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Location of faults in power cables by fault-generated surges Hudak, Nicholas Edward 1951

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IE* ~B? /v/ A 7 LOCATION OF FAULTS IN POWER CABLES BY FAULT-GENERATED SURGES by NICHOLAS EDWARD HTJDAK A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF We accept this thesis as conforming to the standard required from candidates for the degree of MASTER OF APPLIED SCIENCE MASTER OF APPLIED SCIENCE i n the Department of ELECTRICAL ENGINEERING Members of the Department or E l e c t r i c a l Engineering THE UNIVERSITY OF BRITISH COLUMBIA A p r i l , 1 9 5 1 LOCATION OF FAULTS- IN POWER CABLES BY FAULT-GENERATED SURGES ABSTRACT The o b j e c t o f t h i s r e s e a r c h I s t o d e v e l o p a s a t i s f a c -t o r y method f o r l o c a t i n g high-Impedance f a u l t s i n underground c a b l e s . Most methods o f l o c a t i n g f a u l t s r e q u i r e t h a t t h e f a u l t -impedance be r e d u c e d t o a low v a l u e b e f o r e the measurement can be made. A f t e r a c a r e f u l i n v e s t i g a t i o n o f the a v a i l a b l e l i t e r a t u r e , i t was d e c i d e d t h a t t h e most d e s i r a b l e method would be one u t i l i z i n g t h e t r a v e l i n g - w a v e . Of t h e t r a v e l i n g -wave methods, the f a u l t ~ g e n e r a t e d surge method appeared t o have the g r e a t e s t p o s s i b i l i t i e s ; y e t , a c c o r d i n g to t h e a u t h o r ' s knowledge, t h i s method has not been a p p l i e d t o power c a b l e s . I n t h i s method, the c a b l e i t s e l f may be c o n s i d e r e d as t h e n e t -x-jork t h a t g e n e r a t e s t h e r e q u i r e d surges. The c a b l e i s i n i t i a l l y c harged t o a v o l t a g e s u f f i c i e n t l y h i g h to e s t a b l i s h an a r c a t the f a u l t . The sudden c o l l a p s e o f t h e h i g h v o l t a g e a t the f a u l t g e n e r a t e s a surge w h i c h t r a v e l s a l o n g t h e c a b l e t o t h e m o n i t o r i n g end, where i t I n i t i a t e s a t i m i n g d e v i c e and i s r e f l e c t e d back a l o n g the c a b l e t o w a r d t h e f a u l t . The a r c w h i c h i s s t i l l c o n d u c t i n g r e f l e c t s t h e surge back to the s t a t i o n . i i The time i n t e r v a l between t h e f i r s t and second a r r i v a l o f t h e f a u l t - s u r g e a t t h e s t a t i o n i s r e c o r d e d by t h e t i m i n g d e v i c e and i s p r o p o r t i o n a l t o the d i s t a n c e t o t h e f a u l t . I n m a t h e m a t i c a l l y a n a l y z i n g t h e surge phenomena i n c a b l e s , the L a P l a c e o p e r a t i o n a l method o f a n a l y s i s i s used. The c a l c u l a t i o n s f o r t h e t r a n s i e n t produced by t h e d i s c h a r g e o f a d i s t o r t i o n l e s s c a b l e a re worked out i n f u l l d e t a i l . The wave-form c a l c u l a t e d i s p l o t t e d and s u b s t a n t i a t e d w i t h e x p e r i -mental r e s u l t s . The t r a n s i e n t produced i s a r e c t a n g u l a r wave t h a t i s e x p o n e n t i a l l y a t t e n u a t e d and whose p e r i o d i s ^ 6, where 6 i s t h e one-way t r a n s m i s s i o n time o f t h e c a b l e l n seconds. I t i s t h i s wave^form g e n e r a t e d by the c a b l e i t s e l f t h a t i s used to l o c a t e t h e f a u l t . B a s i c a l l y , the f a u l t - l o c a t o r d e v e l o p e d c o n s i s t s of, a h i g h - v o l t a g e l o w - c u r r e n t power pa.ck, a t r i g g e r i n g u n i t , a t i m i n g - p i p g e n e r a t o r , two u n i f o r m d e l a y l i n e s , and a d o u b l e -beam o s c i l l o s c o p e . The b l o c k diagram o f t h e f a u l t - l o c a t o r and t h e c i r c u i t diagrams o f the t r i g g e r i n g u n i t and t i m i n g - p i p g e n e r a t o r a r e g i v e n . The o p e r a t i o n o f t h e c i r c u i t s and the p r o c e d u r e f o r measuring c a b l e f a u l t s a re f u l l y e x p l a i n e d . The f a u l t - l o c a t o r was t e s t e d on c o a x i a l c a b l e o n l y , s i n c e no power c a b l e s were a v a i l a b l e . The r e s u l t s o b t a i n e d were v e r y s a t i s f a c t o r y . The o s c i l l o s c o p e t r a c e s o b t a i n e d were photographed and the e x p e r i m e n t a l r e s u l t s d i s c u s s e d . i i i I t i s c o n c l u d e d t h a t t h e f a u l t - l o c a t o r can be used w i t h o u t m o d i f i c a t i o n f o r l o c a t i n g low and medium-impedance f a u l t s , as w e l l as hlgh-lmpedance f a u l t s i n power c a b l e s . I f t h e t i m i n g - p i p i n t e r v a l i s i n c r e a s e d , t h e f a u l t - l o c a t o r can a l s o be used f o r l o c a t i n g f a u l t s on overhead t r a n s m i s s i o n l i n e s . N. E. Hudak D. B. C. A p r i l l g , 1951. IX ACKNOWLEDGEMENT The a u t h o r w i s h e s t o e x p r e s s h i s a p p r e c i a t i o n t o a l l tho3e who have a3Sl3ted him throughout t h e c o u r s e o f t h e r e s e a r c h and p a r t i c u l a r l y Dr. Frank Noakes f o r h i s guidance and encouragement. Acknowledgement i s a l s o made t o the B r i t i s h C o lumbia Telephone Company L i m i t e d whose s c h o l a r s h i p made t h i s i n v e s t i g a t i o n p o s s i b l e . N i b h o l a s E. Hudak iv CONTENTS Page I I n t r o d u c t i o n 1 I I Review o f L i t e r a t u r e 4-I I I I n v e s t i g a t i o n A. Theory o f Wave P r o p a g a t i o n 1. Fundamental D i f f e r e n t i a l E q u a t i o n s ... 3 • 2. P u l s e s G e n e r a t e d by t h e D i s c h a r g e o f a L o s s l e s s Cable 12 3. T r a n s i e n t s Produced by a Charged C a b l e S h o r t i n g t o Ground l 6 B. R e f l e c t i o n s 1. D e r i v a t i o n o f R e f l e c t i o n O p e r a t o r . . .Zk 2. R e f l e c t i o n L a t t i c e s . . . " 27 C. A t t e n u a t i o n , D i s t o r t i o n and V e l o c i t y . . . 22> D. Equipment 1. G e n e r a l D i s c r i p t i o n 2. H i g h - V o l t a g e Power Pack and L i n e C o u p l i n g 3^ 3. T r i g g e r i n g and T r a c e - B r i g h t e n i n g C i r c u i t ;J6 4. Timing - P i p G e n e r a t o r . . . . . . . . M-0 5. Delay L i n e . ^2 o. P r o c e d u r e i n M e a s u r i n g Cable F a u l t . ^3 E. E x p e r i m e n t a l R e s u l t s . . . . . . . . . . . 5^ IV D i s c u s s i o n V C o n c l u s i o n s . . . . . . . . . . . . . 53 VI Diagrams and I l l u s t r a t i o n s 5^ V I I L i t e r a t u r e C i t e d 66 V3LII B i b l i o g r a p h y . . . . . . . . . . . . . . . . . . 68 . IX Acknowledgement . . . . . . . . . . . . . . . . . . . . 72 V LIST OF ILLUSTRATIONS Page F i g . 1 Schematic C i r c u i t d iagram o f a charged c a b l e d i s c h a r g i n g i n t o a l o a d r e s i s t a n c e . . . . . . . 12 F i g . 2 C u r r e n t and v o l t a g e p u l s e s g e n e r a t e d by a l o s s -l e s s c a b l e d i s c h a r g i n g i n t o a l o a d r e s i s t a n c e .. 15 F i g . 3 Schematic w i r i n g diagram o f a charged c a b l e d i s c h a r g i n g t o ground l6 F i g . k- The v o l t a g e wave g e n e r a t e d by a d i s t o r t i o n l e s s c a b l e d i s c h a r g i n g t h r o u g h a " z e r o " r e s i s t a n c e as c a l c u l a t e d from e q u a t i o n (82) 23 F i g . H-a. O s c i l l o g r a m o f the v o l t a g e wave g e n e r a t e d by an a r c - d i s c h a r g e o f a-zestfr-f oot s e c t i o n o f RG-/2SU c o a x i a l c a b l e • . . 23 F i g . 5 R e f l e c t i o n L a t t i c e — s u c c e s s i v e r e f l e c t i o n s o f a charged c a b l e d i s c h a r g i n g t h r o u g h an impedance 27 F i g . 6 B l o c k diagram showing t h e components of the f a u l t - l o c a t o r 57 F i g . 7 C i r c u i t diagram o f an e x p e r i m e n t a l h i g h v o l t a g e power pack c o u p l i n g c i r c u i t . . . . . . jk-F i g . S Schematic c i r c u i t diagram o f t h e t r i g g e r i n g and t r a c e - b r i g h t e n i n g c i r c u i t 5^ F i g . 9 Schematic c i r c u i t d iagram o f t h e t i m i h g - p i p g e n e r a t o r , 59 F i g . 10 Photograph o f t h e f a u l t - l o c a t o r t i m i n g - p i p g e n e r a t o r , C o s s o r Model 339 double-beam o s c i l l o s c o p e , and t r i g g e r i n g and t r a c e -b r i g h t e n i n g u n i t . . . . . 56 F i g . 11 O s c i l l o g r a m o f a f a u l t at the f a r end of a 951-foot s e c t i o n o f RG/8U c o a x i a l c a b l e . . . . 60 F i g . 12 O s c i l l o g r a m o f a f a u l t l o c a t e d at 951.4- f e e t l n a I 7 S 8 . 2 - f o o t s e c t i o n o f c o a x i a l c a b l e . . . 6 l vc page F i g . 13 O s c i l l o g r a m o f a f a u l t a t " t h e f a r end o f a 12^ 1 . 1-foot s e c t i o n o f c o a x i a l c a b l e . . . . . . 62 F i g . lK O s c i l l o g r a m o f a f a u l t at t h e f a r end o f a 12^ 1 . 1-foot s e c t i o n o f c o a x i a l c a b l e and a d i s c o n t i n u i t y (20 ohms s e r i e s r e s i s t o r ) a t 289-7 f e e t 63 F i g . 15 O s c i l l o g r a m o f a f a u l t l o c a t e d a t 2 ^ 9 . 7 f e e t i n a 1241.1-foot s e c t i o n o f c o a x i a l c a b l e . . . 6h F l g . 16 O s c i l l o g r a m o f a f a u l t a t the f a r end o f a 124-1 .1-foot s e c t i o n o f c o a x i a l c a b l e and a d i s c o n t i n u i t y ( 2 0 ohms s e r i e s r e s i s t o r ) a t 2 8 9 . 7 f e e t . 6 5 LOCATION OF FAULTS IN POWER CABLES BY FAULT-GENERATED SURGES I INTRODUCTION The problem o f l o c a t i n g f a u l t s i n power c a b l e s ha3 p l a g u e d the e l e c t r i c power i n d u s t r y s i n c e the b i r t h o f e l e c t r i c power c a b l e s . The need f o r s a t i s f a c t o r y f a u l t l o c a t i n g equipment i s I n c r e a s i n g as more and more power c a b l e s a r e put i n t o s e r v i c e . Numerous methods o f l o c a t i n g f a u l t s i n c a b l e s have been I n v e s t i g a t e d , namely, the r e s i s t -ance b r i d g e , c a p a c i t a n c e b r i d g e , s e a r c h c o i l , condenser-pop, s t a n d i n g waves, p u l s e d - r a d a r and f r e q u e n c y - m o d u l a t i o n . The t r e n d i n r e c e n t y e a r s has been t o u t i l i z e the t r a v e l ! n g - w a v e method. I n t h i s method t h e d i s t a n c e t o the f a u l t i s d e t e r -mined by measuring the time r e q u i r e d f o r a v o l t a g e o r c u r -r e n t p u l s e t o t r a v e l a l o n g . t h e c a b l e between the f a u l t and the m o n i t o r i n g p o i n t . Messrs. R. F. Stevens and T. W. S t r i n g f i e l d have d i v i d e d the t r a v e l i n g - w a v e method i n t o 1 F o r r e f e r e n c e see l i t e r a t u r e c i t e d 2 t h r e e c a t e g o r i e s : ( l ) P u l s e - r a d a r Method (2) Frequency-m o d u l a t i o n Method and (3) F a u l t - g e n e r a t e d Surge Method, I n t h i s r e p o r t the f a u l t - g e n e r a t e d surge method, w i l l be con-s i d e r e d . T h i s method u n l i k e the p u l s e - r a d a r method r e q u i r e s no p u l s e - g e n e r a t o r and i t e l i m i n a t e s t h e d i f f i c u l t problem o f c o u p l i n g the p u l s e g e n e r a t o r to the c a b l e . The surge o r i g i n a t e s a t the p o i n t o f f a u l t w i t h i n the c a b l e by sudden c o l l a p s e o f t h e h i g h v o l t a g e and t r a v e l s t o t h e s t a t i o n end Of t h e c a b l e where i t s t a r t s a t i m i n g d e v i c e and i s r e f l e c t e d back down t h e c a b l e toward the f a u l t . The f a u l t w h i c h i s s s t i l l c o n d u c t i n g r e f l e c t s t h e surge back t o the s t a t i o n . The time I n t e r v a l between t h e f i r s t and second a r r i v a l o f the surge a t t h e s t a t i o n i s r e c o r d e d by the t i m i n g d e v i c e and i s p r o p o r t i o n a l t o the d i s t a n c e t o the f a u l t . T h i s method o f l o c a t i n g f a u l t s i s i n