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Evaluation of aged transformer oils by microwave absorption measurements. Schroeder, Edgar Henry 1964

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EVALUATION OF AGED TRANSFORMER, OILS B I MICROWAVE ABSORPTION MEASUREMENTS by EDGAR HENRI SCHROEDER B . A . S c , 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 , 1962  A THESIS SUBMITTED I N PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n t h e Department o f Electrical  We a c c e p t t h i s  Engineering  t h e s i s as c o n f o r m i n g t o t h e  standards r e q u i r e d from candidates f o r t h e degree o f Master o f A p p l i e d Science  Members o f t h e D e p a r t m e n t 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 I OF B R I T I S H COLUMBIA J u n e 1964  In presenting  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 of  the requirements for an advanced degree at the U n i v e r s i t y B r i t i s h Columbia, I agree that a v a i l a b l e for reference  and  of  the L i b r a r y s h a l l make i t f r e e l y  study*  I f u r t h e r agree that  per-  mission f o r extensive copying of 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 of my Department or  his representatives.  I t i s understood that; copying or p u b l i -  c a t i o n of t h i s t h e s i s for f i n a n c i a l gain s h a l l not without my  written  by  permission*,  Department of The U n i v e r s i t y of B r i t i s h Columbia, Vancouver 8, Canada  be  allowed  ABSTRACT  The the  d e t e r i o r a t i o n of e l e c t r i c a l  formation  insulating oils  results i n  o f c o m p l e x o x i d a t i o n p r o d u c t s , many o f w h i c h a r e  polar i n structure.  The s i g n i f i c a n c e o f t h e m i c r o w a v e - f r e q u e n c y  d i e l e c t r i c - l o s s m e a s u r e m e n t , when a p p l i e d t o t h e e v a l u a t i o n o f aged t r a n s f o r m e r o i l s ,  i s investigated.  A c y l i n d r i c a l c a v i t y , operating  i n t h e T E Q ^ mode, i s u s e d  t o measure t h e l o s s t a n g e n t o f a g e d t r a n s f o r m e r o i l s .  Q-factor  measurements a r e made by a d y n a m i c method w h i c h i s d e s c r i b e d . The in  p r o b l e m o f mode i n t e r f e r e n c e i n t h e c a v i t y i s i n v e s t i g a t e d detail. I t i s found that the l o s s tangent of transformer  measured a t X-band, i n c r e a s e s oxidation.  The i n c r e a s e  i s influenced  closely p a r a l l e l s the increase not  through  by s e v e r a l f a c t o r s b u t  i n acidity.  S l u d g e p a r t i c l e s do  i n themselves cause a s i g n i f i c a n t i n c r e a s e  losses. the  as t h e o i l d e t e r i o r a t e s  oils,  i n the d i e l e c t r i c  An i n d i r e c t c o r r e l a t i o n b e t w e e n t h e l o s s t a n g e n t and  s l u d g e c o n t e n t o f a n o i l may e x i s t b u t h a s n o t b e e n  established. The  change i n t h e d i e l e c t r i c  c o n s t a n t o f an o i l c a u s e d by  the  p r e s e n c e o f d i s s o l v e d w a t e r , o r by t h e a g e i n g p r o c e s s , i s  too  s m a l l t o be m e a s u r e d b y t h e method u s e d .  measureable increase  i n t h e l o s s t a n g e n t i s p r o d u c e d by t h e  presence of water i n concentrations per  A small but  million.  ii  o f a p p r o x i m a t e l y 75  parts  ACKNOWLEDGEMENT  The w r i t e r w i s h e s t o c o n v e y supervisor,  D r . W. A. G. V o s s ,  and f o r h i s i n t e r e s t , the  duration  h i s s i n c e r e thanks t o h i s  f o r t h e many v a l u a b l e  encouragement and e n t h u s i a s m  discussions  throughout  o f t h e work.  Acknowledgement i s g r a t e f u l l y g i v e n t o t h e N a t i o n a l Research Council  f o r the f i n a n c i a l  assistance  B u r s a r y awarded i n 1962, a S t u d e n t s h i p r e s e a r c h through t h e Departmental  received  from a  i n 1963 and f u n d s f o r  G r a n t , BT-68.  S p e c i a l t h a n k s a r e e x t e n d e d t o D r . P. Noakes f o r suggestions  from which t h e p r o j e c t evolved.  The a s s i s t a n c e  r e c e i v e d f r o m D r . I . H. W a r r e n o f t h e Department o f M e t a l l u r g y , Mr.  J . A. P o r s t e r  Mr.  E . K. L e w i s  o f B. C. Hydro a n d Power A u t h o r i t y and  of Imperial  O i l Enterprises Limited  i s greatly  appreciated. The Mr.  author a l s o wishes  D;. R. M c D i a r m i d ,  t o thank h i s colleagues,  particularly  f o r the i n t e r e s t i n g and h e l p f u l  discussions.  vii  TABLE OP CONTENTS Page LIST OP ILLUSTRATIONS  v  ACKNOWLEDGEMENT 1.  2.  . v i i  INTRODUCTION  1  1.1  Review of Information on Transformer  Oils  1  1.2  T e s t i n g of O i l s i n S e r v i c e  4  1.3  The Low-Frequency Power-Factor Test  6  1.4  Object of the Work  8  1.5  C l a s s i c a l Theory of D i e l e c t r i c Losses  9  THE MEASUREMENT TECHNIQUE AT X-BAND FREQUENCY  15  2.1  Choice of a Method  15  2.2  Apparatus  17  2.3  Design of the C a v i t y  21  2.4  The Coupling Arrangement  24  2.5  Measurement o f Q  28  2.6  I n i t i a l T e s t s with the F i l l e d C a v i t y  32  2.7  Fields  i n the C a v i t y  34  2.8  E x p r e s s i o n f o r Tan 6  37  2.9  P r e l i m i n a r y Tests w i t h the P a r t i a l l y F i l l e d C aV l t y  f o r Q Measurement  Q  and Q  L  . e . « o . « « o o o » « . . o o o o e o e . o . . . . . o « . . . ........  41  2.10 Ghost—Mode Resonances  44  2.11  49  Propagating Modes i n the C a v i t y  2.12 C o r r e c t i o n f o r K l y s t r o n Amplitude  iii  Modulation  50  Page 3.  4.  TESTS AND RESULTS  .  57  3.1  General  Procedure  57  3.2  A r t i f i c i a l l y Ageing the O i l s  57  3.3  E v a l u a t i o n of N e u t r a l i z a t i o n Number  58  3.4  E v a l u a t i o n of Tan 6  3.5  Test I - A r t i f i c i a l l y Aged O i l s  3.6  Test I I - A r t i f i c i a l l y Aged O i l s  61  3.7  T e s t I I I - E f f e c t o f Water  62  3.8  T e s t IV - O i l s Removed from Transformers  62  3.9  Accuracy of the Measurements  66  •  59 *  60  3.10 D i s c u s s i o n of the Results  69  CONCLUSIONS  76  APPENDIX  77  REFERENCES  81  iv  LIST OP ILLUSTRATIONS  Figure  Page  1.1  Frequency Dependence o f P e r m i t t i v i t y  12  2.1  B l o c k Diagram o f Apparatus  18  2.2  Resonance Curve and Markers  22  2.3  C a v i t y and A s s o c i a t e d Equipment  2.4  Coupling C o n f i g u r a t i o n  2.5  Lumped-Parameter E q u i v a l e n t C i r c u i t o f the C a v i t y  2.6  Schematic o f C a v i t y  35  2.7  Normalized Q versus O i l Depth at 8.825 Gc/s  45  2.8  Normalized Q versus O i l Depth at 8.395 Gc/s  45  2.9  O i l Depth versus Frequency f o r Ghost Modes  48  ....  22 25 ..  29  2.10 Frequency Dependence o f Response-Curve Amplitude ..  53  2.11 Normalized K l y s t r o n Power-Output  56  2«X2 Corr€C*fcxon  XGITID  Curve  • o o o o o o o e o * « o » o 0 » o « « o o « * « • •••«•••«•  56  3.1  Temperature C o n t r o l C i r c u i t  63  3.2  Tan 6 and A c i d i t y f o r Test I  64  3.3  Tan 6 and A c i d i t y f o r Test I I  65  3.4  Increase i n A c i d i t y versus Increase i n Tan & ......  70  v  LIST OP TABLES  Table  Page  2.1  Q  2.2  Values o I n i t i a l Measurements of \. and e„ ................ o. r  42  2.3  Ghost-Mode Resonances  49  2.4  Resonances i n the A i r - F i l l e d C a v i t y  51  3.1  Measurements on Service-Aged O i l s  63  3.2  C a l c u l a t e d Values of Tan 6 f o r O i l 2  67  /  vi.  32  lo  1.1.  INTRODUCTION  Review of I n f o r m a t i o n on Transformer O i l s R e f i n e d p e t r o l e u m o i l s have good e l e c t r i c a l  insulating  p r o p e r t i e s and are w i d e l y used as l i q u i d d i e l e c t r i c s i n t r a n s f o r m e r s , s w i t c h gear and power c a b l e s .  However, each  type of a p p l i c a t i o n p l a c e s i t s own s p e c i a l demands upon c e r t a i n p r o p e r t i e s of t h e o i l . For  the case o f t r a n s f o r m e r s , power d i s s i p a t i o n causes a  c o n s i d e r a b l e i n c r e a s e i n temperature and the o i l must a c t as a h e a t - t r a n s f e r f l u i d i n a d d i t i o n t o i t s r o l e as an i n s u l a t o r . For  t h i s reason, chemically stable o i l s w i t h high o x i d a t i o n  r e s i s t a n c e are r e q u i r e d i f s a t i s f a c t o r y s e r v i c e l i f e i s t o be obtained.  The e l e v a t e d temperatures encountered i n normal  s e r v i c e t e n d t o a c c e l e r a t e d e t e r i o r a t i o n of t h e o i l so t h a t , i n t i m e , i t must be r e p l a c e d or r e c l a i m e d i n o r d e r t o a v o i d s e r v i c e f a i l u r e and equipment damage. Transformer o i l s have an i n d e f i n i t e c h e m i c a l c o m p o s i t i o n dependent upon the type of crude from which t h e y are produced and a l s o on the r e f i n i n g p r o c e s s s e l e c t e d f o r t h e i r manufacture.  Both s a t u r a t e d and u n s a t u r a t e d hydrocarbons are  u s u a l l y p r e s e n t so t h a t the o i l i s a complex m i x t u r e c o n t a i n i n g v a r i o u s amounts of napthenes, p a r a f f i n s and a r o m a t i c s .  Olefins  and o t h e r e a s i l y o x i d i z e d substances are removed by t h e r e f i n i n g p r o c e s s s i n c e t h e presence of such components would c o n f e r a low c h e m i c a l s t a b i l i t y on the o i l . used i n Canada are p r i m a r i l y n a p t h e n i c .  Transformer o i l s  Because s p e c i f i c a t i o n s  2.  r e q u i r e them to pour at minus 50°F, they are manufactured imported, wax-free,  napthenic-base  from  crudes.  From an e n g i n e e r i n g viewpoint, the harmful symptoms of transformer o i l d e t e r i o r a t i o n i n s e r v i c e a r e : (a) A decrease i n breakdown v o l t a g e caused mainly by the presence of moisture and  fibres,  (b) The formation of sludge which d e p o s i t s on v a r i o u s p a r t s of the transformer and hinders normal heat d i s s i p a t i o n , (c) The formation of a c i d i c products which  may  damage s o l i d i n s u l a t i o n or cause metal c o r r o s i o n i n the transformer. Moisture and f i b r e s are present as i m p u r i t i e s and can be removed by d r y i n g and f i l t e r i n g or by  centrifuging.  The a c i d s and sludges are formed by o x i d a t i o n of the hydrocarbon c o n s t i t u e n t s of the o i l .  T h i s process i s  a c c e l e r a t e d by the i n c r e a s e d temperature o x i d a t i o n promoters  and the presence of  and c e r t a i n c a t a l y s t s .  A l a r g e volume of  l i t e r a t u r e has been devoted t o a study of o i l o x i d a t i o n , a review of which i s g i v e n by Morton  (2) v  S e v e r a l metals, of  which copper i s the most important, act as c a t a l y s t s d u r i n g oxidation.  (3) '  v  These c a t a l y t i c e f f e c t s occur i n a l l  transformers but can be g r e a t l y reduced by the proper use of (4) a n t i - o x i d a n t s or i n h i b i t o r s .  '  The o x i d a t i o n r e a c t i o n s are complex and only a few general c o n c l u s i o n s may be drawn.  The products formed,  particularly  the a c i d s and sludges, are r e l a t e d to the nature of the o i l  3„  undergoing  o x i d a t i o n , t h e type of c a t a l y s t p r e s e n t , the  temperature  a t which the o x i d a t i o n t a k e s p l a c e and the amount  of oxygen a v a i l a b l e f o r r e a c t i o n ,  G i l s which have been  h e a v i l y r e f i n e d t o remove a r o m a t i c s are r e a d i l y o x i d i z e d t o form a c i d i c p r o d u c t s but g i v e v i r t u a l l y no s l u d g e .  Less  h e a v i l y r e f i n e d o i l s which s t i l l r e t a i n a p o r t i o n of t h e i r o r i g i n a l aromatic hydrocarbon  content are more r e s i s t a n t t o  o x i d a t i o n and do not show t h i s tendency toward development.  acid  However, t h e y w i l l produce more s l u d g e .  I n h i b i t o r s , when added t o good q u a l i t y o i l s which have been properly  r e f i n e d , are v e r y e f f e c t i v e i n r e t a r d i n g a c i d and  sludge f o r m a t i o n .  They are much l e s s e f f e c t i v e when added t o  low q u a l i t y o i l s which c o n t a i n  o x i d a t i o n promoters o r t h o s e  from which the n a t u r a l i n h i b i t o r s have been removed by o v e r refining. Because of t h e i r complex c o m p o s i t i o n , t r a n s f o r m e r o i l s are s u b j e c t e d t o a l a r g e number o f t e s t s i n an e f f o r t t o e v a l u a t e t h e i r q u a l i t y and s u i t a b i l i t y f o r s e r v i c e . S p e c i f i c a t i o n s f o r i n s u l a t i n g o i l s , u s u a l l y c a l l f o r t e s t s of such p h y s i c a l , c h e m i c a l and e l e c t r i c a l p r o p e r t i e s  as pour  point, color, v i s c o s i t y , v o l a t i l i t y , specific gravity, f l a s h p o i n t , n e u t r a l i z a t i o n number or a c i d i t y , f r e e and sulphur content, i n t e r f a c i a l tension s t a b i l i t y , d i e l e c t r i c strength The  oxidation  corrosive  a g a i n s t water,  oxidation  and power f a c t o r .  s t a b i l i t y t e s t i s used t o measure t h e  sludge and a c i d - f o r m i n g t e n d e n c i e s of a new d e f i n i t e c o r r e l a t i o n has been e s t a b l i s h e d  oil.  between  Although  no  laboratory  4.  o x i d a t i o n t e s t s and t h a n any  s e r v i c e l i f e , these t e s t s are more u s e f u l  o t h e r i n j u d g i n g the q u a l i t y of a new  predicting i t s future deterioration.  o i l and  I n the commonly used  t e s t s of t h i s t y p e , o i l samples are s u b j e c t e d t o an atmosphere a t a s p e c i f i e d temperature and i n t e r v a l s , the a c c u m u l a t i o n of a c i d and 1.2.  Testing  of O i l s i n  oxidizing  a f t e r s p e c i f i e d time  sludge i s measured.  Service  Maintenance procedures r e q u i r e t e s t s capable o f measuring the d e t e r i o r a t i o n of an o i l which has been i n s e r v i c e f o r some time.  The  from the  t e s t s n o r m a l l y used f o r t h i s purpose are  s p e c i f i c a t i o n or acceptance t e s t s and  n e u t r a l i z a t i o n number, i n t e r f a c i a l t e n s i o n , strength,  power f a c t o r , r e s i s t i v i t y and  chosen  include  color, dielectric  oxidation l i f e tests.  A rough i n d i c a t i o n of when the o i l should be changed can  be  o b t a i n e d but none of t h e s e t e s t s i s e n t i r e l y s a t i s f a c t o r y . O x i d a t i o n t e s t s which measure sludge a c c u m u l a t i o n are sometimes a p p l i e d to determine the u s e f u l l i f e r e m a i n i n g i n an oil.  Some o i l s , p a r t i c u l a r l y i n h i b i t e d o i l s , have a d e f i n i t e  i n i t i a l i n d u c t i o n p e r i o d d u r i n g which o x i d a t i o n proceeds v e r y slowly, followed  by a p e r i o d  such c a s e s , /the l e n g t h of the can be measured  of more r a p i d d e t e r i o r a t i o n .  i n d u c t i o n p e r i o d which remains  by o x i d a t i o n t e s t s but t h e y are g e n e r a l l y  l i t t l e v a l u e when a p p l i e d t o the more commonly used oils.  In  of  uninhibited  A f t e r an e x t e n s i v e f i e l d - t e s t i n g program w h i c h l a s t e d  (5) t e n y e a r s , McCpnnell;> ' c o n c l u d e d t h a t the t e s t , when c a r r i e d out on u n i n h i b i t e d  sludge-accumulation  o i l s t h a t have been  5 s u b j e c t e d t o s e r v i c e , cannot be c o n s i d e r e d a c c e p t a b l e as an i n d i c a t i o n of o i l q u a l i t y a t t h a t time o r i t s f i t n e s s f o r further service.  He s t a t e d t h a t t h e most u s e f u l t e s t s f o r  t h i s purpose are t h e n e u t r a l i z a t i o n number, i n t e r f a c i a l t e n s i o n and  color. The n e u t r a l i z a t i o n number r e f e r s t o t h e amount of  potassium h y d r o x i d e  (KOH) r e q u i r e d t o n e u t r a l i z e one gram of  o i l and i s t h u s a measure of t h e a c i d i t y of t h e o i l . I n t e r f a c i a l t e n s i o n v a l u e s are h i g h e s t f o r a new o i l and decrease r a p i d l y t o a low v a l u e w h i c h i s approached a s y m p t o t i c a l l y as the o x i d a t i o n p r o g r e s s e s .  This test  measures t h e amount O f s u r f a c e - a c t i v e i n t e r m e d i a t e p r o d u c t s o f o x i d a t i o n p r e s e n t and i s o f v a l u e o n l y d u r i n g the e a r l y of o i l d e t e r i o r a t i o n .  