UBC Theses and Dissertations

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UBC Theses and Dissertations

A study of the high-tension magneto ignition system with special reference to the source and elimination… Smith, Wilbert Brockhouse 1934

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Tho  p r o d u c t i o n o f ene i aprrri; i n v o i v o a « c y c l e o f J  o p a r s t i o o e K h i c h , f o r t h e e o n v o i r l a a e o o f a w e l y u i B eaei r e f e r ence, r.sy be r.ivitJefi i n t o e i x rath«r d f u t i n e t p e x i o a a ,  no  •follows: (l)  "Burin*? t h e £3ret p o r i o t l t h o lot? v o l t s p o  or  primary  a h o r t c i r c u i f c o d h;; tho ti£=Iii;? eontccfca,  ersBtare  rotates o c a r t n i n curront  This current  s t o r e s its tho t&igmtlc  snorter which I s t a r  r.:»d no t h e  I s peuarntec i n t h i s 2 circuit  coil.  joules of  i s uaod to s u p p l y t h o currant; t o t h o sparfe  plui?, together v?i th the I n c i d e n t a l loseos* A few nacrofioeonds ho f o r e n s p a r k i s d e s i r e d s t the  (?) plug  e ears opona t h o tirelng c o n t a c t s , thus fcresSdUig the? p i ' i a -  sry c i r c u i t .  Th® pxim&vy c u r r e n t flocro^soa r a p i d l y , i n d u c i n g  high voltofpea So both p r i s e r y end tseeonczory w J n a i n g a .  *£Ms  high s e c o n d a r y v o l t s go clisrgss up t h e a t r a y aoccnfisiry e n p n c i t i e s to n s u f f i c i e n t l y hi{£h p o t e n t i a l t o tsrask Sojns th© gss be tee cm the e l s e t r e s e s o f t h n spss& p l u g * # p e r i o d 2 i s t ofcefauna i s F « B «  ffheorsr  (5)  of.,.Iftdue.Qa ¥ o I t S | M , . t l l . J ^ ^  JUsbos**} pftpor: " tlG,th«is?itieal r3  £ariod 5 c o n s i s t s o f t h o d i s c h a r g e o f tlw 3aec*idftr y t  r,feray csp&eifcles t h r o u g h tho icmcfe, «?bic!t e r e incSacfcive, sue] the  3ine® u s u a l l y t h e v a l o r s o f c a p a c i t y una laducfcene©  5 a velvet! nr© r e l a t i v e l y s a a l l  &  aiifl mileos  •suppro&sox'a' art*  used tlu) r e s i i i t Q D e e i s a m l l , o s e i l l e - t l c m s o f s v o r j ' high f r e ~ eacney w i l l take p l a c e • (4)  F o l l o w i n g tho '3i.-&ohnrrM c f pxiriod 3 t h o reacdrrlng:  energy i n t h e e l o c f c r i c and- asimofclc c i r c u i t s i s dlc-aipntotf i n thrr jip.nri:., between t h e e l e c t r o d e s  (5)  o f t h e spark pl'ug.  JI120 t o high spoocls o r improper stljastr^oafc o f tho  timing contacts,  i t l a p o s s i b l e th:;t tho p r i j a o r y nay fcocoKc  c h o r t c i r c u i t o a b e f o r e «11 tho <cmarp;y i o ciisfilpntou i n t h e s p a r i i , I K r/hieh ense t h o rosnirifuif? e n o r ^ * i s f.ividoo bets/eon tli© s p a r k and .rotarninf: i n t o th© prlrssr;? c i r c u i t *  fiie c i r c u i t ramalm  (6)  g t i V t f t a z . t S a l l ^ tiood Tor a con-  s i d e r a i l a S i n e , period 6, u n t i l tho s r c m t u r e hm r o t a t e s s i a f f i c i n n t l ^ f o r too c y c l e to bogSn CYS* a g a i n f o r the p r o d u c t i o n of  t h e s s x i sparks  Pr-aC-IilPTlOlT OF /.PH:^4?i),>, 'i'iio raagjieto usnc i s  model 40 ac- jifcosB en P i s t o 1 mounted on the t e s t ba^o.  8  those i n v e s t i g a t i o n s v a u s I d ^ i a  w i t h t h e c o v e r s reiAOvao" cu8  It sa.i d r i v e n a t 900 rpm through' a  gear t r a i n f r o a the s r a e h r o a o u a sjotor Kfcieh o p e r a t e a fcbe t i m i n g c o n t a c t s f o r G CfsBorai E l e c t r i c <mtbo6e r/iy o s c i l l o g r a p h . Tliis eneuroa t h a t t h o v a r i o u s phmzmmm. s s r e n l t c s ^ s el'roniosa T;I th fehs c a c i l l o f - r a p h o  J^ine sni.1uytr.cnt  in  ayn-  o b t M nofl  ~ DicrofijetQr e r r a i i g e r / m t t?fctnch*j<$ to tho rcjf-ialor t i m i n g lever  tho msgnoto*  p3ttg Y&ZQ  £teto&«  Leads i r e : : the sagnato to t h o apart:  of o r c i i K s i j ; if?nitSon oa!