t e n d e d p r i m a r i l y f o r high-impedance f a u l t s . A f a u l t i n a c a b l e i s r a r e l y a dead s h o r t . A f a u l t w i t h l o w v o l t a g e a p p l i e d may measure between 5 0 O O and 1 0 , 0 0 0 ohms even though w e l l c a r b o n i z e d . By a p p l y i n g a r e l a t i v e l y h i g h v o l t a g e t o t h e f a u l t i s can be made to a r c and d u r i n g the a r c i n g p e r i o d the impedance o f the f a u l t d r o p s t o a v e r y low v a l u e . S i n c e m a j o r i t y o f th e f a u l t s a r e i n t e r m i t t e n t i t i s i m p o r t a n t t h a t t h e measure-ment be complete i n a v e r y s h o r t t i m e . I f a h i g h l y s e n s i t i v e l o n g a f t e r - g l o w cathode r a y tube i s a v a i l a b l e o r i f photography i a employed t h e l o c a t i o n o f the f a u l t can he d e t e r m i n e d from one f l a s h o v e r . However, i n t h i s i n v e s t i g a t i o n a c o n s t a n t v i s u a l p a t t e r n on the cathode r a y tube was m a i n t a i n e d by c a u s i n g the c a b l e t o breakdown r e p e a t e d l y . The p o l a r i t y o f e v e r y c o n s e c u t i v e echo a l t e r -n a t e s s i n c e the impedance a t the m o n i t o r i n g end i s h i g h and the impedance at the f a u l t w h i l e t h e a r c i s b e i n g sus-t a i n e d i s low. The echo from the m o n i t o r i n g end i s o f same p o l a r i t y as the i n c i d e n t echo but the echo from the f a u l t i s o f o p p o s i t e p o l a r i t y to t h a t i n c i d e n t t o the f a u l t . T h i s r e v e r s a l i n p o l a r i t y o f c o n s e c u t i v e echos a i d s i n s e g r a g a t i n g t h e f a u l t p i p s from s p u r i o u s surges. The e f f e c t i v e range o f t h i s method i s l i m i t e d t o about 10 m i l e s due t o a t t e n u a t i o n and d i s t o r t i o n p a r t i c u l a r l y o f the h i g h f r e q u e n c y components. I I REVIEW OF LITERATURE The r e q u i r e m e n t s o f the i d e a l f a u l t l o c a t o r were d e f i n e d by Messrs. R. F. Stevens and T. W. S t r i n g f i e l d ^ " The d e s i r a b l e q u a l i t i e s a r e : ( l ) The d e v i c e s h o u l d complete the measurement b e f o r e t h e a r c i s e x t i n g u i s h e d (2) I t s h o u l d have a h i g h a c c u r a c y ( 3 ) The r e s u l t s s h o u l d be r e a d i l y a v a i l -a b l e ( w i t h o u t d e v e l o p i n g p h o t o g r a p h i c f i l m ) and e a s i l y I n t e r -p r e t e d . (4-) The equipment s h o u l d be s i m p l e , p o r t a b l e , rugged, and r e l a t i v e l y i n e x p e n s i v e . (5) I t s h o u l d o p e r a t e w i t h s a f e t y to p e r s o n n e l and s e r v i c e . To f u l f i l l t h e above r e q u i r e m e n t s 3ome system w h i c h u t i l i z e s t h e t r a v e l i n g waves must be employed. The t r a v e l i n g - w a v e method can be d i v i d e d i n t o t h r e e c a t e g o r i e s : (a) The P u l s e - r a d a r (b) Frequency-modulated and ( c ) F a u l t - g e n e r a t e d surge. (a) PULSE-RADAR METHOD - I n t h i s method an a r t -i f i c i a l l y g e n e r a t e d v o l t a g e p u l s e o f s h o r t d u r a t i o n i s impr r e s s e d on one end o f the c a b l e . The p u l s e t r a v e l s down the c a b l e w i t h v e l o c i t y depending upon t h e c a b l e p arameters. Upon meeting the f a u l t a p o r t i o n o f t h e I n c i d e n t p u l s e I s r e f l e c t e d back toward t h e source w h i l e the r e m a i n d e r o f the p u l s e c o n t i n u e s i n the same d i r e c t i o n . One-half t h e time r e q u i r e d f o r the r e t u r n of t h e echo from the f a u l t m u l t i p l i e d by the v e l o c i t y o f p r o p a g a t i o n i s e q u a l t o the f a u l t d i s t a n c e . The minimum r e s i s t a n c e o f a d e t e c t a b l e s e r i e s f a u l t i s about f i v e ohms and maximum r e s i s t a n c e o f a d e t e c t a b l e shunt f a u l t i s about 1000 ohms. The e f f e c t i v e range o f p u l s e - r a d a r method i n power c a b l e s i s about 10 m i l e s . I f t h e impedance o f the f a u l t i s h i g h t h e r e f l e c t i o n p r o d u c e d w i l l not g i v e a c l e a r change i n t h e t r a c e . By a p p l y i n g a r e l a t i v e l y h i g h v o l t a g e t o t h e f a u l t i t can be made to a r c and d u r i n g the a r c i n g i t s Impedance d r o p s to z e r o . S e v e r a l methods have been d e v e l o p e d w h i c h super-impose t h e a r t i f i c i a l p u l s e s on top o f a h i g h d.c. v o l t a g e . p J . P. L o z e s J r . has superimposed 3000 v o l t 3 m i c r o - s e c o n d t e s t surges r e p e a t e d 30 t i m e s p e r second on top o f p e r i o d i c h i g h v o l t a g e h a l f - s e c o n d d-c p u l s e s . When t h e d-c p u l s e i s o f f , t h e t r a c e on the s c r e e n i s same as i f t h e c a b l e were not f a u l t e d s i n c e the f a u l t impedance i s u s u a l l y much h i g h e r t h a n t h e surge impedance o f the c a b l e . When t h e d-c p u l s e s a r e a p p l i e d , the f a u l t a r c s o v e r , i t s " r e s i s t a n c e " goes t o zero and t h e t e s t surges a re r e f l e c t e d . W i t h the d-c c y c l i n g on and o f f a c o n t i n u a l l y a l t e r n a t i n g , t r a c e o f t h e u n f a u l t e d and f a u l t e d c a b l e i s seen. (b) FREQUENCY-MODULATION METHOD- The i n i t i a l a t t r a c t i o n o f t h i s system was the p o s s i b i l i t y o f e l i m i n a t i n g the o s c i l l o s c o p e and r e a d i n g the f a u l t d i s t a n c e d i r e c t l y on a m i l l l a m e t e r . A f r e q u e n c y - m o d u l a t e d v o l t a g e s i g n a l i s 6 Impressed on the c a b l e w h i c h t r a v e l s down the c a b l e t o the f a u l t and i s r e f l e c t e d back t o the source. The f r e q u e n c y o f the Impressed v o l t a g e i s v a r i e d a t a l i n e a r l y r a t e w i t h t i m e . The r e f l e c t e d s i g n a l a r r i v i n g a t t h e source w i l l have a d i f f e r e n t f r e q u e n c y t h a n t h e f r e q u e n c y b e i n g t r a n s m i t t e d at t he same i n s t a n t . The d i f f e r e n c e i n f r e q u e n c i e s i s measured by a s u i t a b l e d i s c r i m i n a t o r c i r c u i t and i s p r o p o r t -i o n a l t o the di'st'ance t o t h e f a u l t . The d e t a i l e d r e q u i r e -ments.of t h i s system were examined by Mr. F. F. R o b e r t s . ^ I n o r d e r t h a t s h o r t p e r i o d s o f time can be measured a c c u r a t e l y t h e f r e q u e n c y o f the modulated c a r r i e r and the b a n d w i t h must be h i g h . T h i s i s u n d e s i r a b l e s i n c e a t h i g h f r e q u e n c i e s the a t t e n u a t i o n and d i s t o r t i o n a r e h i g h . A g a i n , u n l e s s the f a u l t Impedance i s reduced, the s i g n a l r e f l e c t e d from a h i g h im-pedance f a u l t w i l l be s m a l l . The sim p l e f r e q u e n c y - m o d u l a t e d system i s i n c a p a b l e o f d i s t i n g u i s h i n g m u l t i p l e f a u l t s . A more e l a b o r a t e system i n v o l v i n g ah a u t o m a t i c f r e q u e n c y a n a l y z e r and an o s c i l l o s c o p e would be r e q u i r e d . I t i s con-c l u d e d t h a t the f.m. method cannot compete w i t h t h e p u l s e t e c h n i q u e s . ( c ) FAULT-GENERATED SURGE METHOD - Two systems o f a p p l y i n g the f a u l t - g e n e r a t e d surges f o r l o c a t i n g f a u l t s on t r a n s m i s s i o n l i n e 3 have been d e v e l o p e d by the E n g i n e e r s o f the B o n n e v i l l e Power A d m i n i s t r a t i o n . F o r convenience t h e y have d e s i g n a t e d t h e s e as "Type A" and "Type B" f a u l t - l o c a t o r s . I n t h e "Type A" system t h e surge from the f a u l t t r a v e l s t o the s t a t i o n end of the l i n e where I t I n i t i a t e s a t i m i n g d e v i c e . 7 The surge i s r e f l e c t e d from t h e s t a t i o n bus back down the l i n e t o the f a u l t where I t i s r e f l e c t e d and r e t u r n s t o the s t a t i o n . The time between the f i r s t and second a r r i v a l o f the surge a t t h e s t a t i o n I s measured by t h e t i m i n g d e v i c e and I s p r o p o r t i o n a l t o the d i s t a n c e to t h e f a u l t . I n the "Type B" system use i s made o f b o t h surges w h i c h o r i g i n a t e a t t h e f a u l t and w h i c h t r a v e l down the l i n e i n o p p o s i t e d i r e c t i o n s . One o f the s e a r r i v e s a t t h e "near end" o f the l i n e and t r i g g e r s a t i m i n g d e v i c e . The o t h e r t r a v e l s t o the "remote end" and causes a broad-band r a d i o t r a n s m i t t e r t o send out a t i m i n g p u l s e w h i c h i s r e c e i v e d a t t h e near end and s t o p s t h e t i m i n g d e v i c e . The time i n t e r v a l measured l e s s the c o r r e c t i o n f o r t h e r a d i o wave i s p r o p o r t i o n a l t o t h e d i s t a n c e t o the f a u l t . I n b o t h o f t h e s e systems t h e f a u l t l o c a t o r i s c o n t i n o u s l y m o n i t o r i n g the l i n e s . The f a u l t i s r e c o r d e d b e f o r e t h e a r c i s e x t i n g u i s h e d t h u s n o n - s u s t a i n e d as w e l l as permanent f a u l t s can be l o c a t e d . The "Type A" l o c a t o r r e q u i r e s a cathode r a y tube and a camera whereas "Type B" employs a e l e c t r o n i c time i n t e r v a l c o u n t e r . The "Type A" system r e q u i r e s t h a t the c o * e f f i c -i e n t o f r e f l e c t i o n a t the f a u l t be h i g h i n o r d e r t o o b t a i n a good r e f l e c t e d s i g n a l . I n t h e "Type B" system no use i s made o f r e f l e c t i o n s . g I I I INVESTIGATION A. Theory o f Wave P r o p a g a t i o n I t i s d e s i r a b l e t o c a l c u l a t e the shape o f the p u l s e g e n e r a t e d a t the f a u l t and the m o d i f i c a t i o n s i t under-goes as i t t r a v e l s down t h e c a b l e , a l s o the magnitude and shape o f the r e f l e c t i o n t o be exp e c t e d from a d i s c o n t l n u l t y 4 The e x a c t s o l u t i o n o f the d i f f e r e n t i a l e q u a t i o n s g o v e r n i n g t h e t r a v e l i n g waves i s v e r y complex and l e n g t h y . I n o r d e r t o s i m p l i f y t h e mathematics a p p r o x i m a t i o n s w i l l be made. 1. Fundamental D i f f e r e n t i a l E q u a t i o n s C o n s i d e r a s h o r t l e n g t h o f c a b l e L c€x S x . c+ 8c +~ e + Se where r 1 c g s e r i e s r e s i s t a n c e i n ohms p e r u n i t r o u t e l e n g t h s e r i e s i n d u c t a n c e i n h e n r y s " " " " shunt c a p a c i t a n c e i n f a r a d s " " 11 " shunt conductance l n ohms II II 9 Change i n v o l t a g e a l o n g §x Change i n c u r r e n t a l o n g S" 3c 6 6 = - 9e ( 6^)-c | | ( r<S^) I n the l i m i t as <5 ?c — & - O - § # = r L •••••• x _5> e q u a t i o n s ( l ) and ( 2 ) become I n t r o d u c i n g o p e r a t o r p r r J2— r <s>-t 0 > AL. 2 <S>7C Take of (3) and s u b s t i t u t e i n t o (k) Take jE-of U) and s u b s t i t u t e i n t o (3) 2 l e t A - \j(r+s(p)C3i-cp) let C3 ~ JZJL ^ZC T h e r e f o r e , /k - ^ pjfc+P +P)(°<-(3 +p) Then e q u a t i o n s ( 5 ) and ( 6 ) become 11 T r e a t i n g (13) and (1*0 as l i n e a r d i f f e r e n t i a l e q u a t i o n s t h e s o l u t i o n s are, e = A e + B £ 15 L - Ce +£)<? x6 where A,B,C, & D, a r e c o n s t a n t s w i t h r e s p e c t t o X b u t a r e a r b i t r a r y f u n c t i o n s o f time. The s o l u t i o n s a r e i n o p e r a t i o n -a l form o n l y s i n c e & c o n t a i n s t h e o p e r a t o r p. S u b s t i t u t e (15) and ( l 6 ) i n t o (If) Comparing c o e f f i c i e n t s , - J 3+cf * A . . . . . 12 L e t be the surge impedance o p e r a t o r (3+P 12 L e t — =r C h a r a c t e r i s t i c impedance ' C The* \ -=y[^±0±±-^ • O 0 • A 21 From e q u a t i o n s ( l g ) , ( 19) , and ( 2 0 ) , e q u a t i o n s (15) and (16) can he r e - w r i t t e n . 