stages  C o l o r , when c o n s i d e r e d by i t s e l f , i s  m i s l e a d i n g i n e v a l u a t i n g o i l s o f s e r v i c e q u a l i t y but can be h e l p f u l i n conjunction w i t h other t e s t s . None of t h e f o r e g o i n g t e s t s can be c o n s i d e r e d as a r e l i a b l e i n d i c a t o r of how much sludge i s l i k e l y t o be found i n a transformer.  However, e x p e r i e n c e i n t h e f i e l d has shown  t h a t o i l s do n o t u s u a l l y develop a s i g n i f i c a n t amount o f sludge u n t i l t h e i r a c i d i t i e s have reached a c e r t a i n l e v e l .  In  B r i t a i n , i t i s c o n s i d e r e d unwise t o l e a v e an o i l i n s e r v i c e when i t s a c i d i t y has reached a v a l u e o f 1.0 mg KOH p e r gram. Low v a l u e s o f i n t e r f a c i a l t e n s i o n are measured w e l l b e f o r e s i g n i f i c a n t sludge f o r m a t i o n occurs and t h i s t e s t i s found t o be of ao v a l u e . i ^  O l i v e r h a s p o i n t e d out t h a t i n t h e  U n i t e d S t a t e s , most o p e r a t o r s o f power t r a n s f o r m e r s c o n s i d e r  6.  o i l s u i t a b l e f o r s e r v i c e when t h e a c i d i t y i s l e s s than some a r b i t r a r y v a l u e i n t h e 0.4 t o 0.7 mg KOH p e r gram range. t h i s decreased  With  l i m i t p l a c e d on a c i d i t y , i n t e r f a c i a l t e n s i o n  v a l u e s have more s i g n i f i c a n c e and a r e o f t e n used i n c o n j u n c t i o n w i t h n e u t r a l i z a t i o n numbers. The breakdown v o l t a g e o f an i n s u l a t i n g o i l depends p r i m a r i l y on the degree o f c o n t a m i n a t i o n by f i b r e s and moisture.  The d i e l e c t r i c s t r e n g t h t e s t i s o n l y a measure o f  such c o n t a m i n a t i o n and i s a v e r y u n s a t i s f a c t o r y c r i t e r i o n f o r the c o n d i t i o n of an o i l w h i c h has been i n s e r v i c e . 1.3.  The Low-Frequency Power-Factor Test The low-frequency  p o w e r - f a c t o r t e s t i s o f t e n used as a  c r i t e r i o n f o r o i l q u a l i t y , p a r t i c u l a r l y w i t h reference to c a b l e and c a p a c i t o r o i l s .  I t has a l s o been used t o measure  the d e t e r i o r a t i o n of t r a n s f o r m e r o i l s i n t h e f i e l d , r e p l a c i n g both n e u t r a l i z a t i o n number and i n t e r f a c i a l t e n s i o n v a l u e s i n d e t e r m i n i n g the need f o r o i l r e c l a m a t i o n . I n i t s s i m p l e s t form, t h e p o w e r - f a c t o r t e s t c o n s i s t s o f f i l l i n g a c a p a c i t o r w i t h o i l and comparing the d i e l e c t r i c l o s s e s w i t h those of a s t a n d a r d , c a p a c i t o r whose l o s s e s a r e a c c u r a t e l y known.  A type of .Sobering b r i d g e i s used f o r the  comparison and v e r y s t r i c t a t t e n t i o n must be p a i d t o c l e a n l i n e s s o f the t e s t c e l l and o t h e r d e t a i l s i n o r d e r t o o b t a i n r e p e a t a b l e r e s u l t s . (8) (9) (10)  ^  Q  t e s t i s normally  c a r r i e d out a t a temperature between 20°G and 100°C a t powerl i n e frequency.  Under these c o n d i t i o n s , p o l a r i z a t i o n l o s s e s  7  i n t h e o i l a r e n e g l i g i b l e and t h e p o w e r - f a c t o r t e s t i s e s s e n t i a l l y a measurement o f o i l c o n d u c t i v i t y o r r e s i s t i v i t y . The  a c t u a l v a l u e of o i l c o n d u c t i v i t y i s o f importance  o n l y f o r c a b l e and c a p a c i t o r required  o i l s where low c o n d u c t i v i t y i s  i n o r d e r t o p r e v e n t o v e r h e a t i n g t h r o u g h ohmic l o s s e s .  For t r a n s f o r m e r o i l s , t h e a c t u a l v a l u e o f o i l c o n d u c t i v i t y i s u s u a l l y n o t s i g n i f i c a n t b u t i t i s o f i n t e r e s t i f i t can be c o r r e l a t e d t o other important properties  of the o i l .  Attempts  have been made t o c o r r e l a t e c o n d u c t i v i t y and p o w e r - f a c t o r v a l u e s w i t h such p r o p e r t i e s best,  as a c i d and sludge c o n t e n t .  At  such c o r r e l a t i o n s a r e poor because c o n d u c t i v i t y i s v e r y  much dependent upon t h e presence of c e r t a i n t r a c e  impurities.  C h i l d s andStannet^"*" V used r e s i s t i v i t y and a c i d i t y t e s t s to evaluate the c o n d i t i o n of transformer o i l s i n s e r v i c e .  The  c o n d u c t i v i t y was found t o depend s t r o n g l y on t h e t o t a l i r o n c o n t e n t o f t h e o i l s as w e l l as upon a c i d i t y .  F o r an o i l w i t h  an a c i d i t y o f 0.2 mg KOH p e r gram, an i n c r e a s e  i n i r o n content  from 0.1 t o 10 p a r t s p e r m i l l i o n caused a t e n f o l d i n c r e a s e i n conductivity.  There was no apparent c o n n e c t i o n between t h e  occurrence o f i r o n and a c i d i t y i n t h e o i l s .  The l a r g e e f f e c t  of t r a c e s o f i r o n on c o n d u c t i v i t y i s a l s o d i s c u s s e d  by Salomon  He found t h a t a r t i f i c i a l l y ageing a new t r a n s f o r m e r o i l f o r 48 hours a t 1.15°C, i n t h e presence o f an i r o n w i r e ,  increased  the c o n d u c t i v i t y o f t h e o i l by a f a c t o r o f 1000. Other t r a c e i m p u r i t i e s a l s o had l a r g e e f f e c t s .  A f t e r many ageing  experiments he concluded t h a t t h e r e i s no q u a n t i t a t i v e c o r r e l a t i o n between t h e i n c r e a s e sludge v a l u e o f a c i d i t y produced.  i n power f a c t o r and t h e B e n n e t t ^ ^ ^ g i v e s a graph  8.  has on t h e r e s i s t i v i t y o f an o i l .  McConnell  '. s t a t e s t h a t  v  power f a c t o r and dc r e s i s t i v i t y measurements made on transformer  o i l s , d u r i n g h i s program of f i e l d t e s t i n g , appeared  t o have l i t t l e o r no s i g n i f i c a n c e . Prom t h e s e and s i m i l a r e x p e r i m e n t s , one i s l e d t o t h e c o n c l u s i o n t h a t n e i t h e r t h e low-frequency p o w e r - f a c t o r t e s t nor t h e dc r e s i s t i v i t y t e s t i s o f much v a l u e the c o n d i t i o n o f a t r a n s f o r m e r 1.4.  i n determining  o i l i n service.  Object o f t h e Work T r a n s f o r m e r o i l s which have been p r o p e r l y r e f i n e d a r e  almost e n t i r e l y f r e e from p o l a r m o l e c u l e s .  When put i n t o  s e r v i c e t h e y become s u b j e c t t o p o l a r c o n t a m i n a t i o n because many o f t h e i m p o r t a n t d e t e r i o r a t i o n p r o d u c t s formed as a r e s u l t of o x i d a t i o n have m o l e c u l e s w h i c h a r e p o l a r i n s t r u c t u r e . I t should t h e r e f o r e be p o s s i b l e t o e v a l u a t e  the c o n d i t i o n o f an  o i l by measuring t h e p o l a r i z a t i o n l o s s e s a s s o c i a t e d w i t h t h e d e t e r i o r a t i o n products.  A h i g h degree of d e t e r i o r a t i o n would  be i n d i c a t e d by l a r g e l o s s e s . Debye v  ' has shown t h a t f o r d i l u t e s o l u t i o n o f p o l a r  m o l e c u l e s i n n o n p o l a r l i q u i d s , the r e l a x a t i o n time o f t h e d i p o l e s i s g i v e n a p p r o x i m a t e l y by t h e e x p r e s s i o n d where \  4% n. r kT  3  1.1  i s t h e v i s c o s i t y o f the l i q u i d , r i s t h e r a d i u s o f  the s p h e r i c a l d i p o l e , k i s Boltzmann's c o n s t a n t a b s o l u t e temperature.  and T i s t h e  The o r i e n t a t i o n a l p o l a r i z a t i o n l o s s e s  .9.  are  a maximum a t an a n g u l a r f r e q u e n c y , OJ = —  .  Prom  d  Equation 1 . 1 i t f o l l o w s t h a t f o r o r d i n a r y temperatures, o permanent d i p o l e s o f atomic dimensions  ( r = 1 A) have a  r e l a x a t i o n t i m e of a p p r o x i m a t e l y lO "*"^ sec when i n a l i q u i d -  such as t r a n s f o r m e r o i l .  As a r e s u l t , t h e maximum  o r i e n t a t i o n a l p o l a r i z a t i o n l o s s e s s h o u l d occur a t f r e q u e n c i e s near 1 0 ^ c / s .  Due t o t h e l a r g e number o f d i f f e r e n t o x i d a t i o n  p r o d u c t s formed, t h e l o s s peak i s p r o b a b l y v e r y broad w i t h s i g n i f i c a n t l o s s e s o c c u r r i n g throughout t h e microwave spectrum. T h i s t h e s i s uses a microwave t e c h n i q u e t o i n v e s t i g a t e t h e c o r r e l a t i o n between t h e d e t e r i o r a t i o n o f t r a n s f o r m e r o i l and the  r e s u l t a n t i n c r e a s e i n d i e l e c t r i c l o s s e s measured a t X-band.  The purpose of t h e i n v e s t i g a t i o n i s t o determine t h e s i g n i f i c a n c e of the d i e l e c t r i c - l o s s measurement a t microwave frequency when used as a c r i t e r i o n o f q u a l i t y f o r o i l s i n s e r v i c e . (14)  In p r e v i o u s work done i n t h i s Department, Smith  used  lumped-parameter c i r c u i t s t o measure t h e d i s s i p a t i o n f a c t o r o f t r a n s f o r m e r o i l a t v a r i o u s temperatures and a t f r e q u e n c i e s up to  1 0 Mc/s. One o f h i s c o n c l u s i o n s was t h a t t h e d i s p e r s i o n  method f o r t e s t i n g t r a n s f o r m e r o i l s , i n t h e f r e q u e n c y  spectrum  2 0 c/s t o 1 0 Mc/s and a t room t e m p e r a t u r e , was n o t s a t i s f a c t o r y . However, h i s measurements d i d i n d i c a t e t h a t a t room temperature, the  maximum i n t h e d i s s i p a t i o n f a c t o r c o u l d be expected t o  occur a t v e r y h i g h f r e q u e n c y . 1.5.  C l a s s i c a l Theory o f D i e l e c t r i c  Losses  The r e l a t i o n between the e l e c t r i c d i s p l a c e m e n t D, t h e e l e c t r i c f i e l d E and t h e p o l a r i z a t i o n P i s g i v e n by  10.  D = e E + P  ... 1.2  o where e  Q  i s t h e p e r m i t t i v i t y o f f r e e space.  Por l i n e a r  d i e l e c t r i c s , the p o l a r i z a t i o n i s a l i n e a r f u n c t i o n  of the  e l e c t r i c f i e l d and E q u a t i o n 1.2 may be w r i t t e n as D = eE, where e i s the p e r m i t t i v i t y o f the m a t e r i a l c  = e  0  and i s g i v e n by  +|  ... 1.3 p  The r a t i o o f t h e p o l a r i z a t i o n t o the e l e c t r i c f i e l d , g , i s t h e e l e c t r i c s u s c e p t i b i l i t y X,  In general, X  i s frequency  dependent and i t i s t h i s f a c t which g i v e s r i s e t o t h e f a m i l i a r polarization  losses.  The p o l a r i z a t i o n which occurs when a d i e l e c t r i c i s s u b j e c t e d t o an e x t e r n a l the  sum o f t h r e e  e l e c t r i c f i e l d may be c o n s i d e r e d as  contributionss P = P + P e  The s u b s c r i p t s  Q  a  + P, a  e, a and d r e f e r r e s p e c t i v e l y  atomic and d i p o l a r p o l a r i z a t i o n .  ... 1.4  to electronic,  The e l e c t r o n i c  polarization  r e s u l t s from an e l a s t i c d i s p l a c e m e n t o f t h e e l e c t r o n an atom r e l a t i v e t o t h e n u c l e u s .  cloud of  The atomic p o l a r i z a t i o n i s  caused by changes i n bond a n g l e s or i n t e r a t o m i c d i s t a n c e s of atoms w i t h i n t h e m o l e c u l e as a r e s u l t of the a p p l i e d , f i e l d . M o l e c u l e s which have a permanent d i p o l e moment w i l l attempt t o a l i g n themselves i n t h e d i r e c t i o n of t h e a p p l i e d f i e l d . l a t t e r e f f e c t i s known as d i p o l a r or o r i e n t a t i o n a l  This  polarization.  A l l o f the f o r e g o i n g mechanisms l e a d t o d i e l e c t r i c l o s s e s but t h e i r i n d i v i d u a l c o n t r i b u t i o n s  t o the t o t a l losses are  i m p o r t a n t i n d i f f e r e n t p a r t s o f t h e f r e q u e n c y spectrum.  The  11 o  r e l a x a t i o n time, x e  o r T , a s s o c i a t e d w i t h e l e c t r o n i c and a' —13 —15  atomic p o l a r i z a t i o n i s o f t h e o r d e r of 10  t o 10  sec.  S i n c e t h e maximum l o s s e s occur a t a n g u l a r f r e q u e n c i e s such t h a t (OT s 1, t h e d i e l e c t r i c l o s s e s caused by t h e s e p o l a r i z a t i o n s are important i n the i n f r a r e d t o u l t r a v i o l e t range but a r e s m a l l a t lower f r e q u e n c i e s .  Depending on the  n a t u r e o f t h e m a t e r i a l , t h e r e l a x a t i o n t i m e o f permanent -12 d i p o l e s may be somewhere between days and 10 s e c . P o r many —9 —10 slightly polar dielectrics,  i s a p p r o x i m a t e l y 10  o r 10  sec and these d i e l e c t r i c s have a l o s s peak i n t h e microwave r e g i o n o f t h e frequency  spectrum.  Prom E q u a t i o n s 1.3 and 1.4, t h e p e r m i t t i v i t y o f a d i e l e c t r i c may be w r i t t e n as e = eo + ...1.5 e + X a + Xa The f r e q u e n c y dependence o f each e l e c t r i c s u s c e p t i b i l i t y can be c r u d e l y approximated by assuming i t t o be o f the form A  •v  * i  _  ~  *io  1 +  where t h e s u b s c r i p t i ,  jwT  i  '  r e f e r s t o e i t h e r e, a o r d.  Prom t h e  magnitude o f t h e a p p r o p r i a t e r e l a x a t i o n t i m e s , i t f o l l o w s t h a t the e l e c t r o n i c and atomic p o l a r i z a t i o n s c o n t r i b u t e t h e i r  full  share t o t h e t o t a l p o l a r i z a t i o n a t microwave f r e q u e n c i e s . R e f e r r i n g t o F i g u r e 1.1, a h i g h - f r e q u e n c y p e r m i t t i v i t y e be d e f i n e d as c ea = e„ o + * e + X a. p e r m i t t i v i t y e can be d e f i n e d as e aa  S  d e f i n i t i o n s , E q u a t i o n 1.5 becomes  S  Q  may  A s t a t i c or zero-frequency a e  + ©  a>  X J - . U s i n g these QQ  12.  Thus, the frequency dependence of t h e e l e c t r i c  susceptibility  can be d e s c r i b e d by i n t r o d u c i n g t h e concept o f a complex permittivity c  e  c  w r i t t e n as o  where, from E q u a t i o n  .« 1o 7  1.6,  e' = c  ea  s ea ,1 + a)2 T£2  e" = (e s - c ea') v  _J^d  ur%l  1 +  ...  1.8  ...  1.9  These two e q u a t i o n s a r e r e f e r r e d t o as t h e Debye E q u a t i o n s The r a t i o e'/e  0  i s d e f i n e d as t h e r e l a t i v e p e r m i t t i v i t y  a l s o known as the d i e l e c t r i c c o n s t a n t .  The e" term i s  responsible f o r the d i e l e c t r i c l o s s e s .  UHF  to  i I Infrared) i l l I i i I  I  Microwave I  Ultraviolet  > •l-t  a  u  ©  High F r e q u e n c i e s  0 Frequency  F i g . 1.1 Frequency Dependence of  Permittivity  (15)  c, r  13.  When a d i e l e c t r i c o f p e r m i t t i v i t y e„ i s p l a c e d i n a t i m e c v a r y i n g e l e c t r i c f i e l d E = E e*' ^, a c u r r e n t f l o w s . a)  Q  a as the c o n d u c t i v i t y o f t h e d i e l e c t r i c , t h e t o t a l  Defining current  d e n s i t y J^j, i s w r i t t e n as, t a k i n g D = c E , c  J  =  T  oE +  .= (o + we")E + jwe'E  ... 1.10  The component o f t h e c u r r e n t which i s i n phase w i t h E r e s u l t s i n power d i s s i p a t i o n . The average power l o s s w, p e r u n i t volume, i s w  =|  (a + we") E *  ... 1.11  The maximum s t o r e d - e n e r g y d e n s i t y i n t h e d i e l e c t r i c i s equal t o 1 2 •g- e'E  0  .  Hence, d e f i n i n g the Q o f t h e d i e l e c t r i c i n t h e u s u a l  way and t a k i n g a = 0 f o r s i m p l i c i t y , n Maximum S t o r e d Energy Average Power Loss y  =  w  The r e c i p r o c a l o f t h e Q - f a c t o r  =  c e" 51  1  '** -  , , ^  0  i s r e f e r r e d t o as the l o s s  tangent o r t a n 6 and i s g i v e n by e"  tan 6  =  ... 1.13  I n w r i t i n g E q u a t i o n s 1.12 and 1.13, o has been s e t equal t o zero i n order t o s i m p l i f y t h e e q u a t i o n s .  However, t h e s e  e q u a t i o n s may s t i l l be r e g a r d e d as p e r f e c t l y g e n e r a l f o r a l l d i e l e c t r i c s p r o v i d e d t h e q u a n t i t y e" i s r e d e f i n e d t o i n c l u d e the e f f e c t s o f non-zero c o n d u c t i v i t y .  R e f e r r i n g t o E q u a t i o n 1.9,  t h i s i s done by adding a t e r m ^ t o account f o r t h e c o n d u c t i v i t y . W i t h t h i s new d e f i n i t i o n o f e", the t o t a l c u r r e n t d e n s i t y i s w r i t t e n as J  T  = (we" + jwe')E  ... 1.14  14.  The  quantity e  M  now  i n c l u d e s terms f o r a l l the mechanisms  g i v i n g r i s e t o c u r r e n t s w h i c h are i n phase w i t h the  applied  f i e l d and, w i t h t h i s d e f i n i t i o n of e", t h e g e n e r a l i t y of Equations 1.12  and 1.13  follows.  At v e r y low f r e q u e n c i e s , p o l a r i z a t i o n l o s s e s n e g l i g i b l e so t h a t e" - —  .  