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Measurement of the propagation characteristics of shielded and unshielded dielectric-tube waveguides Makino, Ikufumi 1970

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MEASUREMENT  OF THE PROPAGATION CHARACTERISTICS  SHIELDED AND UNSHIELDED DIELECTRIC-TUBE .  OF  WAVEGUIDES  by  IKUFUMI MAKINO B.Sc,  Doshisha  U n i v e r s i t y , 1967  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n the Department o f Electrical  We a c c e p t  this  t h e s i s as conforming  required Research Supervisors  Engineering  to the  standard  •. >  «...  Members o f the Committee  Head o f Department  Members o f the Department o f Electrical  Engineering  THE UNIVERSITY OF BRITISH COLUMBIA  December, 1970  In  presenting  this  thesis  an a d v a n c e d  degree  the L i b r a r y  s h a l l make  I  f u r t h e r agree  for  scholarly  by h i s of  this  written  at  the U n i v e r s i t y  that permission  It  The U n i v e r s i t y o f B r i t i s h V a n c o u v e r 8, Canada  1' ,  shall  tBno^/veerC Columbia  1310  for  the  requirements  Columbia,  I agree  r e f e r e n c e and copying of  this  that  not  copying  or  for  that  study. thesis  t h e Head o f my D e p a r t m e n t  is understood  financial gain  Beefarieg.)  December  British  by  permission.  Department o f  Date  of  for extensive  p u r p o s e s may be g r a n t e d  for  fulfilment of  it freely available  representatives. thesis  in p a r t i a l  or  publication  be a l l o w e d w i t h o u t my  ii  ABSTRACT  Accurate measurements of the propagation c o e f f i c i e n t of the HE^^ mode on polythene-tube waveguides i n a i r and surrounded by a polyfoam s h i e l d are reported.  These were carried out at X-band  frequencies using a cavity-resonance method.  The results obtained  confirm previous t h e o r e t i c a l predictions although there i s an element of uncertainty concerning the exact d i e l e c t r i c properties of the commercial grade polythene tubes used.  The measurements also yielded the phase  c o e f f i c i e n t of the HE^^ mode which was confirmed by measurement of the r a d i a l decay of the e l e c t r i c f i e l d outside the tube. Enclosing the d i e l e c t r i c - t u b e i n a low-density, low-loss polyfoam  s h i e l d resulted i n only a s l i g h t degradation of the attenuation  c h a r a c t e r i s t i c s of the waveguides.  .  -  Measurements of the phase c h a r a c t e r i s t i c s of the higher order T E Q ^ and T M Q ^ modes on the tube at frequencies close to cutoff are also reported.  iii  TABLE OF CONTENTS ABSTRACT .  .  TABLE OF CONTENTS LIST OF ILLUSTRATIONS  Page i i i i i  ...  . iv  LIST OF TABLES  . vi  LIST OF SYMBOLS  v i i  ACKNOWLEDGEMENT  iv  1.  INTRODUCTION  1  2.  SURFACE-WAVE PROPAGATION ON DIELECTRIC-TUBE WAVEGUIDES  3  2.1 2.2  3 6 6 9  3.  F i e l d Components Mode Spectrum 2.2.1 C h a r a c t e r i s t i c Equations 2.2.2 Cutoff Conditions  :  CAVITY-RESONANCE METHOD OF MEASURING ATTENUATION , 3.1 Introduction 3.2 R e l a t i o n Between A t t e n u a t i o n C o e f f i c i e n t and Q F a c t o r ... 3.2.1 R e l a t i o n Between A t t e n u a t i o n C o e f f i c i e n t and Q. F a c t o r f o r Surface-Wave Resonator 3.3 R e l a t i o n Between Unloaded Q and Loaded Q  11 11 11  4.  EXPERIMENTAL APPARATUS 4.1 Introduction 4.2 Surface-Wave Resonator 4.3 Mode E x c i t e r s  18 18 20 26  5.  RESULTS 5.1 Dependence o f C a v i t y Q F a c t o r on S i z e o f C o u p l i n g Aperture 5.2 Measurement o f Guide Wavelength 5.3 Measurement o f R a d i a l Decay o f E l e c t r i c F i e l d 5.4 Measurement o f A t t e n u a t i o n C o e f f i c i e n t  29  CONCLUSIONS  42  6.  REFERENCES  13 16  29 30 36 38  43  iv LIST OF ILLUSTRATIONS Figure  . Page  2.1  The D i e l e c t r i c Tube Waveguide  3  2.2  Mode Spectrum of Polythene Tube, p=0.5  8  2.3  Cutoff Conditions;  3.1  C h a r a c t e r i s t i c s of D i e l e c t r i c Tube Waveguides, H E ^ Mode ...  12  3.2  Transmission C h a r a c t e r i s t i c s of a Resonant Cavity  16  3.3  . V a r i a t i o n of Input Impedance of a Resonant Cavity  16  T E , TM , EH Q 1  Q1  and H E  12  Modes  10  4.1  Layout of Apparatus  19  4.2  General View of Surface-Wave Resonator  4.3  Surface-Wave Resonator  23  4.4  D e t a i l s of Cavity End P l a t e Showing H E ^ Mode E x c i t e r ......  24  4.5  D e t a i l s of Cavity End P l a t e  25  4.6  Diagram of TEQ-^ Mode E x c i t e r and P o s i t i o n of E x c i t e r  .  22  R e l a t i v e to D i e l e c t r i c Tube  26  4. 7  TE  28  4.8 5.1  T M Mode E x c i t e r Measured Dependence of Cavity Q Factor o f H E ^ Mode on Coupling Aperture Diameter  29  5.2  Measurement of Guide Wavelength of H E ^ Mode by F i e l d Perturbing Bead Method  31  5. 3.a  Experimental and T h e o r e t i c a l Phase C h a r a c t e r i s t i c s of HE.. Mode on Polythene Tube I  33  Experimental and T h e o r e t i c a l Phase C h a r a c t e r i s t i c s of HE.^ Mode on Shielded and Unshielded Polythene Tube I I  34  5.3.b 5.3. c  Q 1  Mode E x c i t e r  28  Q1  1  Experimental and T h e o r e t i c a l Phase C h a r a c t e r i s t i c s of HE.. Mode on Polythene Tube I I I  35  5.4. a  R a d i a l Decay of E  f o r H E ^ Mode  36  5.4.b  R a d i a l Decay of E , f o r HE-. Mode r3 11  37  J  z 3  V  Figure 5.5.a  Page Experimental and Theoretical Attenuation C h a r a c t e r i s t i c s of HE Mode on Polythene Tube I  39  5.5.b  Experimental and Theoretical Attenuation C h a r a c t e r i s t i c s of 'HE Mode on Shielded and Unshielded Polythene Tube I I . 40  5.5.c  Experimental and Theoretical Attenuation C h a r a c t e r i s t i c s of HE Mode on Polythene Tube I I I  4  1  LIST OF TABLES Table 3.1  Sample Output from  QFACTOR .  4.1  D e t a i l s of Polythene Tubes ..  5.1  D e t a i l s of Coupling Apertures  vii  LIST OF SYMBOLS a., b .  = constants  A (p..), B (p..)  = functions  c.  = jb /a  ^ z i ' ^rL' ^ f l i  ±  =  of Bessel  functions  ±  ^ - ^ ^ ^ ^ - » a d i a l , azimuthal components of e l e c t r i c on  field,  u  na  r  respectively, i n medium i  f  = frequency  f h.  = resonant frequency = wave number of medium i  H ., H ., H . zi r i 61  = l o n g i t u d i n a l , r a d i a l , azimuthal components of magnetic f i e l d , respectively, i n medium i  I (p..) n *ij  = modified Bessel function of the f i r s t  J  = Bessel function of the f i r s t  1  (p..) n *ij  kind  kind  kg  = phase c o e f f i c i e n t of free space  K (p. .)  = modified Bessel function of the second kind  I  = number of h a l f wavelengths i n resonator  L  = length of resonator  m, n  = mode subscripts  N,  = t o t a l power loss per unit length and power loss p e r unit length i n medium i , respectively  N  = power flow  g  N ,N P P P*4 ij  Q  = t o t a l power loss i n each end plate and power loss i n each plate i n medium i , respectively h.r. i j = q u a l i t y factor  Q  = loaded Q factor 1  Q u  = unloaded Q factor  r  = r a d i a l co-ordinate  r^,  = inner and outer radius of tube respectively  viii  R  = normalized r e s i s t i v e component  R^  = r e s i s t i v e component of wave impedance of a metal  S>A' Sg, S^  = integrals of functions  of Bessel  S_, S„, T , T„  = integrals of functions  of modified Bessel  tan5,  = loss tangent of medium i  VQ , v , v ^ ^  = speed of l i g h t i n free space, group v e l o c i t y and phase v e l o c i t y , respectively  W, W.  = t o t a l energy storage per unit length and t o t a l energy  1  K.  B>  1  K  functions functions  storage per unit length i n medium i , respectively Y (p..)  = Bessel function of the second kind  z  = l o n g i t u d i n a l co-ordinate  Z  = impedance of free space  a  = attenuation  3  = phase c o e f f i c i e n t of tube  3^  = coupling c o e f f i c i e n t  Af e . ri  = bandwidth = r e l a t i v e p e r m i t t i v i t y of medium i  0 .  = azimuthal co-ordinate  X  = free space wavelength  X , X , X c g r  = cutoff, guide and resonant wavelength,respectively  u  = r e l a t i v e premeability  P  -  ui  = angular frequency  c o e f f i c i e n t of tube  r /r ±  2  of medium i  iv ACKNOWLEDGEMENT The author i s deeply indebted to his research supervisors Dr. B. Chambers and Dr. M.M.Z. Kharadly for t h e i r encouragement and guidance throughout the course of t h i s project. Grateful acknowledgement i s made to the National Research Council of Canada for support under grants A3344 and A7243 and to the University of B r i t i s h Columbia f o r the award of a University of B r i t i s h Columbia Graduate Fellowship during the academic years 1968-1970. The author i s also g r a t e f u l to Mr. C.G. Chubb, Mr. D.G. Daines and Mr. J.H. Stuber for building the p r e c i s i o n equipment and to Mr. H.H. Black for the photographic work. The author also wishes to thank Miss Linda Morris f o r typing the manuscript and Mr. B. Wilbee, Mr. F. Scholz and Mr. S. Graf for t h e i r c a r e f u l proofreading of the f i n a l d r a f t .  1. During  the l a s t  INTRODUCTION  f o r t y y e a r s o r so, many i n v e s t i g a t o r s have  c o n s i d e r e d the problem o f surface-wave p r o p a g a t i o n a l o n g tubes.  dielectric  In 1932, Zachoval"'" o b t a i n e d the c h a r a c t e r i s t i c e q u a t i o n f o r  T M Q ^ modes and s o l v e d t h i s g r a p h i c a l l y  f o r a range o f tube  parameters.  2 Two y e a r s l a t e r ,  the e x i s t e n c e o f these modes was v e r i f i e d by L i s k a ,  whose measurements o f guide wavelength showed good agreement w i t h Zachovai's f o r TE  theory.  In 1949, A s t r a h a n  o b t a i n e d the c h a r a c t e r i s t i c  equations  and h y b r i d modes and measured v a l u e s o f guide wavelength f o r  the H E ^ , T M Q ^ and TE  modes which agreed v e r y w e l l w i t h t h e o r y . 4  about the same time, Jakes c i e n t s o f TM„  and TE„  Om  At  gave e x p r e s s i o n s f o r the a t t e n u a t i o n c o e f f i -  modes and measured the a t t e n u a t i o n o f the TM'  Om  01  and TEQ-^ modes on p o l y s t y r e n e tubes.  A t e c h n i q u e f o r o b t a i n i n g the  a t t e n u a t i o n c o e f f i c i e n t o f any mode was o u t l i n e d by Unger^ i n 1954 u s i n g a method s i m i l a r t o J a k e s ' , but the a n a l y s i s was completed  o n l y f o r the  6 ^11  m o c  *  e  o  n  tubes w i t h s m a l l diameter  t o wavelength r a t i o s .  Mallach  made a rough e s t i m a t e o f the a t t e n u a t i o n o f the H E - Q mode by measuring the r a d i u s a t which t h e magnitude o f the e l e c t r i c i t s v a l u e a t t h e tube s u r f a c e .  field  fell  t o 1/e o f  I n 1968 Kharadly and Lewis'' completed  comprehensive study o f t h e p o s s i b l e u s e f u l n e s s o f the d i e l e c t r i c a l o w - l o s s waveguide. propagating  They concluded  the dominant  t h a t a moderately  a  tube as  t h i n - w a l l e d tube  mode c o u l d have p r o p a g a t i o n  characteristics  g r e a t l y s u p e r i o r t o those o f c o n v e n t i o n a l m e t a l l i c waveguides a t m i l l i m e t e r wave f r e q u e n c i e s .  A l s o , they proposed  a method f o r overcoming the problems  of s u p p o r t i n g the tube and the d e g r a d a t i o n o f performance due to adverse weather c o n d i t i o n s o r nearby o b s t a c l e s .  T h i s c o n s i s t e d o f embedding t h e  tube i n a l a y e r o f l o w - d e n s i t y , l o w - l o s s d i e l e c t r i c o f s u f f i c i e n t  radial  extent that a n e g l i g i b l e p o r t i o n of the wave was c a r r i e d outside t h i s dielectric. So f a r as i s known, no accurate measurements of the attenuat i o n c h a r a c t e r i s t i c s of the dominant HE  mode on d i e l e c t r i c - t u b e s have  been made. This seems s u r p r i s i n g i n view of the f a c t that t h i s mode i s the one most l i k e l y to be used i n p r a c t i c e . The o b j e c t i v e s of the i n v e s t i g a t i o n reported here were therefore: (i)  to obtain experimental data on the attenuation and phase c o e f f i c i e n t s  of the HE  mode on commercially a v a i l a b l e polythene tubes from d i r e c t  measurements, using the cavity-resonance method. ( i i ) to a s c e r t a i n experimentally the e f f e c t of s h i e l d i n g the tube w i t h low-density, low-loss polyfoam. Chapter 2 reviews b r i e f l y some of the features of surface-wave propagation on d i e l e c t r i c - t u b e waveguides. i s drawn from reference 7.  