22 e - B e 23 A and B a r e de t e r m i n e d from the boundary c o n d i t i o n s 12 2. PULSES GENERATED BY THE DISCHARGE OF A LOSSLESS CABLE The n a t u r e o f t h e t r a n s i e n t produced, by a l o s s l e s s c a b l e d i s c h a r g i n g i n t o a r e s i s t i v e l o a d (see F i g . l ) w i l l be s t u d i e d by the a p p l i c a t i o n o f o p e r a t i o n a l method a n a l y s i s . C Cable of Characzferistic. Impedance £?e s Load F i g . 1 Schematic' c i r c u i t diagram o f a charged c a b l e d i s c h a r g i n g i n t o a l o a d r e s i s t a n c e The c a b l e l e n g t h oi i s i n i t i a l l y charged t o a v o l t a g e and at time "t=o t h e s w i t c h S i s suddenly clo§ed. The a-c Impedance o f t h e c a b l e from t r a n s m i s s i o n l i n e t h e o r y i s 3 = Coikj€*>S 24-The L a p l a c e t r a n s f o r m impedance i s f o u n d by s u b s t l t u t l n g p f o r j <^> L ' ( Z ) ~ Z =Z.C*-rhpg 25 13 Where p = ^ i s the t r a n s f o r m parameter 6 = ~ i s t h e one-way t r a n s m i s s i o n time o f t h e c a b l e AT ^<^Y% 1 8 t i l e c h a r a c t e r i s t i c impedance o f t h e c a b l e The c u r r e n t t r a n s f o r m E q u a t l o n ( 2 6 ) can be r e - w r i t t e n L e t b»be the r e f l e c t i o n f a c t o r a t l o a d end where Yn - ^ . . . . . 28 ~ T^Ffiby b i n o m i a l theorem s i n c e \Vn£ / Expand ^ - ^  C-0 • • • • • 29 S u b s t i t u t e e q u a t i o n ( 2 9 ) i n t o ( 2 7 ) ..... 30 Ik T a k i n g the I n v e r s e L a p l a c e t r a n s f o r m o f e q u a t i o n (31) - where H(t-%K§)=Q £r(t-***S)<0 as in =r © , / , ^ j 3 I f the l o a d I s matched to the c a b l e the c u r r e n t c o n s i s t s of a s i n g l e r e c t a n g u l a r p u l s e o f a m p l i t u d e Jj — Jsi*. and d u r a t i o n 7"~- <2 8 (see F i g 2a). The e f f e c t o f m ismatching the l o a d produces a s e r i e s o f s t e p s i n t o t h e t r a n s i e n t d i s c h a r g e . (See F i g . 2b and 2 c ) . The s t e p s are a l l of t h e same s i g n when ^ f ^ ^ a n d a l t e r n a t e i n s i g n when ^g^^m . The s t e p s a r e the r e s u l t s o f r e f l e c t i o n s a t t h e t e r m i n a l s o f the c a b l e due to impedance mismatch. The r e f l e c t i o n s t r a v e r s e the c a b l e t o t h e open end i n time ^ , a r e c o m p l e t e l y r e f l e c t e d and t r a v e l back to the l o a d end I n t o t a l t i m e ^ ^ w h e r e they appear as 15 p o s i t i v e o r n e g a t i v e s t e p s depending upon the l o a d r e f l e c t i o n f a c t o r . These r e f l e c t i o n s c o n t i n u e w i t h c o n s t a n t l y d i m i n i s h i n g a m p l i t u d e u n t i l a l l t h e energy i n i t i a l l y s t o r e d i n t h e c a b l e i s d i s s i p a t e d i n t h e l o a d r e s i s t a n c e . As a s p e c i a l case assume t h a t l o a d r e s i s t a n c e i s z e r o , then from (2%) m = 1 and e q u a t i o n (32) becomes 33 T h i s i s a square wave o f a m p l i t u d e • and p e r i o d ^ (See P i g . 2d). To f o l l o w page 15 "Ho ' OL_0i O Zo -4 6 &S <3S /OS 0 Z€ 4-6 €6 36 /OS (a) FRX - Za Ob) f=i,-2. -£~ "1 £ r — ^5 1 I 1 O 2)6 -<? . ; i (d) F*X=0 5 SIS /OS I I F i g . 2. C u r r e n t and v o l t a g e p u l s e s g e n e r a t e d by a l o s s l e s s c a b l e d i s c h a r g i n g i n t o a l o a d r e s i s t a n c e . The s o l i d l i n e r e p r e s e n t the v o l t a g e p u l s e s and the broken l i n e the c u r r e n t p u l s e s . U.B.C. A p r i l , l£, 1951 16 3. TRANSIENTS PRODUCED BY A CHARGED CABLE SHORTING TO GROUND The problem i s to o b t a i n an e x p r e s s i o n f o r the v o l t -age a c r o s s - ? ^ (See F i g . 3) a t any i n s t a n t o f time a f t e r the f a u l t o c c u r s a t ^ j ? s o f f e r s a v e r y h i g h impedance to h i g h f r e q -u e n c i e s o n l y and i ? ^ o f f e r s h i g h impedance to b o t h h i g h and low f r e q u e n c i e s . 3 Hi$h Voltaqe i D.C. Source \ * Fault CCable Arcmg 7b G roun d ) F i g . 3 - Schematic w i r i n g diagram o f a charged c a b l e s h o r t i n g t o ground. The c a b l e I s i n i t i a l c harged t o a v o l t a g e ^ ^ b e f o r e t h e f a u l t o c c u r s . Assume t h a t the " r e s i s t a n c e " o f the a r c i s z e r o . L e t the parameters o f the per u n i t l e n g t h o f t r a n s m i s s i o n d i s t a n c e o f the c a b l e be r , 1, c, and g . X i s measured from t h e p o i n t o f f a u l t . Boundary c o n d i t i o n s a r e eCot) & O for t>o 3^ 35 37-17 The p a r t i a l d i f f e r e n t i a l e q u a t i o n s f o r a u n i f o r m t r a n s m i s s i o n l i n e a r e - § f = ri +Jt"2i l I n s o l v i n g e q u a t i o n s ( l ) and (2) f o r t h e above boundary 7 c o n d i t i o n s the L a p l a c e o p e r a t i o n a l method w i l l be used. The L a p l a c e t r a n s f o r m o f ^ V * t ) b y d e f i n i t i o n i s The L a p l a c e t r a n s f o r m Q f j ^ ^ x t j f a y d e f i n i t i o n i s 2 T a k i n g the L a p l a c e t r a n s f o r m o f e q u a t i o n ( l ) = rZ+Spc - * L f e c ) 3*5 From boundary c o n d i t i o n (35) ^ f e 0 ) ~ 0 (3$) becomes - f f = ( W ^ o r 39 13 M-o T a k i n g the L a p l a c e t r a n s f o r m o f e q u a t i o n ( 2 ) = se+cpe -cqr^o) ••••• From "boundary c o n d i t i o n (34-) 0 ^ " £ a (ho) becomes =(34 Cp) e - c£-0 h i Take o f e q u a t i o n s (39) and ( 4 l ) ^ ? = r ( r ^ ) 2 t * 2 S u b s t i t u t e e q u a t i o n ( h i ) i n t o (k-2) - ( r ^ c 5 T c P ; e - c e r t * ? ) ^ ^ £ £ « * V - v 5^ where A? = * Xp)C$ +G?) 7 and r r, (r+Ap)C£0 ^ S u b s t i t u t e e q u a t i o n (39) i n t o U3) „ J C Z • • • • • ^ T r e a t i n g e q u a t i o n s (4-5) a n ( i & s o r d i n a r y l i n e a r d i f f e r e n t i a l e q u a t i o n s t h e s o l u t i o n s a r e 50 19 Where A, B, F, and G are c o n s t a n t s w i t h r e s p e c t to x o n l y and f u n c t i o n s o f p. S u b s t i t u t e e q u a t i o n s (k-S) and (50) i n t o (39) Comparing c o e f f i c i e n t s F FTTP 3 5 ^ = = 53 & r*>e> ^ R e w r i t i n g e q u a t i o n s (^9) a n d (50) I^ P; = ^ s + B < f * ~ J 56 C o n s t a n t s A and B are d e t e r m i n e d form boundary c o n d i t i o n s (36) and (37) T a k i n g the L a p l a c e t r a n s f o r m o f (37)2^ p^-O and a p p l y i n g t h i s c o n d i t i o n t o ( 5 ° ) - A e^s £^= o §=A£U 57 T a k i n g the L a p l a c e t r a n s f o r m o f (J>6) GC°p}rO and a p p l y i n g t h i s c o n d i t i o n t o e q u a t i o n (55) S o l v i n g e q u a t i o n s (57) and (58) 20 60 S u b s t i t u t i n g f o r A and B i n t o (55) and (56) and s i m p l i f y i n g E q u a t i o n ( 6 l ) can be r e w r i t t e n a3 x r , *Ac*-d) -M^-dfl % ^ # L ' £ ^ J. — — " E q u a t i o n (63) can be s o l v e d by (a) t h e e x p a n s i o n theorem w h i c h g i v e s the s o l u t i o n i n form o f a t r i g o n o m e t r i c s e r i e s o r by (b) the e x p a n s i o n i n terms of t h e s o l u t i o n s f o r semi-i n f i n i t e l i n e s w h i c h has a p h y s i c a l i n t e r p r e t a t i o n l n terms o f d i r e c t and m u l t i p l e - r e f l e c t e d waves. The r i g o r o u s pure ' m a t h e m a t i c a l s o l u t i o n ..of (63) c o n s i s t s o f the a p p l i c a t i o n o f the i n v e r s i o n theorem f o l l o w e d by c o n t o u r i n t e g r a t i o n . The exact s o l u t i o n i n v o l v i n g c o n t o u r i n t e g r a t i o n w i l l not be a t t e m p t e d here. I n s t e a d t h e s o l u t i o n f o r a d i s t o r t i o n l e s s c a b l e w i l l be o b t a i n e d t h r o u g h t h e use o f the e x p a n s i o n theorem g i v i n g the r e s u l t i n a t r i g o n o m e t r i c s e r i e s . R e w r i t i n g e q u a t i o n (63) i n h y p e r b o l i c form OtP) J f t Cosh Ad J 64 21 F o r a d i s t o r t i o n l e s s l i n e r 9 T = -c- 6 5 E q u a t i o n (7) becomes A = + ( % + P ) 66 From (46) and (7) F o r d i s t o r t i o n l e s s l i n e e q u a t i o n (64) i s s ^ ^ /7_ Coshl%+ti(*Sr-)l 63 •vr J S o l v i n g second term o f (63) by the e x p a n s i o n theorem t h e n 6(fy- M.' I&Lgrt 70 3'(ar) F i r s t d e termine t h e z e r o s o f the denominator o f (69) C%i-p)coshC^+P)^=o . . . . . 71 These are at JL (a) P~~ C 72 M P = * J l ^ ^ - # 73 where r) = 0 , 1 , 2,3 F o r the r o o t p = - ^ t h e denominator 3 G a * 9 l 0 : f ^7°) i 3 / 7 4 c 22 F o r the r o o t s o f p g i v e i n (7 3), o f (_&3) i s But c o . 3 h ( g . f p J . S £ : = - 0 f o r a l l v a l u e s o f p g i v e n i n (73) t h e r e f o r e , e q u a t i o n (75) reduces t o Sf&h) = J Z.frn+O s»>hjf& »+/) = c-onH%c*»+d 76 F o r the s o l u t i o n o f (69) s u b s t i t u t e (jk) and (75) i n t o (70) The i n v e r s e t r a n s f o r m o f the f i r s t term o f e q u a t i o n (68) i s 80 23 The complete s o l u t i o n o f (68) i s (79) minus (80) t)~o *C« /Sot The v o l t a g e a t any i n s t a n t o f time a t t h e m o n i t o r i n g end of the c a b l e where TC-<^ i s e> . ^ ^ Z 1 ^ d o l / c o s H+L-nyrtl « T h i s e q u a t i o n r e p r e s e n t s a square wave w h i c h has a p e r i o d and w h i c h I s e x p o n e n t i a l l y a t t e n u a t e d by the a t t e n u a t i o n f a c t o r C . The p l o t o f t h i s c urve i s shown i n F i g . 4. The o s c i l l o g r a m F i g . h a shows the v o l t a g e g e n e r a t e d by the d i s c h a r g e o f a23?,7-foot s e c t i o n o f RG/8U c o a x i a l c a b l e . The t h e o r e t i c a l l y c a l c u l a t e d v o l t a g e wave and the o b s e r v e d wave a r e v e r y s i m i l a r showing t h a t the m a t h e m a t i c a l approx-i m a t i o n s made i n a r r i v i n g at e q u a t i o n ( 8 2 ) a r e j u s t i f i e d . To f o l l o w page 23 t , z % 1ST * IT! *T~6 f , 3 d ouhttre t, = seconds F i g . h. The r o l t a g e wave generated by a d i s t o r t i o n l e s s c a ble d i s c h a r g i n g through a eero r e s i s t a n c e pg c a l c u l a t e d from equation (£2) F i g . 4 a . O s c i l l o g r a m of the voltage wave generated by an arc discharge of a $09-foot s e c t i o n of RG/gU c o a x i a l cable. For c i r c u i t diagram see P i g . 3- Page l 6 U. B. C. A p r i l It, 195X 2k A. R e f l e c t i o n s ( l ) D e r i v a t i o n o f R e f l e c t i o n O p e r a t o r C o n s i d e r a l i n e o f l e n g t h ^ t e r m i n a t e d by an imp-edance j? a . At Tc-O steady s t a t e v o l t a g e I s a p p l i e d t h r o u g h an impedance J£J e ^ = A e + B € F o r the above boundary c o n d i t i o n s at 3G.3=- b • . e - ^ A + m ^ ^ ~ ~ r C A - B ) - 0 1 at ?&&d< e^Ae+B^^^^e -Be J R e w r i t i n g ( 9 0 ) and ( 9 1 ) O L e t 22 23 9 0 9 1 9 2 9 3 9 ^ 25 L e t m# a n d f l ^ b e the r e f l e c t i o n f a c t o r s a t j? / and i * g r e s p e c t i v e l y where _ —, _ / - p . _ 5 96 m ~ = 3 ~ z * 97 S o l v i n g (9^) a 9g From (95) and (98) From (98) and (99) 1 S u b s t i t u t i n g i n t o e q u a t i o n (22) and (23) — C_ - rr\z <f >£" i n i C * y _ * "7177 • • • • 1 0 * , - - 7 - 7 — * — - Z ^ - T I - • • • • 102 Expanding t h e denominator by the b i n o m i a l e x p a n s i o n theorem 7 1 = ^ 7 3 * 1 - 7 = ? = ' * r * r » 1 0 3 E q u a t i o n s (101) and (102) become ^dO+Cd/ * m * t™,">z£ + fo^C -J 26 The f i r s t term g i v e s the e f f e c t o f the d i r e c t wave w h i l e the second term g i v e s the e f f e c t o f the r e f l e c t e d wave from the f a r end, and t h e t h i r d t h a t o f t h e wave r e f l e c t e d from t h e near end. The above e q u a t i o n s g i v e the sum o f the d i r e c t and r e f l e c t e d wave3 w h i c h are e f f e c t i v e at ti m e s £ = 2£-t-= °^^ ~~*r <f=r , e t c . I n d i v i d u a l l y , t h e waves a c t as i f each were t r a v e l i n g a l o n e on an i n f i n i t e l i n e , o r i g i n a t i n g a t the impedance d i s c o n t i n u i t y and d i s p l a c e d from each o t h e r by time t= £~ where dt i s the d i s t a n c e between the lmnedance d i 3 c o n t i n u i t y . The wave o r i g i n a t i n g a t t h e d i s c o n t i n u i t y i s d e t e r m i n e d by t h e i n c i d e n t wave and the r e f l e c t i o n o p e r a t o r . 