Therefore,  0)  are  t a n 6 = ^-t = e/  ~r.» we''  which i s the f a m i l i a r r a t i o of c o n d u c t i o n c u r r e n t t o displacement current i n a c a p a c i t o r .  As the f r e q u e n c y i s  i n c r e a s e d , the p o l a r i z a t i o n l o s s e s a l s o i n c r e a s e , pass t h r o u g h a maximum and t h e n decrease once more t o a low v a l u e . e x p e r i m e n t s , the d i e l e c t r i c l o s s e s a t X-band are due to p o l a r i z a t i o n e f f e c t s .  I n the primarily  15.  2.  2.1.  THE MEASUREMENT TECHNIQUE AT X-BAND FREQUENCY  Choice o f a Method Transformer o i l s i n t h e i r i n i t i a l s t a t e have v a l u e s o f  tan  6 and d i e l e c t r i c c o n s t a n t o f t h e o r d e r o f 0.001 and 2.1  respectively.  A l t h o u g h t h e d e t e r i o r a t i o n o f an o i l was  expected t o be accompanied by an i n c r e a s e i n t a n 6, t h e magnitude o f t h e i n c r e a s e which would o c c u r was n o t known. In  c h o o s i n g a measurement t e c h n i q u e , two b a s i c requirements  were c o n s i d e r e d t o be o f p r i m a r y i m p o r t a n c e : (a) The method must be capable o f making a c c u r a t e and r e p e a t a b l e measurements o f t a n 6 and d i e l e c t r i c c o n s t a n t i n t h e range o f i n t e r e s t . (b) The e x p e r i m e n t a l procedure i n v o l v e d i n making a measurement s h o u l d be as s i m p l e and d i r e c t as p o s s i b l e . B o t h waveguide and r e s o n a n t - c a v i t y methods a r e used f o r measurements on medium-loss d i e l e c t r i c s .  I n waveguide methods,  a s e c t i o n o f t h e guide i s s e a l e d and f i l l e d w i t h the under t e s t , thus s e r v i n g as an a b s o r p t i o n c e l l .  specimen  By  t e r m i n a t i n g t h e c e l l w i t h an o p e n - c i r c u i t o r s h o r t - c i r c u i t and comparing t h e VSWR and the p o s i t i o n s o f t h e v o l t a g e nodes i n the i n p u t waveguide f o r t h e cases o f t h e empty and t h e f i l l e d c e l l , t h e v a l u e s o f t a n 6 and d i e l e c t r i c c o n s t a n t o f t h e sample may be deduced.  A s i m p l i f i c a t i o n o f t h e procedure can be made  by a d j u s t i n g t h e l e n g t h o f t h e a b s o r p t i o n c e l l , o r a l t e r n a t i v e l y , the e x c i t a t i o n f r e q u e n c y , so t h a t an i n t e g r a l number o f h a l f  16.  wavelengths occurs i n the c e l l .  I n t h i s quasi-resonant  method,  o n l y t h e specimen l e n g t h and the VSWR i n t h e i n p u t guide a r e r e q u i r e d f o r a d e t e r m i n a t i o n o f t a n 6.  Many sources o f e r r o r  must be t a k e n i n t o account w i t h the r e s u l t t h a t a c c u r a c i e s a r e g e n e r a l l y n o t comparable t o those o b t a i n a b l e w i t h c a v i t y techniques.  resonant-  The f o r e g o i n g waveguide methods have been (16  V  d i s c u s s e d i n d e t a i l by L u t h r a and Walker • ' who a p p l i e d them to  ceramics. C a v i t y methods are w e l l s u i t e d t o measurements on medium  and l o w - l o s s d i e l e c t r i c s .  The d i e l e c t r i c sample i s p l a c e d  i n t o t h e c a v i t y w h i c h i s c o u p l e d t o t h e i n p u t waveguide and e x c i t e d i n t o t h e d e s i r e d mode o f resonance.  I n order t o  c a l c u l a t e t h e l o s s t a n g e n t and t h e d i e l e c t r i c c o n s t a n t i s i s necessary  t o measure t h e d e p t h o f d i e l e c t r i c i n t h e c a v i t y ,  the l e n g t h o f t h e empty c a v i t y a t resonance, t h e l e n g t h o f t h e c a v i t y a t resonance w i t h t h e d i e l e c t r i c i n p l a c e and t h e Q - f a c t o r s o f t h e c a v i t y , b o t h i n t h e absence and presence o f the d i e l e c t r i c .  For low-loss l i q u i d d i e l e c t r i c s , the c a v i t y  may be c o m p l e t e l y f i l l e d , particularly  simple.  i n w h i c h case t h e c a l c u l a t i o n s a r e  I n almost a l l i n s t a n c e s t h e e f f e c t o f  w a l l l o s s e s can be accounted f o r more r e a d i l y than i n corresponding accuracy  waveguide methods w i t h the r e s u l t t h a t g r e a t e r  i s obtainable.  Q measurements can be c o n v e n i e n t l y made u t i l i z i n g a (17)  sophisticated  dynamic method d e s c r i b e d by Free*  .  In spite  of t h e r e l a t i v e l y l a r g e amount o f equipment w h i c h i s r e q u i r e d f o r t e s t s , the experimental good r e s u l t s .  procedure i s s i m p l e and y i e l d s  17.  Due t o t h e s e c o n s i d e r a t i o n s , a r e s o n a n t - c a v i t y t e c h n i q u e was chosen and used f o r a l l t a n 6 and d i e l e c t r i c c o n s t a n t measurements.  For reasons d i s c u s s e d ii?^ a l a t e r s e c t i o n i t was  found i m p r a c t i c a l t o use a c o m p l e t e l y f i l l e d c a v i t y f o r t a n 6 measurements but good r e s u l t s were o b t a i n e d u s i n g the p a r t l y f i l l e d cavity.  The method f o r Q measurement w i l l now  be  described. 2.2.  Apparatus f o r Q Measurement A b l o c k diagram of t h e equipment i s shown i n F i g u r e 2.1.  An a i r - c o o l e d k l y s t r o n o s c i l l a t o r i s f r e q u e n c y modulated t h e s u p e r p o s i t i o n o f a sawtooth v o l t a g e from the CRO the r e f l e c t o r v o l t a g e .  by  sweep onto  Th^e c a v i t y , used as a t r a n s m i s s i o n  d e v i c e , i s l o o s e l y c o u p l e d t o the i n p u t waveguide and i s tuned to  r e s o n a t e a t the c e n t r e f r e q u e n c y of the k l y s t r o n .  At the  output o f t h e c a v i t y , the t r a n s m i s s i o n resonance curve i s d e t e c t e d , a m p l i f i e d by a l o w - n o i s e audio a m p l i f i e r and d i s p l a y e d on one t r a c e of a dual-beam o s c i l l o s c o p e .  The  Q - f a c t o r o f the c a v i t y i s determined by measuring the f r e q u e n c y s e p a r a t i o n o f the resonance curve h a l f - p o w e r p o i n t s .  This  measurement i s e a s i l y and a c c u r a t e l y made u s i n g markers  of  known f r e q u e n c y s e p a r a t i o n t h a t are d i s p l a y e d on the second t r a c e of t h e o s c i l l o s c o p e . G e n e r a t i o n o f the f r e q u e n c y markers i s accomplished by a s t r a i g h t - f o r w a r d double-heterodyne method.  By means o f the  d i r e c t i o n a l c o u p l e r and h y b r i d - T j u n c t i o n , a s m a l l p o r t i o n of the output power from the frequency-modulated k l y s t r o n i s t r a n s f e r r e d t o the f i r s t c r y s t a l m i x e r .  Here i t i s heterodyned  P.M. Klystron  A t ten'.  D i r . Coupler  Matched Load  Matched Load  Matched Load  Atten.  1  (••  Precision  Atten. Matching — . D e t e c t o r Unit  HybridT  Wave-f-  Meter  1  Xtal Mixer  s t  Klystron  n d  Xtal  Mixer :—z  — . — _ .  Fixe^u^reqs  12  Calibrated Oscillator  Atten.  F i g . 2.1  B l o c k Diagram of Apparatus  Resonance Curve Amplifier •  Frequency Markers A m p l i f ie:=-  19.  w i t h t h e output o f an unmodulated, f i x e d - f r e q u e n c y k l y s t r o n tuned a p p r o x i m a t e l y t o the c e n t r e frequency o f t h e f i r s t . mixer output c o n s i s t s o f a frequency-modulated  The  signal  c o r r e s p o n d i n g t o t h e d i f f e r e n c e frequency between t h e two klystrons.  T h i s s i g n a l i s now combined w i t h t h e output o f a  c a l i b r a t e d o s c i l l a t o r i n a second c r y s t a l mixer.  After  a m p l i f i c a t i o n of t h e output and removal o f h i g h - f r e q u e n c y components, t h r e e markers a r e a v a i l a b l e .  The c e n t r e marker  i s produced when the k l y s t r o n s a r e i n tune and t h e o u t e r two when t h e y d i f f e r by t h e o s c i l l a t o r  frequency.  A d d i t i o n a l s m a l l e r markers, c o r r e s p o n d i n g t o harmonics o f t h e o s c i l l a t o r f r e q u e n c y , a r e produced  i f t h e power l e v e l s a t  the mixer i n p u t s a r e n o t c o r r e c t l y a d j u s t e d .  These e x t r a  markers w i l l n o t be p r e s e n t i f t h e c i r c u i t s have been w e l l a d j u s t e d b u t , i n any c a s e , t h e y a r e s m a l l and cause no c o n f u s i o n even i f they a r e v i s i b l e . The markers may be moved as a group i n a h o r i z o n t a l d i r e c t i o n on t h e CRO t r a c e by s l i g h t l y a d j u s t i n g t h e frequency of t h e second k l y s t r o n , ' A f i n e c o n t r o l o f t h e r e f l e c t o r v o l t a g e i s a good method o f a c h i e v i n g t h i s smoothly.  The  s e p a r a t i o n of t h e o u t e r markers i s c o n t r o l l e d by a d j u s t i n g t h e frequency of t h e c a l i b r a t e d o s c i l l a t o r .  The photographs o f  F i g u r e 2.2 i l l u s t r a t e t h e q u a l i t y o f t h e t r a c e s and markers a v a i l a b l e , as w e l l as t h e use o f t h e markers and p r e c i s i o n a t t e n u a t o r i n measuring t h e frequency s e p a r a t i o n o f t h e resonance  curve h a l f - p o w e r p o i n t s .  The procedure f o r Q measurement i s as f o l l o w s .  The  20.  c a v i t y i s f i r s t tuned u n t i l the peak of the resonance  curve  occurs a t the c e n t r e f r e q u e n c y o f the swept k l y s t r o n .  The  v e r t i c a l p o s i t i o n of the o s c i l l o s c o p e t r a c e upon which the markers are d i s p l a y e d i s a d j u s t e d u n t i l i t i s l o c a t e d a t t h e peak of the resonance c u r v e .  The i n p u t power t o t h e c a v i t y i s  now doubled by a d j u s t i n g the p r e c i s i o n a t t e n u a t o r . r e a d j u s t i n g the resonance  After  curve b a s e l i n e t o i t s o r i g i n a l  level,  the markers occur a t the h a l f - p o w e r l e v e l on t h e v e r t i c a l scale.  By making the n e c e s s a r y w i d t h and h o r i z o n t a l p o s i t i o n  adjustments, the markers are superimposed  on the  resonance  curve h a l f - p o w e r p o i n t s whose frequency s e p a r a t i o n can now  be  determined d i r e c t l y from the s c a l e s e t t i n g of the c a l i b r a t e d oscillator. Important advantages  are g a i n e d by u s i n g t h i s t e c h n i q u e  f o r Q measurement: (a) The measured Q - f a c t o r i s independent  of the  c r y s t a l detector characteristics, (b) S l i g h t i n s t a b i l i t y of the k l y s t r o n frequency d u r i n g the measurement does not a f f e c t t h e a c c u r a c y of the r e s u l t .  I f s m a l l frequency  d r i f t s o c c u r , t h e y are seen as s l i g h t h o r i z o n t a l s h i f t s of the resonance curve On the oscilloscope trace.  The shape of the  resonance  curve i s l e f t unchanged. (c) Measurements are r a p i d and easy t o make. The c h i e f d i s a d v a n t a g e of the t e c h n i q u e i s t h a t the power output o f the k l y s t r o n may not remain*constant over the sweptf r e q u e n c y band.  I n l a t e r experiments i t was found t h a t t h i s  21.  e f f e c t was a p p r e c i a b l e and a c o r r e c t i o n had t o be a p p l i e d . 2.3.  Design o f t h e C a v i t y For t h e a c c u r a t e d e t e r m i n a t i o n  o f d i e l e c t r i c l o s s e s by  c a v i t y methods, t h e mode c h o i c e and c a v i t y d e s i g n a r e n e c e s s a r i l y such t h a t w a l l l o s s e s a r e s m a l l compared w i t h specimen l o s s e s .  T h i s a l l o w s t h e d i e l e c t r i c l o s s e s t o be  c a l c u l a t e d by measuring t h e t o t a l l o s s e s i n t h e c a v i t y and t h e n a p p l y i n g a c o r r e c t i o n term f o r t h e r e s i s t i v e l o s s e s on the w a l l s .  Assuming t h a t t h i s c o r r e c t i o n t e r m can be  c a l c u l a t e d t o an a c c u r a c y o f about 90$, t h e u n c e r t a i n t y i n t r o d u c e d i n t o l o s s tangent v a l u e s w i l l n o t exceed; 1.5$ i f the c a v i t y w a l l l o s s e s a r e l e s s than 15$ of t h e specimen losses. with a Q  T h i s argument l e a d s t o t h e c o n c l u s i o n t h a t a c a v i t y v a l u e of n o t l e s s t h a n 15,000 i s r e q u i r e d f o r l o s s  Q  tangent measurements w i t h a p a r t l y f i l l e d c a v i t y whose measured Q i s about 3000. A c y l i n d r i c a l c a v i t y d e s i g n e d t o operate a t 8.5 Gc/s i n the T B Q ^ mode was used f o r t h e measurements.  The photograph  of F i g u r e 2.3 shows t h e c a v i t y and some of t h e a s s o c i a t e d equipment. The TEQ^ mode o f o p e r a t i o n was chosen because o f t h e h i g h l y d e s i r a b l e f i e l d p a t t e r n a s s o c i a t e d w i t h t h i s mode. S i n c e t h e E - f i e l d i s p u r e l y c i r c u m f e r e n t i a l , t h e r e i s no c u r r e n t f l o w between t h e s i d e w a l l arid t h e end w a l l o f t h e cavity.  Hence, t h e c a v i t y may be tuned by a  non-contacting  p l u n g e r w h i c h h e l p s t o damp out u n d e s i r e d modes of resonance. A f u r t h e r d e s i r a b l e p r o p e r t y of t h e T E  m  mode i s t h a t t h e  P i g . 2.2  Resonance  P i g . 2.3  Cavity  C u r v e and  Markers  and A s s o c i a t e d  Equipment  f i e l d s have no a z i m u t h a l dependence.  As a r e s u l t , t h e T E Q ^  mode i s a s i n g l e t and has no tendency t o s p l i t  o r become  u n s t a b l e due t o s m a l l i r r e g u l a r i t i e s i n t h e c a v i t y .  The f a c t  t h a t t h e TM-^ mode i s a companion mode of t h e T E Q ^ i s n o t a serious disadvantage. to  The c o u p l i n g elements can be l o c a t e d  e x c i t e t h e d e s i r e d mode p r e f e r e n t i a l l y .  I n a d d i t i o n , the  u n d e s i r e d TMj^ mode i s s t r o n g l y p e r t u r b e d by t h e presence o f the gap a t t h e t u n i n g p l u n g e r . The c a v i t y was made e n t i r e l y o f b r a s s .  Choosing  a  diameter o f 3.090 i n c h e s and a maximum l e n g t h o f 2.6 i n c h e s gave a'Q V a l u e i n t h e d e s i r e d range w i t h o u t p l a t i n g t h e cavity.  The t u n i n g p l u n g e r p o s i t i o n , was c o n t r o l l e d by a  micrometer screw o f l e n g t h one i n c h , c a l i b r a t e d t o 0.0001 inc. In order t o p e r m i t p l u n g e r t r a v e l over a d i s t a n c e l a r g e r t h a n one i n c h , t h e c a v i t y b a r r e l was made i n two s e c t i o n s , t h e upper one b e i n g e a s i l y removed.  This permitted the cavity  length.,to be v a r i e d by t h e p l u n g e r from 0.7 t o 2.6 i n c h e s , a range s u f f i c i e n t t o l o c a t e t h e f i r s t t h r e e resonances o f t h e TEQ^ mode i n t h e a i r - f i l l e d  cavity.  O r i g i n a l l y t h e base p l a t e was f a s t e n e d t o t h e c a v i t y by machine screws and was s e a l e d by a g a s k e t .  T h i s arrangement  was i n c o n v e n i e n t f o r two r e a s o n s : (a) The gasket was somewhat c o m p r e s s i b l e .  Therefore  t h e l e n g t h o f t h e c a v i t y as measured by t h e micrometer depended upon t h e t e n s i o n o f t h e basep l a t e mounting (b) The presence cavity  screws.  o f t h e gasket made c l e a n i n g o f t h e  difficult.  24. F o r these r e a s o n s , t h e base p l a t e was s e c u r e l y f a s t e n e d t o t h e c a v i t y b a r r e l and permanently  soldered into place.  A small  h o l e near t h e o u t e r p e r i m e t e r o f t h e base p l a t e served as a drain, 2.4.  The C o u p l i n g Arrangement  For a u n i f o r m waveguide system, t h e guide wavelength X , 6 t h e f r e e - s p a c e wavelength X and t h e c u t - o f f wavelength X a r e o c r e l a t e d by t h e e q u a t i o n n  -!_  -  „  -  g  _  _  :  TMnm":  21  J L c  o  The c u t - o f f wavelengths ° waveguide a r e g i v e n by TE J nm  i  f o r TE  and TM nm  X  nm  waves i n a c y l i n d r i c a l *  = ^nrn  c  « e • 2*2  _ 2na , X_ "c = ~ 3— nm  In t h e s e e x p r e s s i o n s , a i s t h e r a d i u s o f t h e g u i d e ; K m  th  n m  i s the  r o o t o f Jn '(x) = 0;-Snm• i s t h e m root of J n (x) = 0. At a frequency o f 8.5 Gc/s, a c a v i t y o f diameter 3.090 th  i n c h e s w i l l propagate  any mode f o r which t h e r a t i o o f c u t - o f f wavelength t o guide r a d i u s , —c , i s g r e a t e r t h a n 0.9. Thus, X  On  t h i r t e e n modes o f p r o p a g a t i o n a r e p o s s i b l e i n t h e a i r - f i l l e d cavity.  F i l l i n g the cavity with d i e l e c t r i c results i n  a d d i t i o n a l modes of p r o p a g a t i o n b e i n g p e r m i t t e d .  I n order t o  e x c i t e t h e d e s i r e d T E Q ^ mode p r e f e r e n t i a l l y , t h e c o u p l i n g (18) c o n f i g u r a t i o n used by B l e a n e y i n F i g u r e 2.4 was employed.  