"Applied Science, Faculty of"@en . "Electrical and Computer Engineering, Department of"@en . "DSpace"@en . "UBCV"@en . "Hanson, Bradley Everon"@en . "2011-12-14T02:58:26Z"@en . "1964"@en . "Master of Applied Science - MASc"@en . "University of British Columbia"@en . "This thesis is a performance study of the paraboloidal antenna of the Dominion Radio Astrophysical Observatory and is an assessment of the quantity and distribution of radiation reaching the receiver input from all directions.\r\nThis study deals first with the ideal reflector for which the radiation pattern is computed for small off-axis angles and for wide-angle radiation. The latter calculations make use of the stationary-phase principle in evaluating the radiation integrals. It has been found that the half-power beam-width is slightly more than 0.5\u00B0 and the first side-lobe is at least 30 db down.\r\nIn the following chapter, the surface imperfections of the reflector are considered, in addition to the radiation reaching the feed from the ground. The aperture field is divided into a number of zones perturbed slightly in phase so as to approximate the slowly-varying roughness of the reflector. The resulting increase in side-lobe level is then not only related to the surface tolerance, but to the average size of each zone. The radiation reaching the feed from the ground due to spillover, transmission through the reflector mesh and holes, and reflector surface loss, contributes about 16\u00B0K to the equivalent noise temperature of the antenna.\r\nThe hollow dielectric spars supporting the feed horn are considered and are treated first as being infinite in length where the necessary boundary conditions are applied. The concept of scattering in cones about the cylinder axis is also developed. Then, for the finite cylinder, radiation is assumed to result from the same scattering width.\r\nExperimental studies are carried out and with Cassiopeia A as a source, the shape of the main beam is found to agree with the theoretical result, but the level of the first side-lobe is higher than expected. This discrepancy is believed to be due to reflector distortion. The sun is used as a source for detection of spar scattering and the presence of scattering cones is confirmed. An absolute temperature calibration is carried out with a resulting figure 27\u00B0K for the antenna pointed at the zenith. This temperature is measured at the input of a Dicke switch and is consistent with the theoretical 16\u00B0K presented to the input of the feed horn."@en . "https://circle.library.ubc.ca/rest/handle/2429/39683?expand=metadata"@en . "THE RECEIVING PATTERN OF A PARABOL0IDAL ANTENNA USED IN RADIO ASTRONOMY by BRADLEY EVERON HANSON B.A.Sc, U n i v e r s i t y of B r i t i s h Columbia, 1962 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE In the Department of E l e c t r i c a l E n g i n e e r i n g Ve accept t h i s t h e s i s as conforming to the standards r e q u i r e d from candidates f o r the degree of Master of A p p l i e d Science Members of the Department of E l e c t r i c a l E n g i n e e r i n g The U n i v e r s i t y of B r i t i s h Columbia MAY 1964 In 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 the r e q u i r e m e n t s f o r an advanced degree a t 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 , I agree t h a t the 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 and s t u d y . I f u r t h e r agree 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 purposes may be granted by the Head o f my Department or by h i s r e p r e s e n t a t i v e s . I t i s unders tood 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 not 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 . Department o f E l e c t r i c a l E n g i n e e r i n g 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 , Vancouver 8, Canada. -Date May 25, 1964 ABSTRACT This t h e s i s i s a performance study of the p a r a b o l o i d a l antenna of the Dominion Radio A s t r o p h y s i c a l Observatory and i s an assessment of the q u a n t i t y and d i s t r i b u t i o n of r a d i a t i o n r e a c h i n g the r e c e i v e r input from a l l d i r e c t i o n s . This study dea l s f i r s t w i t h the i d e a l r e f l e c t o r f o r which the r a d i a t i o n p a t t e r n i s computed f o r small o f f - a x i s angles and f o r wide-angle r a d i a t i o n * The l a t t e r c a l c u l a t i o n s make use of the stationary-phase p r i n c i p l e i n e v a l u a t i n g the r a d i a t i o n i n t e g r a l s . I t has been found t h a t the half-power beam-width i s s l i g h t l y more than 0.5\u00C2\u00B0 and the f i r s t s i d e - l o b e i s at l e a s t 30 db down* In the f o l l o w i n g chapter, the surface i m p e r f e c t i o n s of the r e f l e c t o r are considered, i n a d d i t i o n to the r a d i a t i o n reaching the feed from the ground* The aperture f i e l d i s d i v i d e d i n t o a number of zones perturbed s l i g h t l y i n phase so as to approximate the s l o w l y - v a r y i n g roughness of the r e f l e c t o r . . The r e s u l t i n g i n c r e a s e i n s i d e \u00E2\u0080\u0094 l o b e l e v e l i s then not only r e l a t e d to the sur-face t o l e r a n c e , but to the average s i z e of each zone* The r a d i a -t i o n r e a c h i n g the feed from the ground due to s p i l l o v e r , t r a n s -m i s s i o n through the r e f l e c t o r mesh and h o l e s , and r e f l e c t o r sur-face l o s s , c o n t r i b u t e s about 16\u00C2\u00B0K to the e q u i v a l e n t noise temper-ature of the antenna* The hollow d i e l e c t r i c spars supporting the feed horn are considered and are t r e a t e d f i r s t as being i n f i n i t e i n l e n g t h where the necessary boundary c o n d i t i o n s are a p p l i e d . The concept of s c a t t e r i n g i n cones about the c y l i n d e r a x i s i s a l s o developed. Then, f o r the f i n i t e c y l i n d e r , r a d i a t i o n i s assumed to r e s u l t i i from the same s c a t t e r i n g width. Experimental s t u d i e s are c a r r i e d out and wit h C a s s i o p e i a A as a source, the shape of the main beam i s found to agree with the t h e o r e t i c a l r e s u l t , but the l e v e l of the f i r s t s i d e - l o b e i s higher than expected* T h i s discrepancy i s b e l i e v e d to be due to r e f l e c t o r d i s t o r t i o n * The sun i s used as a source f o r detec-t i o n of spar s c a t t e r i n g and the presence of s c a t t e r i n g cones i s confirmed. An absolute temperature c a l i b r a t i o n i s c a r r i e d out wi t h a r e s u l t i n g f i g u r e 27\u00C2\u00B0K f o r the antenna p o i n t e d at the z e n i t h . This temperature i s measured at the input of a Dicke switch and i s c o n s i s t e n t w i t h the t h e o r e t i c a l 16\u00C2\u00B0K presented to the input of the f e e d horn. i i i ACKNOWLEDGEMENT The author wishes to thank P r o f e s s o r P. K. Bowers f o r h i s guidance and encouragement i n c a r r y i n g out t h i s r e s e a r c h . F u r t h e r acknowledgement i s given to the s t a f f of the Dominion Radio A s t r o p h y s i c a l Observatory f o r t h e i r v a l u a b l e a s s i s t a n c e and f o r the use of the observatory and equipment. He would a l s o l i k e to acknowledge the h e l p f u l suggestions given by members of the f a c u l t y and s t a f f and by h i s f e l l o w graduate students. This r e s e a r c h was conducted w i t h the f i n a n c i a l a s s i s t a n c e r e c e i v e d from the B r i t i s h Columbia Hydro and Power A u t h o r i t y , the B r i t i s h Columbia Telephone Company and the N a t i o n a l Research C o u n c i l under Grant (BT\u00E2\u0080\u009468) granted to the Department of E l e c t r i c a l E n g i n e e r i n g . TABLE OP CONTENTS Page L i s t of I l l u s t r a t i o n s v Acknowledgement ............................ v i i i 1. INTRODUCTION 1 2. RADIATION PROM AN IDEAL PARABOL01DAL REFLECTOR . 4 2*1 D e r i v a t i o n of the R a d i a t i o n I n t e g r a l ...... 5 2*2 E v a l u a t i o n of the R a d i a t i o n I n t e g r a l ...... 13 2*2*1 E v a l u a t i o n of M f o r Small O f f -Axis Angles \u00E2\u0080\u00A2\u00E2\u0080\u00A2\u00E2\u0080\u00A2\u00E2\u0080\u00A2\u00C2\u00AB\u00E2\u0080\u00A2\u00E2\u0080\u00A2\u00E2\u0080\u00A2\u00E2\u0080\u00A2\u00E2\u0080\u00A2.. 16 2*2*2 E v a l u a t i o n of M f o r Large O f f -Axis Angles 18 3. SURFACE AND FEED IMPERFECTIONS \u00E2\u0080\u00A2 . 29 3.1 Phase E r r o r s \u00E2\u0080\u00A2*. 29 3.2 Surface Loss 37 3*3 Transmission through Mesh *...\u00E2\u0080\u00A2\u00E2\u0080\u00A2\u00E2\u0080\u00A2\u00E2\u0080\u00A2\u00E2\u0080\u00A2**\u00E2\u0080\u00A2\u00C2\u00AB\u00E2\u0080\u00A2*.. 40 3*4 E f f e c t of Holes i n the R e f l e c t o r ......\u00E2\u0080\u00A2\u00C2\u00AB.. 41 3*5 S p i l l o v e r 44 4. SCATTERING BY SPARS \u00E2\u0080\u00A2 47 4*1 S c a t t e r i n g by I n f i n i t e Metal Rods \u00E2\u0080\u00A2\u00E2\u0080\u00A2\u00E2\u0080\u00A2\u00E2\u0080\u00A2*.\u00C2\u00AB.. 48 4*2 S c a t t e r i n g by D i e l e c t r i c Spars ..\u00E2\u0080\u00A2\u00E2\u0080\u00A2\u00E2\u0080\u00A2\u00C2\u00AB\u00C2\u00AB\u00E2\u0080\u00A2\u00E2\u0080\u00A2*.. 53 4*3 Truncated C y l i n d e r s ............\u00E2\u0080\u00A2\u00C2\u00AB\u00E2\u0080\u00A2*\u00C2\u00AB\u00E2\u0080\u00A2\u00C2\u00AB\u00E2\u0080\u00A2\u00E2\u0080\u00A2\u00E2\u0080\u00A2\u00E2\u0080\u00A2 56 5. EXPERIMENTAL VERIFICATION 64 5*1 Measurement of the Main Beam and Near S i d e -Lobes ....\u00E2\u0080\u00A2\u00E2\u0080\u00A2*\u00E2\u0080\u00A2\u00E2\u0080\u00A2\u00E2\u0080\u00A2\u00E2\u0080\u00A2. \u00E2\u0080\u00A2 64 5*2 S o l a r Measurements .*\u00E2\u0080\u00A2\u00E2\u0080\u00A2\u00E2\u0080\u00A2\u00E2\u0080\u00A2\u00E2\u0080\u00A2\u00E2\u0080\u00A2\u00E2\u0080\u00A2\u00E2\u0080\u00A2.. 70 5*3 Absolute Temperature C a l i b r a t i o n .\u00E2\u0080\u00A2\u00E2\u0080\u00A2\u00E2\u0080\u00A2\u00E2\u0080\u00A2*\u00E2\u0080\u00A2\u00E2\u0080\u00A2.. 73 6. CONCLUSIONS V \u00E2\u0080\u00A2*\u00E2\u0080\u00A2*... 82 References 84 r i v LIST OF ILLUSTRATIONS 1. Radio tel e s c o p e of the Dominion Radio A s t r o y p h y s i c a l Observatory near P e n t i c t o n , B.C. 3 2. R e f l e c t i o n of a plane wave at a r b i t r a r y i n c i d e n c e 5 3. Coordinate system f o r r e f l e c t o r a n a l y s i s 7 4. Geometry of o f f \u00E2\u0080\u0094 a x i s r a d i a t i o n 9 5. Coordinate system f o r e Q 11 6. Horn feed f o r p a r a b o l o i d a l antenna . 14 7. Measured r a d i a t i o n - p a t t e r n of horn feed with p o i n t s p l o t t e d from e m p i r i c a l formula .................. 15 8. Current d i s t r i b u t i o n r e s u l t i n g from a l i n e a r l y - p o l a r i z e d source 17 9. Concept of stationary\u00E2\u0080\u0094phase zones . . 1 9 10. S p i r a l formation of the edge zone .. 24 11. Ideal r a d i a t i o n p a t t e r n , small angles 26 12. Envelope of i d e a l r a d i a t i o n p a t t e r n , wide angles 27 13. Aperture f i e l d of antenna subdivided i n t o small c i r c u l a r zones 31 14. A d d i t i o n of phasors perturbed i n phase by small random amounts 34 15. S i d e - r a d i a t i o n l e v e l w i t h phase e r r o r v s . i d e a l l e v e l 35 15(c) S i d e - r a d i a t i o n l e v e l with phase e r r o r v s . i d e a l l e v e l 36 16. Mesh d e t a i l 39 17. R e f l e c t o r - h o l e d e t a i l 42 18. P o s i t i o n and o r i e n t a t i o n of r e f l e c t o r holes 43 v F i g u r e Page 19. S c a t t e r i n g of plane waves from the c e n t r a l r e g i o n of the r e f l e c t o r ............ 48 20. Coordinate system f o r s c a t t e r i n g from c y l i n d e r s ....a................. 49 21. S c a t t e r i n g behaviour of i n f i n i t e c y l i n d e r at oblique i n c i d e n c e 52 22. Spar c r o s s \u00E2\u0080\u0094 s e c t i o n ......................... 54 23. P o l a r p l o t of s c a t t e r i n g - c o n e p o s i t i o n s .... 57 24. Beamwidth det e r m i n a t i o n of s c a t t e r i n g cone \u00E2\u0080\u00A2...\u00E2\u0080\u00A2.\u00E2\u0080\u00A2\u00E2\u0080\u00A2\u00C2\u00AB.\u00E2\u0080\u00A2\u00E2\u0080\u00A2\u00E2\u0080\u00A2\u00C2\u00AB\u00C2\u00AB\u00E2\u0080\u00A2\u00E2\u0080\u00A2\u00E2\u0080\u00A2.. 