>Io eseept whore oiherwiae  f h c nperJL plugs usofi t i c r e ; en AC n u t o K o b i l o  C l o o a v i a t i o n p l u g nre Th5J set-up,  p l a ^ . as  epecln.1 p l u ^ t o be ucscrlho£ l a t e r *  t o g e t h e r vikh  a per 11 en of the n n p l i f i o r ueod  is  ciotorminiiift the c u r r e n t wave f o r i o , i s shovrn on P i s t e 2<* 1/0%' froqueac;;- o s c i l l o g r a m  v. ore  token on a Meeting--  house 6 element o s c i l l o g r a p h * d i r e c t l y v;hon r o a r i h i e , c r rneans c f vacuus tube a m p l i f i e r s whea e i t h e r the v o l t a g e e a r r e a t s ware herons tho £ep -e o l the t n o t r u r x m t , t  i n s e r t i o n o f tho v i f c r n t o r oi-v.- ent constants  to too g r e a t an e x t e n t  c  VJOUIC  altar  or  o r irhen t&e  the c i r c u i t  L 0*meral h l o c t r i e cfithocio  T^-i; o s c i l l o g r a p h t a s used to cbfcnSn o u c S l l o i r r a n s o f the h i f r h f r e q u o B c v components o f "both the v o l t a g e s  am. c o r r a u t e .  A  PLATE 1.  VXAH  2  r e s i s t a n c e c l a p - v o l t a p e n i r i t i o r isorvod t o reduce t h e v o l t e - p e a to v a l u e s s u i t a b l e f o r a p p l y i n g t o t h o o s c i l l o g r a p h  pistes.  deflection  C u r r e n t t r a c e s VQXQ t o k e n t>y osipli£^ii3£ t h e v o l t a g e  drop s e r o a e a 3J?0 efea v & r i a o l o r o o i a t i m e o amplifior*  srifch & ts-o s t a g e .  f i i s above i t a n t i o B s f t a a p l i f i s r -woo c o i i a t r u c t o t l o s  follows*  vijo o s c i l l a t i o n c o i l s wore removed f r o n t h o t i m i n g  wave o s c i l l a t o r -on t h o c a t h o d e r a y o s c i l l o g r a p h and -a p l u g i n o r r a B g e r L s n t o u b s t i t u t o d , vrhlch i n s e r t e d a 1 5 , 0 0 0 ohia r a s i s t nnce i n t h e p l a t o c i r c u i t o f the tuho and eonnoctod t h e R e f l e c t i o n p l a t e s serosa  this resistance*  ?he plat©  f r o m on e x t e r n a l a m p l i f i e r c o n s i s t i n g o f a hl~tm  current  tali©, tms .  s e n t t h r o u g h t h e 10,000 0!® grid- losJs r e s i s t o r i n t h e o s c i l l a t o r , c o i m o e t i o n t w i i i g oMtdjood  means o f t h i n l«go i n s e r t e d  between t h e e n d s o f the m a l e t o r wi& ttia laotmtiag c l i p s ,  iliia  c u r r e n t p r o v i d e d t h e g r i d b i o s f o r t h o 50 w a t t turn froc. t h o 13 d r o p i n t h e 10,000 oh a r e s i s t a n c e *  Aa e precaution spoinat  6&asm t o t h e 50 w a t t s t a g e duo t o l a d * o f g r i d b i a s , t h o p l a t e o a r r o a t o f t h e s x t o r n a l a m p l i f i e r •eras a l o e s e n t t h r o u g h a r e l a j ? v*hich i n t e r r u p t e d  t h o AC power s u p p l y s h m i l t l t h i o c u r r e n t  foil.,  O t h e r tip psrs. t u s i n c l u d e d 3 B u r t e s t hod o ro.:* o s c i l l o scope w i t h which o v i s u a l  stttd> o f t h o i m v a f o r n s wee fnaflo, s  t h r e e tufeo r a d i o s e t w h i c h was? used f o r m o n i t o r i n g i n t e r f e r e n e o , nod m i s c e l l a n e o u s t h e rnagnoto  constants.  the r a d i o  a p p a r a t u s usee" i n d o t G r o i n i n g  1.  