v  . • and i l l u s t r a t e d s c h e m a t i c a l l y  25.  T E Q ^ Magnetic F i e l d i n Cavity  T E ^ Q Magnetic F i e l d i n Guide  F i g . 2.4  Coupling  Configuration  C o u p l i n g i n t o the c a v i t y i s from, the narrow s i d e of a r e c t a n g u l a r waveguide through two s m a l l h o l e s i n the base plate.  C o u p l i n g out of the c a v i t y i s through a t h i r d h o l e i n  t h e base p l a t e i n t o the end of another s e c t i o n of r e c t a n g u l a r waveguide.  The s i z e of the c o u p l i n g h o l e s was e x p e r i m e n t a l l y  a d j u s t e d u n t i l s u f f i c i e n t power was a v a i l a b l e a t the o u t p u t . A h o l e diameter of 0.25  i n c h e s was used.  The c o u p l i n g h o l e s  were s e a l e d w i t h t h i n g l a s s d i s c s g l u e d t o t h e u n d e r s i d e of the base p l a t e . The t h e o r y of t h e c o u p l i n g c o n f i g u r a t i o n i s e a s i l y understood.  The o n l y f i e l d component which e x i s t s a l o n g the  narrow s i d e of a r e c t a n g u l a r waveguide o p e r a t i n g i n the T E ^ Q mode i s t h e l o n g t i t u d i n a l magnetic f i e l d .  By c o u p l i n g from  t h i s s i d e of the guide t h r o u g h two s m a l l h o l e s p l a c e d d i a m e t r i c a l l y o p p o s i t e i n the end w a l l of the c a v i t y , the l o n g t i t u d i n a l magnetic f i e l d i n the guide i s coupled t o t h e r a d i a l magnetic f i e l d i n t h e c a v i t y .  Prom waveguide t h e o r y ,  the r a d i a l magnetic f i e l d a t the end w a l l of a c y l i n d r i c a l c a v i t y i s , ( o m i t t i n g the term, e"J *): w  For TE modes: 2.3a For TM modes: H  r  = "  J°2  wen J ( k r ) s i n nQ rk' 2 n u  The h o l e s are spaced o n e - h a l f wavelength  2.3b  •0 •  a p a r t i n the  r e c t a n g u l a r guide so t h a t the f i e l d s a t the h o l e s are of equal magnitude and o p p o s i t e i n phase^  As a r e s u l t o f the cos  nQ  2 7 .  or s i n n© dependence o f t h e H  R  components, o n l y TE o r T M waves  whose o r d e r o f n i s even w i l l be e x c i t e d i n t h e c a v i t y by f i e l d s phased i n t h i s manner. The  output c o u p l i n g h o l e i s l o c a t e d t o reduce t h e number  of u n d e s i r e d modes a p p e a r i n g  a t the output.  A g a i n , because o f  the form o f t h e ©-dependence, modes c o r r e s p o n d i n g have a zero H  R  to n = 2 w i l l  f i e l d a t an angle o f 4 5 ° t o t h e i n p u t waveguide.  Such modes should be e l i m i n a t e d from t h e output by l o c a t i n g the c o u p l i n g h o l e as i n d i c a t e d i n F i g u r e 2 . 4 . Although t h e e l i m i n a t i o n o f u n d e s i r e d modes by t h i s means may be o f importance i f t h e c a v i t y i s used as a wavemeter, i t does n o t h e l p t o s o l v e t h e fundamental problem o f mode i n t e r f e r e n c e i n the c a v i t y .  T h i s can be done o n l y by p r e v e n t i n g t h e e x c i t a t i o n  of u n d e s i r e d resonances.  Since the primary a p p l i c a t i o n of the  c a v i t y i s f o r t a n 6 measurements, t h e l o c a t i o n o f t h e output c o u p l i n g h o l e i s of secondary importance. The  e f f e c t i v e n e s s o f t h e c o u p l i n g c o n f i g u r a t i o n was  i n v e s t i g a t e d over a wide frequency 8 . 3 t o 8 . 9 Gc/s,  t h e amplitude  band.  W i t h i n t h e range,  of t h e T E Q - ^ resonances a t t h e  output o f t h e a i r - f i l l e d c a v i t y was g r e a t e r than t h a t o f t h e s t r o n g e s t u n d e s i r e d mode by a f a c t o r o f about 2 0 0 .  Upon  f i l l i n g t h e c a v i t y w i t h o i l , t h i s f a c t o r was reduced t o about 30.  The T E Q ^ resonances c o u l d be s a t i s f a c t o r i l y e x c i t e d w e l l  o u t s i d e t h e frequency  range s t a t e d b u t t h e amplitude  of o t h e r modes was n o t n e a r l y as good.  reduction  T h i s i s t o be expected  since the distance separating the input coupling holes corresponds t o e x a c t l y o n e - h a l f wavelength o n l y a t t h e d e s i g n frequency.  For other f r e q u e n c i e s , the f i e l d s a t the coupling  28.  h o l e s are no l o n g e r i n p e r f e c t phase o p p o s i t i o n and modes whose order o f n i s odd can be more e a s i l y e x c i t e d i n t h e cavity. 2.5.  Measurement o f Q  Q  and  (19) Following Ginzton  ', t h e lumped-parameter e q u i v a l e n t  v  c i r c u i t o f a c a v i t y w i t h two i n p u t s i s shown i n F i g u r e 2.5 ( a ) . The i n p u t and output c o u p l i n g t o t h e c a v i t y i s r e p r e s e n t e d by i d e a l t r a n s f o r m e r s , s e l f - i n d u c t a n c e s and r e s i s t i v e components. Assuming t h a t b o t h t h e g e n e r a t o r  and l o a d a r e matched and  n e g l e c t i n g t h e s e l f - i n d u c t a n c e s o f t h e c o u p l i n g elements, t h i s c i r c u i t may be t r a n s f o r m e d  i n t o t h e one of F i g u r e 2.5-(b).  i n p u t and output c o u p l i n g c o e f f i c i e n t s a r e d e f i n e d as 2 ^1 5 2 ^2 = l ^2 2  h  "IT"  n  =  n  s  TT~  The  '  2  4  s  and Zg are t h e c h a r a c t e r i s t i c impedances o f the i n p u t and output waveguides and the e q u i v a l e n t g e n e r a t o r v o l t a g e E i s equal t o n^E-^. The unloaded Q of the c a v i t y i s to L s The loaded Q of t h e c a v i t y i s  Q  L  =  1  +  P  2  ...  2.5  The r e l a t i o n s h i p between c a v i t y Q and the t r a n s m i s s i o n resonance curve i s o b t a i n e d as f o l l o w s :  29.  L Coupled Generator Impedance  R  s  6.B  I s  Coupled Load Impedance  E  (b)  Pig. 2.5  Lumped-Parameter E q u i v a l e n t C i r c u i t of t h e C a v i t y  30.  The t r a n s m i s s i o n l o s s T(w) i s d e f i n e d as  f r  P, T(w) .  ... 2.6  where P  = Maximum a v a i l a b l e power from t h e generator  q  d e l i v e r e d t o a matched l o a d . P^ = A c t u a l power d e l i v e r e d t o t h e l o a d . C a l c u l a t i n g T(u>) f o r t h e e q u i v a l e n t c i r c u i t o f the c a v i t y , T(u>) = -  ±~§  (1 + 0! + 8 )  -p +  2  2  In t h i s expression, A  where f and  Q  —ar——  0  o  i s t h e resonant  4A Q/  l  f  =  *  »»• 2.8  o  frequency  of the c a v i t y  f ^ i s the d e v i a t i o n from t h e resonant  At resonance, A = 0. T(wJ 0  ...2.7  i s d e f i n e d as t h e t u n i n g parameter;  f - f  /\ =  p  2  frequency.  Therefore  = " " ( i + '1  K  2P 'o )  2  and u s i n g E q u a t i o n 2.5 y i e l d s the n o r m a l i z e d  transmission  equation: T(o)) T(w ) 0  1  o 9  1 + 4 A^Q^  The t r a n s m i s s i o n half-power  p o i n t s occur when 2 A Q ^ » 1, from  which i t f o l l o w s t h a t f  Q  0  =%f^  T h i s shows t h a t Q  Q  (1 + P i +  ...2.11  cannot be c a l c u l a t e d d i r e c t l y from t h e  31.  t r a n s m i s s i o n resonance c u r v e .  A separate  experiment t o  measure the c o u p l i n g c o e f f i c i e n t s i s r e q u i r e d .  F o r the case  of v e r y l o o s e c o u p l i n g , p^ and P g a r e s m a l l compared w i t h u n i t y and may be n e g l e c t e d . Q  Q  =  f o r the empty  I f t h i s approximation  i s valid,  cavity.  The i n p u t c o u p l i n g c o e f f i c i e n t P^ can be determined from a measurement o f t h e power f l o w i n t o t h e c a v i t y a t resonance. T h i s measurement i s most e a s i l y made by removing the matchedl o a d t e r m i n a t i o n on t h e waveguide r u n and r e p l a c i n g good s h o r t - c i r c u i t l o c a t e d t o g i v e f i e l d coupling holes.  i t with a  maxima a t the i n p u t  A standing-wave d e t e c t o r p l a c e d  immediately  b e f o r e t h e c a v i t y i n t h e waveguide r u n i s used t o probe t h e VSWR p a t t e r n i n t h e g u i d e . can be c a l c u l a t e d  As o u t l i n e d by G i n z t o n * ' " , p . 20  from t h e v a l u e s o f VSWR measured f o r t h e  cases o f t h e tuned and detuned c a v i t y .  Measurements o f p^ were  made f o r t h e empty, p a r t i a l l y f i l l e d and t h e c o m p l e t e l y cavity.  filled  I n each case, p^ was found t o be a p p r o x i m a t e l y  equal  t o 0.01. The output c o u p l i n g c o e f f i c i e n t P g cannot be measured b u t i t i s assumed t o be o f t h e same o r d e r as p ^ . On the b a s i s o f these measurements, t h e l o o s e - c o u p l i n g approximation  was taken as b e i n g  valid.  The Qo v a l u e s o f t h e f i r s t t h r e e TE,-., (Jl resonances were measured and compared w i t h t h e t h e o r e t i c a l Q v a l u e s . q  The  r e s u l t s a r e l i s t e d i n Table 2.1. I n c a l c u l a t i n g t h e t h e o r e t i c a l Q , a s k i n depth o f Q  1.48 x 10  cm f o r b r a s s has been used.  The f i r s t two  resonances i n d i c a t e t h a t , due t o s u r f a c e roughness, t h e e f f e c t i v e s k i n depth was a p p r o x i m a t e l y  10 p e r c e n t g r e a t e r t h a n  32.  the t h e o r e t i c a l v a l u e . Q  The a d d i t i o n a l r e d u c t i o n i n measured  f o r t h e t h i r d resonance i s probably  q  being c o n s t r u c t e d i n two s e c t i o n s .  a r e s u l t of t h e c a v i t y  The second s e c t i o n i s used  t o l e n g t h e n t h e c a v i t y so t h a t t h e T E Q ^ located.  resonance can be  An i m p e r f e c t j u n c t i o n between the two s e c t i o n s would  i n c r e a s e t h e w a l l l o s s e s i n t h i s area and p r o b a b l y reason f o r t h e reduced Q  observed.  Table 2.1.  Resonance  Theoretical  Q Values o  Experimental 2o  T E  011  T E  012  T E  013  2.6.  i s the  Ratio of Exper./Theor. Q Values *o  9,340  8,250  0.883  16,850  15,000  0.891  28,300  21,000  0.75  I n i t i a l Tests w i t h t h e F i l l e d C a v i t y S e v e r a l d i f f i c u l t i e s were encountered i n a t t e m p t i n g t o  make t a n 6 measurements w i t h a c a v i t y c o m p l e t e l y oil.  f i l l e d with  F o r t h e purpose o f Q measurement, a s i g n a l - t o - n o i s e  r a t i o o f 25:1 was d e s i r a b l e .  T h i s p e r m i t t e d measurements t o  be made w i t h ease b u t r e q u i r e d a resonance curve a m p l i t u d e o f not l e s s t h a n 200 m i c r o v o l t s a t t h e d e t e c t o r output.  Signals  of t h i s a m p l i t u d e c o u l d be o b t a i n e d f o r t h e l o w e r - l o s s samples t e s t e d b u t t h e h i g h e r - l o s s specimens gave an output about an order o f magnitude below t h i s  level.  A second problem i n v o l v e d t h e f r e q u e n c y m o d u l a t i o n  33.  c h a r a c t e r i s t i c s o f the r e f l e x k l y s t r o n .  In order to o b t a i n  maximum power from the k l y s t r o n , i t was o p e r a t e d near i t s a b s o l u t e maximum r a t i n g s .  Under these c o n d i t i o n s the  e l e c t r i c a l t u n i n g a v a i l a b l e was 20 Mc/s p o r t i o n 1 Mc/s  of which o n l y a c e n t r a l  i n w i d t h was f r e e from amplitude m o d u l a t i o n .  For s m a l l d e v i a t i o n s . f r o m the c e n t r e f r e q u e n c y , the power output of the k l y s t r o n decreased s y m m e t r i c a l l y about t  Q  had dropped o f f 0.8 db a t a d e v i a t i o n of 4 Mc/s.  and  For l a r g e r  d e v i a t i o n s , t h e decrease i n output power was more r a p i d and was no l o n g e r s y m m e t r i c a l about t h e c e n t r e f r e q u e n c y . A f u r t h e r c o m p l i c a t i o n was d i s c o v e r e d upon i n v e s t i g a t i o n of the output d e t e c t o r response as a f u n c t i o n o f f r e q u e n c y . Two d i f f e r e n t d e t e c t o r heads and matching u n i t s were employed but no c o m b i n a t i o n of these p e r m i t t e d the d e t e c t o r t o be b r o a d banded s u f f i c i e n t l y to g i v e a f r e q u e n c y independent over the swept-frequency band o f the k l y s t r o n .  response  The optimum  adjustment of the matching u n i t was a compromise between output amplitude and d e t e c t o r bandwidth and y i e l d e d a response which was down o n l y s l i g h t l y a t a d e v i a t i o n o f 4  Mc/s.  Due t o the k l y s t r o n m o d u l a t i o n c h a r a c t e r i s t i c s and the d e t e c t o r response, o n l y t h e c e n t r a l p o r t i o n o f the k l y s t r o n t u n i n g mode c o u l d be used.  For the s y m m e t r i c a l p a r t of the  k l y s t r o n power-output c u r v e , a c o r r e c t i o n f o r amplitude m o d u l a t i o n can be d e r i v e d v e r y e a s i l y .  T h e r e f o r e i t was  d e c i d e d t o l i m i t the w i d t h of the resonance curve so t h a t the h a l f - p o w e r p o i n t s f e l l w i t h i n 4 Mc/s  of the c e n t r e f r e q u e n c y .  I n accordance w i t h t h i s r e s t r i c t i o n , the minimum v a l u e o f loaded Q which c o u l d be measured was a p p r o x i m a t e l y 1000.  34.  Completely f i l l i n g the c a v i t y w i t h the o i l s t e s t e d i n l a t e r experiments r e s u l t e d i n a loaded Q c o n s i d e r a b l y below t h i s value.  As a r e s u l t , i t was  necessary  to use a c a v i t y o n l y  p a r t l y f i l l e d w i t h o i l f o r t h e t a n 6 measurements.  This  a u t o m a t i c a l l y p r o v i d e d adequate power a t the d e t e c t o r output but i n t r o d u c e d some a d d i t i o n a l mode-interference  problems  which are d i s c u s s e d i n a l a t e r s e c t i o n . 2.7.  F i e l d s i n the C a v i t y From waveguide t h e o r y , the f i e l d s i n a c y l i n d r i c a l  resonant  c a v i t y • are g i v e n by  v  ', ( o m i t t i n g the term,  e^ ): w t  For TE Modes: E  = 0 z  H  z  Hr  = J ( k r ) cos nO s i n Bz n s  H_ =  £k J n ' ( k r') cos nO cos Bz x  -  E„ = joou E  e  J ( k r ) s i n n© cos  B  0  = j ^  rk  ...  r  2  Bz  n  J ( k r ) s i n nQ s i n Bz  rk  J ' ( k r ) cos nO s i n B: n  2.12a  For TM Modes: H  = 0  z  E  z  = J ( k r ) cos nQ cos P z  E  r  = - § J '(  E  H  n  k r  n  = 6  D w  s n  © s i n pz  ^s- J ( k r ) s i n nO s i n pz rk^ n  - j  r  ) c°  "-^TT  rk  fi = - j ^ Q  J ( k r ) s i n n© cos p:  J ' ( k r ) cos n© cos B: n  Tuning P l u n g e r P o s i t i o n i n Empty C a v i t y 1  -Plunger P o s i t i o n I with D i e l e c t r i c !  1  Air C , Q  B , t  \ , t  u  Q  Dielectric c  d» Pd». d» Ho X  2a F i g u r e 2.6  Schematic o f C a v i t y  36.  A c y l i n d r i c a l c a v i t y d e s i g n e d t o r e s o n a t e i n t h e T E Q ^ mode and p a r t i a l l y f i l l e d w i t h d i e l e c t r i c i s i l l u s t r a t e d i n F i g u r e 2.6, At resonance, T E Q ^ waves e x i s t i n each s e c t i o n o f t h e c a v i t y . From E q u a t i o n 2.12a, t h e f i e l d e q u a t i o n s f o r t h i s mode a r e written as: In the a i r - f i l l e d p o r t i o n : H  z = t o  H  B  J  C  = C  r  ( k r )  s  i  h2  n  z  J ' ( k r ) cos 6 z  t  0  © - J t "T-  t  2  c  J  o'  (  k  r  )  s  i  n  ... 2.13a  2  t 2  B  z  In the d i e l e c t r i c - f i l l e d p o r t i o n : Hz = C, d Jo ( k r ) s i n B,z, d. 1 B  H E  = C  r  d  d  j = J ' ( k r ) cos 8 ^  ... 2.13b  Q  © = J°d Tr -  V  2  In these equations,  (  k  r  )  s  and  i  n  B  d i z  a r e c o n s t a n t s which a l l o w f o r t h e  p o s s i b i l i t y o f waves o f d i f f e r e n t a m p l i t u d e s i n t h e two s e c t i o n s . The boundary c o n d i t i o n s t o be s a t i s f i e d a t t h e a i r d i e l e c t r i c i n t e r f a c e a r e t h a t t h e f o l l o w i n g f i e l d components be continuous: (a) The t a n g e n t i a l component o f t h e magnetic i n t e n s i t y H, (b) The t a n g e n t i a l component of t h e e l e c t r i c f i e l d E, (c) The normal component o f t h e magnetic i n d u c t i o n B, (d) The normal component o f t h e e l e c t r i c d i s p l a c e m e n t D. Applying  t h e boundary c o n d i t i o n s a t z^ =  Zg  =  " ^» ^  w o  equations are obtained: C  d  sinB  d  ^  d  = - C  t  sinB  t  ... 2.14  37. C S d  cos 8  d  {  d  = C 6  d  t  t  cos 6  ... 2.15  t  D i v i d i n g t h e s e two equations y i e l d s t h e r e s u l t a n t e q u a t i o n which must be s a t i s f i e d f o r a T E Q ^ resonance t o e x i s t i n t h e partly f i l l e d  cavity:  -sr- t a n B J? = - - t - t a n B i ...2.16 d t E q u a t i o n 2.16 may <be p u t i n a d i f f e r e n t form by u s i n g t h e d  relation  u  d  o  &  t  a  c>  t  ), where  sz resonant l e n g t h o f t h e empty c a v i t y ,  ^2 ==. r e d u c t i o n i n resonant l e n g t h due t o t h e addition of the d i e l e c t r i c . Since  $  corresponds t o an i n t e g r a l number o f h a l f ' w a v e l e n g t h s  ^ t , and B 2 becomes  t  = ^  , i t f o l l o w s t h a t t a n 8^ f  = 0 and E q u a t i o n 2.16  Q  t  - a- i j -a< t a n P r  d  = P xT T d:  4  r  t  a  n  M  ^d  ^2  +  )  2  '  1 7  The r i g h t - h a n d s i d e o f t h i s e q u a t i o n i s known i n terms o f t h e measured q u a n t i t i e s  k  .