The theory i n t h i s chapter  In Chapter 3, the theory underlying the c a v i t y -  resonance method f o r measuring the attenuation c o e f f i c i e n t of low-loss waveguides i s discussed.  This i s followed i n Chapter 4 by a d e s c r i p t i o n  of the experimental apparatus used.  Experimental r e s u l t s f o r the propagation  c h a r a c t e r i s t i c s of the H E ^ mode on-polythene  tubes i n a i r and surrounded  by a polyfoam s h i e l d are given i n Chapter 5, together with r e s u l t s f o r the phase c o e f f i c i e n t of the Q ^ and TM ^ modes at frequencies close to c u t o f f . t e  Conclusions drawn from t h i s i n v e s t i g a t i o n and suggestions f o r further work are contained i n Chapter 6.  3  2. 2.1  SURFACE-WAVE PROPAGATION ON DIELECTRIC TUBE WAVEGUIDES  Field  Components The tube c o n f i g u r a t i o n of i n t e r e s t i s shown i n f i g u r e 2.1.  It  c o n s i s t s o f two c o a x i a l d i e l e c t r i c r e g i o n s  r e l a t i v e p e r m i t t i v i t i e s e , and e „ embedded r l r2 v  of r e l a t i v e p e r m i t t i v i t y 3 > e  r  e  and  r2  o f i n f i n i t e l e n g t h and i n a third  infinite  dielectric  where .2.1  > r l e  e _ > e r2 r3 _  In a l l c a s e s ,  i t w i l l be assumed t h a t the r e l a t i v e p e r m e a b i l i t y  r e g i o n , u ., i s u n i t y . ri' w i t h t-9-z  o f the  P r o p a g a t i o n i s assumed i n ' t h e z - d i r e c t i o n ,  dependence o f the form exp j(wt-n0.-6z) i n the l o s s l e s s case.  "r3 Figure  2.1  The D i e l e c t r i c - T u b e  Waveguide  4 Under these c o n d i t i o n s , o m i t t i n g the f a c t o r exp j ( w t - n 6 - $ z ) , the f i e l d  E  E  components a r e g i v e n by  zl = l V l a  h  R = J hT 1  rl  r  )  '  01 2_ "1 h  l  n y  lW >  a  ri  k  n n z  \h, r  +  \  I  1  n  n^l  r  V )  n  1  0 H  zl = l V l > b  h  n  H  rl  h  l  r  ei  =  r  ,2.2.a  , k  e  — Z  i W  a  0  )  +  +  f  ^  Jhfi~ i a  i  ^  ~  10  E  E  z2  J  = 2 a  o  -  n  n  Our)H Z  i  a  '82 " " TT 2 V 2 ^  z2  h  J  = 2 b  n  h  ' nu  •  h 2  2  )  W> « a  _ k Z  A (h r)  2  n  2  " [l h r 2 VV>  r)  r  r  r  Y (h.r) n 2  b  2  * /v  6  a  H  V i  h  1  r2 = ll2 2 V •  i  b  k  e H  \ i )  +  y  r2 0 0 . k  h ~  J  .» . •  Z  b  2  V  h  2  r  )  ^  (h r ) + r 2 b  1 2  Y(h.r) n 2  = b  2  B (h r) n  2  \ = ? 7 2 V 2 - j f 2 VV» a  h  r)  b  2  h rZ 2  £ H  <r <  62  =  2  Q  k  "J z f0 h T2  a  2 n A  ( h  2  r )  "  X " h  b  2  2r  B  n  ( h  2  r )  r  l ±  r  ± 2 r  ,2.2.b  J  z3  r3  a  K (h r)  3  j  n  3  K ' (h„r) +' h „ 3 n i 3  n  ^ .2  y  r  3 9  ° ° ,2 h« r  b„ K (h,r) J n 3  tu \ - r 3 0 0 , ', . a_ K (h r ) - 3 b K_(h,r) 3 n 3 3 n 3  n  y  K  Z  v  0  v  r  r z3  b.K (h„r) 3 n 3  H = r3  H  63  J  r Z  3  3  < r < «> .2.2.c  a  h  2  3 n K  ( h  3  r )  J IT 3 3  +  b  Q  K  n  ( h  3  r )  ^h^ 3 >3 r 7|-- 3 n 3 a  0  K  r)+  b  K  (h  r)  1  where, from the wave equation 2 2 2 h- = 3 - u , * e , k 1 " r l r l 0 n  h  2 2  2 =  y  r2  e  r2 0 " k  2 ,2.3  B  2 2 3 - u e _ k_ r3 r3 0 0  The symbols appearing  i n equations  2.2 and 2.3 are defined i n the l i s t of  symbols. Upon s e t t i n g n=0 (no 6-variation), equations two sets corresponding  2.2 separate  into  to the c i r c u l a r l y symmetric modes designated T M Q ^ and  TE„ . For n^O, equations Om  2.2 describe inseparable combinations of TE and TM  modes which are designated hybrid modes.  In general, one or other of  the component parts of a hybrid mode i s dominant.  I f the TE portion  i s dominant, the mode i s designated HE ; i f the TM component i s dominant, nm i t i s termed EH . The nature of TE or TM dominance and the s i g n i f i c a n c e nm of the subscript m i n the mode designation i s discussed f u l l y i n reference 7.  6 2.2 Mode Spectrum 2.2.1  C h a r a c t e r i s t i c Equations By matching the a x i a l and tangential f i e l d components  and 2 at r=r^ and those i n media 2 and 3 at * *2> l 8 e  =  i n eight unknowns, a.^,.b^, i=l-4, are obtained.  i n media 1  homogeneous equations  n t  These may be solved to  give the following c h a r a c t e r i s t i c equations f o r the hybrid modes:  «  r  / r2 n 22  )  \P 2 n 22  )  £  A  ( p  A  ( p  2  i  , r3 n £  P  K  ( p  3 ¥r2 n P22 B  (  2  32 n 32 A 22 n 22 K  (p  P  )  B  (p  ,2.4.a  3 nn _ 3^2_ ^r _  y  ) +  )  P  K  ( p  32 n 32 K  ( p  )  )  32 J y  and  ^ r2 n 21 £  A  ( p  lP l n 21 A  (p  )  )  ,  Wn^' P  2  ll n I  ( p  f y  r2 n 21 B  ( p  l l ^ ' 21 n 21 )  p  B  (p  +  )  Equation 2.4.a i s applicable f o r EH for HE  nm  modes.  2.4.b  )  Pll „<Pll>I  '21'  modes and equation 2.4.b i s applicable  The r a t i o a./a„ i s given by equation 2.5. 4 2  The r a t i o b./b„  <\ L •  i s obtained from equation 2.5 by interchanging and ^ The characteri s t i c equations for the TE and TM_ modes are obtained by s e t t i n g n=0 i n Om Om e  u  r  rt  M  equation 2.4.b. A t y p i c a l spectrum of modes on a polythene tube i n free space (e  rl  =£  =y =y =y =1 r3 r l r2 r3  A e „=2.26, and P=r../r =0.5) i s shown i n figure 2.2. r2 1 2  The main features of the mode spectrum are: (i)  The HE^^ mode has no lower cutoff frequency.  (ii)  Unlike the case for the d i e l e c t r i c rod (p=0), the T E  and TM„ modes do not have the same value of r„/X Om I  at cutoff.  Q m  This i s  also true f o r HE. ,. and EH. modes. l,m+l lm. (iii)  As P"KL, the phase c h a r a c t e r i s t i c s of the TE^  mode become indistinguishable, as do those of the TM^  and  E H  ]_  and m m  HE^  °des, thus  1  CN  ^—N  rH CN  ft -  rH CN  ft  •w  c CN  i-l  (0  + rH rH  I—1  rH P.  -  a  M  rH rl (J  ft  c  t—1  rH rH  ft  CN ft  rH CN  *—* CN CN  CN ft  ft  c  I  rH CN  >-)  V  rH CN  *-> rH CN ft  c  ft' —  *  a  >< rH CN (X  ft  c  ft  '  CN ft  CN ft  CN ft CN ft  CN ft  CN CN ft  CN CN ft  CN  CN ft CN ft CN ft  CN  U  3-  +  I  CN  CN CO ft  CN  CN CN ft  8  providing  the p h y s i c a l d i s t i n c t i o n between HE and EH modes. (iv)  As p-KL, the n=0 and n=l modes appear i n widely separated  c l u s t e r s , each c l u s t e r c o n s i s t i n g of four modes ( (v) value of  HE lm  >  T E  o ' ™0m m  a n d  E H  lm^'  The HE, and TE. phase c h a r a c t e r i s t i c s i n t e r s e c t at some lm Om . I n most cases, f o r values of r^/A greater than that at the  i n t e r s e c t i o n , the d i f f e r e n c e s  i n the two curves are too small to be seen  g r a p h i c a l l y . However, the degeneracy of the H E ^  a n d  T E  02  be seen i n f i g u r e 2.2.  Figure 2.2  Mode Spectrum of Polythene Tube, p=0.5  m o d e s  ^  o r  san  2.2.2  Cutoff Conditions Lossless surface-wave propagation on the d i e l e c t r i c - t u b e  requires that a l l quantities appearing i n equations 2.3 be r e a l and positive.  If u ~e =u .e then cutoff occurs when h =0 and h =0, or r3 r3 r l r l 3 1 0  generally, when P-j^O  anc  ^ ll ^° p  Hence by applying small argument  =  approximations to c e r t a i n of the Bessel functions i n equations 2.4.a-b, the following cutoff conditions are obtained.  r l 21 Q P 2 1 " T —-, s r l 21 0 2 1 > "  £  P  J  (  )  2 e  R  £  p  Y  (p  2 £  r2 7, r2  : J  l ?21 ~—: (  )  ^ x TM modes A  \<» J 2  0 22 Y (P ) J  ( p  )  Q  2.6.a  2 2  P  21 0  p  21 Y ( p ) -.2Y p  J  ( P  21  0  P  Y  ( p  22  l  _ 1 22  }  Y  l  (P  At cutoff p  (  ( p  2 2  p  2i  l(  }  2]L  TE modes )  2 1  2 1  y  " 1 P21> J (P ) J  )  ,2.6.b  HE, modes lm m > 1  r  22 J  (  1  2 2  Y  1 21>  Y  1 P22  }  r3 r3  }  (P  (  P  '21  21 r l (e ,+e „) r l r2' £  EH, modes lm m >. 1  ,2.6.c  i s given by  p =2.. , 22  21  Y (p )  Y  J  2 1  ( p  HE^^ mode  1  )  )  ( P  l  J (P )  2 2  21  J  1  l  2 J  - 0  2 2  J (P ) 1  -  )  x  )r 2 Jl r2 M  e  _  y  e  .2.7  from which the value of r_/X can be determined. 2 c The v a r i a t i o n of r /X with P for the TE.,, TM , EH 0  and HE  ni  L  C  Ul  U±  i i  a polythene tube (e =2.26) i n free space i s shown i n figure r2  modes on Ll  2.3,  11 3. 3.1  CAVITY-RESONANCE METHOD FOR MEASURING ATTENUATION-  Introduction The  .  cavity-resonance  method appeared to be the one most s u i t a b l e  f o r d i r e c t l y measuring the s m a l l a t t e n u a t i o n c o e f f i c i e n t o f the H E ^ Q mode on d i e l e c t r i c - t u b e waveguides. only a f a i r l y  The main advantages o f the method a r e t h a t  s h o r t l e n g t h o f waveguide i s needed and the problems o f  a c c u r a t e measurement o f power l e v e l s o r s u b s t i t u t e d a t t e n u a t i o n a r e avoided.  The r e l a t i o n s h i p between  attenuation c o e f f i c i e n t  and the Q f a c t o r  of a c a v i t y formed from a s e c t i o n o f the waveguide and two m e t a l l i c end plates i s discussed  3.2  i n the next s e c t i o n .  R e l a t i o n Between A t t e n u a t i o n  C o e f f i c i e n t and Q F a c t o r  A d o p t i n g the nomenclature o f r e f e r e n c e resonator  xs g i v e n by  ITT  w  _j^WL_ 2N +NL  y  7, the Q f a c t o r o f t h e  =  P  L  /  N  1 1  v  g S 2N +2LaN P  .......................  3.1  g  where  W = N /v , N=2aN g g g Then .  I Q  2av . 2N S_ P_ gv coWL  =  . •  +  3.2  p  where 3  =  to/v  For very  P  =2TT/X  • g  long resonators,  and the e x p r e s s i o n  can be  neglected  f o r Q becomes  <; M r ) •• g  the second term i n e q u a t i o n 3.2  ••••••••••  3  -  3  12  Then t h e a t t e n u a t i o n c o e f f i c i e n t a i s g i v e n by  ,3.4  4 9 In p r e v i o u s e x p e r i m e n t a l  i n v e s t i g a t i o n s o f s u r f a c e waveguides ' ,  v a l u e s o f a have been o b t a i n e d by measuring Q and g and u s i n g the t r a n s mission-line  formula, .3.5  a = 2Q which assumes v /v =1 i n e q u a t i o n significant HE^ and  3.4.  T h i s assumption may l e a d t o  errors.  As an example, the f a c t o r v /v f o r t h e dominant P g mode on a p o l y t h e n e tube (e^^=2.26) waveguide has been completed  i s shown i n f i g u r e 3.1.  equation  3.5 i s v a l i d  I n s p e c t i o n o f t h i s f i g u r e shows t h a t  f o r such waveguides when the p h a s e - v e l o c i t y  r e d u c t i o n i s v e r y s m a l l o r v e r y l a r g e , b u t can l e a d t o a p p r e c i a b l e e r r o r s for intermediate values. In the p r e s e n t i n v e s t i g a t i o n , no p r o v i s i o n was made f o r measuring v  g  and hence the r a t i o v /v t o g e t h e r w i t h the term i n e q u a t i o n P g .  3.2 i n v o l v i n g end p l a t e l o s s e s were e v a l u a t e d u s i n g t h e t h e o r y g i v e n below  1.4 p=0.1  v _E v g  f\ I' 0  1.2  // /  -  3  0 , 5  ^ 0 . 8  ^"""^0.9 1.0  0 F i g u r e 3.1  0.4  0.8  r /X 2  1.2  1.6  2.0  C h a r a c t e r i s t i c s o f D i e l e c t r i c - T u b e Waveguide, H E ^ Mode  13  3.2.1  R e l a t i o n Between Attenuation C o e f f i c i e n t and Q Factor f o r Surface-Wave Resonator  From equation 3.2,  a  * /M  A L Y I _ 2Np\  _l 2  J\q  \,v  wWl7  A _ .  2\.v /\Q  2  (  V  2 V\  N  uLO^+W^Wg).  g  3.6  +  P  /  where, f o r the dominant HE^^ mode,  22  a W  1  a  2  _ 3 2 a  f f e  h  : i & T  +  oVi  2 + ( k  ) 2  h-^owl^  ]  1;L  r2  h  2 V  B 2 s  A  0 0 2  + ( k  Z  C  ) 2 s  B  + 4 g k  Z  C  S  K +  4B  h  2  2  = 4  /  (P  A  r 3  V0 3 h  x  Pl  2 2  )  h^ T  K +  [32 (k Z c/]s +  0  0  k o  Z c K 2 (p )  (P  )N  S  I I T + C  ?3 S 2  I T  - 4  C  13 \( : °  o  Z  0  P2  p3  7 T R  J  ^0 r y l A  ( p  2  ~ z r J 0  a  ^lP  L  e  2 2 m  2 2  R  zJ  L> 0  2 a  3 2  L  2a a fTR  N  3  3 2  ^ V ^ n / 1 21  0  0  W<P >,  A  N  .3.7  0 0 2 AB  V0 2 L  a a TTe  3  }  12 \I^(p )  4  4  W  A  21  (p  fl  rl  4 4v„Z„h, 0 01 a  W  v e  m/' l 22 A  ( p  V  ) 1  K p ), l (  3 2  c  2  [ Z T , — :  3  v  4 c  Vr3 u  z  2"  21 ' )  B  l (  p  K (p  3 2  )  1  2 1  ) J. AB  o  The functions S , S,,S . S, S,„ T , T, and T, are i n t e g r a l s of functions I A B AB' K' I A K T  T  r  of Bessel functions which are defined and evaluated i n reference 7. Table 3.1 shows a sample output from a computer program c a l l e d QFACTOR which was used to obtain the unloaded Q f a c t o r of the surface wave resonator, the f a c t o r (v /v ) and the attenuation c o e f f i c i e n t of the P 8  .3.8  .14  dominant coefficient  mode by s o l v i n g e q u a t i o n 2.4.b f o r ^ ( g ) ,  where the. phase  0 was d e c i d e d by the number o f h a l f wavelengths c o n t a i n e d  i n the l e n g t h o f the c a v i t y .  