27 (b) R e f l e c t i o n L a t t i c e s I n a n a l y z i n g the problem o f s u c c e s s i v e r e f l e c t i o n s o f t r a v e l i n g waves, use i s made of r e f l e c t i o n l a t t i c e s . C o n s i d e r a charged c a b l e i n s u l a t e d at b o t h ends s h o r t i n g to ground t h r o u g h an impedance J ? , a t d i s t a n c e ^ from one end, (See F i g . 5 ) . The wave € g e n e r a t e d by the sudden c o l l a p s e o f v o l t a g e t r a v e l s a l o n g t h e c a b l e i n b o t h d i r e c t i o n s from JSf and when i t r e a c h e s the open end i t r e f l e c t s w i t h o u t change o f shape o r s i g n . The wave on r e t u r n i n g to 2f g i v e s r i s e t o two components; t h e r e f l e c t e d wavee^Cand the r e f r a c t e d o r t r a n s m i t t e d wave£3e where °< I s the r e f l e c t i o n o p e r a t o r and (3 the r e f r a c t i o n o p e r a t o r , each b e i n g a f u n c t i o n i n v o l v i n g the p a r a m e t e r s o f the c i r c u i t and the time d e r i v a t i v e P ~ The r e s u l t a n t v o l t a g e as a f u n c t i o n o f time a t any p o i n t i s t h e sum o f a l l waves w h i c h have a r r i v e d up to t h e g i v e n i n s t a n t p r o p e r l y d i s p l a c e d by t h e I n t e r v a l o f t h e i r r e l a t i v e p o s i t i o n on the c a b l e . At d e f i n i t e I n t e r v a l s 3uch as € ^ t h e xsraves a r r i v e s i m u l t a n e o u s l y from the r i g h t and l e f t and add up by s u p e r p o s i t i o n . Thus, t h e l a t t i c e p r e s e n t s a c l e a r t i m e -d i s t a n c e p i c t u r e o f the phenomena o f s u c c e s s i v e r e f l e c t i o n s and shows a t a g l a n c e j u s t what I s happening a t a l l p o i n t s a l o n g the c a b l e a t a l l i n s t a n t s o f t i m e . To f o l l o w page 27 REFLECTION LATTICE F i g . 5. S u c c e s s i v e r e f l e c t i o n s o f a charged c a b l e d i s c h a r g i n g t h r o u g h an Impedance z, U.B.C. A p r i l 1 3 f 1951 23 (2) A t t e n u a t i o n , D i s t o r t i o n and V e l o c i t y As a wave t r a v e l s a l o n g the c a b l e i t i s a t t e n u a t e d and d i s t o r t e d due t o co n d u c t o r r e s i s t a n c e as m o d i f i e d by s k i n e f f e c t , l e a k a g e t o ground, and d i e l e c t r i c l o s s e s . The d i s -3 t o r t i o n i s e l i m i n a t e d i f — •= — and the a t t e n u a t i o n i s a c c o u n t e d <*• f o r by a s i m p l e e x p o n e n t i a l decrement f a c t o r The e x p r e s s i o n s f o r a t t e n u a t i o n and d i s t o r t i o n may be d e r i v e d from g e n e r a l v o l t a g e and c u r r e n t e q u a t i o n s f o r a t r a n s m i s s i o n l i n e . = (Ac - B € J For i n f i n i t e l i n e 22 tyc « f ~ 8 e J . . . . 23 X.—• o o B - O F o r an a p p l i e d v o l t a g e t h a t i s a f u n c t i o n o f time £ ^ » . - o ) - & ( t ) . . . . 106 E q u a t i o n (22) and (23) become - <? £i(t> 4 - 4 : <S ^Cf) • • • • 107 103 Is The a c c u r a t e s o l u t i o n o f e q u a t i o n s (107,) and (10*5) i s d i f f i c u l t and so an a p p r o x i m a t i o n w i l l be made. F o r h i g h r a t e s o f change w i t h time o f v o l t a g e and c u r r e n t , p i 3 l a r g e hence ~ , , \ ( p t ^ •••• 29 ^^<~(s+f> . . . . 1 1 0 E q u a t i o n ( 1 0 7 ) and ( l O g ) reduce t o = c f £ ( i ^ . . . . 1 1 2 ^ ^ ^ ^ / ^ f i ^ ) - ^ f i ' ^ ) d t ] . . . . 1 1 3 The e q u a t i o n s show t h a t the v o l t a g e wave i s p r o p -ag a t e d w i t h o u t d i s t o r t i o n b u t i 3 s u b j e c t to a t t e n u a t i o n o f £ ^ p e r u n i t l e n g t h . The c u r r e n t wave i s s u b j e c t t o same a t t e n u a t i o n but i s a l s o d i s t o r t e d as shown by the i n t e g r a l term. The a t t e n t u a t i o n f a c t o r oc* was d e f i n e d i n e q u a t i o n ( 9 ) At h i g h f r e q u e n c i e s , s k i n e f f e c t and d i e l e c t r i c a b s o r p t i o n l o s s e s change r , 1 , and g. G a p a c i t a n c e f i s r e l a t i v e l y i n d e p -endent o f f r e q u e n c y . The s k i n e f f e c t w i l l c o n c e n t r a t e most o f t h e c u r r e n t a t t h e o u t e r s u r f a c e o f the core and i n n e r s u r f a c e o f the 3heath. R e s i s t a n c e w i l l be I n c r e a s e d by de-c r e a s i n g t h e e f f e c t i v e c r o s s s e c t i o n o f t h e c o n d u c t o r s . The s e l f I n d u c t a n c e o f the c o r e due to i n t e r n a l f l u x l i n k a g e w i l l be reduced. The change i n °C w i t h f r e q u e n c y means t h a t t h e h i g h f r e q u e n c y components are a t t e n u a t e d more r a p i d l y t h a n the l o w f r e q u e n c y components thus c r e a t i n g d i s t o r t i o n w h i c h 3 0 i s not shown i n e q u a t i o n s (112) and ( 1 1 3 ) . S o l u t i o n s (112) and ( 1 1 3 ) a r e approximate s i n c e i t was assumed t h a t p i s l a r g e . * 11,12 Fo r s i n g l e c o n d u c t o r c a b l e , •7 s* x / 0 f a r a d s r>er meter . . 1 1 4 ^r) io? h e n r i e s p e r meter .. 1 1 5 ( a t h i g h f r e q u e n c i e s i n t e r n a l i n d u c t a n c e i s n e g l i g i b l e ) g Where /C0- v e l o c i t y o f l i g h t . = 3 x 10 meter p e r second — — r e l a t i v e p e r m i t t i v i t y o f the i n s u l a t i o n M _ r e l a t i v e p e r m e a b i l i t y o f t h e d i e l e c t r i c /i ( f o r most d i e l e c t r i c s ^ , i s u n i t y ) TP =/^c S u b s t i t u t e (114) and ( 1 1 5 ) i n t o (*$) 116 — 7c0(^< . . . . 1 17 AT= /Caf%0 . . . . H g The v e l o c i t y o f p r o p a g a t i o n a l o n g the c a b l e depends upon the r e l a t i v e p e r m i t t i v i t y o f t h e i n s u l a t i o n . (See t a b l e below) I n s u l a t i o n K (Average) V e l o c i t y o f P r o p a g a t i o n G-as P o l y e t h y l e n e O i l f i l l e d paper V a r n i s h e d cambric Rubber 1 . 0 2 . 2 5 ? ' 5 4 c 6 -9 8 3 f t . p e r second 6 5 5 " " 5 2 5 " " 11 4 6 0 " " 11 400 " « " 31 D. THE EQUIPMENT 1. G e n e r a l D e s c r i p t i o n B a s i c a l l y the equipment c o n s i s t s of a v a r i a b l e h i g h v o l t a g e power-pack, a t r i g g e r i n g and t r a c e - b r i g h t e n i n g c i r c u i t , a t i m i n g - p i p g e n e r a t o r , two d e l a y l i n e s and a d o u b l e -beam C o s s o r " o s c i l l o s c o p e . The b l o c k d i a g r a m o f t h e equipment i s shown i n F i g . 6 . The c a b l e ( l ) i s d i s c o n n e c t e d a t b o t h ends (2 and 3) and the equipment i s s t a t i o n e d a t the n e a r end ( 2 ) . The f a u l t a t (4) i s a s s i m u l a t e d by a p p l y i n g a h i g h v o l t a g e t o the c a b l e f rom the power pack ( 5 ) . The sudden c o l l a p s e o f the h i g h v o l t a g e t o a, v e r y much l o w e r v a l u e a t t h e f a u l t g e n e r a t e s two t r a v e l i n g waves (5 and 6) w h i c h t r a v e l a l o n g t h e c a b l e i n o p p o s i t e d i r e c t i o n s away from t h e f a u l t . The t r a v e l i n g wave (6) i s not r e q u i r e d i n t h i s method and I t s e f f e c t s may be e l i m i n a t e d by t e r m i n a t i n g the c a b l e a t the f a r end (3) i n i t s c h a r a c t e r i s t i c impedance. The f a u l t - s u r g e (5) on a r r i v i n g a t t h e near end (2) meets a h i g h - p a s s f i l t e r (7) w h i c h p a s s e s o n l y the steep wave f r o n t o f the t r a v e l i n g wave. The r e s i s t o r s ( 8 ) , (9) and (10) form a p o t e n t i o m e t e r d e v i c e f o r t a p p i n g a r e d u c e d v a l u e o f the i n c i d e n t v o l t a g e wave ( 5 ) . The i n i t i a l n e g a t i v e v o l t a g e (5.) a p p e a r i n g a c r o s s r e s i s t o r s (S and 9) t r i g g e r s the u n l v i b r a t o r i n c i r c u i t ( l l ) w h i c h g e n e r a t e s two sharp n e g a t i v e p u l s e s (12 and 13) . P u l s e (12) i n i t i a t e s the s i n g l e s t r o k e h o r i z o n t a l sweep i n t h e o s c i l l o s c o p e and p u l s e (13) t r i g g e r s t h e t i m i n g - p i p 32 g e n e r a t o r ( 15) . The u n i v i b r a t o r i n c i r c u i t (11) a l s o g e n e r a t e s a l o n g e r p o s i t i v e p u l s e ( l 6 ) f o r b r i g h t e n i n g t h e o s c i l l o s c o p e t r a c e . The I n c i d e n t v o l t a g e wave (5) a p p e a r i n g a c r o s s the r e s i s t o r (2>) i s f e d i n t o the d e l a y l i n e (17) , t h r o u g h the a m p l i f i e r (18) i f n e c e s s a r y , onto t h e Y2 p l a t e o f the o s c i l l o -scope p r p d u c i n g a v e r t i c a l d e f l e c t i o n . B o t h d e l a y l i n e s ( i k and 17) a r e t e r m i n a t e d i n t h e i r r e s p e c t i v e c h a r a c t e r i s t i c impedance i n o r d e r t o e l i m i n a t e r e f l e c t i o n s . Meanwhile the surge (5) w h i c h s t a r t e d t h e above t r a i n o f e v e n t s i s p a r t i a l l y r e f l e c t e d f r om the h i g h impedance at (2) and i s on i t s way back to the f a u l t ( h ) . At t h e f a u l t (4) w h i c h i s s t i l l c o n d u c t i n g t h e i n i t i a l wave (5) i s a g a i n p a r t i a l l y r e f l e c t e d and t r a v e l s back t o t h e near end ( 2 ) . On i t s second a r r i v a l the p u l s e (5) i s a g a i n f e d onto the Y - p l a t e o f t h e o s c i l l o s c o p e p r o d u c i n g a second p i p on the t r a c e . The second p i p i s d i s p l a c e d f r om the f i r s t p i p by a d i s t a n c e p r o p o r t i o n a l to t h e r e t u r n r o u t e t r a v e l t i m e o f t h e surge between the equipment a t (2) and t h e f a u l t at ( h ) . The second and s u c c e e d i n g a r r i v a l s of wave (5) have no e f f e c t on the u n i v i b r a t o r i n c i r c u i t (11) so t h a t the h o r i z o n t a l sweep o f the o s c i l l o s c o p e i s not i n t e r r u p t e d . The t i m i n g p i p s p r o d u c e d by t i m i n g - p i p g e n e r a t o r (15) a r e f e d onto the Y, t r a c e o f the o s c i l l o s c o p e s i m u l t a -n e o u s l y w i t h t h e echoes.on the Y2 t r a c e . These are o f f i x e d f r e q u e n c y and a r e t h e r e f o r e a means o f measuring e q u a l time I n t e r v a l s on the h o r i z o n t a l t r a c e . 33 I n o r d e r t o keep the t r a c e v i s i b l e on t h e cathode r a y tube the o u t p u t o f the power pack (5) was a r r a n g e d t o a s s i m u l a t e the f a u l t r e p e t i t i v e l y . I f a l o n g a f t e r - g l o w s c r e e n i s a v a i l a b l e o r photography i s used a s i n g l e f l a s h -o v e r o f t h e f a u l t i s s u f f i c i e n t t o l o c a t e i t . 2. H i g h - V o l t a g e Power Pack and L i n e C o u p l i n g I n o r d e r t o m a i n t a i n the t r a c e v i s i b l e on t h e o s c i l l o s c o p e the power pack was c o n n e c t e d t o produce a v o l t a g e t h a t would r e p e a t e d l y cause the f a u l t t o f l a s h -o v e r . F o r e x p e r i m e n t a l purpose the v o l t a g e s U3ed were; (a) 0 - 1200 v o l t s D. C. (b) 0 - 1750 v o l t s peak h a l f - w a v e r e c t i f i e d 6 0 - c y c l e s i n e wave. (c ) 0 - 1750 v o l t s peak f u l l - w a v e r e c t i f i e d 6 0-cycle s i n e wave. Cd) 0 - 4600 v o l t s A. C. 6 0 - c y c l e At f i r s t , a D. C. v o l t a g e was used and t h e power pack was c o u p l e d to t h e c a b l e t h r o u g h the c o u p l i n g c i r c u i t shown i n F i g . 