>? and X^. d  by s o l v i n g an e q u a t i o n of t h e form  Thus, \  may be c a l c u l a t e d  d  ^ = A, where 0 =  Having o b t a i n e d \ , t h e d i e l e c t r i c c o n s t a n t e d  r  may b e " e v a l u a t e d -  by u s i n g E q u a t i o n 2.1 i n t h e form \ { - ± - + -±-) \ ta Kc  ... 2.18  2  G  2.8.  =  E x p r e s s i o n f o r Tan 6 The Q o f a resonant c a v i t y i s d e f i n e d as n y  =  w  T o t a l S t o r e d Energy Average Power Loss  #  o TO " ' " a  x  For a r e s o n a t o r p a r t l y f i l l e d w i t h d i e l e c t r i c , t h i s e x p r e s s i o n i s w r i t t e n as  '  38.  * . J-  Q = co  w  +  r  ... 2.20  d  •where U^. i s the energy s t o r e d i n the a i r p o r t i o n ,  i s the  e n e r g y s t o r e d i n t h e d i e l e c t r i c p o r t i o n , P^ i s t h e average power l o s s on t h e w a l l s and P^ i s t h e average power l o s s i n the  dielectric. The q u a l i t y f a c t o r of t h e d i e l e c t r i c alone i s d e f i n e d as A 1 P j = ialTo" ' U  2d =  u  Hence, t h e l o s s tangent o f t h e d i e l e c t r i c may be d e r i v e d from the measured Q o f t h e p a r t l y f i l l e d c a v i t y by r e a r r a n g i n g t h e terms o f E q u a t i o n 2.20:  4 U  tan 6  = ^  t +1  w coU P  d  The s t o r e d e n e r g i e s and power- l o s s e s on t h e w a l l s a r e c a l c u l a t e d from t h e f i e l d components i n t h e c a v i t y assuming the f i e l d s t o be those w h i c h would occur f o r t h e case of a loss-free dielectric.  The c a l c u l a t i o n s a r e s i m p l i f i e d  c o n s i d e r a b l y by c h o o s i n g t h e depth of d i e l e c t r i c  to  correspond t o an i n t e g r a l number of h a l f wavelengths i n t h e d i e l e c t r i c so t h a t a node o f t h e t r a n s v e r s e E - f i e l d o c c u r s a t the a i r - d i e l e c t r i c i n t e r f a c e . this f i e l d distribution,  I t can e a s i l y be shown t h a t f o r  t h e mean magnetic s t o r e d energy equals  the mean e l e c t r i c s t o r e d energy i n each o f t h e a i r and d i e l e c t r i c - f i l l e d p o r t i o n s , thus e n a b l i n g t h e s t o r e d e n e r g i e s t o be determined from e i t h e r t h e magnetic o r e l e c t r i c alone.  field  Choosing t h e s i m p l e r form, . « a o 2•22  U  d  = 2  B  &• • 2 o 23  E | * dv  d  D i e l e c t r i c Volume  An a p p r o x i m a t i o n f o r t h e w a l l l o s s e s may be o b t a i n e d by assuming the w a l l t o have a u n i f o r m c o n d u c t i v i t y of e f f e c t i v e v a l u e ae .  T h i s determines an e f f e c t i v e s k i n depth A e .  Prom  a consideration  of t h e P o y n t i n g v e c t o r a t t h e w a l l s u r f a c e , t h e (22) power f l o w i n t o t h e w a l l i s w r i t t e n as an i n t e g r a l ': x  P  *  =  ds  V .  2  • • • 2 • 2^L  Wall Area  where H^, i s t h e t a n g e n t i a l component o f the magnetic f i e l d a t the w a l l s u r f a c e . f u n c t i o n of Q,  Ao* i s e x p r e s s i b l e as a e  the experimentally  Q  c a v i t y Q.  The p r o d u c t  e  measured v a l u e of unloaded  T h i s p r o v i d e s a means of e l i m i n a t i n g t h i s product  from E q u a t i o n 2.24. Evaluation  of t h e s t o r e d e n e r g i e s and w a l l l o s s e s has been  c a r r i e d out i n t h e Appendix.  S u b s t i t u t i n g these v a l u e s i n t o  E q u a t i o n 2.21 y i e l d s the r e s u l t :  \ \  n  tan 6 =  1 +  n  2  l r e  3  H_ x  3 d  1  j  1 n,1 e Q • r**<  <  2,3 *d 1  X  3  + 4a  2  "3  + n  l )  + i&^2V „ 3  ••0 where, Q  = t h e measured l o a d e d Q of t h e p a r t l y f i l l e d c a v i t y ,  n^ = t h e number of h a l f wavelengths i n t h e d i e l e c t r i c , n Q  Q  2  = the number of h a l f wavelengths i n t h e a i r p o r t i o n , = t h e measured Q o f t h e empty c a v i t y ,  2«2 5  40  V = t h e number o f h a l f wavelengths i n t h e empty c a v i t y when Q  Q  was measured,  er = the d i e l e c t r i c c o n s t a n t of the d i e l e c t r i c , i Except f o r a s l i g h t l y d i f f e r e n t n o t a t i o n o f n^ and ng, (23) E q u a t i o n 2.25 i s t h e r e s u l t quoted by Penrose  .  A l t h o u g h a g e n e r a l e x p r e s s i o n f o r t a n 6 which i s v a l i d f o r an a r b i t r a r y depth o f d i e l e c t r i c may be d e r i v e d , t h e r e a r e i m p o r t a n t reasons f o r c h o o s i n g  t o be an i n t e g r a l number o f  h a l f wavelengths so t h a t t h e E - f i e l d i s zero a t t h e a i r dielectric  interface:  (a) S i n c e t h e l o s s e s i n t h e d i e l e c t r i c a r e a minimum where t h e e l e c t r i c f i e l d i s a minimum, t h e i n t e r f a c e r e g i o n makes o n l y a s m a l l t o t h e measured l o s s t a n g e n t . errors i n the dimension  contribution  Therefore, small  j f ^ o r poor l e v e l l i n g of  t h e c a v i t y w i l l have o n l y v e r y minor e f f e c t s on the a c c u r a c y o f t h e measurement. (b) Meniscus e f f e c t s a r e n e g l i g i b l e . (c) S m a l l changes i n 1^ do n o t detune t h e c a v i t y . T h i s p r e v e n t s mechanical v i b r a t i o n s which p e r t u r b the  l i q u i d s u r f a c e from c a u s i n g i n s t a b i l i t y o f  the resonance curve d i s p l a y e d  on t h e o s c i l l o s c o p e .  This point i s quite important experimentally. The f a c t t h a t  s m a l l changes i n  c a v i t y can be shown v e r y e a s i l y .  do n o t detune t h e  I f L i s the t o t a l length of  the p a r t l y f i l l e d c a v i t y a t resonance, d i f f e r e n t i a t i n g o = n^ ^d E q u a t i o n 2.16 shows t h a t ^ dL n = 0 f o r X^ ~- . d  41.  2.9.  P r e l i m i n a r y T e s t s w i t h the P a r t i a l l y F i l l e d C a v i t y A s e r i e s o f t e s t s were c a r r i e d out t o determine  how w e l l  the t h e o r e t i c a l e x p e c t a t i o n s were borne out e x p e r i m e n t a l l y f o r a commercial t r a n s f o r m e r o i l .  A t e s t frequency o f 8.71 Gc/s  was s e l e c t e d because t h e o p e r a t i o n o f t h e k l y s t r o n was most s a t i s f a c t o r y at t h i s frequency.  The f i r s t experiment had  t h r e e main o b j e c t i v e s : (a) To i n v e s t i g a t e how a c c u r a t e l y X^ and e be measured w i t h t h e p a r t l y f i l l e d (b) To determine  r  could  cavity,  how s i g n i f i c a n t s m a l l e r r o r s i n  Jl^ and l e v e l l i n g o f t h e c a v i t y a r e when measuring t a n 6, (c) To e l i m i n a t e any mode i n t e r f e r e n c e which might be p r e s e n t . The v a l u e o f X^. was f i r s t determined  d i r e c t l y by measuring  the d i s t a n c e between t h e resonances i n t h e a i r - f i l l e d  cavity.  In a s i m i l a r manner, X^ was o b t a i n e d d i r e c t l y by measuring t h e d i s t a n c e between resonances when t h e c a v i t y was c o m p l e t e l y f i l l e d with oil.. i s obtained.  U s i n g E q u a t i o n 2.18, an a c c u r a t e v a l u e o f e  r  As d i s c u s s e d p r e v i o u s l y , t h e resonance curve  produced by t h e f i l l e d c a v i t y i s t o o broad f o r Q measurement but i s . s u i t a b l e f o r d e t e r m i n i n g X^ and e  r  w i t h an e r r o r o f  about one p a r t p e r thousand. In o r d e r t o i n v e s t i g a t e how a c c u r a t e l y X^ and e  r  c o u l d be  measured w i t h t h e p a r t l y f i l l e d c a v i t y , v a r i o u s depths o f o i l were p l a c e d i n t h e c a v i t y and E q u a t i o n 2.17 was used t o c a l c u l a t e v a l u e s o f X, and e  from t h e measurements c o r r e s p o n d i  42.  t o each depth.  The r e s u l t s a r e g i v e n i n Table 2.2.  o i l depths, t h e c a l c u l a t e d v a l u e s of X^ and e  r  Por s m a l l  contain large  e r r o r s , presumably due t o t h e p e r t u r b i n g e f f e c t s o f t h e coupling holes.  P o r d i e l e c t r i c depths o f a p p r o x i m a t e l y one-  h a l f wavelength,  the values obtained w i t h the p a r t l y  filled  c a v i t y a r e e s s e n t i a l l y the same as those measured w i t h t h e completely f i l l e d c a v i t y . t h a t X^ and e  r  Subsequent experiments  confirmed  c o u l d be measured s a t i s f a c t o r i l y w i t h t h e p a r t l y  f i l l e d c a v i t y p r o v i d e d t h e o i l depth was a p p r o x i m a t e l y  one-half  wavelength. Table 2.2.  Oil  Quantity ml  I n i t i a l Measurements of X, and e d r  O i l Depth inches  10.0 20.0 30.0 40.0 50.0 60.0 65.0 70.0  C a l c u l a t e d X^ inches  0.0814 0.1628 0.2442 0.3255 0.4069 0.4883 0.5290 0.5697  1.067 1.030 1.013 1.005 0.998 0.994 0.994 0.995  Calculated e inches 1.905 2.025 2.085 , 2.110 2.135 2.150 2.150 2.145  T e s t Frequency = 8.71 Gc/s X^ measured w i t h t h e f i l l e d c a v i t y = 0.9940 i n c h e s e r measured w i t h t h e f i l l e d c a v i t y = 2.150 i n c h e s Measured X^ = 1.6030 i n c h e s Theoretical X  t  = 1.604 i n c h e s  r  43.  The measured Q was expected t o remain c o n s t a n t f o r s m a l l changes i n $  d  from t h e h a l f - w a v e l e n g t h v a l u e .  The t u n i n g  p l u n g e r c o u l d be a d j u s t e d so t h a t the resonance curve d i s p l a y e d on t h e o s c i l l o s c o p e corresponded t o e i t h e r t h e resonance.  T E Q J ^  O  R  ^®Qi3  C o n t r a r y t o e x p e c t a t i o n s , i t was found t h a t mode  i n t e r f e r e n c e was p r e s e n t and caused t h e Q o f b o t h resonances t o change q u i t e d r a s t i c a l l y as ^  was v a r i e d s l i g h t l y .  An  attempt t o remove the i n t e r f e r e n c e by changing t h e f r e q u e n c y of t h e k l y s t r o n o s c i l l a t o r by a few Mc/s was n o t s u c c e s s f u l . A new frequency o f 8.825 Gc/s appeared a t f i r s t t o be satisfactory.  I n o r d e r t o i n v e s t i g a t e more s y s t e m a t i c a l l y  the e f f e c t s o f v a r y i n g  Jl^  t  a c a l i b r a t e d p i p e t t e was mounted  as a b u r e t t e and connected t o the d r a i n i n t h e base p l a t e o f the c a v i t y .  T h i s a l l o w e d t h e o i l depth t o be v a r i e d  c o n t i n u o u s l y i n a known manner w h i l e t h e resonance curve was b e i n g observed on the o s c i l l o s c o p e .  Graphs i l l u s t r a t i n g t h e  mode i n t e r f e r e n c e encountered a r e g i v e n i n F i g u r e 2.7. F o r purposes o f curve comparison, the Q - f a c t o r s o f the two resonances have been n o r m a l i z e d . I t i s s i g n i f i c a n t t o note t h a t t h e curve shapes a r e v e r y s i m i l a r , a f a c t which i n d i c a t e s t h e i n t e r f e r i n g mode i s n o t i n f l u e n c e d by p l u n g e r t r a v e l i n t h e a i r s e c t i o n of t h e c a v i t y . At a g i v e n f r e q u e n c y , the presence o r absence of an i n t e r f e r i n g mode appeared t o be determined s o l e l y by t h e depth o f o i l present.  T h i s type o f i n t e r f e r e n c e would n o t be caused by  normal resonances whose waves a r e p r o p a g a t i n g i n b o t h s e c t i o n s of t h e c a v i t y .  However, ghost-mode resonances, c o n s i s t i n g o f  p r o p a g a t i n g waves i n t h e d i e l e c t r i c s e c t i o n and evanescent  waves i n t h e a i r s e c t i o n , c o u l d cause such i n t e r f e r e n c e .  These  resonances do n o t tune w i t h t h e p l u n g e r i f i t i s f a r enough away from t h e l i q u i d s u r f a c e .  I t was t e m p o r a r i l y assumed and  l a t e r c o n f i r m e d t h a t t h e troublesome i n t e r f e r i n g modes were of the ghost-mode v a r i e t y . In view o f t h e severe mode i n t e r f e r e n c e i n t h e v i c i n i t y of the c o r r e c t depth i n F i g u r e 2.7, a s y s t e m a t i c s e a r c h f o r a more s u i t a b l e f r e q u e n c y was made i n t h e band 8.3 t o 8.9 Gc/s. Between 8.3 and 8.4 Gc/s, t h e r e was no i n t e r f e r e n c e observed f o r o i l depths near t h e h a l f - w a v e l e n g t h v a l u e .  The f r e q u e n c y  of 8.395 Gc/s was f i n a l l y s e l e c t e d and used f o r a l l o f t h e later tests.  The graphs o f F i g u r e 2.8, o b t a i n e d i n the same  way as those o f F i g u r e 2.7, i l l u s t r a t e t h e amount o f e r r o r i n p e r m i t t e d b e f o r e t h e measured Q - f a c t o r i s a f f e c t e d . There were no e r r o r s due t o mode i n t e r f e r e n c e d e t e c t a b l e i n any of t h e a c t u a l t e s t s performed l a t e r .  I t was a l s o  confirmed t h a t l e v e l l i n g t h e c a v i t y a p p r o x i m a t e l y by a v i s u a l i n s p e c t i o n was p e r f e c t l y adequate p r o v i d e d t h e o i l depth was near t h e h a l f - w a v e l e n g t h v a l u e .  An a c c u r a t e l e v e l l i n g d i d n o t  produce any measureable change i n Q.  The e f f e c t s o f m e c h a n i c a l  v i b r a t i o n s caused by t h e v a r i o u s c o o l i n g motors i n the power s u p p l i e s were c o m p l e t e l y n e g l i g i b l e . 2.10.  Ghost-Mode Resonances From E q u a t i o n 2.1 i t f o l l o w s t h a t waves which a r e  p r o p a g a t i n g i n the d i e l e c t r i c r e g i o n and evanescent i n t h e a i r r e g i o n can occur f o r any mode whose c u t - o f f wavelength l i e s i n the range such t h a t  45.  1.1 TE  Xc • = 0.488" 2  0 1 2 Resonance  ~ ~ ~ 0 1 3 Resonance € = 2.150 TE  1.0  r  ^ \  X  OJ  \  s \  \  '/ \  '/  \  0.9 S  \  ll  1  o  /  S3  ll  .  ll ll  1  \  V  \  V V \v \\  vv  \\ \\  1  V  \  0.7 0.43  0.45  P i g 2.7  V  V  0.47 0.49 It II I O i l Depth ( i n c h e s )  0.51  0.53  Normalized Q v e r s u s O i l Depth a t 8.825 Gc/s  1.1  K  II  518  1 i  1.0  C  o  |  1  ***  xi <o  \  1  I  OJ  v  \\ \\ \\ \\ \ \ \\  11  1 V  u  1  1  / A\ v  0.8  1  s X. v \  1  N •H rH  1 1  a  g 0.9 o  TE  S3  TE  1 . 0.8 0.47  0 1 2 Resonance 0 1 3 Resonance 6 = 2.150 r  0.49  0.51  0.53  0.55  O i l Depth ( i n c h e s ) P i g . 2.8  Normalized Q v e r s u s O i l Depth a t 8.395 Gc/s  0.57  46.  1  K  "  2  O  1  K  K '  >  2  C  2  !  For these modes, the p r o p a g a t i o n  o  constant  i n the a i r region,  j B ^ , i s r e a l and p o s i t i v e d e f i n i n g t h e a t t e n u a t i o n 1 1  1  = 2n  a  K  constant  1 / 2  • e o 2 « 26  K  2  2  The evanescent waves have c a l o n og t i t u d i n a l dependence d e s c r i b e d by h y p e r b o l i c f u n c t i o n s r a t h e r than by t r i g o n o m e t r i c f u n c t i o n s .  For  the a i r r e g i o n , the f o l l o w i n g s u b s t i t u t i o n s are made: . JB  t  = a  s i n 8^  = - j sinh a  cos 8^ ^  = cosh a  ... 2.27  ^  These s u b s t i t u t i o n s , when a p p l i e d t o E q u a t i o n  2.16, y i e l d  the c o n d i t i o n a l e q u a t i o n which must be s a t i s f i e d f o r a TE g h o s t mode resonance t o be e x c i t e d .  Although Equation  2.16 was d e r i v e d  f o r the s p e c i f i c case of t h e T E Q - ^ resonance, i t c l e a r l y a p p l i e s t o a l l TE resonances i n t h e p a r t l y f i l l e d c a v i t y .  Hence, the  c o n d i t i o n f o r any TE ghost-mode resonance t o o c c u r i s g i v e n by tan  = - — ~ tanh a  ... 2.28  The matching c o n d i t i o n f o r an a r b i t r a r y T M mode can be d e r i v e d i n an i d e n t i c a l manner s t a r t i n g from t h e a p p r o p r i a t e equations  g i v e n by E q u a t i o n 8  d  tan P  d  i  2.12b. d  = - e P r  field  The r e s u l t i s :  t  tan P  t  ...  2.29  For a TM ghost-mode resonance, t h i s becomes tan 6  d  ^  = - p — t a n h a 1^  d  The v a l u e o f the p r o d u c t a  ... 2.30 encountered f o r the v a r i o u s  ghost modes, was g e n e r a l l y l a r g e r t h a n 2.5.  Therefore tanh a  i s a p p r o x i m a t e l y equal t o u n i t y and E q u a t i o n 2.28 and E q u a t i o n (OA)  2.30 t a k e t h e f o l l o w i n g s i m p l i f i e d forms*  ':  For TE ghost modes: 8  ii  d  tan P " a For TM ghost modes:  ... 2.31  =  d  tan S  d  i  d  = e  r  fp  ... 2.32  d  The c u r v e s o f F i g u r e 2.9 have been p l o t t e d from these e q u a t i o n s and show t h e t h e o r e t i c a l depth of o i l f o r a ghost mode t o be e x c i t e d a t a given frequency.  