59 25. T h e o r e t i c a l beam-shape of s c a t t e r i n g cone due to f i n i t e l e n g t h of spar 59 26. E f f e c t of tapered spar on t r a n s m i t t e d and r e f l e c t e d rays (spar deformity exaggerated) \u00E2\u0080\u00A2\u00E2\u0080\u00A2\u00C2\u00BB\u00E2\u0080\u00A2\u00E2\u0080\u00A2\u00C2\u00BB\u00E2\u0080\u00A2\u00E2\u0080\u00A2.. 60 27. S e c t i o n of s c a t t e r i n g cone 61 28. Receiver response of C a s s i o p e i a passing through main beam ( d r i f t scan) ............. 66 29(a). Comparison of experimental and t h e o r e t i c a l beam-shape curves f o r d r i f t scan (E-plane or 0 = 90\u00C2\u00B0) 68 29(b). Comparison of experimental and t h e o r e t i c a l beam-shape curves f o r d e c l i n a t i o n scan (H-plane or 0 = 0\u00C2\u00B0 ) 69 30. Contour p l o t of s o l a r measurements 71 31. Antenna-sun geometry 72 32. Comparison of experimental and t h e o r e t i c a l beam-shape of s c a t t e r i n g cone 73 33. T y p i c a l double lobe observed d u r i n g s o l a r measurements 74 34. Dicke radiometer 75 35. P r i n c i p l e of the absolute-temperature measurement \u00E2\u0080\u00A2\u00C2\u00AB\u00E2\u0080\u00A2\u00E2\u0080\u00A2\u00E2\u0080\u00A2\u00E2\u0080\u00A2\u00E2\u0080\u00A2\u00E2\u0080\u00A2\u00E2\u0080\u00A2......<> 76 v i F i g u r e Page 36\u00C2\u00AB Detector law .. ....................... 76 37. V a r i a t i o n of antenna temperature with d e c l i n a t i o n angle ......... ....\u00C2\u00AB...*..\u00E2\u0080\u00A2\u00E2\u0080\u00A2... 78 38, Receiver f r o n t - e n d ........... ..*\u00E2\u0080\u00A2\u00E2\u0080\u00A2\u00E2\u0080\u00A2.\u00C2\u00BB\u00E2\u0080\u00A2\u00E2\u0080\u00A2... 79 1. INTRODUCTION A r a d i o antenna i s a device whose primary purpose i s to r a d i a t e or r e c e i v e electromagnetic energy. Such a device enables the t r a n s m i s s i o n or r e c e p t i o n of s i g n a l s only i n d e s i r e d d i r e c t i o n s and suppresses such s i g n a l s i n c e r t a i n other d i r e c t i o n s . Antennas are encountered, f o r example, i n l i n e \u00E2\u0080\u0094 o f \u00E2\u0080\u0094 s i g h t microwave communication systems where the primary purpose i s to concentrate as much energy i n a given d i r e c t i o n as p o s s i b l e . An antenna i n t h i s case i s s a i d to have a l a r g e g a i n , since the r a t i o of power d e n s i t y r a d i a t e d i n the d e s i r e d d i r e c t i o n to the average power d e n s i t y i s l a r g e . Furthermore, no d i s t i n c t i o n i s made between an antenna used f o r t r a n s m i t t i n g or r e c e i v i n g as the c h a r a c t e r i s t i c s of both types are the same. That i s r the t r a n s m i t t e d power d e n s i t y i n a given d i r e c t i o n i s p r o p o r t i o n a l to the r e c e i v i n g s e n s i t i v i t y i n the same d i r e c t i o n , by the r e c i p r o c i t y theorem. The antenna considered here i s p a r t of a system engaged i n making s c i e n t i f i c o bservations i n astronomy. This system i s designed s o l e l y f o r the purpose of i n t e r c e p t i n g r a d i a t i o n from beyond the e a r t h and i n f a c t i s used to determine the i n t e n s i t y , s i z e , l o c a t i o n and frequency spectrum of g a l a c t i c -hydrogen r a d i a t i o n . The study of \"radio s t a r s \" i s of i n t e r e s t as w e l l . From the above, i t i s obvious t h a t the antenna must be capable of r e s o l v i n g d i s t i n c t sources separated by small angular d i s t a n c e s and as a r e s u l t , a knowledge of the width of the main beam i s of primary importance. Furthermore, i t i s necessary to determine the q u a n t i t y and d i s t r i b u t i o n of energy t h a t can be r e c e i v e d from o f f \u00E2\u0080\u0094 a x i s p o i n t s . Such r a d i a t i o n could come from t e r r e s t r i a l as w e l l as c e l e s t i a l sources and may be i n d i s t i n g u i s h a b l e from s i g n a l s r e c e i v e d i n the main beam. The concept of g a i n , however, has at best l i m i t e d s i g n i f i c a n c e i n the context of r a d i o astronomy. Thus* i t i s the purpose of t h i s t h e s i s to evaluate the performance of the antenna so as to enable r a d i o astronomers to r e a l i z e i t s l i m i t a t i o n s and to make f u r t h e r c o r r e c t i o n s to r e c e i v e d d a t a . The antenna considered here, being of a type i n common use i n radar and communications j. i s p a r a b o l o i d a l i n shape, i s 25.7 metres i n diameter, has a f o c a l l e n g t h of 7.63 metres and i s used at a frequency of 1420 MHz, the frequency of hydrogen r a d i a t i o n . The antenna i s shown i n Fi g u r e 1. In making a performance e v a l u a t i o n of t h i s antenna, a t h e o r e t i c a l a n a l y s i s i s made along w i t h an experimental v e r i -f i c a t i o n . The t h e o r e t i c a l work deals with the determination of the r e c e i v i n g p a t t e r n of the i d e a l r e f l e c t o r , the s c a t t e r i n g . o f waves due to the supporting s t r u c t u r e s i n f r o n t of the antenna, the r a d i a t i o n d i r e c t l y r e a c h i n g the focus from beyond the rim, and the e f f e c t s due to surface i m p e r f e c t i o n s . For v e r i f i c a t i o n , strong r a d i o s t a r s and the sun have been used to check the antenna p a t t e r n and the s c a t t e r i n g due to spars. F i n a l l y , an absolute temperature c a l i b r a t i o n has been c a r r i e d out i n order to determine the e f f e c t s of the t e r r e s t r i a l environment. Figure 1. Radio te l e s c o p e of the Dominion Radio A s t r o p h y s i c a l Observatory near P e n t i c t o n , B. C\u00C2\u00AB 4 2. RADIATION PROM AN IDEAL PARABOLOIDAL REFLECTOR In p r i n c i p l e * Maxwell's equations can be used to solve any electromagnetic s c a t t e r i n g problem i f the a p p r o p r i a t e boun-dary c o n d i t i o n s can be a p p l i e d . However, the mathematics are u s u a l l y extremely d i f f i c u l t and consequently, approximations supported by p h y s i c a l arguments form the best a l t e r n a t i v e . One approximation to the problem i s based on geometric or ray optics and i s only u s e f u l f o r determining the d i r e c t i o n of propagation of the m a j o r i t y of the electromagnetic energy. This solution i s exact only i n the l i m i t of zero wavelength. For f i n i t e wavelengths, the approach to be taken here i s somewhat more r e a l i s t i c i n t h a t the r a d i a t i o n f i e l d i s c a l c u -l a t e d on the b a s i s of the s u r f a c e - c u r r e n t d i s t r i b u t i o n a l of the r e f l e c t o r . These c u r r e n t s are approximated on the b a s i s of the i n c i d e n t f i e l d where i t i s assumed t h a t an element of surface area and an element of the i n c i d e n t wave behave as i n f i n i t e tangent p l a n e s . Hence at the r e f l e c t o r s u r f a c e , the incident and r e f l e c t e d f i e l d s are equal and the surface c u r r e n t i s n u m e r i c a l l y equal to the t a n g e n t i a l component of the t o t a l magnetic f i e l d . As the f o c a l l e n g t h i s many wavelengths i n magnitude, the r e f l e c t o r i s i n the r a d i a t i o n zone of the f e e d . Consequently, any p e r t u r b a t i o n of the feed by the r e f l e c t o r i s l a r g e l y due to the r a d i a t i o n f i e l d . However, t h i s e f f e c t i s n e g l i g i b l e since the g r e a t e s t p o r t i o n of the feed energy i s r e f l e c t e d i n t o the main beam of the antenna and the amount i n t e r c e p t e d by the horn i s only a small f r a c t i o n of the t o t a l . The amount of energy returned to the source i s then p r o p o r t i o n a l to the square of the r e f l e c t i o n 5 2 c o e f f i c i e n t and i s given approximately by where G q i s the feed g a i n , X i s the wavelength, and f i s the f o c a l l e n g t h . In t h i s case _11 *| i s 0.0174 or the r e f l e c t e d energy i s about 0.03 per cent* Had the r e f l e c t i o n c o e f f i c i e n t been l a r g e , i t would have been necessary to determine the perturbed r a d i a t i o n - p a t t e r n of the source. As a r e s u l t , the new c u r r e n t d i s t r i b u t i o n of the r e f l e c t o r would have been c a l c u l a t e d on the b a s i s of the a l t e r e d feed p a t t e r n . 2.1 D e r i v a t i o n of the R a d i a t i o n I n t e g r a l Consider a pl a n e j i n f i n i t e l y conducting, s e m i - i n f i n i t e body upon which a plane wave i s i n c i d e n t as shown i n Figure 2* The Figure 2. R e f l e c t i o n i n c i d e n t f i e l d s can be of a plane w r i t t e n i n wave at a r b i t r a r y i n c i d e n c e conventional n o t a t i o n as E = E e ^ ( t \" t> e o o o H = s x E \u00E2\u0080\u009E o o o y (x w h e r e e a n d s a r e u n i t v e c t o r s . F o r t h e s u r f a c e - c u r r e n t o o d e n s i t y - K = n x H w h e r e H = H + H , . F u r t h e r m o r e , H = H , o l - o , 1. \u00E2\u0080\u00A2 t a n t a n f o r a p l a n e s u r f a c e . T h e r e f o r e * t h e s u r f a c e - c u r r e n t d e n s i t y c a n b e w r i t t e n a s K = 2 ( n x H ) o o r , f o r a u n i t E - f i e l d , K = 2 ( n x s\" x ~e ) \ I \u00E2\u0080\u0094 e o o' \l \i - j k r . . . 2 - 1 w h e r e k = \u00E2\u0080\u0094 c a n g l e i s 2n X F r o m t h e f e e d , t h e p o w e r p e r u n i t s o l i d w h e r e P ^ i s t h e t o t a l p o w e r f r o m t h e p r i m a r y f e e d a n d G ( \u00C2\u00A3 , ^ 0 i s t h e g a i n f u n c t i o n o f t h e f e e d . T h u s , t h e e l e c t r i c f i e l d a s a f u n c t i o n o f I S P * \u00E2\u0080\u00A2 \u00E2\u0080\u00A2 2\"~ 2 \u00E2\u0080\u0094*. w h e r e E i s t h e p e a k v a l u e o f t h e e l e c t r i c f i e l d , a n d w h e r e as shown i n Figure 3, Fi g u r e 3. Coordinate system f o r r e f l e c t o r a n a l y s i s From Equations 2-1 and 2-2, the s u r f a c e - c u r r e n t d e n s i t y becomes K = 8^'! fe (n x \"s x \"e ) e~^P y o o' p * * # 2~ 3 Now consider the r a d i a t i o n f i e l d of an elemental d i p o l e of l e n g t h d and c a r r y i n g a cu r r e n t C.\u00C2\u00AB Thus f o r a y-component o c u r r e n t , E e ke - j k r where d << \, This r e s u l t can be extended to an element of area c a r r y i n g a surface c u r r e n t K\u00C2\u00AB Hence, the r a d i a t i o n f i e l d can b 8 w r i t t e n f o r the y-component of c u r r e n t as K i 0 - j k r dE* =\" j i \"y e cos s i n f k e - T \u00E2\u0080\u0094 dA For reasons of convenience, the erms can be dropped and r e i n t r o d u c e d when the r a d i a t i o n p a t t e r n i s computed. Thus, a v e c t o r I can be d e f i n e d as - j k r where, i n g e n e r a l , c u r r e n t s can be expected to be f l o w i n g i n the three coordinate d i r e c t i o n s . Since the current elements are i n f a c t on the surface of a l a r g e r e f l e c t o r , i t i s necessary to express I as a f u n c t i o n of i and l/f 1 n magnitude and i n phase* R e f e r r i n g to Figure 4, the d i s t a n c e from the f i e l d p o i n t to the c u r r e n t element becomes r = R - pf0.tR where s and are u n i t v e c t o r s . Therefore I can now be w r i t t e n o i t i n terms of the d i s t a n c e from the f i e l d p o i n t to the o r i g i n as K ...2-4 I t i s assumed t h a t the d i s t a n c e to the f i e l d , p o i n t i s l a r g e compared w i t h the s i z e of the r e f l e c t o r and hence the rays R and r are t r u l y p a r a l l e l as shown i n F i g u r e 4* By combining Equations 2-3 and 2-4 and i n t e g r a t i n g over the r e f l e c t o r s u r f a c e , F i g u r e 4. Geometry of o f f - a x i s r a d i a t i o n I i s now w r i t t e n - j k B I = -3 2u B V u. 2it J p x s x S ) e - ^ k P ^-\"o'V 0 0 dA\u00C2\u00AB ...2-5 The i n c l i n a t i o n f a c t o r s can at t h i s p o i n t be int r o d u c e d , thus g i v i n g the e l e c t r i c f i e l d components E ^ and E ^ . Therefore, E0 =.i, . I and E^ = i ^ * I 10 where I* = i cos 0 cos0 + i cos Q sin(f) + i ( - s i n $ ) 0 X r J X. ( - s i n ( i ) + i x v ^ 7 y = i (-sin0) + i cos 0 \u00E2\u0080\u00A2 ...2-6 The d e r i v a t i o n of these u n i t v e c t o r s can be seen from Figure 3. Before Equation 2-5 can be i n t e g r a t e d , i t i s necessary to express a l l the v e c t o r s i n terms of the i n t e g r a t i o n v a r i a b l e s , For the phase term, s and i n are w r i t t e n * 1 o E !3 = \"l\" c o s S sxny + l s i n \u00C2\u00A3 sinW + \"t (-costy) o x ' y ' z ' ij j = i x cos(f) s i n Q + i sin0 s i n Q + cos Q as can be seen from Figure 3* Hencej 1 - S q . 