7> The r e p e t i t i o n f r e q u e n c y o f t h e f l a s h - o v e r was d e t e r m i n e d l a r g e l y by t h e t i m e c o n s t a n t s o f the c u r r e n t l i m i t i n g r e s i s t o r R and t h e s h u n t i n g condenser C. The condenser C was i n t e n d e d as a r e s e r v o i r o f energy w h i c h would d i s c h a r g e i n t o the c a b l e once the f l a s h - o v e r o c c u r r e d and m a i n t a i n the a r c w h i l e the f a u l t - s u r g e s are t r a v e l i n g up and doxvn th e c a b l e . The H- mh. r a d i o f r e q u e n c y choke c o i l was used to p r e v e n t the f a u l t - s u r g e 3 from s h o r t i n g t o ground t h r o u g h C. I t was f o u n d n e c e s s a r y to p l a c e a 250 ohm damping r e s i s t o r i n s e r i e s w i t h the r . f . choke to e l i m i n a t e the o s c i l l a t i o n s w h i c h were g e n e r a t e d by shock e x c i t i n g the choke each time the f a u l t f l a s h e d o v e r . A f t e r e x p e r i m e n t i n g w i t h t h i s c o u p l i n g c i r c u i t i t was found t h a t L and C c o u l d be o m i t t e d . To follow page Z50 ohms ohn., F<=tOO,OOQ s r.f. Choke: Co/7 High Vo/fage &. C /Power /Pack Fig . 7. Circuit diagram of an experimental high voltage power pack coupling c i rcui t U. B„ C. ^ p r i l 18,1951 35 S a t i s f a c t o r y r e s u l t s f o r any o f the f o u r v o l t a g e s a v a i l a b l e were o b t a i n e d by c o n n e c t i n g t h e power pack d i r e c t l y I n s e r i e s w i t h the c a b l e t h r o u g h a 100,000 ohm n o n - i n d u c t i v e r e s i s t o r . The r e p e t i t i o n f r e q u e n c y o f t h e f l a s h - o v e r , i n case o f d. c., depends upon the time c o n s t a n t o f t h e c u r r e n t l i m i t i n g r e s i s t o r and the c a p a c i t y o f the c a b l e and a l s o upon the magnitude o f the f l a s h - o v e r v o l t a g e . I n case o f a. c. v o l t a g e s the r e p e t i t i o n : f r e q u e n c y " i s d e t e r m i n e d p r e d o m i n a n t l y by f r e q u e n c y o f a. c. v o l t a g e . The c u r r e n t l i m i t i n g r e s i s t o r i s a v o l t a g e r e g u l a t o r whose v a l u e s h o u l d be h i g h t o keep the f a u l t c u r r e n t . l o w so t h a t t h e f a u l t w i l l f l a s h - o v e r r e p e t i t i v e l y , and not conduct c o n t i n u o u s l y . 36 3' T r i g g e r i n g ; and T r a c e - B r i g h t e n i n g C i r c u i t The t r i g g e r i n g and t r a c e b r i g h t e n i n g c i r c u i t p e r m i t s th e f i r s t i m p u l s e f r o m t h e f a u l t t o t r i g g e r the h o r i z o n t a l sweep and s i m u l t a n e o u s l y b r i g h t e n t h e t r a c e , but b l o c k s the subsequent echoes 30 they do not i n t e r f e r e w i t h the h o r i z o n t a l sweep. B a s i c a l l y the c i r c u i t c o n s i s t s o f a d i o d e l i m i t e r , a u n i v i b r a t o r and a cathode f o l l o w e r . The complete c i r c u i t i s shown s c h e m a t i c a l l y i n F i g . 8>. I n the q u i e s c e n t c o n d i t i o n , i n t h e u n i v i b r a t o r i s c o n d u c t i n g s t r o n g l y ( a p l a t e c u r r e n t o f 11 ma), and Vty. a r e n o n - c o n d u c t i n g . The cathode o f V-j_, the d i o d e l i m i t e r , i s h e l d p o s i t i v e r e l a t i v e to the anode by the cathode b i a s p o t e n t i o m e t e r w h i c h can m a i n t a i n a p o s i t i v e p o t e n t i a l 0 - 150 v o l t s on the cathode. The d i o d e w i l l c onduct o n l y when the cathode i s d r i v e n f a r enough n e g a t i v e l y so t h a t t h e anode i s p o s i t i v e r e l a t i v e t o the cathode. T h i s means t h a t o n l y an i n p u t s i g n a l w h i c h has a n e g a t i v e v o l t a g e g r e a t e r t h a n the p o s i t i v e b i a s on the cathode w i l l cause t o conduct and upset t h e b a l a n c e o f the u n i v i b r a t o r . The b i a s i n g p o t e n t i o m e t e r can be set so t h a t e i t h e r a l a r g e o r s m a l l n e g a t i v e p u l s e w i l l t r i g g e r t h e u n i v i b r a t o r . When V i conducts a n e g a t i v e s i g n a l i s Impressed on t h e g r i d o f Vg w h i c h s t o p s Vg from c o n d u c t i n g s e n d i n g the p l a t e o f Vg p o s i t i v e . The h i g h p o s i t i v e v o l t a g e on the p l a t e o f Vg i s Impressed ori t h e g r i d s o f V^and Vij. c a u s i n g b o t h t u b e s t o conduct v e r y s t r o n g l y . W h i l e V-^  i s c o n d u c t i n g , 37 i t s p l a t e i s d r i v e n about 150 v o l t s n e g a t i v e . . T h i s n e g a t i v e v o l t a g e i s Impressed on the g r i d o f V 2 t h r o u g h t h e c o u p l i n g condenser C i w h i c h s t o p s Vg f r o m c o n d u c t i n g u n t i l 0± d i s c h a r g e s t h r o u g h RT.. Gnce C i has d i s c h a r g e d t h r o u g h R i , V2 b e g i n s to conduct a g a i n and V^ i s cut o f f and the c i r c u i t r e t u r n s to t h e q u i e s c e n t p e r i o d a w a i t i n g the nex t d i s t u r b a n c e . The time c o n s t a n t i s about 725 m i c r o - s e c o n d s . D u r i n g t h i s p e r i o d o f time t h e echoes a p p e a r i n g on Vi have no e f f e c t on V2 s i n c e V2 I s a l r e a d y cut o f f . Thus t h e u n i v i b r a t o r r e s ponds to t h e f i r s t n e g a t i v e p u l s e and b l o c k s a l l s u c c e e d i n g p u l s e s f o r a p e r i o d o f 725 m i c r o s e c o n d s . The n e g a t i v e p u l s e g e n e r a t e d a t the p l a t e o f Vj, i 3 d i f f e r e n t i a t e d and a p p l i e d t o the "Synch" t e r m i n a l o f the o s c i l l o s c o p e f o r t r i g g e r i n g t h e h o r i z o n t a l sweep . The P u c k l e time base i n the C o s s o r Model 339 o s c i l l o s c o p e "^3 can be s t a r t e d and stopped- by an e x t e r n a l t r i g g e r v o l t a g e a p p l i e d to the "synch" t e r m i n a l s when t h e i n t e r n a l s e l f - r e p e a t i n g v o l t a g e i s s h o r t c i r c u i t e d . When t h e "synch" t e r m i n a l i s d i s c h a r g e d and the beam f l i e s back t o the l e f t s i d e o f the s c r e e n and remains t h e r e u n t i l the "synch" t e r m i n a l i s d r i v e n p o s i t i v e a t w h i c h time the h o r i z o n t a l sweep b e g i n s . The n e g a t i v e p u l s e s h o u l d o n l y be o f s u f f i c i e n t d u r a t i o n t o d i s c h a r g e the condenser i n t h e P u c k l e time-base c i r c u i t . S i n c e t h e S y n c h r o n i z i n g p u l s e has a st e e p l e a d i n g edge and l e s s s t eep t r a i l i n g edge, t h e "synch" p o t e n t i o m e t e r on t h e - o s c - i i i o s c o p e i s used as a v e r n i e r t o v a r y the time a t w h i c h 3& t h e h o r i z o n t a l 3weep w i l l b e g i n . The "synch" p o t e n t i o m e t e r i d e t e r m i n e s what p e r c e n t a g e o f the "synch" i s a p p l i e d t o the g r i d o f t h e b u f f e r tube. As soon as the g r i d o f t h e b u f f e r tube r e t u r n s t o les3 than 12 v o l t s n e g a t i v e the b u f f e r tube s t a r t s c o n d u c t i n g and t h e h o r i z o n t a l sweep i s i n i t i a t e d . The h o r i z o n t a l sweep can be d e l a y e d as much as 10 micro-seconds f o r t h e f a s t e s t sweep and t h e e f f e c t i v e l e n g t h o f t h e t r a c e can be expanded s i m p l y by r o t a t i n g the "synch" c o n t r o l c l o c k -w i s e . The n e g a t i v e p u l s e f o r t r i g g e r i n g t h e t i m i n g - p i p g e n e r a t o r i s t a k e n from t h e p l a t e o f Vj. : S i n c e the f l y -back on t h e o s c i l l o s c o p e i s not b l a c k e d - o u t , t h e t i m i n g p i p s appear on the f l y - b a c k t r a c e and i n t e r f e r e w i t h t h o s e o n t t h e f o r w a r d t r a c e . To a v o i d t h i s i n t e r f e r e n c e the n e g a t i v e t r i g g e r i n g p u l s e i s d e l a y e d 6.1 micr o s e c o n d s by 335 eras o f G e n e r a l E l e c t r i c Company u n i f o r m d e l a y l i n e t o make c e r t a i n t h a t t h e f l y - b a c k I s complete b e f o r e t h e t i m i n g - p i p s appear on the t r a c e . The p o s i t i v e p u l s e g e n e r a t e d a t the p l a t e o f V2 I s a p p l i e d t o g r i d o f the cathode f o l l o x ^ e r Vij.. The ou t p u t o f the cathode f o l l o w e r , a 5°°- microsecond 9 0 - v o l t p o s i t i v e p u l s e , i s f e d onto g r i d A4. o f the cathode r a y tube t h r o u g h a 0.01 m i c r o f a r a d condenser shunted by a 0,1 megohm r e s i s t o r . T h i s l a r g e b r i g h t e n i n g p u l s e i s a p p l i e d each time, the h o r i z o n t a l sweep i s t r i g g e r e d t o make the t r a c e v i s i b l e at" h i g h w r i t i n g 39 speeds. T h i s b r i g h t e n i n g p u l s e dannot be a p p l i e d c o n t i n -u o u s l y as i t would b u r n the f l u o r e s c e n t c o a t i n g on t h e cathode r a y tube. T i m i n g - P i p G e n e r a t o r On t h e Co s s o r Model 339 double-beam o s c i l l o s c o p e ^ whose h o r i z o n t a l ' s w e e p i s not l i n e a r w i t h time, t h e most c o n v e n i e n t way o f measuring e q u a l time i n t e r v a l s i s by p l a c i n g t i m i n g p i p s on t h e YT. t r a c e . The t i m i n g p i p s appear on t h e Y i t r a c e s i m u l t a n e o u s l y w i t h , t h e f a u l t - s u r g e p i p s on th e Y2 t r a c e and a r e l o c k e d i n s t e p by the I n i t i a l f a u l t -surge so t h a t the sweep can be expanded and the p o s i t i o n o f the echoes measured more a c c u r a t e l y . The t i m i n g - p i p g e n e r a t o r i s a m o d i f i e d H a r t l e y 12 o s c i l l a t o r w h i c h was' b u i l t by T. K. N a y l o r . I t was r e -m o d i f i e d so t h a t i t c o u l d be t r i g g e r e d f r om the u n i v i b r a t o r . The s c h e m a t i c c i r c u i t d iagram i s shown i n F i g . 9 . V£A i s a s h u n t i n g t r i o d e w h i c h i s c o n d u c t i n g d u r i n g t h e q u i e s c e n t p e r i o d and b i a s i n g t h e o s c i l l a t o r t r i o d e V&B beyond c u t o f f by means o f the common cathode r e s i s t o r R-2h. The $00 ohm r e s i s t o r R31 was added t o unbalance the o p e r a t i n g c h a r a c t e r -1 s t i e s o f V£A and V^g and t h e g r i d o f V^A was b i a s e d 33 v o l t s p o s i t i v e t o i n s u r e t h a t V"6A i s c o n d u c t i n g c o n t i n u o u s l y except when t r i g g e r e d by a l a r g e n e g a t i v e p u l s e from t h e u n i v i b r a t o r . The s i n e wave o u t p u t o f Vgg I s c l i p p e d by the a s y m m e t r i c a l cathode f o l l o w e r ( V y ^ ) . A second cathode f o l l o w e r , a b u f f e r t r i o d e V y B , d r i v e s a d i f f e r e n t i a t i n g c i r c u i t w h i c h d i f f e r e n t -i a t e s the r e c t i f i e d s i n e wave from Vy^. T h i s peaked -waveis impressed,on a s m a l l i n d u c t a n c e (Lh) w h i c h tends to square 41 t h e p i p s hy r e d u c i n g t h e a m p l i t u d e and i n c r e a s i n g t h e w i d t h o f the peak. The f r e q u e n c y o f t h e t i m i n g p i p s i s 4.47 megacycles so the pip3 are spaced 6.224 m i c r o s e c o n d s a p a r t . They a r e 0.03 m i c r o s e c o n d s wide and 1$ v o l t s i n a m p l i t u d e . These p i p s a r e i n d i s t i n g u i s h a b l e a t low sweep speeds but a r e o n l y 12 mm a p a r t on the f a s t e s t sweep. A 6.1 m i c r o s e c o n d G e n e r a l E l e c t r i c Company u n i f o r m d e l a y l i n e i s u sed between t h e t i m i n g - p i p g e n e r a t o r and the t r i g g e r i n g c i r c u i t so t h a t the t i m i n g p i p s do not appear on the f l y b a c k t r a c e and be c o n f u s e d w i t h those on the f o r w a r d t r a c e . 