I t i s of i n t e r e s t t o note t h a t  the i n t e r f e r e n c e d i s c u s s e d p r e v i o u s l y and i l l u s t r a t e d i n F i g u r e 2.7 can be a t t r i b u t e d t o t h e e x c i t a t i o n o f the TEgg» TMgg  an<  * p r o b a b l y a c o m b i n a t i o n of t h e TMg^ and TE^g g h o s t -  mode resonances. An experiment was performed t o i n v e s t i g a t e how s t r o n g l y the v a r i o u s ghost modes were e x c i t e d a t 8.395 Gc/s. The r e s u l t s a r e shown i n Table 2.3.  S e v e r a l o f t h e resonances were  t o o weak t o be observed d i r e c t l y b u t t h e s e c o u l d be d e t e c t e d by n o t i n g t h e i r e f f e c t on the T E Q - ^ modes.  As b e f o r e , the o i l  depth was v a r i e d c o n t i n u o u s l y w h i l e t h e T E Q ^ resonance was b e i n g observed on t h e o s c i l l o s c o p e .  curve  At the depth  c o r r e s p o n d i n g t o t h e e x c i t a t i o n o f a ghost mode, a d i s t i n c t broadening o f the curve and decrease i n a m p l i t u d e o c c u r r e d f o r both T E Q ^  and T E Q ^  resonances.  The TEgg ghost mode was much  oo;  Frequency Figo  2o9  Oil  (Gc/s)  Depth v e r s u s Frequency f o r Ghost Modes  weaker t h a n t h e o t h e r s but c o u l d s t i l l be p o s i t i v e l y  identified. 7  I t was a l s o observed t h a t t h e TEgg mode was somewhat t u n a b l e with the plunger.  T h i s was t o be expected s i n c e f o r jf^  a p p r o x i m a t e l y equal t o one i n c h , p u t t i n g t a n h a  1^ equal t o  u n i t y i s n o t a good a p p r o x i m a t i o n . Table 2.3 Resonance  ™221 ™031  Amplitude H volt  a inch"  100  *  021  T E  611  T E  321  T E  131  T E  711  *  J  d  Exper. inches  3.11  0.295  0.295  3.38  0.337  0.341  25  3.50  0.357  0.361  50  0.802  0.368  0.384  1.895  0.448  0.456  *  2.63  0.537  0.545  *  3.25  0.656  0.659  3.29  0.671  0.676  0.802  0.738  0.741  *  ™122  Theor. inches  ™511 T E  Ghost-Mode Resonances  v  1^  -  I n d i c a t e s ^ presence d e t e c t e d i n d i r e c t l y T e s t Frequency = 8.395 Gc/s 2.11  P r o p a g a t i n g Modes i n t h e C a v i t y The modes e x c i t e d i n t h e a i r - f i l l e d c a v i t y were i d e n t i f i e d  by u s i n g E q u a t i o n 2.1 t o c a l c u l a t e t h e t h e o r e t i c a l l e n g t h a t which a p a r t i c u l a r resonance  cavity  should occur.  T a b l e 2.4  l i s t s t h e resonances e x c i t e d s t r o n g l y enough t o be o b s e r v a b l e and compares t h e i r approximate a c t u a l amplitudes a t t h e detector.  Some of t h e weaker resonances found were due t o t h e  e x c i t a t i o n o f modes i n t h e space behind t h e t u n i n g p l u n g e r r a t h e r t h a n i n t h e main p o r t i o n of the c a v i t y .  These c o u l d be  e a s i l y d i s t i n g u i s h e d from t h e normal ones by n o t i n g t h a t  since  the space b e h i n d the p l u n g e r i s lengthened as t h e c a v i t y i t s e l f i s s h o r t e n e d , t h e t u n i n g b e h a v i o u r o f resonances e x c i t e d behind t h e p l u n g e r w i l l be r e v e r s e d . I n a s i m i l a r manner, Equations 2.16 and 2.29 were used t o i d e n t i f y t h e modes i n t h e p a r t l y f i l l e d c a v i t y .  Por t h e o i l  depth chosen, t h e T M ^ resonances a r e t h e o r e t i c a l l y degenerate w i t h t h e T E Q ^ resonances b u t a r e not e x c i t e d because o f t h e c o u p l i n g c o n f i g u r a t i o n used.  No evidence o f i n t e r f e r e n c e from  the TMj^ mode c o u l d be d e t e c t e d .  Other p r o p a g a t i n g modes i n  the c a v i t y a r e s u f f i c i e n t l y f a r removed t o e l i m i n a t e the p o s s i b i l i t y o f i n t e r f e r i n g w i t h t h e T E Q - ^ resonances. 2.12.  C o r r e c t i o n f o r K l y s t r o n Amplitude M o d u l a t i o n Amplitude m o d u l a t i o n o f t h e k l y s t r o n  causes t h e frequency  s e p a r a t i o n o f t h e resonance curve h a l f - p o w e r p o i n t s t o be l e s s t h a n t h e t r u e s e p a r a t i o n which would be measured i f t h e power output o f t h e k l y s t r o n remained c o n s t a n t over t h e sweptf r e q u e n c y band.  Por t h i s reason, the value of  from E q u a t i o n 2.10 i s l a r g e r t h a n t h e t r u e v a l u e .  calculated An  approximate c o r r e c t i o n f o r t h i s e r r o r w i l l now be d e r i v e d f o r t h a t p o r t i o n o f t h e k l y s t r o n power-output n e a r l y s y m m e t r i c a l about t h e f r e q u e n c y f  Q  curve which i s .  51. T a b l e 2.4  Resonances i n t h e A i r - P i l l e d  Cavity  T e s t Frequency 8.395 Gc/s Amplitude  Mode  \i v o l t  * T E  111  T E  211  A c t u a l Cav. Length inches  Theor. Cav. Length inches  4  0.644  30  0.731  0.730  120  0.787  0.784  75,000  0.844  0.845  011 Possibly TM  i;L1  40  0.855  0.845  Possibly T E  3 1 1  10  0.901  0.886  20  0.952  10  1.021  300  1.059  1.051  40  1.105  1.102  200  1.110  1.106  20  1.460  1.460  240  1.570  1.568  70,000  1.688  1.690  4  1.708  60  1.872  T E  *  ™211 T E  411  T E  121  T E  112  T E  212  T B  012  *  P o s s i b l y TE or  511 TM  T E  113  T E  412  T E  122  Possibly  1.886  3 n  ™212  TM  T E  213  T E  013  Q 2 2  1.900  240  2.112  2.103  10  2.185  2.189  40  2.206  2.203  60  2.209  2.212  20  2.351  2.340  200  2.356  2.352  50,000  2.532  2.534  I n d i c a t e s Resonance behind Tuning P l u n g e r  R e f e r r i n g t o t h e e q u i v a l e n t c i r c u i t o f F i g u r e 2.5(b), t h e presence o f amplitude m o d u l a t i o n can be accounted f o r by assuming t h e g e n e r a t o r v o l t a g e t o be o f t h e form B = E(f) = B ( f ) Q  ... 2.33  g(t ) x  Since the c o r r e c t i o n i s l i m i t e d t o the symmetrical p o r t i o n of the power-output c u r v e , g ( f ^ ) i s an even f u n c t i o n d e s c r i b i n g the f r e q u e n c y dependence o f t h e output i n terms o f t h e deviation f^.  With t h i s s u b s t i t u t i o n , t h e n o r m a l i z e d  t r a n s m i s s i o n through t h e c a v i t y becomes T(u))  g (f ) 2  1  ______ _ T(a) ) 1 + 4A^QL  ... 2.34  0  T (to) 1 The h a l f - p o w e r p o i n t s occur when )• ' > = . Therefore, fi o r e c a l l i n g t h a t A = j - - , t h e t r u e v a l u e o f Q^ i s c a l c u l a t e d o from E q u a t i o n 2.34 and i s g i v e n by 1/2 ... 2.35 2g*(f ) - 1 1  [2g 2 (fj_) - l l1  1/2 , can be o b t a i n e d by  u s i n g a v e r y s i m p l e e x p e r i m e n t a l t e c h n i q u e t o p l o t a graph o f the f u n c t i o n g ( f - ^ ) .  At any g i v e n f r e q u e n c y , t h e s i g n a l  level  a t t h e d e t e c t o r i s r e l a t e d t o t h e power output of t h e k l y s t r o n , Quite g e n e r a l l y , t h e power t r a n s m i t t e d t h r o u g h the c a v i t y and d e l i v e r e d t o t h e l o a d r e p r e s e n t e d by t h e matched d e t e c t o r i s P (f) = T L  ... 2.36  T^jrP  2 s R  C o n s i d e r the case o f t h e c a v i t y tuned t o resonance frequency f = f  Q  + f^.  at a  At resonance, t h e c a v i t y a c t s as a  pure r e s i s t a n c e o f t h e v a l u e R  and hence, e v a l u a t i n g E, , t h e s  ju  power d e l i v e r e d t o the l o a d at t h i s frequency i s g i v e n by P  T  (f) =  Po (1 +  P  +  l  fi )\  .  .. 2.37  B (f )g (f ) 2  2  0  1  2  S i m i l a r l y , w i t h t h e c a v i t y tuned t o resonance a t the f r e q u e n c y f , t h e power d e l i v e r e d t o the l o a d a t the frequency f i s Q  Q  MO =  2.38  . E^(f ) (i + Pi +  W \  D i v i d i n g t h e s e two e q u a t i o n s y i e l d s the n o r m a l i z e d power l e v e l at the d e t e c t o r as a f u n c t i o n o f f r e q u e n c y : ... 2.39 I n each case the c a v i t y has been tuned t o resonance a t t h e frequency i n question.  f -f, o 1  1  Trace 1 "Markers g (f ) 2  x  i • i  i  P i g 2.10  Trace 2 "Resonance Curve  Frequency Dependence o f Response-Curve  Amplitude  Prom t h i s a n a l y s i s , i t f o l l o w s t h a t the peak of the resonance curve observed on the o s c i l l o s c o p e t r a c e s out the  54.  f u n c t i o n g ( f - ^ ) , as the c a v i t y i s tuned a c r o s s the sweptfrequency band o f t h e k l y s t r o n . Figure 2.10. the  This i s i l l u s t r a t e d i n  The c a v i t y i s f i r s t tuned t o t h e frequency f  amplitude o f the resonance curve i s n o t e d .  and  Q  The c a v i t y i s  then tuned t o a s l i g h t l y d i f f e r e n t f r e q u e n c y f = f  + f^.  The  response-curve amplitude w i l l be somewhat lower due t o the reduced power output of t h e k l y s t r o n a t the frequency t o which the  c a v i t y i s tuned.  The o r i g i n a l l e v e l i s r e s t o r e d by  i n c r e a s i n g the power i n p u t t o the c a v i t y w i t h an adjustment of the  precision attenuator.  of F i g u r e 2.11  C o n t i n u i n g i n t h i s manner, the graph  i s o b t a i n e d from the c a l i b r a t i o n o f the  p r e c i s i o n attenuator.  T h i s graph i s c o n v e r t e d from t h e d e c i b e l  s c a l e and i s used t o produce the r e q u i r e d c o r r e c t i o n c u r v e o f Figure 2.12.  The c o r r e c t i o n curve i s c o m p l e t e l y independent  of t h e d e t e c t o r square-law c h a r a c t e r i s t i c . Two  assumptions w h i c h r e q u i r e some e x p l a n a t i o n have been  made i n the f o r e g o i n g a n a l y s i s .  I t has been assumed t h a t the  c o u p l i n g c o e f f i c i e n t s are independent of f r e q u e n c y and a l s o t h a t t h e d e t e c t o r s t a y s matched over the f r e q u e n c y range o f interest.  That 8^ and 8  constant i s f a i r l y  2  clear.  do, i n f a c t , remain e s s e n t i a l l y The f i e l d s i n t h e c a v i t y a t t h e end  w a l l are independent of f r e q u e n c y .  I n t h e waveguide, the s m a l l  changes i n guide wavelength caused by the f r e q u e n c y d e v i a t i o n s from f  Q  produce c o m p l e t e l y n e g l i g i b l e e f f e c t s as f a r as the  o p e r a t i o n of the c o u p l i n g h o l e s i s concerned. The matching o f t h e d e t e c t o r i s a s l i g h t l y more problem.  difficult  N e a r l y a l l of the observed decrease i n the output  l e v e l was due t o t h e k l y s t r o n but a s m a l l p o r t i o n was  caused  by t h e frequency-response c h a r a c t e r i s t i c o f t h e d e t e c t o r . The two e f f e c t s a r e not e a s i l y separated e x p e r i m e n t a l l y and the graph o f t h e f u n c t i o n g ( f ^ ) i n c l u d e s b o t h . purposes o f s i m p l i c i t y , t h e c o r r e c t i o n  However, f o  has been d e r i v e d f o r  an i d e a l d e t e c t o r and g ( f ^ ) i s assumed t o r e p r e s e n t t h e amplitude  m o d u l a t i o n c h a r a c t e r i s t i c of t h e k l y s t r o n .  -1. 2  :  F i g 2.11  1  1  u  :  1  N o r m a l i z e d K l y s t r o n Power-Output Curve  Frequency D e v i a t i o n  (Mc/s)  5.0  F i g . 2.12  C o r r e c t i o n Term  57.  3.  3.1.  TESTS AND RESULTS  G e n e r a l Procedure Two t r a n s f o r m e r o i l s of commercial q u a l i t y were s e l e c t e d  f o r the main s e r i e s o f t e s t s .  They w i l l be r e f e r r e d t o as  O i l s 1 and 2 and were of the f o l l o w i n g g e n e r a l t y p e s : Oil 1 - a lightly inhibited o i l , O i l 2 - an u n i n h i b i t e d o i l . These o i l s were a r t i f i c i a l l y aged by o x i d i z i n g them a t e i t h e r 110 or 115 °C.  The c o r r e l a t i o n of t a n 6 w i t h d e t e r i o r a t i o n  was i n v e s t i g a t e d by making t a n 6 measurements on samples  aged  d i f f e r e n t p e r i o d s of t i m e . The c o n d i t i o n of the aged o i l s was a l s o determined c h e m i c a l l y by e v a l u a t i n g t h e n e u t r a l i z a t i o n number of each sample.  Because of t h e complex and l e n g t h y procedure which i s  r e q u i r e d f o r a sludge d e t e r m i n a t i o n , the amount of sludge p r e s e n t i n the o x i d i z e d o i l s was i n s p e c t e d v i s u a l l y but was  not  measured q u a n t i t a t i v e l y . 3.2.  A r t i f i c i a l l y Ageing t h e O i l s The b a s i c procedure o u t l i n e d i s the one used f o r the f i r s t  set  of t e s t s .  The m o d i f i c a t i o n s made p r i o r t o a second s e t o f  t e s t s are d i s c u s s e d i n a f o l l o w i n g s e c t i o n . Pour o i l samples of 120 ml each were put i n t o t h o r o u g h l y c l e a n , 250-ral Erlenmeyer f l a s k s .  The f l a s k s , unstoppered and  exposed t o t h e normal room atmosphere, were p l a c e d i n a t h e r m o s t a t i c b a t h whose temperature was h e l d c o n s t a n t a t 110  °C.  58. An 1 8 - i n c h l e n g t h of 12-gauge s o l i d copper w i r e , c a r e f u l l y c l e a n e d w i t h f i n e emery and a dry c l o t h , was  c o i l e d i n the  form of a s p i r a l and p l a c e d i n the bottom of each f l a s k .  This  served as a c a t a l y s t t o speed up the o x i d a t i o n of the o i l . Every 48 h o u r s , one  of the samples was  removed from the heat  b a t h and a l l o w e d t o c o o l t o room temperature.  Determinations  of n e u t r a l i z a t i o n number and t a n 6 were t h e n made. The  heat b a t h c o n s i s t e d of a w e l l - i n s u l a t e d metal  c o n t a i n e r l a r g e enough t o accommodate f o u r samples at one T h i s c o n t a i n e r was and was  time.  f i l l e d t o the p r o p e r depth w i t h p a r a f f i n  heated by a hot p l a t e .  The temperature o f the b a t h  c o u l d be a d j u s t e d t o any v a l u e between 80 °C and 140 °C.  Once  a d j u s t e d , a simple e l e c t r o n i c c i r c u i t employing a t h e r m i s t o r immersed i n the p a r a f f i n , a u t o m a t i c a l l y h e l d t h e temperature constant  t o w i t h i n - 1 °C of the set v a l u e .  shown s c h e m a t i c a l l y i n F i g u r e 3.3.  The  circuit is  3.1.  E v a l u a t i o n of N e u t r a l i z a t i o n Number The  n e u t r a l i z a t i o n number o f the o i l was  determined  f o l l o w i n g the ASTM C o l o r T i t r a t i o n Method, D974-58T^ ^.  The  25  method c o n s i s t e d of d i s s o l v i n g a 50-ml o i l sample i n 100 ml  of  a t i t r a t i o n s o l v e n t , adding the i n d i c a t o r and t h e n t i t r a t i n g w i t h a standard reached.  a l c o h o l i c base s o l u t i o n u n t i l the end p o i n t  The t i t r a t i o n s o l v e n t i t s e l f was  very s l i g h t l y  was  acidic  and r e q u i r e d a few drops of base s o l u t i o n f o r n e u t r a l i z a t i o n . A b l a n k t i t r a t i o n on 100 ml of the s o l v e n t p r o v i d e d correction for this.  a  59. The t i t r a t i o n s o l v e n t was p r e p a r e d by adding 5 ml o f d i s t i l l e d water and 495 ml of i s o p r o p y l a l c o h o l t o 500 ml of toluene.  The i n d i c a t o r s o l u t i o n was made up by d i s s o l v i n g  2.5 gm of p - n a p t h o l b e n z e i n  (orange i n a c i d , green-brown i n  base) i n 250 ml o f the t i t r a t i o n s o l v e n t . 0.5 ml of t h i s  For each t i t r a t i o n ,  i n d i c a t o r s o l u t i o n was used.  The s t a n d a r d base  s o l u t i o n was p r e p a r e d by d i s s o l v i n g 2.5 gm of NaOH i n one l i t r e of i s o p r o p y l a l c o h o l .  T h i s base was s t a n d a r d i z e d  f r e q u e n t l y by t i t r a t i n g w i t h an aqueous 0.1 N s t a n d a r d solution.  The c o n c e n t r a t i o n o f the base s o l u t i o n was  HC1 0.068 N.  In o r d e r t o express the n e u t r a l i z a t i o n number i n mg KOH gram, t h e c a l c u l a t i o n s were done as though KOH  per  had been used  i n t h e p r e p a r a t i o n of the base s o l u t i o n . 3.4.  E v a l u a t i o n o f Tan 6 For the measurements of l o s s t a n g e n t , the c a v i t y  was  f i l l e d t o a depth c o r r e s p o n d i n g t o o n e - h a l f wavelength o i l f o r the T E Q ^ mode. t h e f i l l i n g was  i n the  Rather than measure the depth of l i q u i d ,  done v o l u m e t r i e a l l y w i t h a p i p e t t e .  of o i l r e q u i r e d t o g i v e t h e c o r r e c t depth was the measured v a l u e of e  The volume  c a l c u l a t e d from  and t h e known diameter of the c a v i t y . r  For o i l s which c o n t a i n e d s l u d g e , care was t a k e n t o ensure t h a t a r e p r e s e n t a t i v e sample was p l a c e d i n the c a v i t y . The Q - f a c t o r s c o r r e s p o n d i n g to the T E Q ^ resonances were measured f o r each sample.  a n d  ^*013  These were c o r r e c t e d  f o r amplitude m o d u l a t i o n of the KLystron a c c o r d i n g t o E q u a t i o n and were t h e n s u b s t i t u t e d i n t o E q u a t i o n 2.25 values.  