1 J J = 1 + costy cos (9 - sinljf s i n (9 cos(\u00C2\u00A3-0). ...2-7 Furthermore^ an element of r e f l e c t o r area, dA, can be expressed as d A = p 2 s i n ^ d ^ d \u00C2\u00A3 . cos 2 .2-8 Before the s u r f a c e \u00E2\u0080\u0094 c u r r e n t v e c t o r (n x s* x e ) can be o o' derivedy i t i s necessary to express e i n terms of \u00C2\u00A3 and f . I t i s assumedj f i r s t of a l l , t h a t the primary feed produces a s p h e r i c a l , l i n e a r l y \u00E2\u0080\u0094 p o l a r i z e d wave and hence e* i s i n the d i r e c t i o n of i n c r e a s i n g a as shown i n Fi g u r e 5\u00C2\u00AB 11 F i g u r e 5. Coordinate system f o r e Q In terms of (a, 8) c o o r d i n a t e s * e Q i s w r i t t e n e = i (-sin a cos B) + i \u00E2\u0080\u009E cos a + i s i n a s i n 8. o x v y z However* s i n a and cos 8 can be expressed i n terms of \u00C2\u00A3 and^/ , thus g i v i n g e = i o x - s i n T s m b c o s o .-^1 - s i n 2 ^ sin 2f J s i n !A s i n \u00C2\u00A3 . 2 1// . 2'\u00C2\u00A3 s m r s i n \u00C2\u00A3 + i cos tyl - s i n 2 ^ s i n 2 \u00C2\u00A3 J From Fig u r e 3 , n i s simply \u00C2\u00A3 ) + i (\u00E2\u0080\u0094sin ~ s m \u00C2\u00B0 y 2 n = 1 ( \" S I D ~X C O S ^ ; T J- \ \u00E2\u0080\u0094 BXU \u00E2\u0080\u009E o J - ^ / T J- ^ \u00C2\u00AB-< O ~ X ^ V Z Z \"A C O S \u00E2\u0080\u00A2 12 Ther e f o r e , a f t e r performing the t r i p l e c r o s s - p r o d u c t , the s u r f a c e -c u r r e n t v e c t o r c i s w r i t t e n c = \u00E2\u0080\u0094 s i n -jr s i n 2 \u00C2\u00A3 s i n \jj -\Jl - s i n 2 1)1 s i n 2 | s m 7j s m y/cos2\u00C2\u00A3 + cos l// cos c = y 1 - s i n 2 ! / / s i n 2 \u00C2\u00A3 \u00C2\u00A3 cos \// c = s m s i n i ,^ 1 - s i n 2 ! / / s i n 2 f ...2-9 For purposes of c a l c u l a t i n g the r a d i a t i o n p a t t e r n , a new v e c t o r M i s d e f i n e d , where 2TI M = 0 0 \ . 4%i c e~ J ~ T ~ s m 1 + c o s ^ c o s ^ - s i n ^ s i n C ^ cos (\u00C2\u00A3\u00E2\u0080\u0094 + cos y/ cos 3 V ...2-10 In terms of M, the e l e c t r i c f i e l d i s then expressed as i -JkB 2TX R -jkR E , = - 3 ^ ^ 2TX R \u00C2\u00A3 h. u 2TC M 9 M where U0 = M.i, M,* = M.i^ \u00C2\u00BB Hence, f o r purposes of c a l c u l a t i n g the p a t t e r n shape, i t i s only necessary to compute the x^y\u00E2\u0080\u0094 and z-components of M and to m u l t i p l y by the i n c l i n a t i o n f a c t o r s i n order to a r r i v e at the 0- and 0 - components of M. 3 For the primary feed* an electromagnetic horn f l a r e d xn the E\u00E2\u0080\u0094plane i s used and i s shown i n Figure 6. I t s r a d i a t i o n p a t t e r n i s p l o t t e d i n F i g u r e 7 and i s approximated by the e m p i r i c a l formula^ G F(^/) 2 = c o s 2 ^ + 0.1026 iff 2 f o r ^ i n r a d i a n s . ( (5 \u00E2\u0080\u00A2 \u00E2\u0080\u00A2 -k a. cos (\u00C2\u00A3.-(/))sin 0 i = l j = l Zm ^ _ . k a . c o s ( \u00C2\u00A3 . -0) s i n Q L e y i i Sij \u00E2\u0080\u00A2\"3 1 3 \u00E2\u0080\u00A2 \u00E2\u0080\u00943\"2 i=l J'=l 3 I f each elemental phasor from 3-1 i s p l o t t e d i n the complex plane, the t o t a l e f f e c t on a l l phasors can be added as shown on F i g u r e 14* Upon p e r t u r b a t i o n of each by a small random the unperturbed d i r e c t i o n , on the average, i f the q u a n t i t y of elements i s l a r g e * Thus, the - r e s u l t a n t of these p r o j e c t e d \u00E2\u0080\u0094 l e n g t h v e c t o r s i s simply a scaled-down v e r s i o n of the o r i g i n a l one and consequently, the outcome of the f i r s t term of 3-2 i s then a l s o 33 p r o p o r t i o n a l to 1 \u00E2\u0080\u0094 6^rms. Furthermore, the p e r p e n d i c u l a r com-2 ponent of the perturbed phasor given i n the second term can be t r e a t e d as a random\u00E2\u0080\u0094walk problem where the l i k e l y outcome, f o r N elements, is\"VN 0 A i n magnitude. Thus to a good ' rms rms . approximation, the power s e n s i t i v i t y i n a given d i r e c t i o n can be w r i t t e n E * (1 - 6 2 r m s ) 2 | V \u00C2\u00A3 G y e - J k a ^ o s C ^ . - ^ s i n S + A Z_ I e U rms . . I y = (1 /S2 \ 2 \u00E2\u0080\u009E 2 x c 2 .2 X T I r2/ 2,2 - U rms) E + O A NK (%T ) . , -, ^ rms rms x 7 i d e a l 2 J-^ur) ur At $ = 0\u00C2\u00B0, the i d e a l p a t t e r n i s w r i t t e n A I 2 N 2 avgl and by n o r m a l i z i n g the p a t t e r n to 0 = 0\u00C2\u00B0, the s e n s i t i v i t y i s g i v e n by P = (1 - 6 f r O S ) 2 P \u00C2\u00B1 D E A L \u00E2\u0080\u00A2 6^ 2 N rms 2 J x ( u r ) 2 A rms ur _ A a v S . ...3-3 where Im Fi g u r e 14* A d d i t i o n of phasors perturbed i n phase by small random amounts and 35 36 This r e s u l t i s not s u r p r i s i n g as the phasors c o n s t i t u t i n g the i d e a l p a t t e r n add on a v o l t a g e b a s i s while the random phasors add on a power b a s i s . However, each zone has a r a d i a t i o n p a t t e r n of i t s own and would t h e r e f o r e concentrate the s c a t t e r e d J (ur) r a d i a t i o n i n the forward d i r e c t i o n according to the \u00E2\u0080\u0094\u00E2\u0080\u0094 term. & ur F i g u r e 15 summarizes the r e s u l t s of Equation 3-3 where the m o d i f i e d p a t t e r n i s p l o t t e d a g a i n s t values f o r the i d e a l p a t t e r n . Curves are p l o t t e d f o r s e v e r a l v a l u e s of N and 0 , The surface t o l e r a n c e i n a l l cases i s f o r + 1 cm as s t a t e d by the manu-f a c t u r e r . I t can be seen that the main lobe i s lowered s l i g h t l y r e l a t i v e power l e v e l without phase e r r o r (db) F i g u r e 1 5 ( c ) . S i d e \u00E2\u0080\u0094 r a d i a t i o n l e v e l with phase e r r o r v s . i d e a l l e v e l 37 i n magnitude while the side lobes are i n c r e a s e d depending on the value of 9 \u00C2\u00AB For small values of 9 , the s i d e - l o b e l e v e l i n c r e a s e i s g r e a t e r than at l a r g e r values of 9 . T h i s e f f e c t i s due to the d i r e c t i v i t y of the i n d i v i d u a l zones i n the a p e r t u r e . Thus i n the v i c i n i t y of the main beam, the general s i d e \u00E2\u0080\u0094 l o b e l e v e l i s r a i s e d to a greater extent than at l a r g e r o f f \u00E2\u0080\u0094 a x i s a n g l e s . 3.2 Surface Loss Since the antenna i s of f i n i t e c o n d u c t i v i t y , i t would be expected t h a t some l o s s i n the s i g n a l s t r e n g t h would occur on r e f l e c t i o n . Even an apparently t r i v i a l l o s s , say 0.1 per cent, can have s e r i o u s consequences as an a b s o r p t i v e m a t e r i a l i s a l s o e m i s s i v e . Consequently, i t i s p o s s i b l e t h a t r a d i a t i o n from the r e f l e c t o r surface could make a s i g n i f i c a n t i n c r e a s e i n the noise l e v e l of the system. Such noise from the r e f l e c t o r a r i s e s from i t s temperature, which i s about 300\u00C2\u00B0K. I t i s w e l l known that a r e s i s t a n c e R develops a voltage across i t s t e r m i n a l s g i v e n by v 2 4k TRB rms where k i s Boltzmann's constant, T i s the absolute temperature, and B i s the bandwidth. I t f o l l o w s that i f t h i s r e s i s t a n c e i s connected to a matched l o a d , the power d e l i v e r e d i s kTB. As the noise power from an a b s o r p t i v e m a t e r i a l v a r i e s with the temperature and the a b s o r p t i o n c o e f f i c i e n t , the power i s o f t e n quoted i n terms of i t s e q u i v a l e n t noise temperature. That i s , 38 the k and B terms are dropped. Thusj T e q u i v a l e n t = \u00C2\u00A3 where \u00C2\u00A3 i s the a b s o r p t i o n c o e f f i c i e n t of the r e f l e c t o r which w i l l now be determined. Consider a plane wave normally i n c i d e n t upon a plane, f i n i t e l y conducting s u r f a c e . For a good conductor, the r e f l e c t e d and i n c i d e n t waves are almost equal i n magnitude and the r e s u l t i n g s u r f a c e \u00E2\u0080\u0094 c u r r e n t d e n s i t y , K , i s 2 |H^ |. The power absorbed per u n i t area i s \u00C2\u00A5 = 2 6 0 -K 6cr H. 1 Here (5 and Cf are the s k i n depth and c o n d u c t i v i t y r e s p e c t i v e l y . The i n c i d e n t power d e n s i t y i s P.' = 77 He ( E x S*) . 1 2 As a r e s u l t , the a b s o r p t i o n c o e f f i c i e n t of the m a t e r i a l i s C = p i = 1.31 x 10~ 4. The r e f l e c t o r , however, i s a mesh and the c u r r e n t s are thus r e s t r i c t e d along the i n d i v i d u a l conductors thereby i n c r e a s i n g the e f f e c t i v e s u r f a c e \u00E2\u0080\u0094 r e s i s t a n c e approximately by a f a c t o r of [ 12. See Figure 16. 39 F i g u r e 16. Mesh d e t a i l Hence, \u00C2\u00A3 = 1.57 x 10~ 3. The f o r e g o i n g c o n s i d e r a t i o n s deal only with the noise power d e n s i t y emitted from the r e f l e c t o r s u r f a c e . Consequently, \u00C2\u00A3 i s only meaningful when i t i s considered along w i t h the feed p a t t e r n and i n t e g r a t e d over the e n t i r e s u r f a c e . I t was mentioned on page 13 that G^Off) represents only the shape of the feed p a t t e r n . I t i s necessary to know i t s absolute g a i n i n a given d i r e c t i o n . From c o n s e r v a t i o n of energy, i t i s obvious that Q where P^ i s the t o t a l power. Thus, G = A % o where G ( ^ ) = G^G^i^S), From a numerical i n t e g r a t i o n of G^{\jl), G q i s approximately 7.94 and hence the g a i n or power s e n s i t i v i t y per u n i t s o l i d angle of the feed i s 0.632 G^{^JJ). Thus, f o r the temperature c o n t r i b u t i o n of the r e f l e c t o r , the noise 40 power d e l i v e r e d to the feed i s d e f l e c t o r \"j J \u00C2\u00A3 M 6 B ( G Q ^ \u00E2\u0080\u0094 ) S i n ^ d \u00C2\u00A3 . 0 0 Dropping k and B and i n t e g r a t i n g , the equivalent temperature due to r e f l e c t o r l o s s i s T 0 - , . n T , = 0.978/T ...3-4 r e f l e c t o r ^ e = 0.46\u00C2\u00B0K f o r T = 300\u00C2\u00B0K ,-3 \u00C2\u00AB and \u00C2\u00A3 = 1.57 x 10\" I t must be noted here t h a t the power a b s o r p t i o n - c o e f f i c i e n t i s not independent of the i n c i d e n c e angle when the E - f i e l d i s tangent to the s u r f a c e . T h i s dependence can be found by-imposing the boundary c o n d i t i o n s f o r an a i r - m e t a l i n t e r f a c e . How-ever, such an e f f e c t would only lower the above temperature m a r g i n a l l y as the feed i s most s e n s i t i v e f o r waves at normal incidence- to the r e f l e c t o r . 3.3 Transmission through Mesh As shown i n F i g u r e 16, the mesh i s small compared to a wavelength of 21 cm and the t r a n s m i s s i o n c o e f f i c i e n t would consequently be small as w e l l . A t h e o r e t i c a l a n a l y s i s of the t r a n s m i s s i o n of waves through m u l t i p l e diamond-shaped holes i s formidable and i s not t r e a t e d here. However, the manufacturer has s t a t e d a maximum value of 1 per cent f o r the t r a n s m i s s i o n c o e f f i c i e n t which i s roughly confirmed by a nomograph p u b l i s h e d 41 r^cently\"*\"^. Thus, E q u a t i o n 3-4 can be a p p l i e d ,in t h i s case, i f \u00C2\u00A3 i s taken as the mesh t r a n s m i s s i o n - c o e f f i c i e n t . The temperature c o n t r i b u t i o n i s then approximately 3\u00C2\u00B0K f o r the whole r e f l e c t o r i f the ground behind i s at 300\u00C2\u00B0K and covers the whole antenna area. Such would be the case i f the antenna were p o i n t i n g s t r a i g h t up. Presumably, the f i g u r e of 1 per cent s t r i c t l y a p p l i e s to normal i n c i d e n c e and since the angle of i n c i d e n c e to the r e f l e c t o r surface reaches a maximum of 40\u00C2\u00B0 at the rim, the temperature con-t r i b u t i o n due to t r a n s m i s s i o n through the mesh would be somewhat short of the 3\u00C2\u00B0K f i g u r e . 