1+2 5. D e l a y L i n e As the minimum time r e q u i r e d t o I n i t i a t e t he h o r i z o n t a l sweep on the o s c i l l o s c o p e i s about 4 micr o s e c o n d s the f a u l t - s u r g e had t o be d e l a y e d b e f o r e b e i n g a p p l i e d t o the Y2 d e f l e c t o r p l a t e s . I t was thought d e s i r a b l e t o see s e v e r a l m i c r o s e c o n d s o f the t r a c e b e f o r e the f i r s t f a u l t -surge a r r i v e d and 30 the p u l s e was d e l a y e d a n o t h e r 6 m i c r o -seconds. The d e l a y was a c c o m p l i s h e d by 55° c m s ° f G e n e r a l E l e c t r i c Company u n i f o r m d e l a y l i n e . The i n n e r c o n d u c t o r i s a l o n g t h i n c o i l wound on a 3 / l 6 i n c h d i a m e t e r Saran f l e x i b l e p l a s t i c t u b i n g and the o u t e r c o n d u c t o r I s a m e t a l b r a i d s u r r o u n d i n g t h e i n n e r one. The i n n e r w i n d i n g i s made of AWG- No. ho copper w i r e , formex i n s u l a t e d , 1 0 9 t u r n s p e r c e n t i m e t e r and i n s u l a t e d from the o u t e r c o n d u c t o r by a 0 . 0 0 1 5 i n c h c e l l u l o s e a c e t o b u t y r o t e tape s i n g l e wrap, 5° P e r cent o v e r l a p . The c h a r a c t e r i s t i c impedance of the l i n e i s 1 1 0 0 ohms and the d e l a y i s 1 m i c r o s e c o n d i n 55 cms. The v o l t a g e r a t i n g i s 500° v o l t s D. C. The a t t e n u a t i o n p e r m i c r o s e c o n d i s 2 to 3 d e c i b e l s a t 2 megacycles per second and 4 t o 6 d e c i b e l a t 4 megacycles p e r second. The d e l a y l i n e i s c o r r e c t l y t e r m i n a t e d a t each end by a 1 1 0 0 ohms ca r b o n r e s i s t o r I n o r d e r t o a v o i d r e f l e c t i o n s . 3^ 6. P r o c e d u r e F o r M e a s u r i n g The Cable Fa,ult Make c e r t a i n t h e c a b l e i s d i s c o n n e c t e d a t b o t h ends and f r e e from s t r a y i n d u c e d v o l t a g e s . Connect the power pack t o t h e c a b l e t h r o u g h a c u r r e n t l i m i t i n g r e s i s t o r u s i n g e i t h e r 60 c y c l e a.c. o r f u l l - w a v e r e c t i f i e d a.c. v o l t a g e . Connect t h e v a r i o u s u n i t s o f the f a u l t - l o c a t o r as shown i n F i g . 6 u s i n g s h o r t l e n g t h s o f c o a x i a l l i n e . The r e s i s t o r s i n t h e d e t e c t i n g c i r c u i t (7) a r e chosen so t h a t t h e maximum v o l t a g e a p p e a r i n g a c r o s s t h e t r i g g e r i n g c i r c u i t does not exceed 300 v o l t s and 200 v o l t s a c r o s s the d e l a y l i n e . The p o t e n t i o m e t e r on t h e d i o d e l i m i t e r i s s e t h a l f - w a y . On t h e o s c i l l o s c o p e s e t p l a t e s - a m p l i f i e r s w i t c h t o A. C. p l a t e s , condenser to p o s i t i o n "9" , t r i g g e r maximum c o u n t e r c l o c k w i s e , synch, b r i l l i a n c y and v e l o c i t y h a l f - w a y , a m p l i t u d e maximum c l o c k w i s e , YT and Y g - s h i f t s so t h a t Y i beam i s above Y2, and and the X- s h i f t so t h a t t h e r e s t i n g spot o f the beam i s j u s t o f f to the r i g h t o f t h e s c r e e n . Keep i n c r e a s i n g the v o l t a g e on the c a b l e by i n c r e a s i n g the v a r i a c \ s e t t i n g i n the h i g h v o l t a g e power-pack u n t i l t h e f a u l t b e g i n s t o f l a s h o v e r . A d j u s t f o c u s and r o t a t e v e l o c i t y and Synch c l o c k w i s e t o expand sweep. Examine the Y2 t r a c e c a r e f u l l y . I f t he d e f l e c t i o n s a re s m a l l , the Output o f t h e d e l a y l i n e i s f e d onto the A i t e r m i n a l o f the o s c i l l o s c o p e and a m p l i f i e d . The i n t e r n a l a m p l i f i e r s a re cascaded by s e t t i n g the p l a t e s - a m p l i f i e r s s w i t c h to 2-HFY^. The g a i n i s i n c r e a s e d by r o t a t i n g . A i and Ap G a i n c l o c k w i s e . The a m p l i f i e r s w i l l 44 produce o n e - h a l f o f t h e i r f u l l s c a l e d e f l e c t i o n w i t h o u t d i s t o r t i o n when cascaded. O v e r l o a d i n g produces d i s t o r t i o n . A f t e r t h e f a u l t has been a p p r o x i m a t e l y l o c a t e d on the compressed sweep, the t r a c e i s expanded by s e t t i n g condenser t o p o s i t i o n "10" and r o t a t i n g Synch and V e l o c i t y s l o w l y c l o c k w i s e . The X - s h i f t i s used to examine any p o r t i o n o f the expanded t r a c e . The d i s t a n c e s between the echoes on the expanded t r a c e a re measured l n terms o f the 0.224 m i c r o s e c o n d t i m i n g p i p s . A l l measurements a r e made t o t h e b e g i n n i n g o f the p u l s e and not t h e peak. 45 E. EXPERIMENTAL RESULTS S i n c e no power c a b l e s were a v a i l a b l e a l l e x p e r i m e n t s were c a r r i e d out on t h r e e l e n g t h s o f c o a x i a l c a b l e . Two lengths, one 289 .7 f e e t l o n g and the o t h e r 9 5 1 . 4 - ! f e e t l o n g , o f RG/8U c a b l e and a t h i r d l e n g t h 8 3 7 . 8 " f e e t l o n g w h i c h r e s e m b l e s v e r y c l o s e l y the RG-63/U cable^were used. The 14 s p e c i f i c a t i o n s o f the c a b l e s used a re l i s t e d below. RG-8/U G e n e r a l purpose medium-size f l e x i b l e c a b l e . I n n e r c o n d u c t o r - 7/21 AWG copper D i e l e c t r i c m a t e r i a l - p o l y e t h y l e n e S h i e l d i n g b r a i d - copper P r o t e c t i v e c o v e r i n g r - v i n y l Nominal, d i a m e t e r o f d i e l e c t r i c - 0 . 285 i n . Nominal o u t s i d e d i a m e t e r - 0 . 4 0 5 i n . Maximum o p e r a t i n g v o l t a g e rms - 4000 v o l t s Nominal c a p a c i t a n c e - 2 9 . 5 ^ i f d / f t . Nominal impedance - 5 2 . 2 ohms V e l o c i t y o f p r o p a g a t i o n - 6 5 5 f t / ^ u sec. Lengths o f c a b l e used - 2 8 9 . 7 f e e t and 9 5 1 . 4 f e e t 4 6 RG-63/U Medium s i z e l o w - c a p a c i t a n c e a i r - s p a c e d - d i e l e c t r i c c a b l e . I n n e r c o n d u c t o r - 1/22 AWG- eopperweld D i e l e c t r i c m a t e r i a l - a i r and p o l y e t h y l e n e S h i e l d i n g b r a i d - copper P r o t e c t i v e c o v e r i n g - v i n y l Nominal d i a m e t e r o f d i e l e c t r i c - 0. 2&5 I n . Nominal o u t s i d e d i a m e t e r - 0.405 i n . Maximum o p e r a t i n g v o l t a g e rms - 1000 v o l t s Nominal c a p a c i t a n c e - 10 yuuafd/ft Nominal impedance - 125 ohms V e l o c i t y o f p r o p a g a t i o n - 311 . 5 ft/p. sec« L e n g t h o f cable, used - S37. S f e e t The photographs o f the o s c i l l o s c o p e t r a c e s a re shown i n f i g u r e s 11 to l 6 i n c l u s i v e . The d i s t a n c e s between t h e s u c c e s s i v e f a u l t - p i p s on the t r a c e were measured i n terms o f the t i m i n g - p i p s on a f u l l y expanded t r a c e and then averaged. The d i s t a n c e t o t h e f a u l t was c a l c u l a t e d by one o f two methods; (a) from t h e v e l o c i t y o f p r o p a g a t i o n o f the wave i n the c a b l e and t h e t i m i n g - p i p i n t e r v a l . (b) from the r a t i o o f t h e d i s t a n c e to the f a u l t t o t h a t o f a know d i s c o n t i n u i t y . 47 The r e s u l t s o b t a i n e d a r e t a b u l a t e d l n t h e t a b l e shown below. T r i a l R e f e r e n c e Average D i s -t ance t o the f a u l t measurec i n t i m i n g - p i p Measured d i s t a n c e ' i t h e f a u l t i n f e e t A c t u a l ;o D i s t a n c e to t he f a u l t i r f e e t E r r o r i n f e e t % E r r o r 1 2 F i g . 1 5 3 .8-. 9 . 1 278 828 2 8 9 . 7 8 3 7 . 8 " 1 ] - Z - 9 . 2 4 . 0 3 1 . 1 7 3 F i g . 1 1 1 3 . 1 9 6 l 9 5 1 . 4 + 1 0 . 4 1 . 0 9 4 . F i g . 1 2 1 3 . 0 9 5 4 9 5 1 . 4 + 3 . 4 0 . 3 5 5 F i g . 1 3 1 6 . 6 1 2 1 8 1 2 4 1 . 1 - 2 3.1 I . 8 5 6 7 F i g . 16 17.O 2 1 . 7 5 1247 1 7 4 5 1 2 4 1 . 1 1 7 8 8 . 2 . + 5 . 9 - 4 3 . 2 0 . 4 7 2.41 Sample C a l c u l a t i o n  Method (a) d = N v T 0 where d = d i s t a n c e t o the f a u l t i n f e e t N = number o f t i m i n g - p i p to the f a u l t v =s v e l o c i t y o f p r o p a g a t i o n l n f e e t p e r m i c r o s e c o n d T o - time i n t e r v a l between t i m i n g - p i p s l n mic r o s e c o n d s C o n s i d e r T r i a l 3 . Method (b) where N]_ N2 d = 6 ^ ( 0 . 2 2 4 ) ( 1 3 . 1 ) ' 2 = 9 6 l f e e t d = _NJL ( ^ ) N2 number o f t i m i n g - p i p s t o t h e f a u l t number o f t i m i n g - p i p s to the end of the c a b l e l e n g t h o f the c a b l e i n f e e t C o n s i d e r T r i a l 1 d = 3 . 8 ( 1 2 4 1 . 1 ) . 2 7 8 f e e t 17 kg IV DISSCUSION The r e s u l t s o b t a i n e d on c o a x i a l c a b l e a r e i n d e e d g r a t i f y i n g . No power c a b l e s were a v a i l a b l e and so t h e p r e -formance o f t h e f a u l t - l o c a t o r on s i n g l e - c o n d u c t o r o r t h r e e -c o n d u c t o r c a b l e s c o u l d not be t e s t e d . The o s c i l l o g r a m s , f i g s . 1 1"to l 6 i n c l u s i v e , appear t o be out o f f o c u s because the t r a c e a t h i g h sweep speeds i s r a t h e r dim, p a r t i c u l a r l y f o r photography, and a time-exposure was n e c e s s a r y . I n t a k i n g the photographs t h e time-exposure f o r the compressed sweep was 6. seconds and 15 seconds f o r the expanded sweep. At the h i g h e s t sweep 3peed the w r i t i n g speed o f the c a t h o d e - r a y beam i s about 3 ' 5 c e n t i m e t e r s p e r microsecond. To make the t r a c e v i s i b l e a t such h i g h sweep speeds e x t e r n a l b r i l l i a n c y c o n t r o l was n e c e s s a r y . I t can be seen from the o s c i l l o g r a m s t h a t t h e t r a c e i s w e l l behaved s i n c e i t remained f i x e d i n p o s i t i o n and a m p l i t u d e d u r i n g the time-exposure. The t r a c e s are f r e e from s p u r i o u s r e f l e c t i o n s and e a s i l y i n t e r p r e t e d . The e f f e c t s o f a 20-ohm s e r i e s r e s i s t o r p l a c e d at a c a b l e j u n c t i o n a r e shown i n F i g s . Ik- and l 6 . The c a b l e j u n c t i o n i t s e l f d i d not produce a n o t i c e a b l e d e f l e c t i o n i n the t r a c e and so a l a r g e impedance d i s c o n t i n u i t y was p l a c e d a t a known p o i n t to study i t s e f f e c t on t h e surge'phenomena. I t w i l l be noted t h a t the r e s i s t o r a t t e n u a t e s the t r a v e l i n g surge v e r y r a p i d l y and t h a t i t s p o s i t i o n on t h e t r a c e a i d s I n d e t e r m i n g the d i s t a n c e to the f a u l t . 4-9 The h i g h - p a s s f i l t e r o r d i f f e r e n t i a t i n g c i r c u i t (7) i n F i g . 6 p l a y s a l a r g e r o l e i n d e t e r m i n g t h e wave shape appear-i n g on t h e t r a c e and the a c c u r a c y o f the measurement. The wave produced a t the f a u l t i s a square wave e x p o n e n t i a l l y a t t e n u a t e d whose p e r i o d i s 4-d. F i g . h a shows the square wave v g e n e r a t e d by t h e d i s c h a r g e o f a cL&S.I-footi s e c t i o n o f c a b l e when the condenser (19) (See F i g . 6,) i n the h i g h - p a s s f i l t e r c i r c u i t (7) i s 150 yuufd and r e s i s t o r (10) i s removed. F i g . 15 i s t h e d i s c h a r g e o f the same c a h l e but t h e condenser (19) was r e d u c e d to l 6 ^uufd to d i f f e r e n t i a t e the square wave. A c a p a c i t o r . a c t s l i k e a s h o r t c i r c u i t at t h e f i r s t i n s t a n t , but f i n a l l y , i f the wave i s s u f f i c i e n t l y l o n g the c a p a c i t o r becomes f u l l y charged and t h e r e a f t e r a c t s l i k e an open c i r c u i t . R e s i s t o r (10) s h o u l d be k e p t low so t h a t the a m p l i t u d e o f t h e f a u l t - s u r g e s a p p e a r i n g on t h e Yg t r a c e a r e l a r g e . F o r a l a r g e f a u l t - s u r g e t h e l e a d i n g edge i s s t e e p and the b e g i n n i n g o f the wave i s more a c c u r a t e l y d e t e r m i n e d . F or p r e c i s e measurement between t h e f a u l t - p i p s i t i s i m p o r t a n t t h a t t h e t o e o f the p u l s e be a c c u r a t e l y d e t e r m i n e d . F i g . 16 i s . a s p e c i a l case where an a.c. breakdown v o l t a g e was a p p l i e d t o t h e c a b l e and the h i g h ^ p a s s f i l t e r (7) i n F i g . 