tausmc  cimiiT,' The e o n s t r u e felon o f t h e s e g u e t o xsae ouch t h a t t h o  e o i l a r e s s l n o - d s t a t i o n e r y one t h e r o t a t i o n o f t h e orr.oturo . a i r o c t o f l th© f l u x t h r o u g h t h e c o i l s f i r s t i n one? d i r e c t i o n una  than i n tho o t h e r *  ? h s t i d i n g c o n t a c t s were o p e r a t e d by e eara  on t h e end o f t h e armature shntt  ancl change o f t i i a i n g was  s e c u r o u b y r o c k i n g tho e n t i r e c o i l aosocibljy about t h o 0r13n.tu.ro axis*  Figure  1 shows a aehoreatic d i a g r a m o f the m i m e t i c  c u i t s h o e i n g : the. p r i n c i p a l dissensions.*  •.g&p was. O.OjJ. cm.  cir-  f h e I c a g t h - .©£ th© a i r  •. .  2-. K&ECTBIC&T* CIS-GUI?. The e l e c t r i c a l c i r c u i t i s shcv?n c l i a g r a s a t i c a l l j ? i n f i g u r e 2«  Tnlz  c i r c u i t represents conditiowo.prevailing  f a i r oograa o r a e e a r a e j tm& s i l l  to a  f o r e fcha b a s i c c i r c u i t f o r  tho - s a t b o f t s t l o a l e n a X y a i a w h i c h f o l l o w s I n a l a t e r s e c t i o n *  It  ma,;? oe v / e l l t o note- t h a t some o f tnea©- so c a l l e d c o n s t a n t s &rs not c o n s t a n t  hut a r e ftraofciosa o f c u r r a n t o r f r e q u e n c y *  this  i n t r o d u c e s complications I n t o t h e jsstfaesatlcal a n a l y s i s as  &G tilting 3.  mil  i t d i f f i c u l t t o o b t a i n s u i t a b l e numerical values.  3DS5;^IJIA?Io:i 0 ? SHS 3C0SI,AHY 3?HAY C/.MClrT. A stanflorft r e s o n a n t e i r c o . i t c o n s i s t i n g o f a kiwmi inductance i n p a r a l l e l  Kith  a v a r i a b l e coiidaosor o f known  c o p a e i t r srao i n s e r t e d i n t h o p l a t e c i r c u i t o f a ut 224 a e r e o n g r i d tucn connected oaeillotor,  as i n f i g u r e 3 t o o p e r a t e na a d j - n o t r o n  Tho r e s u l t i n g o s c i l l a t i o n r;as viov.oo o n tho  screen o f t h e cathode r a y o s c i l l o s c o p e o r locator: with the rodic set.  Ths s e c o n d a r y o f t h e nagneto was t h e n c o n n e c t e d i n  p a r a l l e l r i t f c t h o v a r i a b l e condonaor mm f o r t h e esfss f r e q u e n c y  s spreviously*  the l a t t e r  adjusted  9lm d e c r e a s e i n c a p a c i t y  cf th© s t a n d a r d c o n d e n s e r t?as t h e n nuKcr.i c a l l y e q u a l t o t h o s t r a y secondary c a p a c i t y a t that freqaoncy. c h o o s i n g veluea o f inductance  By s u i t a b l y  and c a p a c i t y Dcasaraments wcyo  nade over a ^ide. r a n g e o f f r e q u e n c i e s , a n d the v a l a o s found p l o t t e d a g a i n s t f r e q u e n c y  thus  a s in f i g u r e 4 , The e f f e c t o f  t h o i n d u c t a n c e o f t h e s e c o n d a r y B i n d i n g vm& n e g l e c t e d s i n c e i t weo vers? l a r g o a s compared tvifch t h o o s c i l l a t i n g bK-?;.i^i:r>?jo!? O F S E K %mra on m&  inductances.  sxiDxa&u  A s e a r c h c o i l c o n s i s t i n g o f 10 t u r n s o f n o . 30 M C t . l r e V - 2 S woantl o n t h e l a m i n a t e s c o r e a s n e a r s s p o s s i b l e t o  the zsoir* c o i l s .  ZBVO f o r o s o f t h o  r o t a t i o n a l v o l t a g e genera-  toe I n t h i s c o i l a n d i n t h e p r i m a r y w i n d i n g t?cre triewod  fcanoously  slcral-  on trie • leotlnfthouso o s c i l l o g r a p h s a d t h e s e r i e s  resistance© s o a d j u s t e d t h a t t h e d e f l e c t i o n s vara t h e etna©. £s the s e n s i t i v i t y o f the v i b r a t o r s teas found t o b e v e r y  neorly  i d e n t i c a l , t h o t u r n s r a t i o was t a k e n a s t h o r a t i o o f t h e t o t a l  a o r l o s r e s i s t a n c e s , tho value being of p r i o r y  p i v i n g s s t h e number  tarns-2?3* fho r a t i o o f t u r n s between t h o p r i m a r y a n d s e c o n d a r y  •»"fia f o u n d by applying windings  fcncsu  AC v o l t a g e s t o the respoet5 vo  and ««asuring t h o v o l t a g e g e n e r a t e d i n t h e o t h e r .  