R1=0.012700(M) T1=0.0  L  95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 1 10 111 112 113 114 115 116 117 118 119 120  R2=0.015875(M)  T2=0.0005  F( H Z ) 7.8842E 7.9606E 8 .0368E 8.1130E 8.1889E 8.2648E 8.3405E 8.4161E 8 .4916E 8.5669E 8 .6421E 8.7172E 8.7922E 8.8671E 8 .9418E 9.0164E 9.0909E 9.1653E 9.2396E 9.3138E 9 .3878E 9.4617E 9.5356E 9.6093E 9 .6829E 9.7564E  T3=0.0  R2/LAMBDA  09 4 . 1 7 4 8 E -01 09 4 . 2 1 5 3 E -01 09 4 . 2 5 5 7 E -01 09 4 . 2 9 6 0 E -01 09 4.3362E -01 09 4 . 3 7 6 4 E -01 09 4.4165E -01 09 4 . 4 5 6 5 E -01 09 4.4965E -01 09 4 . 5 3 6 4 E -01 09 4 . 5 7 6 2 E -01 09 4 . 6 1 6 0 E -01 09 4 . 6 5 5 7 E -01 09 4 . 6 9 5 3 E -01 09 4.7349E -01 . 09 . 4 . 7 7 4 4 E -01 09 . 4 . 8 1 3 8 E- 0 1 4 . 8 5 3 2 E -01 09 09 • 4 . 8 9 2 6 E- 0 1 09 .4 . 9 3 1 8 E -01 09 • 4.9710E -01 0 9 • 5 . 0 1 0 2 E -01 09 5 . 0 4 9 3 E -01 0 9 . 5 . 0 8 8 3 E -01 09 5.1273E -01 09 5 . 1 6 6 2 E -01  Rl/R2=0.8000  ER1=1.000  SIGMA=0.3536E  KO/BETA 9.7252E -01 9 . 7 1 7 1 E -01 9.7091E -01 9.7010E -01 9.6930E -01 9 . 6 8 4 9 E -01 9.6769E -01 9 . 6 6 8 9 E -01 9 . 6 6 0 9 E -01 9 . 6 5 2 9 E -01 9.6449E -01 9 . 6 3 6 9 E -01  08(MHO/M)  VP/VG  9.6289E -01 9 . 6 2 1 0 E -01 9 . 6 1 3 1 E -01 9 . 6 0 5 2 E -01 9.5973E -01 9.5895E -01 9 . 5 8 1 6 E =01 9.5738E -01 9 . 5 6 6 0 E -01 / 9 . 5 5 8 2 E -01 9.5505E -01 . 9 . 5 4 2 7 E -01 9 . 5 3 5 0 E -01 9.5273E -01  ER2=2.260  1.0854E 1.0865E 1.0875E 1.08S5E 1.0895E 1.090 5E 1.0915E 1.0924E 1.0933E 1.0942E 1.0951E 1.0960E 1.0968E 1.0977E 1.0985E 1.0993E 1.1001E 1. 1 0 0 9 E 1.1017E 1. 1 0 2 5 E 1.1033E 1.1041E 1. 1 0 4 8 E 1. 1 0 5 6 E 1.1063E 1.1071E  00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00  LENGTH  QU 1. 0 0 8 1 E 9. 8 8 6 2 E 9. 7 0 0 2 E 9. 5 2 2 2 E 9. 3 5 1 9 E 9. 1 8 8 6 E 9. 0 3 2 2 E 8. 8 8 1 8 E 8.7372E 8. 5 9 8 0 E 8 .4641E 8. 3 3 4 9 E 8. 2 1 0 3 E 8. 0 8 9 8 E 7.9735E 7. 8 6 1 1 E 7. 7 5 2 1 E 7. 6 4 6 6 E 7. 5 4 4 3 E •7. 4 4 5 1 E 7. 3 4 8 9 E 7. 2 5 5 3 E 7. 1 6 4 5 E 7. 0 7 6 1 E 6. 9 9 0 2 E 6. 9 0 6 5 E  ER3=1.000  OF  THE  RES0N4TOR=1.757(M)  ALPHA(DB/M)  04 03 03 03 03 03 03 03 03 03 03 03 03 03 03 03 03 03 0.3 03 03 03 03 03 03 03  7 . 8 6 1 1 E -02 8 . 1 1 0 5 E =02 8 . 3 6 2 2 E -0 2 8 . 6 1 6 5 b -02 8 . 8 7 3 1 E -02 9 . 1 3 2 1 E -02 9 . 3 9 3 4 E -0 2 9 . 6 5 7 3 E -02 9 . 9 2 3 6 E -02 1 . 0 1 9 2 E -01 1.0463E -01 L . 0 7 3 7 E -01 1.1013E -01 1 . 1 2 9 2 E -01 1.1574E -01 I . 1 8 5 7 E -01 1.2144E -01 1 .2433E -01 1.2725E -01 1 . 3 0 2 0 E -01 1.3317E -01 1 . 3 6 1 7 E -01 1.3920E.- 0 1 .1 . 4 2 2 6 E -01 1.4534E -01 1 .4846E-01  ALPHA(D8/FT) 2 . 3 9 6 1 E -0 2 2 . 4 7 2 L E -02 2 . 5 4 8 8 E -02 2 . 6 2 6 3 E -02 2 . 7 0 4 5 E -0 2 2 . 7 8 3 5 E -02 2 . 8 6 3 1 E -0 2 2 . 9 4 3 6 6 -02 3 . 0 2 4 7 E -0 2 3 . 1 0 6 7 E -02 3 . 1 8 9 3 E -0 2 3 . 2 7 2 7 E -02 3 . 3 5 6 9 E -0 2 3 . 4 4 1 9 E -02 3 . 5 2 7 7 E -0 2 3 . 6 1 4 ^ E -02 3 . 7 0 1 6 E -0 2 3 . 7 8 9 7 E -02 3 . 8 7 8 7 E -0 2 3 . 9 6 8 5 E -02 4 . 0 5 9 1 E -0 2 4 . 1 5 0 6 E -02 4 . 2 4 2 9 E -0 2 4 . 3 3 6 0 E -02 4 . 4 3 0 1 E -0 2 4 . 5 2 5 0 E -02 . Ln  Table 3.1  Sample Output from QFACTOR  16  3.3  R e l a t i o n Petween Unloaded Q and Loaded"Q In  p r a c t i c e the loaded Q f a c t o r , Q , o f a c a v i t y r e s o n a t o r i s  g i v e n by amplitude  ,3.9  rv \  where f  i s the resonant  frequency and  Af i s the bandwidth at the h a l f - p o w e r S  p o i n t s o f the t r a n s m i s s i o n c h a r a c t e r istic.  i l  1,0  1  0.707  \ .  f-f  phase  To determine e i t h e r the amplitude  the bandwidth A f ,  -"^  —X . 1 r  o r the phase o f the  t r a n s m i s s i o n c h a r a c t e r i s t i c o f the r e s o -  0 45°  n a t o r can be used  90°'  (figure  The unloaded  3.2"^).  Q can be o b t a i n e d  by measuring the l o a d e d Q and the  90° 45°  r  J X.  Af f-f r  -*  F i g u r e 3.2 Transmission C h a r a c t e r i s t i c s of a Resonant Cavity  c o u p l i n g c o e f f i c i e n t s o f the c a v i t y i n put and output  a p e r t u r e s . . In the case--  where t h e r e a r e two c o u p l i n g a p e r t u r e s , the unloaded  % =V In  Q . i s g i v e n by 1 + f  W  undercoupled  .....3.10  the case where the output  R=0 coupling  $2 i  e q u a t i o n 3.10  Q  u  s  becomes  - Q^a+B-p  6^,  R=°°  negligibly small,  ...3.11  To o b t a i n the c o u p l i n g c o e f f i cient  overcoupled /critically coupled  i t i s necessary  to measure the  F i g u r e 3.3 V a r i a t i o n o f Input Impedance o f a Resonant C a v i t y  17  input impedance of the resonator at resonance.  If the normalized  r e s i s t i v e component R, which i s equal to the coupling c o e f f i c i e n t $ • i s ' found to be greater than unity, the cavity i s overcoupled.  I f R i s found  to be less than unity, the cavity i s undercoupled and i f R i s found to be unity the cavity i s c r i t i c a l l y coupled.  18 4. 4.1  EXPERIMENTAL APPARATUS  Introduction Although  d i e l e c t r i c - t u b e waveguides would be most  used a t m i l l i m e t e r - w a v e  f r e q u e n c i e s , i t was  more convenient  advantageously to conduct  p r e s e n t i n v e s t i g a t i o n at X-band f r e q u e n c i e s . ' T h i s p l a c e d l e s s t o l e r a n c e requirements to  use c o m m e r c i a l l y The  on the dimensions  available  the  stringent  o f the tube, making i t p o s s i b l e  tubes.  