6 was i m p r o p e r l y p r o p o r t i o n e d . When r e s i s t o r (10) was removed from c i r c u i t (7) the t r i g g e r i n g i m p u l s e was e x c e e d i n g l y l a r g e . The t r i g g e r i n g u n i t was i n i t i a t i n g t h e h o r i z o n t a l sweep on b o t h the p o s i t i v e and n e g a t i v e f a u l t - s u r g e s . There are two t r a c e s superimposed upon one a n o t h e r , one t r a c e r e s u l t i n g from a f l a s h - o v e r o f 5 0 t h e f a u l t on t h e p o s i t i v e h a l f - c y c l e o f t h e s i n e wave and t h e o t h e r on t h e n e g a t i v e h a l f - c y c l e . When t h e 5 0 0 0 ohm r e s i s t o r ( 1 0 ) was r e p l a c e d j t h e a.c, breakdown v o l t a g e gave the same t r a c e as t h e d.c. breakdown v o l t a g e . I f the c i r c u i t (7) i s c o r r e c t l y p r o p o r t i o n e d t h e t r a c e i s the same f o r e i t h e r a.c. o r d. c. breakdown v o l t a g e . I n t h e exp e r i m e n t s conducted t h e f a u l t was a s s i m -u l a t e d e i t h e r by d r i v i n g a n a i l t h r o u g h the armour u n t i l i t n e a r l y t o u c h e d the c e n t r e c o n d u c t o r o r by p l a c i n g a s p a r k -gap a t t h e c a b l e j u n c t i o n and a p p l y i n g a h i g h v o l t a g e t o g e n e r a t e an a r c . A c o n s t a n t v i s u a l t r a c e on the o s c i l l o -scope was m a i n t a i n e d by r e p e t i t i v e l y c a u s i n g the f a u l t t o f l a s h o v e r . A f t e r c o n s i d e r a b l e amount o f e x p e r i m e n t i n g i t was c o n c l u d e d t h a t t h e most e f f e c t i v e means o f c o u p l i n g the h i g h - v o l t a g e power pack t o the c a b l e was t h r o u g h a h i g h v a l u e ( 1 5 0 , 0 0 0 ohms) n o n - i n d u c t i v e s e r i e s r e s i s t o r . T h i s c u r r e n t l i m i t i n g r e s i s t o r ( 2 0 ) ( s e e F i g . 6 ) t o g e t h e r w i t h t h e c a p a c i t y o f t h e c a b l e , the f a u l t breakdown v o l t a g e , and the a p p l i e d v o l t a g e d e t e r m i n e the r e p e t i t i o n r a t e o f t h e a r c . The r e p e t i t i o n r a t e f o r a l a r g e 6 0 c y c l e a.c. a p p l i e d v o l t a g e was g r e a t e r than 1 2 0 c y c l e s f o r s h o r t l e n g t h s o f c a b l e s i n c e the c a b l e c o u l d be r e - c h a r g e d s e v e r a l t i m e s i n h a l f a c y c l e . The magnitude o f the r e s i s t o r ( 2 0 ) was m a i n t a i n e d a t a h i g h v a l u e t o l i m i t the s u p p l y c u r r e n t t o the o r d e r o f 1 0 m i l l l a m p e r e s so t h a t t h e f a u l t w i l l not conduct c o n t i n u o u s l y once i t has f l a s h e d o v e r . F o r an a p p l i e d v o l t a g e o f 2 0 0 v o l t s , i t was f o u n d t h a t w i t h a r e s i s t o r ( 2 0 ) o f 1 5 0 , 0 0 0 ohms t h e s p a r k i n g 5 1 a t t h e f a u l t appeared t o he p e r i o d i c (about 1 2 5 s p a r k s p e r second) and t h e t r a c e on the o s c i l l o s c o p e was s t a t i o n a r y and v e r y c l e a r , W i t h a r e s i s t o r ( 2 0 ) o f 2 5 , 0 0 0 ohms the s p a r k i n g a t t h e f a u l t was r a p i d and e r r a t i c (about 2 5 0 s p a r k s p e r second) and the t r a c e was s t a t i o n a r y but s l i g h t l y b l u r r e d . The d i s t a n c e t o the f a u l t may be de t e r m i n e d by e i t h e r method (a) o r method (b) as o u t l i n e d p r e v i o u s l y . Assuming t h a t the v e l o c i t y o f p r o p a g a t i o n a l o n g the c a b l e remains c o n s t a n t , the a c c u r a c y w i t h w h i c h the f a u l t i s l o c a t e d depends p r i m a r i l y upon the st e e p n e s s o f t h e wave f r o n t appear-i n g on t h e t r a c e . The r i s e time o f t h e l e a d i n g edge-of t h e i m p u l s e can be improved by c h o o s i n g t h e para m e t e r s i n the h i g h - p a s s f i l t e r (7) such t h a t t h e f a u l t - p i p s a p p e a r i n g on Yp t r a c e a re l a r g e i n a m p l i t u d e . As the p u l s e t r a v e l s a l o n g the c a b l e i t 3 l e a d i n g edge i s f l a t t e n e d due to a t t e n u a t i o n and d i s t o r t i o n c a u s i n g the i p u l s e t o appear d e l a y e d . F o r a c c u r a t e r e s u l t s i t i s i m p o r t a n t t h a t a l l measurements be made to the toe o f the p u l s e . T h i s method o f l o c a t i n g f a u l t s was i n t e n d e d p r i m a r i l y f o r high-impedance f a u l t s . The complete b u r n i n g -down o f the f a u l t i s unn e c e s s a r y and u n d e s i r a b l e . The a r c g e n e r a t e d a t t h e f a u l t p r o v i d e s the n e c e s s a r y surge and a l s o r e d u c e s t h e f a u l t - i m p e d a n c e t o a v e r y low v a l u e so t h a t a good r e f l e c t i o n i s o b t a i n e d from the f a u l t . From t h e o s c i l l o -grams i t i s seen t h a t the a r c conducts s t r o n g l y f o r a p e r i o d about s i x t i m e s t h e one-way t r a n s m i s s i o n time o f t h e l o n g e s t l e n g t h o f u n f a u l t e d c a b l e . The f a u l t impedance d u r i n g the a r c i n g p e r i o d i s low. Thi3 i s v e r i f i e d by t h e r e v e r s a l i n 52 p o l a r i t y o f every c o n s e c u t i v e echo and by t h e absences o f s p u r i o u s r e f l e c t i o n s from beyond the f a u l t . These f a c t s are borne out v e r y c l e a r l y i n F i g . 12. I t i s not u n t i l the a r c b e g i n s to fade t h a t Bpurious r e f l e c t i o n s from beyond th e f a u l t appear on the t r a c e . S i n c e the a r c i n g p e r i o d v a r i e s d i r e c t l y w i t h the l e n g t h o f the c a b l e and I s o f s u f f i c i e n t d u r a t i o n h t o r e f l e c t s e v e r a l echoes n o t h i n g i s g a i n e d by u s i n g an e x t e r n a l s o u r c e o f c u r r e n t to m a i n t a i n the a r c c o n d u c t i n g f o r a l o n g e r p e r i o d . The energy s t o r e d w i t h i n the c a b l e b e f o r e t h e d i s c h a r g e t a k e s p l a c e i s s u f f i c i e n t t o l o c a t e t h e f a u l t . Thi3 f a u l t - l o c a t o r can e a s i l y be used t o l o c a t e medium and low-Impedance f a u l t s s i m p l y by p l a c i n g the f a u l t -l o c a t o r a t one end and r e p e t i t i v e l y d i s c h a r g i n g a l a r g e con-d e n s e r i n t o the o t h e r end o f t h e c a b l e . The r e p e t i t i o n r a t e o f the d i s c h a r g e need not be p e r i o d i c s i n c e the t r i g g e r i n g u n i t w i l l i n i t i a t e the h o r i z o n t a l sweep f r o m the f i r s t n e g a t i v e i m p u l s e t h a t a r r i v e s a t the m o n i t o r i n g end. The r e p e t i t i o n r a t e s h o u l d be s u f f i c i e n t l y h i g h to g i v e a c l e a r v i s u a l t r a c e on the o s c i l l o s c o p e . The f a u l t - l o c a t o r can a l s o be used as an echo-ranger t o "sound-out" th e impedance d i s c o n t i n u i t i e s by p l a c i n g t h e equipment a t one end o f t h e c a b l e and a spark-ga.p a t t h e o t h e r end. 53 V CONCLUSIONS A f a u l t - l o c a t o r has been d e v e l o p e d f o r l o c a t i n g high-impedance f a u l t s i n power c a b l e s by u s i n g the f a u l t -g e n e r a t e d surge. The r e s u l t s o b t a i n e d i n the l a b o r a t o r y e x p e r i m e n t s a re h i g h l y s a t i s f a c t o r y . I t i s r e g r e t t e d t h a t no power c a b l e s were a v a i l a b l e t o te3t t h e f a u l t - l o c a t o r under a d v e r s e c o n d i t i o n s . However, t h e r e i s every r e a s o n t o b e l i e v e t h a t i t s performance i n f i e l d w i l l be j u s t as e f f e c t i v e as i t i s i n the l a b o r a t o r y . The equipment i s s i m p l e , rugged, p o r t a b l e , I n e x p e n s i v e and r e s u l t s a r e r e a d i l y a v a i l a b l e and e a s i l y i n t e r p r e t e d . The a c c u r a c y and t h e e f f e c t i v e range o f t h i s method o f l o c a t i n g f a u l t s depends g r e a t l y on the t y p e o f ;" o s c i l l o s c o p e t h a t i s a v a i l a b l e and on the d i s t o r t i o n o f the wave i n t h e c a b l e . F o r a c c u r a t e measurement i t i s i m p o r t a n t t h a t t h e h o r i z o n t a l sweep be h i g h l y e x p a n d i b l e . The average a c c u r a c y o b t a i n e d i n the e x p e r i m e n t s conducted i s w i t h i n Due t o a t t e n u a t i o n and d i s t o r t i o n p a r t i c u l a r l y of the h i g h f r e q u e n c y components, t h e e f f e c t i v e range i s l i m i t e d t o about 10 m i l e s . T h i s f a u l t - l o c a t o r can be used t o l o c a t e b o t h t r a n s i e n t and permanent f a u l t s . F o r t r a n s i e n t f a u l t s the equipment must be c o u p l e d c o n t i n u o u s l y t o the cable<x and the t r a n s i e n t d i s t u r b a n c e photographed. F o r high-impedance permanent f a u l t s t h e v o l t a g e . r e q u i r e d to cause the f a u l t t o f l a s h o v e r can be e i t h e r a.c. o r d.c. The c a b l e i s c o u p l e d 54 t o t h e h i g h - v o l t a g e power pack by means o f a h i g h v a l u e non-i n d u c t i v e s e r i e s r e s i s t o r . The a r c g e n e r a t e d a t the f a u l t p r o v i d e s the surge n e c e s s a r y to l o c a t e t h e f a u l t and a l s o r e d u c e s the f a u l t impedance to a v e r y low v a l u e so t h a t a good r e f l e c t i o n i s o b t a i n e d . The l e n g t h o f time d u r i n g which the a r c conducts s t r o n g l y i s o f s u f f i c i e n t d u r a t i o n t o o b t a i n s e v e r a l c l e a r r e f l e c t i o n s so t h a t no e x t e r n a l source o f c u r r e n t i s r e q u i r e d t o m a i n t a i n t h e a r c . The t r a c e i s f r e e f r om s p u r i o u s r e f l e c t i o n s f r om beyond the f a u l t u n t i l t h e a r c b e g i n s to fade. The a r c b e g i n s t o f a d e a f t e r about t h e t h i r d r e f l e c t i o n and the t r a c e b e g i n s t o show s p u r i o u s r e f l e c t i o n s . The f a u l t - p i p s a r e e q u a l l y spaced a l o n g the t r a c e and a l t e r -n a t e c o n s e c u t i v e l y i n p o l a r i t y . The sttfeep can be compressed to examine the t r a c e i n i t s e n t i r e t y o r expanded to examine any p o r t i o n i n d e t a i l . A c o n s t a n t v i s u a l t r a c e on the o s c i l l o -scope was m a i n t a i n e d by c a u s i n g t h e f a u l t t o f l a s h o v e r r e p e t i -t i v e l y . . T h i s f a u l t - l o c a t o r can be U3ed f o r l o c a t i n g medium and low-impedance f a u l t s by p l a c i n g i t a t one end o f t h e c a b l e and r e p e t i t i v e l y d i s c h a r g i n g a l a r g e condenser i n t o t h e o t h e r . T h i s equipment can be used t o st u d y s w i t c h i n g t r a n s i e n t s , and measure v e l o c i t y o f p r o p a g a t i o n , a t t e n u a t i o n , and d i s t o r t i o n o f t r a v e l l i n g waves i n c a b l e s . The surges can be g e n e r a t e d by an e x t e r n a l source o r a spark-gap p l a c e d at the end o f the c a b l e . I f the t i m i n g - p i p I n t e r v a l i s i n c r e a s e d , the f a u l t -55 l o c a t o r can a l s o be used f o r l o c a t i n g f a u l t s on overhead tr a n s , m i s s i o n l i n e s . The o b s e r v e d v o l t a g e wave (See F i g . Ita) and t h e t h e o r e t i c a l c a l c u l a t e d v o l t a g e wave ( F i g . h) a r e v e r y s i m i l a r showing t h a t t h e m a t h e m a t i c a l a p p r o x i m a t i o n s made i n the t h e o r e t i c a l c a l c u l a t i o n s a r e j u s t i f i e d . Other phases o f the t h e o r y have a l s o been v e r i f i e d . 56 VI DIAGRAMS AND ILLUSTRATIONS F i g . 10. -Photograph of the f a u l t - l o c a t o r Timing-pip generator, Coseor model 339 double-beam o s c i l l o s c o p e , and the t r i g g e r i n g and t r a c e - b r i g h t e n i n g u n i t . (One-tenth f u l l 3 i z e ) BLOCK DIAGRAM OF  , FAULT-LOCATOR r(EE (3) o.2&4/<- sec "'• Os\ apart -yrrrr <f:4y M. C. Timing - f^ip Getiei-a'to r • (/*) ('3) J 6.