1+Z**2)*CDSIN(BETO)/(2.0*Z))*DCMPLX(O.DO, 1.00) 254 WWT^UT+VT 255 Z2=Z**2 25G UR*(Z2+1)/(Z2-1) 257 VR=(2.0'Z*CDCOS(BETD)/(<1-Z2)*C0SIN(BETD)) )*DCMPLX(0 258 WWR=UR+VR 259 FN=CDABS(WWT)/TXRCP*CDABS(WWR)/RXRCP-1 260 RETURN 26 1 END 262 C 263 C 264 C 265 FUNCTION DABS(X) 266 IF (X . L T . 0 . 0 ) D A B S « - 1 . 0 » X 267 DASS'X 268 RETURN 269 END End o f F i l e 1 .DO) h-1 117 8.3 Strength (M.O.R) Results The homodyne system measurements and the modulus of rupture (M.O.R) t e s t r e s u l t s f o r board samples #01 to #19 corresponding t o F i g . 8.3 through F i g . 8.21 are given i n t h i s s e c t i o n . Each f i g u r e has the f o l l o w i n g s c a l e : y - a x i s : 3 cm : 1 v o l t , x - a x i s : 6.8 cm : 100 cm (d i s t a n c e along the board). The top chart gives the upper (U) scan which i s 3/4 inches from the top edge while the bottom chart shows the lower (L) scan which i s 1 1/2 inches from the top edge. The dark s o l i d trace shows the c r o s s - p o l a r s i g n a l w h i l e the l i g h t s o l i d t r a c e gives the RF phase s i g n a l . 118 i . 2. 3. 4. 5. Board - tOl Cause of Failure - Failure close to wide face knot, at edge, on tension side. Position of Failure at Knot: #2 Strength of Board (Modulus of Rupture, pal) 4063 Correlation between microwave measurements and location of weakest point of board - Positive: Cross-polar signal indicates steepest slope of grain 045°) and the phase signal indicates a large defective area near knot #2 in the mid-region of the board. 119 1. Board - #02 2. Cause of Failure • Failure close to vide face knot, at edge, on tension side. 3. Position of Failure at Knot: #4 4. Strength of Eoard (Modulus of Rupture, psi) - 7446 5. Correlation between microwave measurements and location of weakest point of board • Negative: The region around knot #3 eeems to be the weakest, as indicated from the chart recording. 120 1. Board • #03 2. Cause of Failure - Failure close to wide face knot, at edge, on tension side. 3. Position of Failure at Knot: #4 4. Strength of Board (Modulus of Rupture, psi) - 4642 5. Correlation between microwave measurements and location of weakest point of board - Positive: CroBs-polar signal shows steepest slope of grain (>45°) near knot 04 and phase signal indicates a large defective area near thiB knot in the mid-region of the board. 121 1. Board - tO'i 2. Cause of Failure - Failure close to narrow faced or spike knot, on tension side. * 3. Position of Failure at Knot: #3 4. Strength of Board (Modulus of Rupture, psi) - 3943 5. 1. Board , - #05 2. Cause of Failure - Failure close to narrow faced or spike knot, on tension side. 3. Position of Failure at Knot: #2 4. Strength of Board (Modulus of Rupture, psi) - 7640 5. Correlation between microwave measurements and location of weakest point of board - Positive: Cross-polar signal shows a large slope of grain (about 25*) and the phase signal indicates a medium-sized defective area In the mid-region of the board. L23 Board - #06 Cause of Failure - Failure close to narrow faced spiked knot, on tension side. 3. Position of Failure at Knot: #4 4. Strength of Board (Modulus of Rupture, psi) - 7972 5. Correlation between microwave measurements and location of weakest point of board - Positive: Cross-polar signal shows a large slope of J»J» (about 20*) and the phase signal indicates a large defective area in the raid-region of the board. 124 Board #07 Cause of Failure - Failure close to narrow faced spiked knot, on tension side. Position of Failure at Knot: 12 Strength of Board (Modulus of Rupture, psi) - 3220 Correlation between microwave measurements and location of weakest point of board » Positive: Cross-polar signal shows a large Elope of grain (about 30°) and the phase signal Indicates a large defective area in the mid-region of the board. 1. Board - #08 2. Cause of Failure - Failure close to narrow faced spiked knot, on tension side. 3. Position of Failure at Knot: #3 ' 4. Strength of Board (Modulus of Rupture, psi) - 5588 5. Correlation between microwave measurements and location of weakest point of board - Positive: Cross-polar signal Indicate a large slope of grain over a wide region near knot #3. 