g e n e r a l l a y o u t o f the microwave apparatus  i s shown i n f i g u r e  4.1. To improve the frequency s t a b i l i t y  of the X-13  klystron,  the  l a t t e r was  water c o o l e d and a k l y s t r o n s y n c h r o n i z e r (FEL Model 136-AF)  was  F o r measurement o f the Q f a c t o r o f the surface-wave  used.  i t was  resonator,  n e c e s s a r y t o measure the bandwidth Af o f the r e s o n a t o r Q c u r v e  accurately.  T h i s was  f a c i l i t a t e d by use o f a b e a t - f r e q u e n c y  t e c h n i q u e which  made i t p o s s i b l e to measure f r e q u e n c i e s i n the X-band range w i t h an of  not more than ± 50 KHz.  cavity  f r e q u e n c y meter has  frequency  By comparison,  error  the o r d i n a r y r e a c t i o n type o f  a t y p i c a l a c c u r a c y o f ± 1MHz  i n the same  range. D e t a i l s o f the components o f the surface-wave  i n the f o l l o w i n g  sections.  r e s o n a t o r are g i v e n  klystron synchronizer  power supply-  attenuators coarse fine  *y>A— water cooled  \psc  tapered waveguide  f i e l d perturbing bead  VL  isolator surface-wave resonator  m u l t i p l i e r mixer  JHF  slotted section  J  frequency meter  x3-  .8-4.2GHz  •a digital counter  chart recorder  0 . 1 msec/cm saw/cw modulation  Figure 4.1  Layout of Apparatus  20  4.2  Surface-Wave Resonator The surface-wave, resonator, shown i n figures 4.2-4.5, consisted  of a length of d i e l e c t r i c tube [1]  approximately  both ends by f l a t , c i r c u l a r , aluminum plates, 0.61m  1.78m  long bounded at  i n diameter and 1;2  i n thickness, mounted at right angles to the waveguide.  cm  Since i t was  desirable to use as long and as straight a tube as possible i n order to obtain accurate measurements of the attenuation c o e f f i c i e n t , i t was necessary to devise some method of adequately supporting and tensioning the tube.  This was  achieved by passing the ends through holes i n the  end plates of the resonator and r a d i a l l y gripping the•tube walls between these plates and close f i t t i n g , c i r c u l a r , s h o r t - c i r c u i t i n g plugs, [2 and 3], inside the tube.  Leakage of energy outside the resonator  through the d i e l e c t r i c - f i l l e d , annular apertures thus formed i n the end plates was  prevented by the use of annular s h o r t - c i r c u i t i n g plungers  [4] at each end of the d i e l e c t r i c tube.  The end plates of the resonator  were kept p a r a l l e l and i n alignment by four t i e rods [5]. the end plates was  Alignment of  carried out using a laser i n a manner s i m i l a r to that  used f o r aligning o p t i c a l c a v i t i e s . polythene tubes,used  Table 4.1 shows d e t a i l s of the  i n the i n v e s t i g a t i o n .  The other end plate of the resonator had a number of holes [7],  0.13  which was  cm i n diameter, l y i n g along a radius of the p l a t e ,  through  inserted a small wire probe s e n s i t i v e to the l o n g i t u d i n a l  component of the e l e c t r i c f i e l d within the resonator.  By moving the  probe from one sampling hole to another the r a d i a l f i e l d decay could be investigated. Normally, a l l the holes i n the end p l a t e , except  the  one containing the probe, were closed by t i g h t l y f i t t i n g aluminum plugs.  *  The numbers given i n the text correspond to those appearing i n f i g u r e s 4.3-5.  21  For the measurement of the r a d i a l decay of the r a d i a l  tube  r (cm) 1  r (cm) 2  P=r /r 1  2  component of the e l e c t r i c f i e l d inside the resonator,  I  0,953  1.270 .  0.750  II  1.270  1.588  0.800 •  III  1;588  1.905  0.833  another probe, mounted on a modified s l o t t e d - l i n e carriage, was moved r a d i a l l y across some cross-sectional plane inside the resonator.  Table 4.1  Details of Polythene Tubes  F i g u r e 4.2  G e n e r a l View of Surface-Wave  Resonator  Figure 4.3  Surface-Wave Resonator  scale  1/10  25  26 4.3  Mode E x c i t e r s E x c i t a t i o n o f the dominant H E ^ mode on t h e d i e l e c t r i c tube  was  achieved  by means o f a s m a l l c i r c u l a r a p e r t u r e  [6] f e d by a c i r c u l a r  waveguide, which a l s o formed one o f the tube t e n s i o n i n g p l u g s  [3] mentioned  i n s e c t i o n 4.2. E x c i t a t i o n o f the T E ^ mode was a c h i e v e d annular  s h o r t - c i r c u i t i n g plunger  by r e p l a c i n g the  [4] a t the i n p u t end o f t h e r e s o n a t o r  by two p o l y s t y r e n e - f i l l e d r e c t a n g u l a r waveguides o f t r a n s v e r s e dimensions 0.8 cm by 1.3 cm ( f i g u r e 4.7), which b u t t e d up a g a i n s t the exposed end o f polythene  tube I I I .  The waveguides were e x c i t e d 180° ( f i g u r e 4,6.b) out o f  phase by u s i n g the s e t —  .  .  up shown i n f i g u r e tapered waveguides  4.6.a. The dimensions  - c a v i t y end p l a t e  o f t h e tapered wavequides  / / s ; ; / ; ;i  were such as / /  to e q u a l i z e the phase JO  v e l o c i t i e s o f the TE  10  and t h e T E °  / ; ? / s A  dielectric tube  phase shifter.  mode o f t h e e x c i t e r  7  (a)  mode o f  the s u r f a c e waveguide. T h i s arrangement  could  a l s o be used t o e x c i t e the dominant H E ^ mode by f e e d i n g b o t h d i e l e c t r i c waveguides i n phase.  An a l t e r n a t i v e  method o f e x c i t i n g t h e TE^  mode, t h a t due t o  (b)  (c)  F i g u r e 4.6 Diagram o f TE Mode E x c i t e r and the P o s i t i o n o f E x c i t e r R e l a t i v e to D i e l e c t r i c Tube  27 Astrahan  3  , i s shown i n Figure  2 . 6 . C .  This was t r i e d i n the present  investi-r-  gation, but proved to be unsatisfactory, since i t excited both the H E . ^ and T E Q ^ modes  simultaneously.  For e x c i t a t i o n of the T M Q ^ mode, the c i r c u l a r waveguide and aperture were replaced by a section of coaxial l i n e , having a tapered inner conductor.  This i s shown i n f i g u r e 4.8.  29 RESULTS 5.1  Dependence of Cavity Q Factor on Size of Coupling Aperture Figure 5.1 shows the dependence of the cavity Q factor of  the H E ^ mode on coupling aperture size f o r tube I I at a frequency of 8.328 GHz.  •'•  For aper-  ture sizes of less than about 5 mm, both the  tube  loaded Q factor and the unloaded Q factor became v i r t u a l l y constant and the coupling c o e f f i c i e n t 3^ was smaller than 0.01.  I  7.1  II  6.4  III  6.4  Hence  the amount of cavity loading f o r this range of aperture sizes was n e g l i g i b l e .  diameter of aperture (mm)  Table 5.1 shows  the actual size of aperture used with each p a r t i c u l a r size of tube.  In a l l cases,  Table 5.1 Details of Coupling. Apertures  the apertures were small enough to ensure that the errors i n the measurements were small.  7000  •  6000 Q 5000  X  4000 5  Diameter  (mm)  10  Figure 5.1 Measured Dependence of Cavity Q Factor of H E ^ Mode on Coupling Aperture Diameter, tube I I , f=8.328GKz O experimental points f o r unloaded Q factor A experimental points f o r loaded Q factor  30 5.2  Measurement o f Guide Wavelength Measurement of the wavelength* a l o n g  tube mounted i n s i d e the r e s o n a t o r was  the s u r f a c e o f the  c a r r i e d out  method s i m i l a r to t h a t d e s c r i b e d by Barlow and the method i n v o l v e d the d e t e r m i n a t i o n contained  using a perturbation . .  Karbowiak"''''".  bead s u p p o r t e d cotton thread  of the number of h a l f wavelengths  T h i s was  achieved  i n close proximity  with  cords  one  to the d i e l e c t r i c waveguide by  While no  made to t r a v e r s e the l e n g t h o f the  appreciable disturbance  bead was to  moved a l o n g  field.  and  the wavelength was  o f the method was the r e s o n a t o r was  achieved  the bead except when  i t was  i n the probe output  only  Thus, the  reso-  accuracy  dependent on the p r e c i s i o n w i t h which the l e n g t h  c o u l d be measured. to an a c c u r a c y  In the p r e s e n t  b e t t e r than ± 1 mm,  shows a t y p i c a l probe o u t p u t ,  the  to  d i s t r i b u t i o n o f the  t h e r e f o r e determined.  the  i n traversing  of  investigation, this l e a d i n g to an e r r o r i n  the measurement of guide wavelength of not more than 1 p a r t i n F i g u r e 5.2  of  -  necessary  number o f maxima c o r r e s p o n d e d  the number of nodes i n the l o n g i t u d i n a l f i e l d nator  produced  e x h i b i t e d s u c c e s s i v e v a r i a t i o n s as  count the number of o s c i l l a t i o n s The  dielectric-  Thus the output  the d i e l e c t r i c waveguide, and  the l e n g t h of the r e s o n a t o r .  resonator,  o f the f i e l d was  s c a t t e r e d by  s i t u a t e d at a node of the e l e c t r i c  probe connected to the r e s o n a t o r  running  the same d i s t a n c e from the  the c o t t o n t h r e a d , some energy was  i t was  running  and d i a m e t r i c a l l y  By simultaneous a x i a l movement of the  throughout at a p p r o x i m a t e l y  waveguide. by  another.  at  a  s t r e t c h e d t r a n s v e r s e l y between tiro p a r a l l e l n y l o n  the s m a l l bead was  remaining  resonant  the a i d o f a s m a l l aluminum  cords mounted l o n g i t u d i n a l l y o u t s i d e the r e s o n a t o r opposite  Essentially  i n the l e n g t h of the r e s o n a t o r when the l a t t e r was  a known f r e q u e n c y .  dielectric-  obtained  when the f i e l d  1780. perturbing  i •! i  • i ft-!'  •U- i-  .Li,.l  4..,..  3  pu  .....  r  .  •U P O  <u  fi o r-l  P.  ~ .1.  0.5  L(m)  1.0  F i g u r e 5.2 Measurement o f Guide Wavelength o f HE Method, Tube I I I , f=8.323 GHz, 4=101  1.5  Mode by F i e l d P e r t u r b i n g Bead  1.757  32  bead was moved along the length of the resonator.  From t h i s , i t was  deduced that there were 1 0 1 h a l f wavelengths i n the length of the resonator at a frequency of  8.323  GHz.  The measured and t h e o r e t i c a l l y predicted v a r i a t i o n of the guide wavelength of the H E ^  i s shown i n figures 5 . 3 . a - c for  mode with ^ A  tubes I , I I and I I I . The experimental, results agree well with p a r t i c u l a r t h e o r e t i c a l curves computed for values of r e l a t i v e p e r m i t t i v i t y ' i n the range 2 . 2 6 to 2 . 3 1 .  (The exact d i e l e c t r i c properties of the commercially  availabl  polythene tubes used were not known.) As a check on the cutoff frequencies of the higher order TEQ-^ and T M Q ^ modes, the l a t t e r were i n d i v i d u a l l y excited  on tube I I I , using the  appropriate mode exciter and the v a r i a t i o n of guide wavelength with r^/X at frequencies close to cutoff was measured. and theory was for tube  I I I  Good agreement between experiment  obtained using the p a r t i c u l a r value of r e l a t i v e p e r m i t t i v i t y  found before,  £^=2.26.  These results are shox-m i n figure  5.3.c  Figure 5 . 3 . b shows the e f f e c t of surrounding tube I I by a lowdensity polyfoam s h i e l d of cross-sectional  dimensions  5 0 cm by 5 0 cm.  As  can be seen, the dispersion c h a r a c t e r i s t i c s of the shielded tube are l i t t l e d i f f e r e n t from those of the unscreened  tube.  The experimental  results  agreed most closely with the t h e o r e t i c a l ones when the r e l a t i v e p e r m i t t i v i t y of the polyfoam s h i e l d was  assumed to be  1.041.  33  34  X X  0.95  0.9 0.4  0.5  r /X 2  0.6  F i g u r e 5.3.b E x p e r i m e n t a l and T h e o r e t i c a l Phase C h a r a c t e r i s t i c s o f -Q Mode on S h i e l d e d and U n s h i e l d e d P o l y t h e n e Tube I I (i) u n s h i e l d e d tube O experimental points t h e o r e t i c a l curve f o r e „=2.28 ( i i ) s h i e l d e d tube • experimental points t h e o r e t i c a l curve f o r e =2.28, e =1.041 he  35  vj\ =0.7380 2 c  r / A =0.5285 2 c 0  1.0  0.95  0.9  F i g u r e 5.3.c of EE , T E  Q 1  (i)  HE O  1]L  E x p e r i m e n t a l and T h e o r e t i c a l Phase C h a r a c t e r i s t i c s and T M Modes on P o l y t h e n e Tube I I I Q 1  mode. experimental points t h e o r e t i c a l curve f o r e 2 2 . 