3.4 E f f e c t of Holes i n the R e f l e c t o r There are two u n d e s i r a b l e e f f e c t s of: l a r g e holes i n the r e f l e c t o r . As i n the case of the mesh, t r a n s m i s s i o n from the ground through the holes would c e r t a i n l y r a i s e the antenna temperature. In a d d i t i o n * d i s t o r t i o n of the i d e a l r a d i a t i o n p a t t e r n could r e s u l t and i t i s necessary then to get at l e a s t an order of magnitude of the e f f e c t of an absence of r a d i a t i o n from c e r t a i n areas of the r e f l e c t o r . Transmission of r a d i a t i o n through the holes i s very d i f f i c u l t to t r e a t on a t h e o r e t i c a l b a s i s , e s p e c i a l l y when the shape i s i r r e g u l a r as shown i n Figure 17. Since the dimensions are of the order of a wavelength, i t i s d i f f i c u l t to say how c l o s e l y the r a d i a t i o n p a s s i n g through the aperture obeys geomet-r i c a l o p t i c s . However, some i n f o r m a t i o n i s r e a d i l y a v a i l a b l e on the t r a n s m i s s i o n c o e f f i c i e n t of i n f i n i t e s l o t s ^ . For the E - f i e l d t r a n s v e r s e to the s l o t , i t i s found that the c o e f f i c i e n t approaches u n i t y as the s l o t width approaches the wavelength. As the s l o t becomes very small, the 42 F i g u r e 17* R e f l e c t o r - h o l e d e t a i l c o e f f i c i e n t r i s e s s h a r p l y thus making the e f f e c t i v e t r a n s m i s s i o n area r e l a t i v e l y i n s e n s i t i v e to changes i n p h y s i c a l s i z e . In the present case however, the corners i n the hole c o u l d a l t e r t h i s behaviour. N e v e r t h e l e s s , i t i s u s e f u l to assume that the hole passes r a d i a t i o n p r o p o r t i o n a l to i t s geometrical area and to c o n s i d e r the r e s u l t i n g e f f e c t on the antenna temperature. In Figure 18, the p o s i t i o n of the holes i s shown. Assume, f o r the moment, that the holes have an e f f e c t i v e t r a n s m i s s i o n area ^ e f f * w h e r e and where \u00C2\u00A3 i s the t r a n s m i s s i o n c o e f f i c i e n t . A i s the geometrical area of the a p e r t u r e . Consequently, the s o l i d angle subtended at the feed i s A e f f 2 a = = 0.0136 A e f f where p i s the d i s t a n c e from the horn to the r e f l e c t o r . In t h i s Consequently f o r s i x 43 F i g u r e 18. P o s i t i o n and o r i e n t a t i o n of r e f l e c t o r h oles h o l e s , the e f f e c t i v e s o l i d angle i s then 0.0817 A e f f . As shown on page.39. the power s e n s i t i v i t y of the feed per u n i t s o l i d angle i s G QG^ (^)/47t and hence the t o t a l power reaching the horn i s simply T h o l e S \" 6 a o G f < ^ Ktt -= 5 . 5 7 A e f f \u00C2\u00B0 K where i s the ground temperature of 300\u00C2\u00B0K and where i t i s assumed t h a t the s e n s i t i v i t y of the horn does not vary over the small area of the h o l e . From Fi g u r e 17, the geometrical area of 2 2 the hole i s 0.167 m or 0.157 m as seen by the feed when pro-r j e c t e d . Hence, the temperature c o n t r i b u t i o n of the s i x holes i s then 0.875\u00C2\u00B0K. Up to now, only the e f f e c t of the holes on the noise temperature of the antenna has been co n s i d e r e d . I t i s a l s o 44 expected t h a t the holes would a l t e r the r a d i a t i o n p a t t e r n i n some manner. The exact r e s u l t s are v e r y d i f f i c u l t to p r e d i c t as the r e f l e c t o r c u r r e n t - d i s t r i b u t i o n i n the v i c i n i t y of each hole may be a l t e r e d c o n s i d e r a b l y * Since the holes are of the order of a wavelength, resonances may a l s o occur. I t can at l e a s t be s a i d t h a t f o r a t r a n s m i t t i n g antenna, some r a d i a t i o n w i l l be removed from the main beam and w i l l t h e r e f o r e r a i s e the s i d e - r a d i a t i o n l e v e l i n some d i r e c t i o n s . I t i s a n t i c i p a t e d , however, t h a t i n c r e a s e s i n s i d e \u00E2\u0080\u0094 l o b e l e v e l due to surface e r r o r s c o u l d e a s i l y be more s i g n i f i c a n t than any e f f e c t of the h o l e s . Thus f o r p r a c t i c a l purposes, the e f f e c t of the holes on the r a d i a t i o n p a t t e r n could then be i g n o r e d . 3.5 S p i l l o v e r While not a d e f e c t of the r e f l e c t o r , but r a t h e r a de-f e c t of the f e e d , s p i l l o v e r can c o n s t i t u t e a major p o r t i o n of the antenna temperature. Along w i t h the t r a n s m i s s i o n from the ground through the mesh and h o l e s , r a d i a t i o n p a s s i n g over the antenna rim i s to be c o n s i d e r e d at t h i s p o i n t . Owing to the s i z e of the r e f l e c t o r , g e ometrical o p t i c s are to be assumed t h e r e -by n e g l e c t i n g any d i f f r a c t i v e e f f e c t s of the edge. Thus, the where the f e e d becomes i n s e n s i t i v e or where the h o r i z o n i s reached. I t i s assumed, as b e f o r e , t h a t the antenna i s pointed v e r t i c a l l y such t h a t the c o n t r i b u t i o n from the ground i s constant over the circumference of the r i m . I f the ground were e n t i r e l y f l a t , the surrounding h i l l s c o uld extend t h i s l i m i t to about 105 . At c o n t r i b u t i o n i s assumed to come As can be seen i n F i g u r e 1, the t h i s p o i n t , the feed i s r e l a t i v e l y i n s e n s i t i v e and any v a r i a t i o n i n r a d i a t i o n around the p e r i p h e r y due to mountain peaks can be ig n o r e d . As i n previous s e c t i o n s , the power s e n s i t i v i t y of the feed per u n i t s o l i d angle i s &0&f( ^)/4TI and the r e s u l t i n g noise temperature from s p i l l o v e r i s then = G.0385 T g = 11.6\u00C2\u00B0K f o r a ground temperature of 300\u00C2\u00B0K. This f i g u r e can, of course, v a r y a c c o r d i n g to the p o s i t i o n of the antenna w i t h r e s p e c t to the ground. I f the antenna i s i n c l i n e d from the v e r t i c a l , the horn does not r e c e i v e any r a d i a t i o n from above the h o r i z o n over a p o r t i o n of the rim. E v e n t u a l l y , the amount of s p i l l o v e r would be reduced by h a l f when the antenna i s h o r i z o n t a l . However, r a d i a t i o n from the surrounding h i l l s would by t h i s time enter the f e e d by way of the r e f l e c t o r and the antenna temperature would r i s e . For the t o t a l antenna temperature, the c o n t r i b u t i o n s from surface l o s s , t r a n s m i s s i o n through the mesh and h o l e s , and s p i l l o v e r can be added to give an approximate value of 16\u00C2\u00B0K as l i s t e d below. Table of Antenna\u00E2\u0080\u0094Temperature C o n t r i b u t i o n s Surface Loss 0.5 Transmission through mesh 3.0 Transmission through holes 0.9 S p i l l o v e r 11.6 16.0\u00C2\u00B0K 47 4. SCATTERING BY SPARS Up to t h i s p o i n t , the r e f l e c t o r and feed and t h e i r imper-f e c t i o n s have been c o n s i d e r e d . However, i t i s c l e a r l y evident from F i g u r e 1 t h a t f u r t h e r d e f e c t s could a r i s e from .scattering by the three hollow d i e l e c t r i c spars supporting the feed horn. In a d d i t i o n , c o a x i a l cables and metal tubing are clamped along the s i d e of each spar f o r purposes of supplying the equipment at the f o c u s . I t would be expected t h a t these spars would reduce the s e n s i t i v i t y of the antenna i n the d e s i r e d d i r e c t i o n , and cause i t to be more s e n s i t i v e to r a d i a t i o n from o f f - a x i s d i r e c t i o n s . I f the antenna i s assumed to be t r a n s m i t t i n g , then the horn would emit p o l a r i z e d waves which would be r e f l e c t e d from the surface of the antenna M The emerging plane wave, of known p o l a r i z a t i o n , would then a r r i v e at the three spars. As a r e s u l t , the spars would s c a t t e r some of the r a d i a t i o n from the c e n t r a l r e g i o n of the r e f l e c t o r as shown i n F i g u r e 19. I t would be of i n t e r e s t to know the q u a n t i t y of s c a t t e r e d power and it's d i s t r i b u t i o n i n v a r i o u s d i r e c t i o n s . U n f o r t u n a t e l y , the complicated geometry of the s p a r s , t h e i r tapered shape, and the assortment of metal cables clamped to them, make an exact a n a l y t i c a l s o l u t i o n v i t u r a l l y i m p o s s i b l e . However, i t i s of i n t e r e s t to consider a few b a s i c q u e s t i o n s . I t would f i r s t be u s e f u l to determine the amount of power s c a t t e r e d by one metal cable i n the absence of a l l other o b s t r u c t i o n s . In a d d i t i o n , the d i r e c t i o n of s c a t t e r e d power would be r e q u i r e d . Then as a comparison, the e f f e c t of the d i e l e c t r i c spar a c t i n g alongi would be of i n t e r e s t . Although these q u e s t i o n cannot be answered 48 Fi g u r e 19, S c a t t e r i n g of plane waves from the c e n t r a l r e g i o n of the r e f l e c t o r e x a c t l y , at l e a s t an approximate s o l u t i o n can be found and an order of magnitude can be obtained f o r the combined e f f e c t of the spars w i t h t h e i r assortment of s e v e r a l c a b l e s . 4.1 S c a t t e r i n g by I n f i n i t e Metal Bods In order to f i n d the s c a t t e r i n g t h a t would occur from one of the cables clamped to a s p a r , i t i s p o s s i b l e to consider the e f f e c t of a plane wave i n c i d e n t on the surface of a long , i s o l a t e d metal c y l i n d e r . One of the spars l i e s i n the plane of p o l a r i z a t i o n of the i n c i d e n t wave* For the other two, i t i s convenient to r e s o l v e the i n c i d e n t wave i n t o t ransverse magnetic 49 (TM) and tran s v e r s e e l e c t r i c (TE) components. That i s , the spar l i e s i n the plane of p o l a r i z a t i o n and at r i g h t angles to i t r e s p e c t i v e l y . Before c o n s i d e r i n g the case of oblique i n c i d e n c e on a rod of f i n i t e wavelength* the si m p l e r case shown i n Figure 20 w i l l be t r e a t e d f i r s t . The metal rod i s assumed to be of i n f i n i t e l e n g t h w i t h a broadside i n c i d e n t wave. The c y l i n d e r i s a l s o z s c a t t e r e d ray F i g u r e 20. Coordinate system f o r s c a t t e r i n g from c y l i n d e r s assumed to be a p e r f e c t conductor* The TM and TE p o l a r i z a t i o n s are c o nsidered s e p a r a t e l y * The s c a t t e r e d f i e l d from a c y l i n d e r with an i n c i d e n t plane wave can be found by a p p l y i n g the appropriate boundary 50 c o n d i t i o n s to the general s o l u t i o n of the wave equation i n c y l i n d r i c a l c o o r d i n a t e s , Such a problem i s t r e a t e d i n the 12 l i t e r a t u r e and the s o l u t i o n i s summarized here. Thus, f o r the case of a plane i n c i d e n t wave* the t o t a l f i e l d can be w r i t t e n oo E = E e - J k r c o s ^ + E ) A ( j ) \" n H ( 2 ) ( k r ) e ^ z z^ z i / n V J / n v ' n = - oo ...4-1 f o r TM i n c i d e n c e . For the TE case, H i s s i m i l a r l y w r i t t e n 7 z J o o H = H e - J k r c o s ^ + H > B ( j ) \" 1 1 H ( 2 ) ( k r ) e J n ^ z z. z. / n v 0 ' n v '\u00E2\u0080\u00A2 n \u00E2\u0080\u0094 \u00E2\u0080\u0094 oo ...4-2 where k = P^, n i s an i n t e g e r , and H ^ 2 ^ ( k r ) i s a Hankel A n f u n c t i o n of the second k i n d . A and B are the undetermined n n c o e f f i c i e n t s . The f i r s t term i n e i t h e r p o l a r i z a t i o n represents the i n c i d e n t plane-wave and the second term d e s c r i b e s the c y l i n d r i c a l l y d i v e r g i n g scattered\u00E2\u0080\u0094wave, In order to f i n d the c o e f f i c i e n t s A n and B n, the boundary c o n d i t i o n s must be s a t i s f i e d . For the TM case, E must v a n i s h z on the c y l i n d e r surface and i n the TE case, E^must v a n i s h . Using the i d e n t i t y o o (j,;)\" 1 1 J n ( k r ) e J n ^ y - j k r c d s * . n = - o o i t f o l l o w s t h a t f o r a c y l i n d e r of ra d i u s a 5 1 J (ka) A n T 2 j H ^ ' ( k a ) n v . . . 