126 m m 1. Board - # 09 2. Cause of Failure - Failure close to narrow faced spike knot, on tension side. 3. Position of Failure at Knot: #3 A. Strength of Board (Modulus of Rupture, psi) - 7930 5. Correlation between microwave measurements and location of weakest point of board » Uncertain: - Cross-polar signal Indicates a large slope of grain and the phase signal shows a medium-size deffective area near knot #2. 1. Board - #10 2. Cause of Failure - Failure close to wise face knot, at edge, on tension side 3. Position of Failure at Knot: #3 4. Strength of Board (Modulus of Rupture, psl) — 5587 .5* Correlation between microwave measurements and location of weakest point, of board - Positive: Cross polar signal indicates a large slope of grain, (lower scan)* 128 tension side 3. Position of Failure at Knot: #4 4. Strength of Board (Modulus of Rupture, psl) - 6212 5. Correlation between microwave measurements and location of weakest point of board - Positive; Cross-polar shows a large slope of grain near knot #4 (both lower and upper scan). 129 Board Cause of Failure #12 Failure close to aide face knot, at edge, on tension side. Position of Failure at Knot: #4 Strength of Board (Modulus of Rupture, psi) 4235 Correlation between microwave measurements and location of weakest point of board - Positive: Cross-polar signal shows a large slope of grain or ooara ^ ^ ^ l n d l c a t e s a l a r g e d e f e c t l v a area near knot #4 In the mid-region of the board. 130 p i p i l i l i p i l i s : 1. Board - #13 2. Cause of Failure Tension failure between load points; laterally buckled. 3. Position of Failure at Knot: clear material 4. Strength of Board (Modulus of Rupture, psl) - 9406 5. Correlation between microwave measurements and location of weakest point of board - Positive: The variations of the cross-polar and phase signals are minimal. Indicating that i t is a strong board. 131 1. Board - H « 2. Cause of Failure « Tension failure between support and load point; failure close to narrow faced or spiked knot. 3. Position of Failure at Knot: #1 4. Strength of Board (Modulus of Rupture, psl)^ - 3464 - 5. Correlation between microwave measurements and location of weakest point of board - Positive: Cross-polar signal shows a large slope of grain (about 35°) and the phase signal Indicates a large defective area in the mid-region of the board. 132 1. Board - #15 2. Cause of Failure » Failure close to narrow faced spiked knot, on tension side. 3.. Position of Failure at Knot: #4 4. Strength of Board (Modulus of Rupture, pal) - 7369 5. Correlation between microwave measurements and location of weakest point of board - Testing not complete. 133 1. Board » tl(> 2. Cause of Failure - Tension failure between load points; laterally buckled. 3. Position of Failure at Knot: clear material 4. Strength of Board (Modulus of Rupture, psi) - 8709 5. Correlation between microwave measurements and location of weakest point of board - Positive: The variations of the cross-polar and phase signals are minimal, Indicating that le i s a strong board. 134 1. Board 2. Cause of Failure #17 Failure close to narrow faced spiked knot, on tension side. 3. Position of Failure at Knot: #4 4; Strength of Board (Hodulus of Rupture, pal) - 7340 5 . Correlation between nlcrowave -surements Z?^**??^? ° f • ^ o u t i s ' / e n r ^ . » — area near knot #4 In the Bid-region. 135 1. Board 2. Cause of Failure #18 Failure close to narrow faced spiked knot, on tension side-3696 3. Position of Failure at Knot: #3 4 Strength of Board (Modulus of Rupture, psi) Correlation between -crow^easurements ^ / ^ I ^ T T o f board - *^;. ) CnS" t{: 1^.lg Ml indicates a large defective area near knot #3 in the mid-region. 136 1. Board - #19 2. Cause of Failure ~ Failure close to narrow faced spiked knot, on tension side. 3. Position of Failure at Knot: #2 4. Strength of Board (Modulus of Rupture, psi) - 7990 5. Correlation between microwave measurements and location of weakest point of board - Positive: Cross-polar signal shows a large slope of grain. (about 35°) and the phase signal Indicates a medium-size defective area near knot #2 in the mid-region. 137 8.4 I l l u s t r a t i o n s of the Homodyne System F i g . 8.22 through F i g . 8.26 show the v a r i o u s p a r t s of the system. 138 F i g . 8.22 The homodyne system F i g . 8.23 The t r a n s m i t t i n g branch 139 F i g . 8.25 The homodyne b r i d g e F i g . 8.26 The balanced raixe 

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