2 6 =  r  •(ii) T E O  Q 1  mode experimental points t h e o r e t i c a l curve f o r e =2.26 r2 mode experimental points t h e o r e t i c a l curve f o r e „=2.26 • r2 0  (iii) TM •  Q 1  '  36 5.3  Measurement of Radial Decay of E l e c t r i c F i e l d As a check on the dispersion c h a r a c t e r i s t i c s of the H E ^ mode  on the-unscreened  tube, the r a d i a l decay of the longitudinal and r a d i a l  components of the e l e c t r i c f i e l d was measured when the resonator was resonant i n the HE, , .. „~ mode at a frequency of 8.328 GHz.  The r e s u l t s  obtained f o r tube I I are plotted i n figures 5.4.a-b together with the t h e o r e t i c a l curves computed from-equations  2.2.c f o r e  =2.28.  37  experimental points t h e o r e t i c a l curve f o r e  =2.28  . •5.4  38  Measurement of Attenuation C o e f f i c i e n t The cavity-resonance method was used to"measure the r e l a t i v e l y  small attenuation c o e f f i c i e n t of the polythene-tube waveguide.  The  eval-  uation of the attenuation c o e f f i c i e n t from the measured Q factor of the resonator was  carried out using equation  3.6.  The measured and t h e o r e t i c a l l y predicted v a r i a t i o n of the attenuation c o e f f i c i e n t with r^/\ of the H E ^  mode i s shown i n figures 5.5.a-c  for the same polythene tubes used previously. Assuming that the tubes had the values of r e l a t i v e p e r m i t t i v i t y found i n section 5.3, i t was  found that  the experimental points agreed with the t h e o r e t i c a l curves f o r loss i n the range 0.00058 to 0.00085. tube II by the polyfoam s h i e l d .  Figure 5.5.b  tangents  shows the e f f e c t of surrounding  It can be seen that the attenuation c o e f f i -  cient of the shielded tube i s only s l i g h t l y higher than that of the unshielded tube.  The experimental results agree best with the t h e o r e t i c a l ones when  the loss tangent i s taken to be 0.00007.  40  0.4  0.3  a (dB/m)  0.2  ^  ^  ^  ^  ^  0.1  0.4  0.5  r /X 2  0.6  F i g u r e 5.5.b E x p e r i m e n t a l and T h e o r e t i c a l A t t e n u a t i o n C h a r a c t e r i s t i c s o f HE Mode on S h i e l d e d and U n s h i e l d e d P o l y t h e n e Cha Tube n Tub u n s h i e l d e d tube (i) O experimental points t h e o r e t i c a l curve f o r e =2.28, tan6 =0.00068 s h i e l d e d tube (ii) • experimental points t h e o r e t i c a l curve f o r e _ 2.28, e =1.041, r2 r3 . tan6 =0.00007 r2  3  2  6.  CONCLUSIONS  A c c u r a t e measurements o f the a t t e n u a t i o n c o e f f i c i e n t  o f the H E ^  mode on c e r t a i n d i e l e c t r i c - t u b e waveguides have been made u s i n g a c a v i t y - r e s o nance method. t i o n s although  The r e s u l t s o b t a i n e d c o n f i r m p r e v i o u s t h e o r e t i c a l p r e d i c t h e r e i s an element o f u n c e r t a i n t y c o n c e r n i n g t h e exact  d i e l e c t r i c p r o p e r t i e s o f t h e commercial grade p o l y t h e n e measurements a l s o y i e l d e d t h e phase c o e f f i c i e n t o f the c o n f i r m e d by measurement o f r a d i a l decay o f t h e e l e c t r i c the tube.  E n c l o s i n g the d i e l e c t r i c  tubes used.  The  mode which was field  outside  tube i n a l o w - d e n s i t y , l o w - l o s s p o l y -  foam s h i e l d r e s u l t e d i n o n l y a s l i g h t d e g r a d a t i o n o f t h e a t t e n u a t i o n c h a r a c t e r i s t i c s o f t h e waveguide. Areas dielectric  i n which f u t u r e t h e o r e t i c a l and e x p e r i m e n t a l work on  tube waveguides might be c a r r i e d out (i)  include the following:  E f f e c t s o f d i s c o n t i n u i t i e s and bends on t h e p r o p a g a t i o n c h a r a c t e r i s t i c s o f the H E ^ mode  (ii)  Measurement o f v  o f t h e HE g  mode  11  (iii)  C o u p l i n g between waveguides  (iv)  Development o f e f f i c i e n t mode e x c i t e r s and f i l t e r s  (v)  E x t e n s i o n o f a l l these t o p i c s t o m i l l i m e t e r - w a v e  frequencies  43  REFERENCES 1.  Z a c h o v a l , L. , "'Elektromagnetische W e l l e n an d i e l e k t r i s c h e n Rohren",Ceska Akademic Ved a Umeni Praze B u l l e t i n I n t e r n a t i o n a l , 1932, V o l . 33, P. 136.  2.  L i s k a , J . , " E l e k t r o m a g n e t i c k e V l y n na d i e l e k t r i c y c h T r u b i c i c h " , pro P e s t o v a n i M a t e r n a t i k y a F y s i k y , 1934, V o l . 63, P. 97.  3.  A s t r a h a n , M.M., " D i e l e c t r i c Tube Waveguides", Ph.D. D i s s e r t a t i o n , Northwestern U n i v e r s i t y , I l l i n o i s , 1949.  4.  J a k e s , W.C.,"Attenuation arid R a d i a t i o n C h a r a c t e r i s t i c s o f D i e l e c t r i c Tube Waveguides", Ph.D. D i s s e r t a t i o n , N o r t h w e s t e r n U n i v e r s i t y , I l l i n o i s , 1949.  5.  Unger, H., " D i ' e l e k t r i s c h e Rohre a l s W e l l e n l e i t e r " , A r c h i v d e r E l e k t r i s c h e n Ubertragung, 1954, V o l . 8, P. 241.  6.  M a l l a c h , "Untersuchungen an d i e l e k t r i s c h e n W e l l e n l e i t e r n i n S t a b - und Rohrform", Fernraeldetech Z., 1955, V o l . 8, No. 1, P. 8.  7.  K h a r a d l y , M.M.Z., and L e w i s , J.E., " P r o p e r t i e s o f D i e l e c t r i c - T u b e Waveguides", P r o c . I E E , 1969, V o l . 116, No. 2, P. 214-224.  8.  Bourk, T.R., K h a r a d l y , M.M.Z., and L e w i s , J.E., "Measurement o f Waveq u i d e A t t e n u a t i o n by Resonance Methods", E l e c t r o n i c s L e t t e r s , 1968, V o l . 4, No. 13, P. 267-8.  9.  S c h i e b e , E.H., K i n g , B.G., Van Z e e l a n d , D.L., "Loss Measurement o f S u r f a c e Wave T r a n s m i s s i o n L i n e s " , J o u r n a l o f A p p l i e d Physics, 1954, V o l . 25, P. 790.  Casopis  10.  Sucher, M., and Fox, J . , "Handbook o f Microwave Measurement", V o l . 3, P. 470, P o l y t e c h n i c P r e s s , 1963.  11.  Barlow, H.M., and Karbowiak, A.E., "An I n v e s t i g a t i o n o f the C h a r a c t e r i s t i c s o f C y l i n d r i c a l S u r f a c e Waves", P r o c . I E E , 1953, V o l . 100, P t . I l l , P. 321.  

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