//4-Sec Arrtp hfier To J3ht/.fiance Grid Cossor Model *'33 9> Oouble -Beani Osci Ii'OSCO p& 3 (/) Cable - A A A A A A -Trigger/hq 6\ Trace -Sriqhi 50/u/tA. -Fd. Mica Cond. 5000 ohms > 00) Z Sriyh ten-mq Cif~Cui -r J Ol) /50J000 Ohms Current Limiting /Resistor-. High Va/tage /OOO ohms (9) >(7) High - Pass Fitter Delay Line 07) //OO Ohms (3) F i g . 6. B l o c k d i a g r a m showing the components o f the f a u l t - l o c a t o r U.B.C, A p r i l 18, 1951 i TRIGGERING AND TRACE-BRIGHTENING CIRCUIT • o-, Sz70n F>osts \(Norrria.L. 5G0X> ZOK<? /OOK IO00K. &Acr a i Potent 10-meter ,5 X.7K < O.OZJL. -o +300 _Q_ Sec Deki<f Line, Timing • T To "Sunch" J — L 'e >ZSOK 2 .1 -o-HI ,. I A . To /3t~i//iancc ZSK • G,rid ID/ode. Z.imi+er- Cat hade '/^oftov/et Fig . £ . Schematic c i rcu i t diagram of the triggering and trace-brightening c i rcui t T J . B . C , Apri l 1 8 , 1 9 5 1 TIMING-MP GENERATOR o + 3 00 Volts ([Filtered ) Triggering O.OI^. Impulse F'rom Urn w o ret to tr 33 Volts r ~ . / U U U -y. To A , Terminal & i-4~3! On Oscilloscope Peakino Coil Shunting OSClHator AsymmefnCGf Suffer JZ>ifferent/aT,rT^ Triads Tnode Cathode Follower Triode Circuit -o G nd. F i g . 9. Schematic c i r c u i t diagram o f the t i m i n g - p i p g e n e r a t o r U.B.C. A p r i l 18, 1951 F i g . 11. O s c i l l o g r a m o f a f a u l t a t t h e f a r end o f a 9 5 1-foot s e c t i o n o f RG/gU c o a x i a l c a b l e . Top - compressed t r a c e Bottom - expanded t r a c e ( t h e t i m i n g - p i p I n t e r v a l i s 0.224 m i c r o s e c o n d s ) F i g . 12. O s c i l l o g r a m o f a f a u l t l o c a t e d a t 951A f e e t i n a 1788.2-foot s e c t i o n o f c o a x i a l c a b l e . Top - compressed t r a c e Bottom - expanded t r a c e ( t h e t i m i n g - p i p i n t e r v a l i s 0.224 mi c r o s e c o n d s ) F i g . 13. O s c i l l o g r a m o f a f a u l t o f the f a r end o f a 1241. I - f o o t s e c t i o n o f c o a x i a l l i n e . Top - compressed t r a c e Bottom - expanded t r a c e ( t h e t i m i n g - p i p I n t e r v a l i s 0.224 m i c r o s e c o n d s ) F i g . 14. Oscillogram of a f a u l t at the f a r end of a 1241.1-foot s e c t i o n of c o a x i a l cable and a d i s c o n t i n u i t y (20 ohms s e r i e s r e 3 i s t o r ) a t 2^9.7 f e e t F i g . 1 5 . Oscillogram of a f a u l t l o c a t e d at 289 .7 f e e t i n a 1241.1-foot s e c t i o n of c o a x i a l cable. Thi3 i s an expand trace showing only the f i r s t two wave forms. The t l m l n g -p l p I n t e r v a l i s 0.224 mieroseconds. 6 5 Abnormal Trace F i g . l b . O s c i l l o g r a m o f a f a u l t a t t h e f a r end o f a 1241.1- f o o t s e c t i o n o f c o a x i a l c a b l e and a d i s c o n t i n u i t y a t 2 8 9 . 7 f e e t . The br e a k -down v o l t a g e used was 6 0 c y c l e a.c. The t i m i n g - p i p i n t e r v a l i s 0.224 m i c r o s e c o n d s . V l l LITERATURE CITED 66 1. S t e v e n s , R. F, and S t r i n g f i e l d , T. W., " T r a n s m i s s i o n L i n e s F a u l t - L o c a t o r u s i n g F a u l t - G e n e r a t e d Surges", T r a n s -a c t i o n s o f t h e American I n s t i t u t e o f E l e c t r i c a l E n g i n e e r s , New York, V o l . 67, P a r t 1, pp. 1168-78, August, 194-8. 2. L o z e s , J . P. J r . , "Improved S u r g e - R e f l e c t i o n System L o c a t e s C a b l e F a u l t s " . E l e c t r i c a l World. A l b a n y , N. Y., V o l . I 3 0 , No. 19, pp. 89-91 , November 6, 194-8. 3 . R o b e r t s , F. F., "New Methods f o r L o c a t i n g Gable F a u l t s P a r t i c u l a r l y on H i g h Frequency C a b l e s " , J o u r n a l o f t h e I n s t i t u t e o f E l e c t r i c a l Engineers,, London, V o l . 93 , P a r t 3 , pp. 389-95, November, 194-6. 4-. S p a u l d i n g , L. R. and Diemond, C. C , "A T r a n s i e n t F a u l t - L o c a t o r f o r H i g h V o l t a g e T r a n s m i s s i o n L i n e s " , T r a n s a c t i o n s o f the American I n s t i t u t e o f E l e c t r i c a l  E n g i n e e r s . New York, V o l . 68, P a r t 2, pp. 1005-10, 194-9. 5. G l a s o e , G. N. and Lebacoz, J . V., P u l s e G e n e r a t o r s . S e r i e s number 5, pp. 175-213, M a s s a c h u s e t t s I n s t i t u t e o f Technology R a d i a t i o n L a b o r a t o r y S e r i e s , New Yor k , McGraw-H i l l Book Go. I n c . , 194-8. 6. J a e g a r , J . C., I n t r o d u c t i o n t o the L a P l a c e T r a n s f o r - m a t i o n w i t h E n g i n e e r i n g A p p l i c a t i o n s , Melbourne, r e p r o -duced by C o u n c i l f o r S c i e n t i f i c and I n d u s t r i a l R e s e a r c h , pp. 89-113, J a n u a r y , 1$H6. 6 7 .1. Gardner, M, F. and Barnes, J . L., T r a n s i e n t s l n L i n e a r Systems. V o l . 1 , New York, J o h n W i l e y and Sons I n c . , 1 9 4 2 . 8 . C o u l t h a r d , W. B.,. T r a n s i e n t s I n E l e c t r i c C i r c u i t s . London, S i r I s a a c Pitman and Sons L t d . , pp. 1 0 9 - 1 1 5 , 1 9 4 6 . 9. D o w e l l , J . C., " A t t e n u a t i o n and S u c c e s s i v e R e f l e c -t i o n s o f T r a v e l i n g Waves", T r a n s a c t i o n s o f American , I n s t i t u t e o f E l e c t r i c a l E n g i n e e r s , New York, V o l . 5 0 , pp. 5 5 1 - 5 6 0 , June, 1 9 3 1 . 1 0 . Bewley, L. V., " T r a v e l i n g Waves on T r a n s m i s s i o n System", T r a n s a c t i o n s o f American I n s t i t u t e o f E l e c t r i c a l  E n g i n e e r s , New Y o r k , V o l . 5 0 , P a r t 2 , pp. 5 3 2 - 5 0 , 1 9 3 L 1 1 . Ware, L. A., and Reed, H. R., Communication C i r c u i t s , second ed. , New Y o r k , John W i l e y and Sons, I n c . , 1 9 4 4 . 1 2 . N a y l o r , T. K., The Echo-Ranger A F a u l t - l o c a t o r f o r Power C a b l e s , M a s t e r 1 s Thesl3 i n the Department o f E l e c t r i c a l E n g i n e e r i n g , U n i v e r s i t y o f B r i t i s h Columbia, September, 1 9 4 8 . 1 3 . - C o s s o r , A. C. L t d . , C o s s o r Double Beam O s c i l l o g r a p h Model 339 I n s t r u c t i o n Manual. CB. 5 5 E . , S i x t h ed., A. C. C o s s o r L t d . , London, pp. 1 5 - 1 8 , F e b r u a r y , 1 9 4 6 . 1 4 . B l a c k b u r n , J . F., Components Handbook S e r i e s 1 7 , pp. 1 5 - 3 2 , M a s s a c h u s e t t s I n s t i t u t e o f Techology R a d i a t i o n L a b o r a t o r y S e r i e s , New Y o r k , M c G r a w - H i l l Book Co. I n c . , 1 9 4 9 . V l l l BIBLIOGRAPHY 1. A l l l b o n e , T. E., Hawley, W. G., and P e r r y , P. R., "Cathode-Ray O s c i l l o g r a p h i c S t u d i e s o f Surge Phenomena", J o u r n a l o f t h e I n s t i t u t e o f E l e c t r i c a l E n g i n e e r s , London, V o l . 75, No. 4-55, pp. 670~6gg, November, 1934-. 2. B e r g , E. J . , H e a v l s l d e ! s O p e r a t i o n a l C a l c u l u s , New York, M c G r a w - H i l l Book Co. I n c . , 1929. 3. Blankmeyer, W. H., "Power L i n e F a u l t - L o c a t o r " , E l e c t r o n i c s , New York, V o l . 17, p. 166, J a n u a r y , 194-6. h. • B r i t i s h E l e c t r i c a l and A l l i e d I n d u s t r i e s R e s e a r c h A s s o c i a t i o n , Surge Phenomena, seven y e a r s ' r e s e a r c h f o r the C e n t r a l E l e c t r i c i t y Board (1933-194-0) R e f e r e n c e s/T35, London, 194-1. 5. Buck, F. W., "Condenser Pop L o c a t e s A e r i a l C a b l e F a u l t s " , E l e c t r i c a l World, A l b a n y , N. Y., V o l . 125-11, p. I l l , May 25, 194-6. 6. Bush, V., O p e r a t i o n a l C i r c u i t A n a l y s i s , New York, J o h n W i l e y and Sons, 1929. 7. C e n t r a l S t a t i o n E n g i n e e r s o f t h e Westlnghouse E l e c -t r i c & M a n u f a c t u r i n g Company, E l e c t r i c a l T r a n s m i s s i o n  and D i s t r i b u t i o n R e f e r e n c e Book, t h i r d ed., C h i c a g o , The L a k e s i d e P r e s s , R. R. D o n n e l l e y and Sons Company, 1944. . . . 69 $. C h u r c h i l l , R. V,} Modern O p e r a t i o n a l Mathematics I n E n g i n e e r i n g . F i r s t ed., New York, M c G r a w - H i l l Book Co. I n c . , 1944. 9 . D a v i s , R., "Impulse S t r e n g t h o f H i g h - V o l t a g s C a b l e s " , J o u r n a l o f t h e I n s t i t u t e o f E l e c t r i c a l E n g i n e e r s , London, P a r t 1, V o l . gS - 8 9 , pp. 199^.202, 194l~42. 10. Evans, D. J . , " L o c a t i o n o f F l a s h o v e r s on T r a n s m i s s i o n L i n e s " , M a s t e r s * T h e s i s i n Department of E l e c t r i c a l E n g i n e e r i n g , U n i v e r s i t y o f B r i t i s h Columbia, 194-9. 11. E v e r i t t , W. L,, Communication E n g i n e e r i n g , f i r s t ed., New York, M c G r a w - H i l l Book Co. I n c . , 1932. 12. G o l d l n g , E. W., E l e c t r i c a l Measurements and Measur- i n g I n s t r u m e n t s , t h i r d ed., London, S i r I s a a c P i t m a n and Sons L t d . , 194-6. 13. H o n n e l l , M. A., " L o c a t i o n o f L i n e F a u l t s " , E l e c t r o n i c s . New York, V o l . 17, I I , p..110, November, 1944. 14-. Jahnke, E., and Emde, F., T a b l e of F u n c t i o n s w i t h Formulae and Curves, f o u r t h ed., New York, Dover P u b l i c a -t i o n s , 194-5. 15. Lempert, I . E., and F e l d t , R., "The 5 RP M u l t i b a n d Tube", an I n t e n s l f i e r - T y p e Cathode-Ray Tube f o r H i g h -V o l t a g e O p e r a t i o n , New York, P r o c e e d i n g s o f the I n s t i t u t e  o f R a d i o E n g i n e e r s , V o l . 34-, No. 7, pp. 4-32-4-4-0, J u l y , 1946. 16. L e s l i e , J . R., and K i d d , K. H., "The L i n a s c o p e " Echo-Ranging Type F a u l t - L o c a t o r f o r H i g h V o l t a g e L i n e s , T r a n s a c t i o n s o f the American I n s t i t u t e o f E l e c t r i c a l  E n g i n e e r s . New York, V o l . 67, P a r t 2, pp. 1162-6, 1948. 17. M o r g o u l i e s , 3., and F o u r m a r l e r , P., " L o c a l i z a t i o n s o f F a u l t s on Overhead L i n e s by Means o f Impulse Waves", Paper 3 G 7 o f Conference I n t e r n a t i o n a l e des Grands Reseaux E l e c t r i q u e s a Haute T e n s i o n , P a r i s , F r a n c e , G a u t h i e r -V l l l a r s , June 24 to J u l y 3 , 1948. 18. Noakes, F., "High Frequency Method f o r L o c a t i o n o f F a u l t s i n Power C a b l e s " , E l e c t r i c a l News. V o l . 53, No. 13, pp. 46-7 , J u l y 1, 1944. 19. N o l a s , E. J . , "High Frequency Method o f L o c a t i n g Power Cable F a u l t s " , M a s t e r ' s T h e s i s l n Department o f E l e c t r i c a l E n g i n e e r i n g , U n i v e r s i t y o f B r i t i s h Columbia, August, 1947. 20. P u c k l e , U. 3.,. Times Bases. New York, J o h n W i l e y and Sons I n c . , 1943. 21. Ramo, 3., and Whinnery, J . R., F i e l d s and Waves l n Modern R a d i o f New York, John W i l e y and Sons I n c . , 1932. 22. Savage, J . H. " L o c a l i z a t i o n o f F a u l t s i n Low V o l t a g e C a b l e s w i t h S p e c i a l R e f e r e n c e t o F a c t o r y Technique", J o u r n a l o f t h e I n s t i t u t e o f E l e c t r i c a l E n g i n e e r s . London, V o l . 9 2 , P a r t 2, pp. 580-93, December, 1945. 71 Simmons, D. M. " C a l c u l a t i o n o f t h e E l e c t r i c a l P roblems o f Underground C a b l e s " , The E l e c t r i c a l J ournal ,, V o l . 29, May to November, 1932. S k i l l i n g , H. H., T r a n s i e n t s i n E l e c t r i c C u r r e n t s r f i r s t ed., New York, M c G r a w - H i l l Book Co. I n c . , 1937. S t a r r , A. T. and Gooding, H. T., " L o c a l i z a t i o n o f F l a s h i n g F a u l t s l n C a b l e s , J o u r n a l o f the I n s t i t u t e o f  E l e c t r i c a l E n g i n e e r s . London, V o l . No. 510, pp. 699-709, June, 1939. Terman, E. F., Radio E n g i n e e r s Handbook, f i r s t ed., New York, M c G r a w - H i l l Book Go. I n c . , 1943. 

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