4 - 3 S i m i l a r l y B = -n J T ( k a ) n v ' 7(27 H t v w ( k a ) . . . 4 - 4 s i n c e E ^ vanishes i f d Rz/dr i s zero. The primes i n d i c a t e d i f f e r e n t i a t i o n w i t h r e s p e c t to the argument. When c o n s i d e r i n g the t o t a l amount of power s c a t t e r e d from an o b j e c t , i t i s o f t e n convenient to express t h i s q u a n t i t y by s p e c i f y i n g the \" s c a t t e r i n g c r o s s - s e c t i o n \" , the r a t i o of the t o t a l s c a t t e r e d power to the i n c i d e n t power d e n s i t y . In the case of an i n f i n i t e metal rod* the s c a t t e r i n g c r o s s - s e c t i o n per u n i t l e n g t h or the \" s c a t t e r i n g width\" would be found. For the two p o l a r i z a t i o n s , the widths are oo TM 4 k A n and n \u00E2\u0080\u0094 \u00E2\u0080\u0094 oo oo TE 4 k B n . . . 4 - 5 n = - i oo The l a r g e s t of the cab l e s used has a diameter of 4 . 1 cm and f o r t h i s c a b l e , the s c a t t e r i n g widths f o r 2 1 cm wavelength are 1 3 o 6 cm and 2 \u00C2\u00AB 3 cm f o r TM and TE p o l a r i z a t i o n s r e s p e c t i v e l y . 52 From the asymptotic expressions f o r the B e s s e l f u n c t i o n s , i t can be seen t h a t f o r a \u00C2\u00AB l / k , the s c a t t e r i n g width i s a monotonically decreasing f u n c t i o n of the r a d i u s a. The f o r e g o i n g a n a l y s i s has considered the case of broad-sid e i n c i d e n c e where the s c a t t e r e d wave propagates r a d i a l l y outward from the c y l i n d e r * For oblique i n c i d e n c e , i t i s reasonable to expect a s c a t t e r i n g width of the same order of magnitude. However, from Huygen Ts P r i n c i p l e i t f o l l o w s t h a t the s c a t t e r e d wave emerges i n a cone about the a x i s of the c y l i n d e r as shown i n F i g u r e 21, T h i s r e s u l t would a l s o have been R i n c i d e n t ray s c a t t e r i n g cone y F i g u r e 21, S c a t t e r i n g behaviour of i n f i n i t e c y l i n d e r at oblique i n c i d e n c e expected from geometrical optics assuming specular r e f l e c t i o n , 53 13 and i s f u r t h e r proven by Mentzer where i t i s shown that the s c a t t e r e d wave i s of the form C O E + + , = E ) A (aT nH ( 2 ) ( k r c o s X ) e ^ ^ e J k z s i n X z s c a t t e r e d z^ / n 0 n n = \u00E2\u0080\u0094 co E - g k ( r c o s X - zsinX) \u00E2\u0080\u009Ej^/ 4 z^ y TxkrcosX oo A e ^ A n e n=\u00E2\u0080\u0094 oo as r \u00C2\u00BB\u00E2\u0080\u00A2 oo \u00E2\u0080\u00A2 I f z = -R sinXand r = R cosX the exponential term e-0kR reduces to the form \u00E2\u0080\u0094 \u00E2\u0080\u0094 which t h e r e f o r e i n d i c a t e s specular r a d i a t i o n i n the R \u00E2\u0080\u0094 d i r e c t i o n . As long as the rod i s assumed to be i n f i n i t e i n l e n g t h , the beamwidth of the s c a t t e r i n g cone i s zero. When the f i n i t e c y l i n d e r i s considered i n S e c t i o n 4.3, the beamwidth becomes f i n i t e . However at t h i s p o i n t , i t i s w e l l to consider f i r s t the s c a t t e r i n g from the d i e l e c t r i c s p a r s . 4.2 S c a t t e r i n g by D i e l e c t r i c Spars As i n the case of the metal c y l i n d e r , i t i s again d e s i r a b l e to d e al f i r s t w i t h an i s o l a t e d , i n f i n i t e l y long, d i e l e c t r i c tube and to assume broadside i n c i d e n c e * The a n a l y s i s i s more complicated because of the existence of three f i e l d s i n the regions shown i n Fi g u r e 22. F u r t h e r , these f i e l d s must be matched at the two boundaries before the s c a t t e r i n g c o e f f i c i e n t outside the c y l i n d e r can be determined. This problem i s s t r a i g h t f o r w a r d at broadside 54 a = 14.0 cm b = 14.9 cm e m = 4.4 m F i g u r e 22. Spar c r o s s - s e c t i o n i n c i d e n c e as only E z ~ and H ^ \u00E2\u0080\u0094 f i e l d s or E^- and E ^ - f i e l d s must be matched at the boundaries f o r TM and TE i n c i d e n c e r e s p e c t i v e l y . In the broadside TM case, three f i e l d s can be w r i t t e n , one f o r each r e g i o n , as oo E E and J (kr) + A.H ^ ( k r ) + B H ^ ( k r ) n x ' n n > ' n n . ' e t n = - oo oo C H ^ ( k r ) + D H ^ ( k r ) n n x ' n n e i n = \u00E2\u0080\u0094 oo oo E = E J (kr) + F I (kr) n n ' n n n = - cxi In the f i r s t equation, the f i r s t term i s p r o p o r t i o n a l to the i n c i d e n t plane-wave, and si n c e o n l y c y l i n d r i c a l l y d i v e r g i n g waves are assumed, A^ = 0. In the second equation, converging and d i v e r g i n g waves are p o s s i b l e , and hence and are non-zero. In the l a s t equation, the f i e l d i s bounded at r - 0, thus making P n = 0. The boundary c o n d i t i o n s r e q u i r e that at r = a and r = b, E = E and E = E r e s p e c t i v e l y , and H a = H a and H = Ea z2 z 3 z l z 2 ^2 ^3 ^1 ^2 r e s p e c t i v e l y . The t a n g e n t i a l H \u00E2\u0080\u0094 f i e l d s are s a t i s f i e d i f d E d E z l z 2 d r - ^ r * S i m i l a r l y f o r the TE p o l a r i z a t i o n , H - f i e l d s are w r i t t e n as f o r the z E ^ - f i e l d s , except the E ^ - f i e l d s are r e l a t e d at the boundaries by z \u00C2\u00B0 z l 1 z 2 ^ r e A r * a m c These c o n d i t i o n s a l s o ensure t h a t the r a d i a l B- and D - f i e l d s are continuous across the boundaries of the d i e l e c t r i c tube. From t h i s a n a l y s i s , the s c a t t e r i n g c o e f f i c i e n t can be s o l v e d and can then be used to f i n d the s c a t t e r i n g c r o s s - s e c t i o n . For a h y p o t h e t i c a l tube of d i e l e c t r i c constant 4.4, an inner diameter of 17.5 cm and an outer diameter of 18.5 cm, the s c a t t e r i n g widths were computed to be 15 cm and 5 cm f o r TM and TE p o l a r i z a t i o n s r e s p e c t i v e l y . These are of the same order of magnitude as the tube diameter which i n d i c a t e s that the spars are behaving o p t i c a l l y . For the general problem of oblique i n c i d e n c e , the reader 14 i s r e f e r r e d to K i e l y , where the d i e l e c t r i c - t u b e antenna i s c o n s i d e r e d . In t h i s case, a d d i t i o n a l boundary c o n d i t i o n s must 56 be s a t i s f i e d and the problem becomes much more complicated. However, from Huygen's P r i n c i p l e i t again f o l l o w s that the s c a t t e r e d f i e l d t r a v e l s i n a cone about the c y l i n d e r a x i s , as i n the case of the metal rod. I t may a g a i n be assumed that the s c a t t e r i n g width i s of the order of the tube diameter and i s t h e r e f o r e comparable with t h a t of the metal rods t r e a t e d i n S e c t i o n 4.1. The p r o x i m i t y e f f e c t of the d i e l e c t r i c and metal c y l i n d e r s r e s u l t s i n a d i s t r i b u t i o n around the hollow s c a t t e r i n g - c o n e which w i l l now be complicated* However, the composite spar can be assigned an e q u i v a l e n t s c a t t e r i n g width which i s probably somewhat l a r g e r than that due to each of the separate elements. I t i s e v i d e n t , from the spar c o n f i g u r a t i o n i n F i g u r e 1, t h a t three d i s t i n c t s c a t t e r i n g \u00E2\u0080\u0094 c o n e s are present and can be represented on a p o l a r p l o t as i n Figure 23. The o r i g i n i s the antenna a x i s * In a d d i t i o n , i t can be seen from the p l a n view of the spars t h a t while spar 1 e x h i b i t s TM s c a t t e r i n g o n l y , the other two spars w i l l have both TM and TE s c a t t e r i n g . Thus, i t would be expected t h a t the s c a t t e r e d power from spar 1 would d i f f e r from the other two. 4*3 Truncated C y l i n d e r s I n the l a s t two s e c t i o n s ^ the i n f i n i t e c y l i n d e r has been , considered and i t i s now necessary to d i s c u s s the c y l i n d e r of f i n i t e l e n g t h . I t i s e v i d e n t , from elementary antenna theory, t h a t a d i p o l e of l e n g t h comparable to the wavelength e x h i b i t s resonance e f f e c t s . Hence, i t i s a n t i c i p a t e d t h a t a t h i n wire of the order of a wavelength l o n g would act as a resonant s c a t t e r e r . 57 F i g u r e 23. P o l a r p l o t of s c a t t e r i n g - c o n e p o s i t i o n s The c u r r e n t d i s t r i b u t i o n over i t s l e n g t h would be d i f f e r e n t than i f i t were a s e c t i o n of an i n f i n i t e l y long w i r e . However, i n the case of the c o a x i a l c a b l e s , i t can be argued t h a t l i t t l e resonance occurs because of t h e i r l e n g t h and t h i c k n e s s . I t i s expected t h a t r a d i a t i o n damping would cause l i t t l e v a r i a t i o n i n surface c u r r e n t over the c y l i n d e r l e n g t h . These are a l s o the 15 assumptions made by Mentzer i n determining the radar c r o s s -s e c t i o n of the t r u n c a t e d , t h i c k c y l i n d e r . Hence, i t i s reasonable to assume that the e f f e c t i v e s c a t t e r i n g width of the metal c y l i n d e r would not change g r e a t l y i f i t were cut to a f i n i t e l e n g t h * but one s t i l l ; l ong compared to 21 cm. S i m i l a r l y , the d i e l e c t r i c spar i s not expected to e x h i b i t resonance e f f e c t s as i t s dimensions are a l s o l a r g e compared to the wavelength. Hence, a d i e l e c t r i c tube of many wavelengths long would behave as an i n f i n i t e c y l i n d e r over most of i t s l e n g t h * The s c a t t e r i n g near the ends of the spar would not be p r e d i c t e d by the theory o u t l i n e d i n S e c t i o n 4 . 2 , but such an e f f e c t would become i n c r e a s i n g l y n e g l i g i b l e as the spar i s lengthened. Owing to the f i n i t e l e n g t h of the spar, i t was a l r e a d y p o i n t e d out t h a t the s c a t t e r i n g cone would widen i n the X-d i r e c t i o n . That i s , the s c a t t e r e d beamwidth would be f i n i t e r a t h e r than i n f i n i t e s i m a l . The beamwidth could b e ^ e a s i l y computed i f the i n c i d e n t plane-wave were uniform. However, as a r e s u l t of the i l l u m i n a t i o n f u n c t i o n of the horn, the beamwidth of the s c a t t e r e d wave i s even g r e a t e r * s i n c e i n e f f e c t only a p o r t i o n of the composite spar i s i l l u m i n a t e d * At a great d i s t a n c e away, the s c a t t e r e d f i e l d would behave s i m i l a r l y to r a d i a t i o n coming from a d i r e c t i v e p o i n t source. Hence* r a d i a t i o n from an element of p r o j e c t e d c y l i n d e r l e n g t h can be w r i t t e n dE x= A e ^ R ( 1 - 0 . 2 3 1 - 1 . 9 3 i 2 ) d i where A i s a constant and the polynomial i n JL d e s c r i b e s the i l l u m i n a t i o n d i s t r i b u t i o n over the p r o j e c t e d spar l e n g t h (See d e f i n i t i o n of H i n F i g u r e 1 9 ) . From the geometry of Figure 2 4 , R can be r e p l a c e d by R + / . A s i n X and the r a d i a t e d f i e l d i s approximately F i g u r e 25\u00C2\u00BB T h e o r e t i c a l beam\u00E2\u0080\u0094shape of s c a t t e r i n g cone due to f i n i t e l e n g t h of spar 0.42 Ae -jkR R rJ k ^ s i n X ( l ^ 0a23\u00C2\u00A3_ i . 9 3 / 2 ) d / . 60 T h i s f u n c t i o n i s e a s i l y i n t e g r a t e d and w i t h the help of the computer, the r e l a t i v e power l e v e l was c a l c u l a t e d f o r a few v a l u e s of X as shown i n F i g u r e 25\u00C2\u00BB I t can be seen from F i g u r e 1 that the d i e l e c t r i c spars are roughly e l l i p s o i d a l or even b i c o n i c a l i n shape. I t f o l l o w s that on the b a s i s of g e o m e t r i c a l o p t i c s ^ the s c a t t e r e d beam-width would be increased.even f u r t h e r as can be seen i n F i g u r e 26* The d i v e r g i n g angle, 2(5* f o r waves r e f l e c t e d from the spar, 6 = 2\u00C2\u00B0 Figure. 