2.35  to y i e l d the t a n 6  60. E q u a t i o n 2.25 t a k e s a simple form when n u m e r i c a l v a l u e s are a s s i g n e d t o t h e v a r i o u s parameters.  F o r example, c h o o s i n g  v = 2 corresponds t o a Q v a l u e of 15,000 from Table 2.1. T h i s Q  value of Q  d i d n o t change d u r i n g the e n t i r e p e r i o d t h a t t h e  Q  c a v i t y was used.  The r a d i u s a i s f i x e d a t 1.545 i n c h e s , t h e  c u t - o f f wavelength  X  C  f o r t h e TEQ^ mode i s equal t o 2.533 i n c h e s  and the guide wavelength e  r  X^ i s e q u a l t o 1.688 i n c h e s .  i s e q u a l t o 2.165 and hence, X^ = 1.032 i n c h e s .  F o r O i l 2,  A l l the  measurements were made w i t h n^ = 1 and n^ equal t o e i t h e r 1 o r 2. W i t h t h e s e s u b s t i t u t i o n s , E q u a t i o n 2.25 becomes n  2  = 1:  Tan 6  =  • ~ - - 0.000249  ... 3.1  n  2  = 2:  Tan 6  =  - 0.000275  ... 3.2  3  2  These e q u a t i o n s p e r m i t t a n 6 t o be c a l c u l a t e d from t h e Q - f a c t o r of e i t h e r t h e T E  Q 1 2  or T E  and X^ = 1.035 i n c h e s .  Q 1 3  resonance.  F o r O i l 1, e  T h e r e f o r e , a p a i r o f almost  r  = 2.150  identical  equations are obtained. 3.5.  Test I  - A r t i f i c i a l l y Aged O i l s  Samples of O i l s 1 and 2 were aged by t h e method d i s c u s s e d previously.  Both o i l s were c l e a r and b r i g h t i n appearance and  s l i g h t l y y e l l o w i n c o l o r a t the s t a r t o f t h e t e s t .  The i n h i b i t e d  o i l showed o n l y a s l i g h t d i s c o l o r a t i o n and a b a r e l y p e r c e p t i b l e t r a c e o f l i g h t grey sludge a f t e r 192 hours o f ageing a t 110 °C. The u n i n h i b i t e d o i l darkened  r a p i d l y i n c o l o r and began t o  produce dark brown sludge when aged f o r about 36 hours. 192 hours, t h e o i l was a reddish-brown a c o n s i d e r a b l e amount o f s l u d g e .  After  i n c o l o r and c o n t a i n e d  Tan 6 and a c i d i t y measurements  61. were made on samples aged f o r v a r i o u s p e r i o d s o f t i m e .  The  r e s u l t s a r e g i v e n i n g r a p h i c a l form i n F i g u r e 3.2. The d i e l e c t r i c c o n s t a n t o f t h e o i l s was o r i g i n a l l y measured as 2.150 and 2.165 f o r O i l s 1 and 2 r e s p e c t i v e l y . These v a l u e s had not changed measureably  a f t e r ageing t h e o i l s  in this test. 3.6.  T e s t I I - A r t i f i c i a l l y Aged O i l s I t was d e s i r a b l e t o make measurements on o i l s which were  more h i g h l y o x i d i z e d t h a n those o f T e s t I.  For t h i s reason,  t h e o i l s f o r Test I I were o x i d i z e d a t t h e h i g h e r temperature of 115 °C.  I n a d d i t i o n t o r a i s i n g t h e temperature o f t h e heat  b a t h , t h e procedure was m o d i f i e d by b u b b l i n g f i l t e r e d a i r which was d r i e d w i t h s i l i c a g e l , t h r o u g h each o i l sample. T h i s ensured an adequate process.  s u p p l y o f oxygen f o r t h e d e t e r i o r a t i o n  A sample was removed from the heat b a t h every  24 h o u r s . A g a i n , t h e i n h i b i t e d o i l was d e t e r i o r a t e d t o a much lower degree t h a n t h e u n i n h i b i t e d o i l .  The s l i g h t amount o f  sludge formed by O i l 1 was l i g h t grey i n c o l o r and the o i l i t s e l f was g o l d e n y e l l o w .  The aged samples o f O i l 2 were v e r y  d a r k i n c o l o r and were h e a v i l y s l u d g e d .  Tan 6 and a c i d i t y  v a l u e s a r e g i v e n by t h e s o l i d - l i n e graphs o f F i g u r e 3.3. I t was a g a i n found t h a t t h e d i e l e c t r i c c o n s t a n t s o f t h e o i l s had not changed a measureable  amount as a r e s u l t o f t h e a g e i n g  process, A s i m p l e t e s t was performed t o determine what s i g n i f i c a n c e the presence o f sludge had on t h e t a n 6 and a c i d i t y measurements.  62.  The h e a v i l y sludged samples of O i l 2, upon which t a n 6 measurements had a l r e a d y been made, were f i l t e r e d t o remove t h e sludge.  Tan 6. and a c i d i t y measurements were then made on t h e s e  filtered oils. the r e s u l t .  The d a s h e d - l i n e graphs of F i g u r e 3.3(b) show  The n e u t r a l i z a t i o n number o f t h e o i l was found t o  be l e s s a f t e r sludge removal but the t a n 6 v a l u e was e i t h e r t h e same o r s l i g h t l y i n c r e a s e d . 3.7.  T e s t I I I - E f f e c t o f Water S i n c e water has a p o l a r s t r u c t u r e and e x h i b i t s a l a r g e  l o s s tangent a t microwave f r e q u e n c y , t h e t a n 6 measured f o r an o i l w i l l be i n f l u e n c e d by m o i s t u r e c o n t e n t .  An experiment was  performed t o determine t h e magnitude o f t h i s  effect.  A few drops o f d i s t i l l e d water were added t o a q u a n t i t y of O i l 1 i n a g l a s s - s t o p p e r e d f l a s k .  T h i s m i x t u r e was s t o r e d  f o r t h r e e weeks u n t i l t h e o i l had t a k e n on a c l o u d y i n d i c a t i n g p a r t i c l e s of moisture i n suspension.  appearance,  A measurement  of t a n 6 was then made on t h e o i l and was found t o have i n c r e a s e d —4 —4 from t h e i n i t i a l v a l u e o f 10.8 x 10 t o 11.8 x 10 . No change in dielectric 3.8.  c o n s t a n t was measured.  T e s t IV - O i l s Removed from  Transformers  Three o i l samples, removed from t r a n s f o r m e r s i n s e r v i c e , were o b t a i n e d from t h e Standards L a b o r a t o r y o f t h e B.C. Hydro and Power A u t h o r i t y .  A l l t h r e e of t h e s e o i l s were regarded as  worn out and were i n t h e p r o c e s s o f b e i n g d i s c a r d e d . tangent and d i e l e c t r i c  The l o s s  c o n s t a n t v a l u e s measured f o r t h e s e o i l s  are l i s t e d i n Table 3.1.  63.  Table 3.1..Measurements on S e r v i c e - A g e d O i l s  T e s t s by B.C. Hydro L a b o r a t o r y  T e s t IV #*  Sample  Appearance  ASTM Color  I FT*  Oil 3  Sludge, foggy  2.75  14.5  0.40  35.9  2.150  Oil 4  Sludge, foggy  2.75  13.7  0.76  45.4  2.165  0.98  52.1  2.220  N.N.  Oil 5  Tan 6 x 104  I n t e r f a c i a l T e n s i o n i n dynes per cm N e u t r a l i z a t i o n Number i n rag KOH per gram  -12 v.  R, :  Decade Box  Q,  R_:  GC32A1 T h e r m i s t o r  K^s  Magnetic reed Relay  K : f  Power Relay  p, , Q : ' ^ 9  x  q  2N1382 (Selected pair) F i g . 3.1  9  p.: 2N1304  Temperature C o n t r o l  Circuit  c  r  0  0  48  96  144  192  Hours a t 110 °C • (b) P i g . 3.2  Oil 2  Tan§ and A c i d i t y f o r Test I  0.40  s  a oo  u u  <u 0.30  •tfo  O (30  B 0.20  CO  •H •H O  a  0.10  o- :-yy-;;-.. 48 ;  V^v V:'.'.v :  . ,. Hours a t 115 "C (b)  P i g 3.3  Oil 2  T a n 8 and A c i d i t y f o r T e s t I I  66. 3.9.  Accuracy of t h e Measurements The e r r o r c o n t a i n e d i n t h e measured t a n 6 v a l u e s depends  p r i m a r i l y on t h e f o l l o w i n g f a c t o r s : (a) C a l i b r a t i o n e r r o r of the p r e c i s i o n  attenuator,  (b) Random e r r o r i n measuring t h e Q - f a c t o r  of t h e  cavity, (c) The presence of amplitude m o d u l a t i o n i n t h e output o f t h e swept k l y s t r o n , (d) The accuracy o f E q u a t i o n 2.25 i n c o r r e c t i n g f o r t h e w a l l l o s s e s i n the c a v i t y . A l t h o u g h t h e amount o f e r r o r i n t a n 6 caused by the c a l i b r a t i o n o f the p r e c i s i o n a t t e n u a t o r i t i s e s t i m a t e d t o be l e s s t h a n ifo.  cannot be measured,  F o r t h e purpose o f Q -  measurement, i t i s r e q u i r e d t o have two c a l i b r a t i o n p o i n t s the a t t e n u a t o r  which c o r r e s p o n d t o a power d i f f e r e n c e of  e x a c t l y 3 db.  The a b s o l u t e amount o f a t t e n u a t i o n  not be a c c u r a t e l y known.  The a t t e n u a t o r  with a rotary-vane attenuator  on  p r e s e n t need  used was compared  whose a b s o l u t e a c c u r a c y i s c l a i m e d  t o be 2fo o r 0.1 db, whichever i s g r e a t e r .  I n view o f t h i s , the  e s t i m a t e o f l e s s than 1$ e r r o r seems r e a s o n a b l e . The r e p e a t a b i l i t y of Q measurement was determined by c a r r y i n g out a number of i d e n t i c a l measurements.  When  measurements on o i l s were b e i n g made, the Q - f a c t o r s generally  were  l e s s than 3500 and t h e r e p e a t a b i l i t y was lfo.  For  the measurement of unloaded Q - f a c t o r s i n excess of 15,000, o s c i l l o s c o p e t r a c e j i t t e r and broadening of t h e markers reduced the r e p e a t a b i l i t y t o 3$.  This uncertainty  of 3$ i n Q  q  would  not produce an e r r o r l a r g e r than 0.5$ i n t h e v a l u e o f t a n 6.  67. The e r r o r s i n t a n 6 caused by amplitude m o d u l a t i o n of the k l y s t r o n are e s t i m a t e d t o be l e s s t h a n 2fo a f t e r a p p l y i n g t h e correction described previously.  S i n c e t a n 6 i s a c o n s t a n t of  t h e d i e l e c t r i c , E q u a t i o n s 3.1 and 3.2 s h o u l d y i e l d v a l u e s i f t h e r e i s no amplitude m o d u l a t i o n p r e s e n t .  identical In the  case when t h e swept k l y s t r o n i s a l s o amplitude modulated, t h e v a l u e o f t a n 6 c a l c u l a t e d from the T E Q ^  resonance w i l l be  c o n s i s t e n t l y lower t h a n t h a t c a l c u l a t e d from t h e  resonance.  T E Q ^ Q  T h i s i s i l l u s t r a t e d i n Table 3.2 which g i v e s t h e u n c o r r e c t e d and c o r r e c t e d v a l u e s o f t a n 6 c a l c u l a t e d f o r t h e aged samples o f O i l 2 i n T e s t I I . The c o r r e c t e d v a l u e s o f t a n 6 d i f f e r by l e s s t h a n 2$ i n a l l c a s e s . T a b l e 3.2  Hours a t 115 °C  Resonance  0  T E  012  0  T E  013  24  T E  012  24  T E  013  48  T E  012  T E  013  T E  012  T E  013  96  T E  012  96  T E  013  120  T E  012  120  T E  013  48 72 72  ,  C a l c u l a t e d V a l u e s of Tan 6 f o r O i l 2 Uncorrected t a n 6 x 10^  Corrected 4 t a n 6 x 10  1.93 + 0.01  11.4  11.9  1.23 + 0.01 2.48 + 0.02  12.0  12.1  15.3  16.6  1.59 + 0.01  16.3  16.8  2.70 + 0.02  16.9  18.7  1.72 + 0.01 2.72 + 0.02  17.9  18.5  17.1  18.9  1.74 + 0.01  18.1  18.7  2.98 + 0.03  19.0  21.4  1.92 + 0.01  20.3  21.2  3.14 + 0.03  20.1  23.0  2.04 + 0.02  21.8  22.9  l Mc/s f  68. The  c l o s e agreement o f t h e c o r r e c t e d v a l u e s o f t a n 6 i n  Table 3.2 a l s o i n d i c a t e s t h a t t h e w a l l l o s s e s i n the c a v i t y have been p r o p e r l y  accounted f o r .  I t i s not p o s s i b l e to  determine e x a c t l y t h e magnitude of t h e e r r o r i n t r o d u c e d  by t h e  c o r r e c t i o n f o r w a l l l o s s e s s i n c e i t depends oh t h e v a l i d i t y o f the assumptions made i n d e r i v i n g E q u a t i o n 2.25. An e s t i m a t e of t h e e r r o r l i m i t i s o b t a i n e d by t h e f o l l o w i n g r e a s o n i n g . The  two b a s i c assumptions made i n d e r i v i n g E q u a t i o n 2.25  were t h a t (a) Except f o r a magnitude f a c t o r  s  the f i e l d s i n the  c a v i t y a r e those which would o c c u r f o r a l o s s free  dielectric,  (b) The w a l l l o s s e s can be c a l c u l a t e d i n terms o f a effective wall conductivity The  a» Q  f i r s t o f these assumptions i s i n g e n e r a l use and i s t a k e n  as b e i n g v a l i d .  The second i s a l s o i n g e n e r a l use and can be  partially justified.  A value for a  can be c a l c u l a t e d from an  e x p e r i m e n t a l measurement o f Q f o r a p a r t i c u l a r resonance i n Q  the a i r - f i l l e d  cavity.  Using t h i s value of O , the Q of other q  Q  resonances can t h e n be p r e d i c t e d w i t h an e r r o r o f l e s s than 10$.  Thus, i t seems reasonable t o use t h i s same v a l u e o f a  g  when c a l c u l a t i n g t h e w a l l l o s s e s i n t h e d i e l e c t r i c - f i l l e d cavity.  On t h i s b a s i s , s i n c e the w a l l l o s s e s were l e s s than  20$ of t h e d i e l e c t r i c l o s s e s , t h e e r r o r i n t a n 6 from t h i s source i s regarded as b e i n g l e s s t h a n 1.5$. I n view o f t h e f o r e g o i n g  sources o f e r r o r , the a b s o l u t e  e r r o r o f t h e measured t a n 6 v a l u e s i s e s t i m a t e d t o be l e s s t h a n 6$.  F o r the purpose o f comparing t a n 6 v a l u e s o f d i f f e r e n t  69. samples w i t h o u t r e g a r d t o t h e a b s o l u t e v a l u e , t h e e r r o r i s l e s s t h a n 2$. D i e l e c t r i c c o n s t a n t measurements made w i t h t h e c o m p l e t e l y f i l l e d c a v i t y have an e r r o r o f l e s s than 0.1$. Measurements of d i e l e c t r i c c o n s t a n t f o r t h e aged samples were made w i t h the cavity partly f i l l e d .  F o r t h e s e , the e r r o r i s l e s s than 0.25$.  The r e p e a t a b i l i t y o f t h e a c i d i t y measurements can be summarized b r i e f l y as f o l l o w s .  The samples o f O i l 1 were a l l  l i g h t l y c o l o r e d so t h a t t h e e s t i m a t e d r e p e a t a b i l i t y i s b e t t e r than 0.01 mg KOH p e r gram.  F o r t h e aged samples o f O i l 2, t h e  d a r k e r c o l o r made o b s e r v a t i o n o f t h e end p o i n t more d i f f i c u l t and t h e e s t i m a t e d r e p e a t a b i l i t y i s 0.03 mg KOH p e r gram. 3.10.  Discussion of Results The graphs o f F i g u r e 3.2 and 3.3 show t h a t a c o r r e l a t i o n  e x i s t s between t h e measured v a l u e s o f t a n 6 and a c i d i t y f o r t h e aged o i l s .  Some o f t h e q u a l i t a t i v e a s p e c t s of t h i s c o r r e l a t i o n  may be deduced from the graphs o f F i g u r e 3.4 which have been prepared by p l o t t i n g the i n c r e m e n t a l changes o c c u r r i n g d u r i n g t h e a g e i n g experiments.  R e f e r r i n g t o F i g u r e 3.4, s e v e r a l  o b s e r v a t i o n s c a n be made: (a) The r e l a t i o n between t a n 6 and a c i d i t y i s a p p r o x i m a t e l y l i n e a r except f o r t h e v e r y e a r l y stages o f o x i d a t i o n , (b) The i n c r e a s e i n l o s s tangent which o c c u r s i s r e l a t e d t o t h e nature of t h e o i l and a l s o t o the c o n d i t i o n s under which t h e o x i d a t i o n t a k e s place,  70.  ( c ) P o r t h e same i n c r e a s e i n a c i d i t y , l o s s tangent for  the increase i n  f o r O i l 2 i s approximately  twice t h a t  O i l 1.  0.40 Oil 2 Test II  00  u 0)  3*  0.30  o to  Oil 2 Test I  \  a i  \  0.20  •H  Oil 1 Test I I  T3 •H O  V  / 0  /  \  >> +>  \  v. / /  fl 0.10  /  y  J3 ^ 0  5  10 4  Increase Pig. Although acidity is  3.4  Increase  i s very d e f i n i t e ,  without  being a c i d i c .  initial  t a n g e n t and tangent  It i s quite  l o s s e s have a p o l a r s t r u c t u r e  This fact During  tan 6 increases rapidly the  i n Tan 6  some o f t h e o x i d a t i o n p r o d u c t s  t o the d i e l e c t r i c  shown by F i g u r e 3.4.  Increase  t h e measurement o f t h e l o s s  measurement o f a c i d i t y .  that at least  contributing  i n A c i d i t y versus  t h e c o r r e l a t i o n between t h e l o s s  not merely a d i r e c t  probable  i n T a n 6 x 10  i s b o r n e o u t e x p e r i m e n t a l l y as  the very  early  stages of o x i d a t i o n ,  compared w i t h a c i d i t y ,  o x i d a t i o n products  indicating  are p o l a r but not a c i d i c .  that However,  71. except f o r t h i s i n i t i a l  p e r i o d , the q u a n t i t y of a c i d i c  oxidation  p r o d u c t s f o r m e d i n a p a r t i c u l a r o i l i n c r e a s e s more o r l e s s i n step w i t h the q u a n t i t y of p o l a r i z a b l e products g i v i n g r i s e the d i e l e c t r i c It w i l l  losses.  be r e c a l l e d t h a t t h e a g e d s a m p l e s o f O i l 2, were  more h i g h l y s l u d g e d t h a n t h o s e o f O i l 1 and h e n c e , one led  to  might  be  t o b e l i e v e t h a t t h e h i g h e r v a l u e s o f t a n 6 f o r O i l 2 were  c a u s e d by t h e e x t r a s l u d g e . correct.  The  This conclusion  would not  l o s s t a n g e n t measurements made on t h e o i l s  w h i c h t h e s l u d g e had b e e n r e m o v e d by f i l t r a t i o n , decrease  i n t a n 6.  In fact,  c a s e s b u t t h i s was  process.  