26. E f f e c t of tapered spar on t r a n s m i t t e d and r e f l e c t e d rays (spar deformity exaggerated) i s approximately f o u r degrees as shown. On the other hand, f o r waves passin g through-the spar i n the forward d i r e c t i o n , no 61 a d d i t i o n a l divergence occurs provided t h a t the v a i l t h i c k n e s s i s constant over i t s l e n g t h . Prom the above c o n s i d e r a t i o n s , i t i s p o s s i b l e to v i s u a l i z e the hollow s c a t t e r i n g - c o n e as i n Fig u r e 27 where i t s t h i c k n e s s i s spar a x i s F i g u r e 27. S e c t i o n of s c a t t e r i n g cone roughly two degrees i n the forward d i r e c t i o n . The t h i c k n e s s of the cone i n the backward d i r e c t i o n i s between two and fo u r degrees as shown, as a r e s u l t of the taper of the spar. The estimated d i s t r i b u t i o n of the s c a t t e r e d power about the spar a x i s i s a l s o suggested i n F i g u r e 27. The t o t a l amount of s c a t t e r e d power due to a l l spars i s not easy to es t i m a t e a c c u r a t e l y . However, from the fo r e g o i n g c o n s i d e r a t i o n s , the e f f e c t i v e s c a t t e r i n g widths may be as much as 30 cm f o r spar 1 and 15 cm f o r spars 2 and 3, thereby g i v i n g 2 a t o t a l c r o s s \u00E2\u0080\u0094 s e c t i o n of 3.3 m . This f i g u r e represents 0.9 per 62 cent of the e f f e c t i v e area of the r e f l e c t o r or 0,9 per cent of the power r a d i a t e d i n the main beam. I t must be emphasized t h a t t h i s f i g u r e i s d e r i v e d from an order of magnitude c a l c u l a t i o n only, and probably represents an upper l i m i t f o r the s c a t t e r e d power. Turning now to the case of a r e c e i v i n g antenna,.it f o l l o w s from the r e c i p r o c i t y theorem that the e f f e c t of the spars w i l l reduce the s e n s i t i v i t y i n the main beam by about 0.9 . per cent and the antenna w i l l now be i n c r e a s i n g l y s e n s i t i v e to r a d i a t i o n coming from the d i r e c t i o n s forming the three hollow s c a t t e r i n g - c o n e s shown i n Figure 23. The t o t a l noise power that can be r e c e i v e d i n these cones would then be 0.9 per cent of the average b r i g h t n e s s temperature as seen by the cones them-s e l v e s . This c o n t r i b u t i o n i s i n s i g n i f i c a n t . Most of the r e c e i v i n g s e n s i t i v i t y of the cones i s i n the forward d i r e c t i o n of the antenna where the b r i g h t n e s s temperature i s much l e s s than t h a t of the ground. The s c a t t e r i n g cones are important f o r another reason, however. I f a strong r a d i o source l i e s i n the d i r e c t i o n of any one of these cones, a spurious s i g n a l would be picked up by the r e c e i v e r . The h i g h e s t s e n s i t i v i t y i n these cones i s estimated to be 40 db down from the main beam and as a r e s u l t , the sun would be powerful enough to be d e t e c t e d . The experimental r e s u l t s shown i n the next chapter confirm t h i s c o n c l u s i o n . Although not considered as one of the spars, i t can be seen from F i g u r e 1 that the c a n i s t e r at the antenna focus may have some s c a t t e r i n g e f f e c t s . A r i g o r o u s treatment of t h i s problem would be very d i f f i c u l t but some idea of i t s s c a t t e r i n g c r o s s -63 s e c t i o n can be obtained from i t s geometrical area. I t s diameter 2 i s about two f e e t or i t s area i s about 0.29 m as presented to a plane wave emerging from the r e f l e c t o r . Since the s i z e i s some-what l a r g e r than the wavelength, the geometrical approximation i s s t i l l u s e f u l . As a comparison, the spars and metal rods have been estimated to have a t o t a l s c a t t e r i n g c r o s s - s e c t i o n of about 2 3*3 m . Thus, the s c a t t e r i n g area of the c a n i s t e r i s almost an order of magnitude below t h a t of the spars. Furthermore, i t i s not expected that the s c a t t e r e d energy would be concentrated i n any p a r t i c u l a r d i r e c t i o n due to i t s c i r c u l a r symmetry and any e f f e c t s on the antenna p a t t e r n are not expected to be measurable. Before d e a l i n g w i t h the experimental aspects of t h i s t h e s i s , a b r i e f review of the t h e o r e t i c a l work should remind the reader of the most important f e a t u r e s of the theory as r e l a t e d to the expected r e s u l t s * From Chapter 2, the antenna r a d i a t i o n -p a t t e r n was c a l c u l a t e d and i t was found that the half-power width of the main beam i s about a h a l f degree and the l e v e l of the f i r s t s i d e - l o b e i s more than 30 db down. In Chapter 3* the antenna i m p e r f e c t i o n s were considered and i t was found that the e f f e c t i v e antenna temperature i s around 16\u00C2\u00B0K. The surface rough-ness i n the p a r a b o l o i d was t r e a t e d and some i n d i c a t i o n was given of the e f f e c t of s m a l l , random i m p e r f e c t i o n s . In Chapter 4, the e f f e c t s of spars were found and i t was p r e d i c t e d that lobes would appear at p o i n t s o f f the a x i s of the antenna as d e f i n e d t h e i r s c a t t e r i n g cones* T h e i r e f f e c t on the antenna temperature i s b e l i e v e d to be n e g l i g i b l e * 64 5* EXPERIMENTAL VERIFICATION Inoorder t h a t some check on the t h e o r e t i c a l work be made, experimental s t u d i e s were c a r r i e d out on the antenna i n 1963* The p a r t i c u l a r o b j e c t i v e s of the t e s t s were to measure the antenna r a d i a t i o n \u00E2\u0080\u0094 p a t t e r n * to determine the e f f e c t of spars* and -to f i n d the absolute temperature and i t s v a r i a t i o n as a f u n c t i o n of the antenna p o s i t i o n wi,,th r e s p e c t to the e a r t h . T h i s absolute measurement would provide a check on the e f f e c t s of s p i l l o v e r * l o s s e s and t r a n s m i s s i o n through the r e f l e c t o r * The p a t t e r n measurements would at l e a s t p a r t i a l l y v e r i f y the c a l c u l a t i o n s and may show up e f f e c t s due to surface t o l e r a n c e s * 5*1 Measurement o f the Main Beam and Near Side-Lobes To determine the antenna r a d i a t i o n - p a t t e r n experimentally* i t would be necessary to i s o l a t e the antenna from a l l surrounding o b j e c t s and to p l a c e a p o i n t e x c i t a t i o n - s o u r c e a great d i s t a n c e away* The p a t t e r n d e t e r m i n a t i o n could then be e a s i l y c a r r i e d out by simply changing the o r i e n t a t i o n of the antenna and measuring the r e c e i v e r response. However, such i s c e r t a i n l y not a simple matter since the antenna i s on the surface of the e a r t h . That i s * a t r a n s m i t t e r l o c a t e d on one of the nearby h i l l s would be u n s a t i s f a c t o r y as the ground would provide a l t e r n a t e paths of t r a n s m i s s i o n from t r a n s m i t t e r to antenna* As the i n c i d e n c e angle from the: t r a n s m i t t e r to the r e f l e c t i o n p o i n t on the ground i s near grazing* a strong* r e f l e c t e d s i g n a l would reach the antenna at a s l i g h t l y d i f f e r e n t angle than t h a t of the d i r e c t s i g n a l * I s o -l a t i n g the two e f f e c t s would be n e a r l y impossible* However* a 65 t r a n s m i t t e r a great d i s t a n c e above the antenna would be almost i d e a l and could c e r t a i n l y be r e a l i z e d by an a r t i f i c i a l e a r t h \u00E2\u0080\u0094 s a t e l l i t e o p e r a t i n g near 1420 MHz. An a l t e r n a t i v e method makes use of c e l e s t i a l sources and would allow at l e a s t a d e t e r m i n a t i o n of the shape of the main beam. In the measurements c a r r i e d out, C a s s i o p e i a A, a strong r a d i o source, was used to measure the beam shape and the l e v e l of f i r s t sider-lobe* At p o i n t s f u r t h e r o f f the antenna a x i s , the s i g n a l f a l l s below the noise l e v e l of the r e c e i v e r and i s not d e t e c t a b l e . However, the sun i s a very strong source and could be used t o measure the s i d e - l o b e l e v e l at p o i n t s w e l l removed from the main beam. U n f o r t u n a t e l y , the source i s approximately a h a l f degree wide and i t s r a d i a t i o n or b r i g h t n e s s d i s t r i b u t i o n i s not uniform. F u r t h e r from time to time* b u r s t s of i n t e n s e r a d i a t i o n occur at d i f f e r e n t p o i n t s on the s o l a r s u r f a c e . Thus, as f a r as making meaningful p a t t e r n measurements i s concerned, the sun i s r e a l l y only u s e f u l i n d e t e c t i n g the presence of p o s s i b l e i s o l a t e d s i d e \u00E2\u0080\u0094 l o b e s or f o r determining the e f f e c t s of spars* The l a t t e r i s to be d i s c u s s e d i n the next s e c t i o n . In making observations on C a s s i o p e i a , a number of d r i f t scans were made w i t h the antenna set i n a f i x e d p o s t i o n w i t h r e s p e c t to the e a r t h * Then with the t u r n i n g of the e a r t h , the r e c e i v e r response was t r a c e d out as shown i n F i g u r e 28. The sharp spikes on e i t h e r side of the main beam are due to changes i n the r e c e i v e r g a i n since i t was necessary to c o n t a i n the t r a c e w i t h i n the r e c o r d e r range* Upon examination of t h i s t r a c e , i t can be seen t h a t i t i s necessary to e s t a b l i s h a zero r e f e r e n c e . 66 o w u o ft fH \u00E2\u0080\u00A2H H r e c e i v e r g a i n G = 200 G = 20 G = 2 d e c l i n a t i o n 6 =. 58\u00C2\u00B0 40' 2 3 h 4 0 m 2 3 h 3 0 m 2 3 h 2 0 m 2 3 h 1 0 m zero l i n e r i g h t a scension F i g u r e 28* Receiver response of C a s s i o p e i a passing through main beam ( d r i f t scan) In t h i s case, the zero l i n e was connected between the lowest l e v e l s on e i t h e r side of the main lobe. In Figure 29(a), the measured beam\u00E2\u0080\u0094shape i s p l o t t e d with the t h e o r e t i c a l curve f o r comparison. For the H-plane or 0 = 0\u00C2\u00B0, a d e c l i n a t i o n scan was t r i e d and i t was found that the v a r i a t i o n of the temperature from the ground gave erroneous r e s u l t s . However, a s e r i e s of d r i f t scans were made where the antenna always remained f i x e d with r e s p e c t to the e a r t h . Along the H-plarie from each successive scan, the v a r i a t i o n due to the antenna p a t t e r n was found and i s p l o t t e d i n Figure 29(b). For the main beam there i s good agreement between t h e o r e t i c a l and experimental r e s u l t s but the side lobes d i f f e r by as. much as an order of magnitude\u00E2\u0080\u00A2 In order to r e s o l v e t h i s discrepancy, at l e a s t two explanations can be advanced. I t could f i r s t be argued that the antenna s u r f a c e - e r r o r s c o n t r i b u t e to the i n c r e a s e i n s i d e -lobe l e v e l . However* the theory of Chapter 3 only p r e d i c t s i n c r e a s e s that are (j) \u00E2\u0080\u0094 i n v a r i a n t , which i s only roughly true f o r the measured p a t t e r n * From Figure 15(a), an i d e a l s i d e \u00E2\u0080\u0094 l o b e l e v e l of -3d db g i v e s a new l e v e l of -26 db at Q - 1 \u00C2\u00B0 . This r e -s u l t checks approximately.with the experimental values i n F i g u r e s 29(a) and 29(b), The zones d e p i c t e d i n Figure 13 are about 2 metres i n diameter which i n d i c a t e s that the r e f l e c t o r d i s t o r t i o n s cover f a i r l y wide areas. This s i z e suggests a misalignment of some r e f l e c t o r panels or a m u l t i p l e warpage over the r e f l e c t o r s u r f a c e . The s i d e - l o b e increase i s concentrated around the antenna a x i s i n d i c a t i n g f u r t h e r that l a r g e s e c t i o n s of the r e f l e c t o r are out of adjustment by only small amounts. Phase e r r o r s due to s m a l l , long-range d i s t o r t i o n s such as de\u00E2\u0080\u0094 1 7 f o c u s s i n g and warpage are d i s c u s s e d f u r t h e r i n S. S i l v e r where the behaviour shown can be compared q u a l i t a t i v e l y with the experimental r e s u l t s ^ Aside from d e f e c t s i n the r e f l e c t o r , some experimental d i f f i c u l t y i s suspected where i r r e g u l a r i t i e s i n background r a d i a t i o n could enter the main beam and cause the r e c e i v e r output to change more than the source a c t i n g on the f i r s t s i d e \u00E2\u0080\u0094 l o b e . Since C a s s i o p e i a i s at 250 K, i t s e f f e c t on the f i r s t s i d e -lobe i s of the order of 0\u00C2\u00AB25\u00C2\u00B0K, but the v a r i a t i o n i n background 68 Fig u r e 29(a)* Comparison of experimental and t h e o r e t i c a l beam-shape curves f o r d r i f t scan (E-plane or m = 90\u00C2\u00B0) 69 + \u00E2\u0080\u0094 1 ! : \" * ; \u00E2\u0080\u00A2 2 1 0 1 2 Q (degrees) F i g u r e 29(b), Comparison of experimental and t h e o r e t i c a l beam-shape curves f o r d e c l i n a t i o n scan (H-plane or(/) : 0\u00C2\u00B0) ^ 70 r a d i a t i o n could e a s i l y v a r y by t h i s amount. As a r e s u l t * there i s some u n c e r t a i n t y i n s e t t i n g the zero l i n e on the output t r a c e . I f t h i s v a r i a t i o n i n background l e v e l were known, i t could be s u b t r a c t e d from the output t r a c e and the v a r i a t i o n due to the antenna p a t t e r n c o u l d be found. Although the expected si d e \u00E2\u0080\u0094 l o b e v a r i a t i o n i s about 0.25\u00C2\u00B0K* the r e c e i v e r i s p r e s e n t l y capable of d e t e c t i n g changes of about 0.1\u00C2\u00B0K\u00C2\u00AB Hence, there i s no u n c e r t a i n t y i n the s i d e - l o b e l e v e l due to the r e c e i v e r t h r e s h o l d . 