due  from  showed no  a s l i g h t i n c r e a s e was  undoubtedly  t h e samples w i t h w a t e r , filtration  be  n o t e d i n some  to inadvertently  contaminating  o r some o t h e r p o l a r i m p u r i t y , d u r i n g t h e  I t must t h e r e f o r e be  sludge p a r t i c l e s themselves  do n o t make a  concluded t h a t the significant  c o n t r i b u t i o n t o t h e v a l u e of l o s s t a n g e n t measured w i t h t h e technique The  employed. f o r e g o i n g a n a l y s i s does not n e c e s s a r i l y i m p l y t h a t  t h e s l u d g e c o n t e n t o f an o i l and t h e m e a s u r e d l o s s t a n g e n t not r e l a t e d . may  I t i s q u i t e p o s s i b l e t h a t t h e s e two  be r e l a t e d i n d i r e c t l y .  tendency  towards  quantities  F o r i n s t a n c e , an o i l s h o w i n g  sludge f o r m a t i o n might a l s o tend t o  other oxidation products polarization losses.  are  a  form  (not n e c e s s a r i l y a c i d s ) having h i g h  I n t h i s way,  a high l o s s tangent  might  be i n d i r e c t l y i n d i c a t i v e o f a h i g h s l u d g e c o n t e n t e v e n t h o u g h the sludge i t s e l f The  i s not r e s p o n s i b l e f o r the d i e l e c t r i c  experimental evidence  s u g g e s t s t h i s p r o p o s a l as  p o s s i b i l i t y b u t i t has n o t b e e n a d e q u a t e l y  a  demonstrated.  losses.  72.  A p o s s i b l e reason f o r the n e g l i g i b l e c o n t r i b u t i o n of t h e sludge t o the p o l a r i z a t i o n l o s s e s i s t h a t the i n s o l u b l e p a r t i c l e s s e t t l e out r a p i d l y t o t h e bottom o f the c a v i t y where the B - f i e l d i s weak.  Thus, even i f the s t r u c t u r e of the  p a r t i c l e s happens t o be p o l a r , the d i e l e c t r i c l o s s e s a s s o c i a t e d w i t h them w i l l be s m a l l .  I f the p a r t i c l e s c o u l d be p l a c e d i n a  r e g i o n of h i g h B - f i e l d , p o s s i b l y by a d i f f e r e n t mode c h o i c e , the l o s s e s measured would p r o b a b l y be l a r g e r .  However, i t i s  f e l t t h a t the l o s s e s caused d i r e c t l y by the presence o f the sludges would s t i l l be a s m a l l percentage o f the t o t a l .  This  o b s e r v a t i o n i s based p a r t i a l l y on the r e l a t i v e l y s m a l l e f f e c t w h i c h s l u d g e removal had on the a c i d i t y of t h e Because the i n h i b i t o r s added t o t r a n s f o r m e r  samples. o i l s are  often  p o l a r compounds, t h e i n i t i a l l o s s tangent measured f o r new may  v a r y over a c o n s i d e r a b l e range.  T h i s a s p e c t was  oils  not  i n v e s t i g a t e d i n d e t a i l but a few measurements on new  o i l s were -4 made. An u n i n h i b i t e d o i l had a l o s s t a n g e n t of 11.3 x 10 w h i l e a h e a v i l y i n h i b i t e d o i l , known t o be of h i g h q u a l i t y , had —4  a t a n 6 v a l u e o f 14.1  x 10  .  As a r e s u l t , i t i s c l e a r t h a t a  measurement of l o s s t a n g e n t , when a p p l i e d t o new  oils,  cannot  be used as a c r i t e r i o n of q u a l i t y . At a f r e q u e n c y of 8.5 constant  Gc/s, t h e l o s s tangent and  of water are a p p r o x i m a t e l y  T e s t I I I was  0.5  dielectric  and 65 r e s p e c t i v e l y .  a b l e t o show t h a t the presence of water d i d  produce a measureable i n c r e a s e i n t a n 6 but the magnitude of the i n c r e a s e was  small.  T h i s i s e x p l a i n e d by n o t i n g t h a t the  s o l u b i l i t y of water i n a new  o i l i s low, b e i n g of the o r d e r  75 p a r t s per m i l l i o n (ppm).  For a used o i l c o n t a i n i n g  of  73.  m o i s t u r e - a b s o r b i n g m a t e r i a l such as c e l l u l o s e f i b r e s or h y d r o p h i l i c o x i d a t i o n p r o d u c t s , a somewhat h i g h e r moisture content i s p o s s i b l e but the i n c r e a s e i n t a n 6 caused by the water would s t i l l not be l a r g e .  I t may  t h e r e f o r e be  concluded  t h a t the i n c r e a s e i n t a n 6 i n aged or used o i l s i s caused p r i m a r i l y by p o l a r i z a b l e substances o t h e r t h a n water. The changes i n t h e d i e l e c t r i c c o n s t a n t caused by the ageing or by the presence  of water were of no  f o r any o f the o i l s t e s t e d .  significance  Even c o n t a m i n a t i o n w i t h a m a t e r i a l  of h i g h d i e l e c t r i c c o n s t a n t such as water, produced in e  which was  r  error.  a change  s m a l l enough t o be masked by the e x p e r i m e n t a l  T h i s seems a t f i r s t t o be somewhat s u r p r i s i n g but i t  i s f u l l y p r e d i c t a b l e i f one c o n s i d e r s a contaminated  or  o x i d i z e d o i l t o be the normal o i l , l o a d e d w i t h s m a l l p a r t i c l e s (26)  having a d i f f e r e n t d i e l e c t r i c constant.  Lewin  v  ' g i v e s an  e q u a t i o n f o r c a l c u l a t i n g the e f f e c t i v e b u l k d i e l e c t r i c  constant  of a p a r t i c l e - l o a d e d d i e l e c t r i c :  er  = e ro  1 +  3$)  e + 2c e - e p  where er  ...  3 o3  V  ro  = e f f e c t i v e b u l k d i e l e c t r i c c o n s t a n t of the particle-loaded material,  c c  ro P  (^)  = d i e l e c t r i c c o n s t a n t of the main m a t e r i a l , ' = d i e l e c t r i c c o n s t a n t of t h e p a r t i c l e s , = r a t i o of t o t a l p a r t i c l e volume t o t o t a l volume.  E q u a t i o n 3.3,may be used when the r a d i u s of the p a r t i c l e s  74.  i s v e r y much s m a l l e r t h a n the wavelength i n t h e d i e l e c t r i c . A p p l y i n g t h e e q u a t i o n t o a t r a n s f o r m e r o i l c o n t a i n i n g water p a r t i c l e s , i t i s seen t h a t a c o n c e n t r a t i o n o f a p p r o x i m a t e l y 800 ppm would be r e q u i r e d t o produce a change i n t h e d i e l e c t r i c c o n s t a n t of 0.25$.  I t f o l l o w s t h a t t h e much  s m a l l e r c o n c e n t r a t i o n s of water found i n p r a c t i c e do n o t produce a measureable change i n c_. S i n c e t h e o x i d a t i o n o f an o i l a f f e c t s o n l y a s m a l l percentage o f t h e hydrocarbon m o l e c u l e s ,  l e a v i n g the others  unchanged, t h e same argument may be used t o show t h a t t h e bulk d i e l e c t r i c constant the ageing p r o c e s s .  should be a f f e c t e d o n l y s l i g h t l y by  T h i s was borne out e x p e r i m e n t a l l y by t h e  measurements made on t h e a r t i f i c i a l l y aged o i l s .  The s e r v i c e -  aged o i l s examined i n Test IV showed a c o n s i d e r a b l e v a r i a t i o n in c  r  w i t h t h e most s e v e r e l y d e t e r i o r a t e d o i l having t h e  highest d i e l e c t r i c constant. coincidental.  I t i s f e l t that t h i s i s  The v a l u e s o f e t h a t were measured a r e r  p r o b a b l y determined by t h e o r i g i n a l d i e l e c t r i c constant o f each o i l r a t h e r t h a n by t h e degree o f d e t e r i o r a t i o n . The t e c h n i q u e  employed f o r measuring t h e d i e l e c t r i c  l o s s e s a t X-band produced v e r y good r e s u l t s . experimental  The most s e r i o u s  d i f f i c u l t y encountered when f i r s t t r y i n g out t h e  method c o n s i s t e d o f ghost-mode i n t e r f e r e n c e i n t h e p a r t l y f i l l e d cavity.  T h i s problem c o u l d be reduced by u s i n g a c a v i t y  w i t h a s m a l l e r diameter,  say f o r i n s t a n c e , 2.1 i n c h e s .  guide wavelength c o r r e s p o n d i n g  t o a frequency  The  o f 8.5 Gc/s would  t h e n be 2.35 inches and o n l y 6 modes c o u l d be propagated i n the a i r - f i l l e d cavity.  When p a r t i a l l y f i l l e d w i t h a m a t e r i a l whose  75.  d i e l e c t r i c c o n s t a n t i s 2.15, an a d d i t i o n a l could e x i s t .  5 ghost modes  The d i e l e c t r i c depths c o r r e s p o n d i n g t o t h e  e x c i t a t i o n o f these ghost modes c o u l d be avoided much more e a s i l y i n t h i s c a v i t y t h a n i n t h e l a r g e r diameter  cavity.  Because o f t h e l o n g e r guide w a v e l e n g t h o f 2.35 i n c h e s , the c a v i t y b a r r e l should be made l o n g e r and a micrometer whose t r a v e l i s n o t l e s s t h a n 4 i n c h e s i s recommended. The d e t a i l e d d e s i g n s h o u l d be worked out so t h a t w i t h t h e d e s i r e d depth of d i e l e c t r i c i n t h e c a v i t y , t h e t u n i n g p l u n g e r i s capable o f b e i n g a d j u s t e d t o y i e l d any o f t h e resonances, inclusive.  The t h e o r e t i c a l unloaded  T E Q - ^  "to  T E Q - J ^  Q of these resonances  would be between 18,000 and 22,000 i n a b r a s s c a v i t y a t 8,5 Gc/s.  T h i s c a v i t y d e s i g n would permit the same type o f  measurements t o be made w i t h a c o n s i d e r a b l e r e d u c t i o n i n t h e mode-interference  problem.  76.  4.  The  CONCLUSIONS  s i g n i f i c a n c e of the microwave-frequency d i e l e c t r i c -  l o s s measurement when a p p l i e d t o the e v a l u a t i o n of aged t r a n s f o r m e r o i l s has been i n v e s t i g a t e d . The  t e c h n i q u e of u s i n g a TBQ^-mode c y l i n d r i c a l c a v i t y ,  c o n t a i n i n g a depth of o i l c o r r e s p o n d i n g t o o n e - h a l f wavelength, proved t o be a v e r y s a t i s f a c t o r y method of measuring the d i e l e c t r i c l o s s e s a t X-band. employed was  The  Q-measurement t e c h n i q u e  s u f f i c i e n t l y s o p h i s t i c a t e d t o reduce the random  e r r o r i n the measured l o s s tangent v a l u e s t o l e s s than The  absolute  1.5$.  e r r o r i n the l o s s tangent v a l u e s i s l e s s t h a n  I t has been e s t a b l i s h e d e x p e r i m e n t a l l y  t h a t the  6$.  loss  tangent of t r a n s f o r m e r o i l s , measured at X-band, i n c r e a s e s the o i l d e t e r i o r a t e s t h r o u g h o x i d a t i o n .  The  increase  tangent c l o s e l y p a r a l l e l s the i n c r e a s e i n a c i d i t y but  as  i n loss also  depends on o t h e r f a c t o r s such as the n a t u r e of the o i l and  the  c o n d i t i o n s under which the o x i d a t i o n t a k e s p l a c e . Sludge p a r t i c l e s , when p r e s e n t i n an aged t r a n s f o r m e r o i l , do not i n themselves cause a s i g n i f i c a n t i n c r e a s e d i e l e c t r i c losses.  The  i n the  p o s s i b i l i t y of an i n d i r e c t r e l a t i o n s h i p  between the l o s s tangent and the sludge c o n t e n t of an o i l i s i n d i c a t e d but has not been e s t a b l i s h e d . The  change i n the d i e l e c t r i c c o n s t a n t of an o i l ,  caused  by the presence of d i s s o l v e d w a t e r , or by the a r t i f i c i a l p r o c e s s , i s too s m a l l t o be measured by the method used.  ageing A  s m a l l but measureable i n c r e a s e i n the l o s s tangent i s produced by the presence of water i n c o n c e n t r a t i o n s 75 p a r t s per  million.  of a p p r o x i m a t e l y  77. APPENDIX  E v a l u a t i o n of t h e S t o r e d E n e r g i e s Prom E q u a t i o n 2.23, t h e e x p r e s s i o n f o r t h e d i e l e c t r i c s t o r e d energy U  d  i s g i v e n by = | e  J\E\  2  d  dv  ... A . l  D i e l e c t r i c Volume S u b s t i t u t i n g t h e v a l u e f o r t h e e l e c t r i c f i e l d g i v e n by E q u a t i o n 2.13b i n t o E q u a t i o n A . l and r e f e r r i n g t o P i g u r e 2.6, the f o r e g o i n g e q u a t i o n becomes ^d U  a  j j C ( ^ ) J ( k r ) s i n 6 ^ 2*r d r dz z=0 r=0 ... A.2 The depth of t h e d i e l e c t r i c i s chosen so t h a t ^ = n ^ ( ^ )  d = I d e  2  2  d  2  2  ±  x  d  and  1^ =  ( _ i ) where n^ and  are i n t e g e r s .  N o t i n g t h a t J ^ ( k a ) = 0 f o r t h e T E Q - ^ mode, E q u a t i o n A.2 (27)  integrates* U  ' to y i e l d  d = * d C e  2 d  (^)  |! J ( k a ) n ( ^ )  2  2  G  x  ... A.3  A s i m i l a r i n t e g r a t i o n f o r the a i r - s t o r e d energy g i v e s t h e following D  result:  t  0/(fi)  £  2  J (ka) „ (^) 2  0  2  ... A.4  For t h e d i e l e c t r i c depth chosen, an i n s p e c t i o n of E q u a t i o n 2.15 shows t h a t C C  t  f% c  d  X  2  2  2  H  * 2 ^d  «• • Ao 5  and hence  _______  3 A 6  where c_. i s t h e d i e l e c t r i c c o n s t a n t e^/e « Q  Evaluation of the Wall  Losses  The w a l l l o s s e s a r e c a l c u l a t e d from E q u a t i o n 2.24:  2  A °e e  Wall  Area  On t h e s i d e w a l l i n t h e d i e l e c t r i c , H- = H  z  = C J ( k a ) s i n p^z d  Q  T h e r e f o r e , t h e s i d e - w a l l l o s s i n t h e d i e l e c t r i c i s g i v e n by  sihr  c  d  2 J  o  2 ( k a  '  s  i  n  2  B  d l z  2  ™  d  z  l  z=0 I n t e g r a t i n g , t h e s i d e - w a l l l o s s i n t h e d i e l e c t r i c i s equal t o 2 2 C, J (ka) ira n.\, d o I d 4  A  7  Ae oe  On t h e end w a l l i n t h e d i e l e c t r i c , H_- = H_."= -C (j£—) J ^ ( k r ) . d  T h e r e f o r e , t h e e n d - w a l l l o s s i n t h e d i e l e c t r i c i s g i v e n by P  a  2 A a e  C qd (ki ^ ) 2  J r=0  v  2  J , ( k r ) 2wr d r 2  I n t e g r a t i n g , t h e e n d - w a l l l o s s i n t h e d i e l e c t r i c i s equal t o «sl (^) "•e e  2  In the a i r - f i l l e d  c/  J (ka) 2  0  ...A.S  s e c t i o n of t h e C a v i t y , t h e w a l l  losses  are c a l c u l a t e d i n a s i m i l a r manner by s t a r t i n g w i t h E q u a t i o n 2.24 and u s i n g t h e e x p r e s s i o n s f o r H_ which a p p l y i n the a i r - f i l l e d p o r t i o n .  The r e s u l t s a r e as f o l l o w s :  79.  The  s i d e - w a l l l o s s i n the a i r - f i l l e d p o r t i o n i s equal t o C^.  J  Q  (ka)na i ^ X ^  • •• Ao 9  4 A o* The  end-wall l o s s i n the a i r - f i l l e d p o r t i o n i s equal t o Tta"  / tx2  2  6  TJ^rT e e ^  C  l  n  2/, v  T  t  J  ... A.10  0  ( k a )  Th'e.-total w a l l l o s s i n the c a v i t y i s obtained 1  by summing X  c  the q u a n t i t i e s A.7 t o A.10. Using the r e l a t i o n ^ = ^ s i m p l i f y the r e s u l t a n t expression, by  ? w The  = TtaX,, C^" J^"(ka)  quantity  n  O  +  4  a  7 S  d J • o• Ao X1  V i s an i n t e g e r , the s t o r e d  Of  energy i s obtained  The  2  Por the empty c a v i t y of length  = V (TJ^-) where  O  n  i s determined from a measurement of  A °e  the unloaded Q of the c a v i t y . such t h a t  +  the t o t a l w a l l l o s s i s given  ^d  e  $  i  to  from Equation A.4 and i s equal t o  w a l l l o s s i n the empty c a v i t y may be obtained  from the  q u a n t i t i e s A . 9 and A.10 and i s equal to C  2  0  J ( k a ) n a V X. 2  0  4  1 +  X  A O  ^e e  Qo=-o^)  2  §  4a X. V X,  • •« A* X2  A a { e  2  e  4a X  (  i +  VX,  Equation A.12 i s used t o e l i m i n a t e the q u a n t i t y  from  80.  E q u a t i o n A.11,  w i t h the r e s u l t . X 7Tf 3  n  2  K  l  +  n  1  2  +  X ~3 2  +  4 a  4a X  ... The q u a n t i t i e s P^, s u b s t i t u t i o n i n t o Equation  and U^/U^ 2.21.  are now  available for  A.13  81.  REFERENCES  1.  Rogers, A. G,, " I n s u l a t i n g O i l s from Petroleum", Unpublished Report, Imperial O i l Limited, T o r o n t o , 1963.  2.  Morton, F. and B e l l , R.T.T., "The Low Temperature L i q u i d Phase O x i d a t i o n o f Hydrocarbons: A L i t e r a t u r e Survey", J . I n s t . P e t r o l . , V o l . 44, 1958, p.260.  3.  Thompson, C. N., "Mechanism of Copper C a t a l y s i s i n Insulating O i l Oxidation", J . Inst. P e t r o l . , V o l . 44, 1958, p.295.  4.  Wood-Mailock, J . C , S t e i n e r , H. and Wood, L. G., "The E f f e c t o f M e t a l s on Transformer O i l s and Some Methods o f P r o t e c t i o n A g a i n s t Adverse E f f e c t " , J . I n s t . P e t r o l . , V o l . 44, 1958, p. 320.  5.  M c C o n n e l l , T. A., " E v a l u a t i o n o f L a b o r a t o r y T e s t s as Indicators of the Service L i f e of Uninhibited E l e c t r i c a l I n s u l a t i n g O i l s " , Symposium on I n s u l a t i n g O i l s , ASTM S p e c i a l T e c h n i c a l P u b l i c a t i o n No. 218, 1957, p.3.  6.  G o s s l i n g , P.W.L., I n G e n e r a l D i s c u s s i o n , Symposium on I n s u l a t i n g O i l s , ASTM S p e c i a l Tech. Pub. No. 218, 1957, p.34.  7.  O l i v e r , F. S., i b i d . , p.36„  8.  S t a r k , K. H., " D i e l e c t r i c Loss o f I n s u l a t i n g O i l " , P r o c . I . E . E . , V o l . 100 I I A , 1953, p.89.  9.  M a r t i n , R. G. and P a t t e r s o n , E„ A., "The Measurement of the Power F a c t o r s o f I n s u l a t i n g L i q u i d s a t 50 c/s", P r o c . I . E . E . , V o l . 100 I I A , 1953, p.68.  0  10.  B e n n e t t , G. E., " E l e c t r i c a l Measuring Techniques and their Application to Insulating O i l s " , J . Inst. 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