5.2 S o l a r Measurements As mentioned i n 5.1, the d e t e c t i o n of side lobes and e f f e c t s due to spars r e q u i r e s a v e r y strong source. The sun, 4 o at a temperature of 5 x 10 K, would be s u f f i c i e n t l y powerful to show up lobes at about \u00E2\u0080\u009450 db. I t was p o i n t e d out, however, th a t t h i s source i s broad and non-uniform and as a r e s u l t * the p a t t e r n would be smaared. That i s , the response i s simply the c o n v o l u t i o n i n t e g r a l of the antenna p a t t e r n and the s o l a r d i s t r i b u t i o n . In a one\u00E2\u0080\u0094dimensional system, the response as a f u n c t i o n of 0 i s w r i t t e n * v(0) \u00E2\u0080\u00A2 A(y-i?) sdf) dfi where A(Q ) i s the antenna power p a t t e r n and S ( ^ ) i s the angular power d i s t r i b u t i o n of the source. U n f o r t u n a t e l y , the d i s t r i -b u t i o n i s only known f o r the \" q u i e t \" sun or when there are no strong b u r s t s of r a d i a t i o n from p o i n t s on the s o l a r s u r f a c e . 71 Consequently for present purposes, the general effect of the sun i s of interest and i s useful for showing up the effects of spars and metal rods. In Figure 30, a contour map of the solar measurements i s plotted along with curves indicating the positions of expected radiation from spars. At the centre, the effects of the main beam and near side\u00E2\u0080\u0094lobes are dominant. However, the effects of spars begin to appear along the curved l i n e s as shown. The contour levels are proportional to the receiver response or temperature. Some features here may be spurious as i t i s Figure 30\u00C2\u00AB Contour plot of solar measurements 72 p o s s i b l e t h a t the main beam may p i c k up i r r e g u l a r i t i e s i n the background r a d i a t i o n from sources not l i s t e d i n standard c a t a l o g u e s . In a d d i t i o n * r e f l e c t i o n s from nearby h i l l s may cause some e r r o r s . I n F i g u r e 31* the antenna-sun geometry i s shown f o r the time when the observations were made. The sun was about -5 degrees i n d e c l i n a t i o n and the observations were made at angles as much as 12 degrees below the sun. These obs e r v a t i o n s are p l o t t e d I n re g i o n s around = 180\u00C2\u00B0 and Q = 12\u00C2\u00B0* Furthermore* t h i s s i t u a t i o n i s only true when the sun i s hi g h e s t i n the sky at noon* L a t e r i n the day, the sun sets lower onto the surrounding h i l l s and the s i t u a t i o n d e t e r i o r a t e s * A g r a z i n g angle of 10 degrees i s s u f f i c i e n t l y small to permit strong r e f l e c t i o n s . Thus* i t i s necessary to repeat the measurements at a d i f f e r e n t time of the year and to compare the Figure 31* Antenna-sun geometry two contour maps. The f e a t u r e s common to both would then be a t t r i b u t e d to the antenna and spars and not to e f f e c t s of h i l l s and unknown c e l e s t i a l sources* 73 In Figure 32, the measured beam-shape of the s c a t t e r i n g cone i s p l o t t e d along w i t h the t h e o r e t i c a l r e s u l t of Chapter 4. T h i s p a t t e r n i s taken from a po i n t Q = 9\u00C2\u00B0 and0= 170\u00C2\u00B0 on the contour map. However, many of the s c a t t e r i n g lobes appear i n p a i r s as shown i n Figure 33. In Chapter 4, the s c a t t e r e d f i e l d was found only and no c o n s i d e r a t i o n was g i v e n to the a d d i t i o n a l 2 1 0 1 2 X (degrees) F i g u r e 32. Comparison of experimental and t h e o r e t i c a l beam-shape of s c a t t e r i n g cone e f f e c t of r a d i a t i o n from the r e f l e c t o r . I t i s suggested here t h a t such i n t e r f e r e n c e e f f e c t s appear i n the s c a t t e r i n g cone and cause the r e s u l t i n g b i \u00E2\u0080\u0094 l o b e p a t t e r n . Thus, the t h e o r e t i c a l beam-width from Chapter 4 can at best be regarded as an approximation and should only serve as a guide i n determining the r a d i a t i o n c h a r a c t e r i s t i c s of the spars. 5.3 Absolute Temperature C a l i b r a t i o n In Chapter 3, the absolute temperature of the antenna 74 Fi g u r e 33 \u00E2\u0080\u00A2 T y p i c a l double lobe observed during s o l a r measurements was estimated to be approximately 16\u00C2\u00B0K and was due mainly to s p i l l o v e r , surface l o s s e s and t r a n s m i s s i o n through the mesh and h o l e s . In t h i s s e c t i o n , an experimental d e t e r m i n a t i o n of the antenna temperature i s to be d e s c r i b e d and the r e s u l t s are compared w i t h the above f i g u r e . In F i g u r e 34, a s i m p l i f i e d v e r s i o n of the ra d i o r e c e i v e r i s shown where the output v o l t a g e i s p r o p o r t i o n a l to the d i f f e r e n c e i n temperature of the two sources, antenna and r e f e r e n c e . Such an arrangement i s the c l a s s i c a l Dicke r a d i o \u00E2\u0080\u0094 18 meter . I f the switch operates at a s u f f i c i e n t speed, the f l u c t u a t i o n s i n r e c e i v e r noise have no e f f e c t on the output and as a r e s u l t , only changes i n antenna temperature a f f e c t s the response. Thus, to measure the absolute antenna temperature, i t i s only necessary to determine the change i n output vo l t a g e f o r a g i v e n temperature change i n the antenna. Instead of the antenna, matched loads at known temperatures can be s u b s t i t u t e d 75 T antenna r e f e r e n c e Rx 9 1 I X > T l t Figure 34. Dicke radiometer f o r c a l i b r a t i n g the output. The r e f e r e n c e - l o a d temperature need not be known p r e c i s e l y but i t must remain constant* In t h i s experiment, c a l i b r a t i n g loads at m e l t i n g - i c e and l i q u i d - o x y g e n temperatures were used while the refer e n c e l o a d remained at room temperature. Thus, the change i n output v o l t a g e f o r a g i v e n change i n temperature was e s t a b l i s h e d . Then by e x t r a p o l a t i o n , the absolute antenna\u00E2\u0080\u0094temperature was found from the new output v o l t a g e . Figure 35 i l l u s t r a t e s the p r i n c i p l e used. In p r i n c i p l e , the method o u t l i n e d above i s s t r a i g h t -forward and y i e l d s the exact answer. U n f o r t u n a t e l y , f u r t h e r c o r r e c t i o n s must be a p p l i e d i n c a l c u l a t i n g the antenna temperature, I t can be seen t h a t the r e c e i v e r i s i n l a r g e - s i g n a l o p e r a t i o n and i t i s expected t h a t n o n - l i n e a r i t y of the output would r e s u l t . In Figure 36, the r e c e i v e r output as a f u n c t i o n of input power i s p l o t t e d where the refere n c e p o i n t shown i s d e f i n e d when the source and r e f e r e n c e temperatures are equal. As the source temperature drops, the output d e f l e c t i o n v a r i e s as shown while 76 i n t e g r a t o r m e l t i n g r-xce ( 2 7 3 \u00C2\u00B0 K ) l i q u i d oxygen* ( 9 0 \u00C2\u00B0 K ) Rx T 1 c out r e f antenna AV T . = 90 - 2 AT ant \u00E2\u0080\u0094 \u00E2\u0080\u0094 out r e f 1 273\u00C2\u00B0 K \"1 - 2 9 0 \u00C2\u00B0 K -AV 2 3 AT ant recorder trace F i g u r e 35\u00C2\u00BB P r i n c i p l e of the absolute-temperature measurement V o u t 6 1 A V , A V , 1 AT ^ h r e l a t i v e temperature Figure 36, Detector law 77 the refer e n c e p o i n t remains f i x e d . Thus, the antenna temperature i s simply T . = T - \u00E2\u0080\u0094 - AT antenna oxygen AP where AT = T. - T \u00E2\u0080\u00A2 i c e oxygen C o r r e c t i o n s must a l s o be made to the noise temperatures from the i c e and l i q u i d \u00E2\u0080\u0094 o x y g e n l o a d s . Short lengths of RG 9B/U c o a x i a l cable were used i n making the v a r i o u s c o n nections. The m e l t i n g i c e was contained i n a l a r g e Dewar a few f e e t from the switch and the e l e v e n \u00E2\u0080\u0094 f o o t connecting cable had a l o s s of 1.1 db. As a r e s u l t , the e f f e c t i v e noise temperature from the l o a d was r a i s e d to 278\u00C2\u00B0K* S i m i l a r l y , the two-foot cable from the oxygen l o a d i n c r e a s e d the temperature to 99.3\u00C2\u00B0K. These: r e v i s e d temp-er a t u r e s were based on an ambient temperature of 296\u00C2\u00B0K. Applying these temperatures and the detector\u00E2\u0080\u0094law c o r r e c t i o n to the above equation, the antenna temperature i s 28\u00C2\u00B0K. During the course of the experiment, i t was necessary to take extreme c a u t i o n i n ensuring that, the three sources, i c e , oxygen and antenna were a l l equal i n impedance* Thus, any v a r i a t i o n i n noise d e l i v e r e d to the r e c e i v e r due to d i s c r e p a n c i e s i n l o a d impedance were e l i m i n a t e d w i t h the use of c o a x i a l double\u00E2\u0080\u0094stub tuners i n s e r t e d i n the i c e and oxygen c a b l e s . The antenna admittance was measured w i t h a General Radio admittance meter and the tuners were set so t h a t the loads appeared to have the same admittance as the antenna. Subsequently, the antenna temperature was then measured as d e s c r i b e d e a r l i e r . The r e c e i v e r bandwidth was set at 200 KHz. In the t h e o r e t i c a l c a l c u l a t i o n s , the antenna temperature was found f o r the case when the a x i s was pointed at the z e n i t h or s t r a i g h t up* However* the absolute measurements were c a r r i e d out at the c e l e s t i a l pole and hence, i t was necessary to r e c o r d the antenna t e m p e r a t u r e ^ v a r i a t i o n as a f u n c t i o n of i t s p o s i t i o n w i t h r e s p e c t to the ground* This v a r i a t i o n i s p l o t t e d i n Fi g u r e 37 f o r the d e c l i n a t i o n motion running p a r a l l e l w i t h the north-south d i r e c t i o n of the earth* (0*1 0 0 m 00 s hour a n g l e ) * I t can be seen t h a t the temperature at the z e n i t h drops by 1\u00C2\u00B0K froift t h a t at the pole and hence, the antenna temperature at the z e n i t h i s 27 K* Note f u r t h e r the in c r e a s e i n temperature i n (5 d e c l i n a t i o n (degrees) F i g u r e 37* V a r i a t i o n of antenna temperature with d e c l i n a t i o n angle 79 the v i c i n i t y of (5 \u00E2\u0080\u0094 50\u00C2\u00B0. This e f f e c t i s due to the v a r i a t i o n i n s p i l l o v e r as d i s c u s s e d i n S e c t i o n 3,5, At t h i s p o i n t , a discrepancy of 11\u00C2\u00B0K remains between a c a l c u l a t e d 16\u00C2\u00B0K and a measured 27\u00C2\u00B0K f o r the antenna temperatures* However* i t i s necessary to p o i n t out that a d d i t i o n a l noise enters the feed from the oxygen and, to a l e s s e r extent, the 19 water vapour i n the atmosphere \u00C2\u00BB At the z e n i t h , the c o n t r i -b u t i o n from the sky i s approximately 2\u00C2\u00B0K, thus p u t t i n g the temperature at 18\u00C2\u00B0K at the horn input* The l a r g e i n c r e a s e s i n temperature shown i n Figure 37 f o r angles w e l l removed from the z e n i t h are l a r g e l y due to the f a c t t h a t the beam passes through more atmosphere and r e s u l t s i n gre a t e r a b s o r p t i o n . r e v e r s i b l e [ M motor horn balance discharge XM\u00E2\u0080\u0094 v a r i a b l e attenuator c a l i b r a t i n g discharge ~Rx ~ l i q u i d oxygen reference F i g u r e 38. Receiver f r o n t - e n d \u00E2\u0080\u00A2 80-The remaining discrepancy of 9\u00C2\u00B0K can be a t t r i b u t e d to the e f f e c t s of the feed horn and d i r e c t i o n a l c o u p l e r . Since the temperature was measured at the switched i n p u t , i t can be seen from F i g u r e 38 t h a t noise amounting to 3\u00C2\u00B0K i s i n s e r t e d by the coupler, which i n t u r n comes from the v a r i a b l e attenuator. (In t h i s experiment, the discharge tubes are not used). Hence, the 6\u00C2\u00B0K d i f f e r e n c e may be a t t r i b u t e d to l o s s e s i n the horn, d i r e c t i o n -a l c o u p l e r , and v a r i o u s connectors and would r e s u l t from a s i g n a l a t t e n u a t i o n of 0.1 db. This l o s s i s t y p i c a l of c o a x i a l - t y p e couplers at these f r e q u e n c i e s . I t i s suggested, however, that the horn (and d i r e c t i o n a l coupler) might be c a l i b r a t e d by p l a c i n g an a b s o r p t i v e enclosure around the horn. A subsequent a b s o l u t e -temperature measurement s i m i l a r to that j u s t d e s c r i b e d would be compared wi t h that r e g i s t e r e d by a thermometer placed i n the e n c l o s u r e . The d i f f e r e n c e would then be a t t r i b u t e d to l o s s e s i n the horn and c o u p l e r . The procedure j u s t d e s c r i b e d i s not the only method a v a i l a b l e f o r making absolute-temperature measurements. I t i s worth c o n s i d e r i n g a n r a l t e r n a t e scheme as a p o s s i b l e method f o r f u t u r e work. In many e l e c t r i c a l measurements, n u l l techniques o f f e r the advantage of e l i m i n a t i n g the e f f e c t s of the d e t e c t i n g d e v i c e . An abvious method would only r e q u i r e t h a t the r e f e r e n c e temperature be a l t e r e d so t h a t the noise l e v e l s on both s i d e s of the switch be equal. The balance and c a l i b r a t i n g discharge tubes as shown i n F i g u r e 38 would not be used here. However, t h i s method would r e q u i r e a c o n t i n u o u s l y - v a r i a b l e thermal source f o r the r e f e r e n c e at around 30\u00C2\u00B0K. A l t e r n a t i v e l y , the r e f e r e n c e can be set at the p r e s e n t l y a v a i l a b l e l i q u i d - o x y g e n temperature, and a 81 known amount of noise can be added on the antenna side of the switch making both sides 90\u00C2\u00B0K. This method r e q u i r e s the use of an accurate, v a r i a b l e attenuator i n s e r t e d between the switch and antenna. In t h i s case, the measured antenna temperature i s 28\u00C2\u00B0K and the r e f e r e n c e i s about 90\u00C2\u00B0K. An a t t e n u a t i o n of 1.124 +0.017 db i s r e q u i r e d i f the antenna temperature i s to be known to w i t h i n + 1\u00C2\u00B0K. A t o l e r a n c e of t h i s order i s im-p o s s i b l e to achieve with even the best attenuators and i t would be necessary to use more p r e c i s e methods. For example, RG 9 B/U cable has a l o s s of about 10 db per 100 f e e t at 1420 MHz and i s e a s i l y measured -to 0.1 db. Thus,11.24 f e e t of cable would give the r e q u i r e d l o s s to a t o l e r a n c e of + 0.01124 db. This method would r e q u i r e s u b s t i t u t i o n of v a r i o u s lengths of cable u n t i l the r e c e i v e r output i s n u l l e d . For t h i s reason, the procedure i s tedious unless the n u l l i s reached a f t e r one or two t r i a l s . Other means of measuring the absolute temperature of the antenna can be c e r t a i n l y be proposed. However, i t i s beyond the scope of t h i s t h e s i s to consider a l l p o s s i b i l i t i e s . The a l t e r -n a t i v e method d i s c u s s e d here should acquaint the reader with the approach to be taken i n e v a l u a t i n g other p o s s i b l e schemes. For a f u r t h e r d i s c u s s i o n of antenna-temperature measurements, the 20 reader i s r e f e r r e d to Schuster, et a l , where an 85-foot para-b o l o i d o p e r a t i n g at 960 and 2388 MHz i s considered. 82 6. CONCLUSIONS This t h e s i s has attempted to give some understanding and f e e l i n g f o r the behaviour of the p a r a b o l o i d a l antenna and some of i t s unavoidable i m p e r f e c t i o n s . Chapter 2 has d e a l t w i t h the i d e a l r e f l e c t o r and methods were developed f o r c a l c u l a t i n g i t s wide-angle r a d i a t i o n p a t t e r n . Although the c u r r e n t - d i s t r i \u00E2\u0080\u0094 b u t i o n method i s not new* i t has r a r e l y been used i n the study of such antennas and the methods developed here may prove u s e f u l f o r c a l c u l a t i o n of other wide-angle p a t t e r n s . Chapter 3 has attempted to estimate the e f f e c t s of i m p e r f e c t i o n s i n the r e f l e c t o r and f e e d . Surface roughness has been t r e a t e d from a s t a t i s t i c a l standpoint whereas most attempts i n the l i t e r a t u r e have Considered s p e c i f i c types of surface e r r o r * R a d i a t i o n from the ground and from surface l o s s e s have been estimated to b r i n g the e q u i v a l e n t noise temperature of the antenna to 16\u00C2\u00B0K* Small surface e r r o r s are not expected to a f f e c t t h i s f i g u r e * The spars have been s t u d i e d i n Chapter 4 and a t h e o r e t i c a l b a s i s has been e s t a b l i s h e d f o r t h e i r general behaviour. The s i t u a t i o n i s complicated by the f a c t t h a t both the c o a x i a l cables and d i e l e c t r i c spars s c a t t e r the i n c i d e n t f i e l d . However* the sCattering-cone concept d i s c u s s e d here remains v a l i d . I t i s t h e r e f o r e p o s s i b l e to p r e d i c t the d i r e c t i o n of the s c a t t e r e d r a d i a t i o n and to assess i t s e f f e c t on the general behaviour of the antenna* The experimental work i n Chapter 5 has attempted to v e r i f y : some of the t h e o r e t i c a l c l a i m s i n previous c h a p t e r s . A check on 83 the small\u00E2\u0080\u0094angle p a t t e r n was c a r r i e d out using the powerful r a d i o s t a r C a s s i o p e i a A. V h i l e agreement was achieved f o r the main beam, the f i r s t s i d e - l o b e was higher than expected. Surface e r r o r s are probably the p r i n c i p l e cause although i r r e g u l a r i t i e s i n background r a d i a t i o n could a l s o c o n t r i b u t e to t h i s d i s c r e p a n c y . An a r t i f i c i a l e a r t h - s a t e l l i t e would c e r t a i n l y be u s e f u l i n making p a t t e r n measurements and would c l e a r away much of the doubt u s i n g n a t u r a l s ources. In order to check the spars, the sun was used to r e v e a l the p r e d i c t e d s c a t t e r i n g cones. However, the h i l l s are b e l i e v e d to have caused some tr o u b l e i n the observations near (7j) = 180\u00C2\u00B0, These obser v a t i o n s should be repeated at a d i f f e r e n t time of the year and a comparison could then be made. F i n a l l y , an absolute noise-temperature measurement was c a r r i e d out and i t was found, a f t e r s e v e r a l c o r r e c t i o n s , to be about 27\u00C2\u00B0K f o r the antenna poi n t e d at the z e n i t h . However, t h i s f i g u r e i n c l u d e s the e f f e c t s of l o s s i n the feed horn and d i r e c t i o n -a l coupler whereas the 18\u00C2\u00B0K f i g u r e i s the temperature at the horn i n p u t . A p o s s i b l e c a l i b r a t i o n procedure d e s c r i b e d i n Chapter 5 would c l e a r away any doubts about t h e i r noise c o n t r i b u t i o n s . I t i s hoped that t h i s t h e s i s w i l l i n s p i r e f u r t h e r i n v e s t i -g a tions i n t o pattern-measurement techniques f o r r a d i o t e l e s c o p e s and space\u00E2\u0080\u0094communication antennas. Furthermore, the study of p r e c i s e noise\u00E2\u0080\u0094measuring methods could be expanded so t h a t improve-ments co u l d be made i n the temperature c a l i b r a t i o n of la r g e an-tennas and i n the o b s e r v a t i o n a l techniques of r a d i o astronomy. 84 REFERENCES 1. S i l v e r , S. , Microwave Antenna Theory and Design, MIT R a d i a t i o n Laboratory S e r i e s , V o l . 12, New York, McGraw-Hill (1949), pp. 415-423. 2. S i l v e r , S., op* c i t . * p. 440* 3. M i l l a r , R.F., \"A Horn Feed f o r an 84-Foot P a r a b o l o i d \" * ERB-533* N a t i o n a l Research C o u n c i l of Canada, Radio and E l e c t r i c a l E n g i n e e r i n g D i v i s i o n , Ottawa (January, I960)* 4* C a r t e r * D., \"Wide\u00E2\u0080\u0094Angle R a d i a t i o n i n P e n c i l Beam Antennas\"* J o u r n a l of A p p l i e d P h y s i c s * V o l . 26, No. 6 (June, 1955), p. 645. ~ 5. \" E v a l u a t i o n of L i m i t s ; Use of Recurrence R e l a t i o n s \" , Modern Computing Methods, Na t i o n a l P h y s i c a l Laboratory* Her Majesty's S t a t i o n e r y O f f i c e ( l 9 6 l ) , pp. 122-123* 6. S i l v e r , S., op* c i t * * pp. 119-122. 7. B r a c e w e l l , R.N*, \"Tolerance Theory of Large Antennas\", IRE T r a n s a c t i o n s o'fe Antennas and Propagation* V o l . AP-9* No* 1 (January, 1961), p. 49. 8. Swarup, G* and Yang, K.S^, \"Monitoring P a r a b o l o i d a l Antennas\", Proceedings of the IRE, V o l . 48, No. 11 (November, 1960), p. 1918(Correspondence). 9. Dragone, C* and Hogg* D.C., \"Wide-Angle R a d i a t i o n due to Rough Phase F r o n t s \" , B e l l System T e c h n i c a l J o u r n a l * V o l . 42* No* 5 (September 1963), p. 2285. 10. Mumford, W.W., \"Some T e c h n i c a l Aspects of Microwave R a d i a t i o n Hazards\"* Proceedings of the IRE* V o l . 49, No. 2 (February^ 1961), p. 445. 11. H a r r i n g t o n * R.F*, Time\u00E2\u0080\u0094Harmonic Electromagnetic F i e l d s * New York* McGraw-Hill (1961), pp. 365-371. 12* King, R.W.P. and Wuy T.T., The S c a t t e r i n g and D i f f r a c t i o n of Waves, Cambridge, Massachusetts, Harvard U n i v e r s i t y Press (1959)* p. 22. 13. Mentzer, J.R., S c a t t e r i n g and D i f f r a c t i o n of Radio' Waves* London, Pergamon Press (1955), pp. 62-64* 14. K i e l y * D.G*, D i e l e c t r i c A e r i a l s , London* Methuen and Co* L t d . (1953), p. 81* ~~~ 85 15. Mentzer, J . R., op, cit\u00C2\u00AB, p. 102. 16. Brueckmann, H., \"Antenna Pattern Measurement by S a t e l l i t e \" , IEEE Transactions on Antennas and Propagation. V o l . AP-11, No. 2 (March, 1963), p. 143. ^ 17. S i l v e r , S., op. c i t * , p. 190. 18. Dicke, R. H., \"The Measurement of Thermal Radiation at Microwave Frequencies\", The Review of S c i e n t i f i c Instruments. V o l . 17, No. 7 (July 1946), p. 268. 19* Hogg, D* C., \"Sources of Noise i n Centimeter Wave Antennas\"* Low Noise Electronics, London, Pergamon Press, (1962), pp. 307-309* \" 20. Schuster, D., S t e l z r i e d , C* T*, and Levy, G* S., \"The Determination of Noise Temperatures of Large Paraboloidal Antennas\", IRE Transactions on Antennas and Propagation* V o l . AP-10, No. 3, (May, 1962), p* 286* "@en . "Thesis/Dissertation"@en . "10.14288/1.0103234"@en . "eng"@en . "Electrical and Computer Engineering"@en . "Vancouver : University of British Columbia Library"@en . "University of British Columbia"@en . "For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use."@en . "Graduate"@en . "The receiving pattern of a paraboloidal antenna used in radio astronomy"@en . "Text"@en . "http://hdl.handle.net/2429/39683"@en .