5?his r a t i o \-?sc f o u n d .to bo 5 0 : 1 w h i c h gave a s tho number o f seconder;- t u r n s , 15,7GG«  i^mmsiBimm  OF  mmmicss*  The s e l f i n d u c t a n c e o f t h e s a g a s t o secondary measured by aeana o f tm Anderson I n d u c t a n c e B r i d g e ,  i;  f r e q u e n c y range o f 300 t o 1000  cycles  e  was  for a  and. was found t o d i f f e r  l i t t l e frora j>0 h e n r y s o v e r t h i s f r e q u e n c y r a n g e .  t'he p r i m a r y  i n a n e t a n c e was aieasured w i t h on AC a s s e t e r and v o l t m e t e r a t 60 c y c l e s f o r a c u r r e n t range o f 0.1 t o 1.0 amperes and the v a l u e was found t o be c o n s t a n t a t 0.02  henrya.  Because o f t h e v e r y  h i g h r a t i o or* t u r n s and t h e f a c t t h a t t h e e o i l s were c o n n e c t e d t o g e t h e r i n t e r n a l l y , c o n v e n t i o n a l methods o f measuring  the  m u t u a l i n d u c t a n c e c o u l d n o t be u s e d , so the c o e f f i c i e n t o f c o u p l i n g K> was found f r o a the r e l a t i o n the m u t u a l i n d u c t a n c e c a l o u l a t e d .  n^/n-  x 1 - IC  A proof o f this r e l a t i o n i s  g i v e n i n iippendiK I .  P r o a t h i s r e l a t i o n K was found t o be  0.9?  henry.  ana K t o be 0.75  M ^ B C T K A f l t f f l 0? m  and  SSUCSD/iEY !5FFE01?JfB HSSIS^AESIS*  -In o r d e r t o d e t e r m i n e th©  e f f e c t i v e r e s i s t a n c e o f tho  secondary w i n d i n g a t v a r y i n g f r e q u e n c i e s , t h o scheme shown i n the  f i g u r e 5 «?as u s e d ,  v a r i a b l e condcaiser G was v a r i e d u n t i l  the power f a c t o r o f the c i r c u i t C, E^,  r  8  and the o s c i l l a -  t o r o u t p u t , became u n i t y a s i n d i c a t e d by the vacuum tube v o l t ~ rioter,  "he v a r i a b l e r e s i s t a n c e lip was t h e n s u b s t i t u t e d f o r  t h e n a g n e t o secondary and v a r i a b l e c o n d e n s e r , I-U., L j . and  C,  and a d j u s t e d so t h a t the vacuum tube v o l t e e t e r r e a d the ssiae a s f o r m e r l y , when R  p  s 3-^.  I n t h i s n a n u s r the e f f e c t i v e  r e s i s t a n c e o f the magneto secondary was d e t e m i n e d f o r a  f r e q u e n c y r a n g e o f 600 t o 5500 c y c l e s *  Figure 6 i s a graph  showing the v a r i a t i o n , o f t h i s r e s i s t a n c e with  frequency,  fhe  d i r e c t c u r r e n t r e s i s t a n c e u a s o n l y 3000 oJaas b u t a s may be aeeu, t h e e f f e c t i v e r e s i s t a n c e i s e n c m o u s l y g r e a t e r , r e a c h i n g 700,000 ohras a t t h e r e s o n a n t f r e q u e n c y o f 3500 c y c l e s .  r^easurcfasnt o f t h e d i r e c t c u r r e n t r e s i s t a n c e o f t h e w i n d i n g s was made w i t h an a n n e t e r and v o l t e s t e r , and t h e p r i & ~ a r y c o n d e n s e r V7as no a sure d by means o f a c a p a c i t y b r i d g e , a s was  the c a p a c i t y o f t h e s p a r k p l a g e *  So u r e a l * p r e t e n c e a t  p r e c i s i o n was made in. t h e d e t e r m i n a t i o n  o f any o f t h e magneto  c o n s t a n t s s i n c e i t was f o u n d t h a t a l a r g e , u n a v o i d a b l e e x p e r i * d e n t a l e r r o r was a l w a y s p r e s e n t .  Jtar i n s t a n c e , an i a p e r e e p -  t i b l e movement o f t h e armature caused, a s nueh a s 3% e r r o r i n the measurement o f i n d u c t a n c e . l i s t o f the c i r c u i t c o n s t a n t s the a m a t u r e  teae&iately  Tlx?, f e - l l o s & s g t a b i c g i v e s a dsteraincd f o r the p o s i t i o n o f  f o l l o w i n g th© o p e n i n g o f t h e t i m i n g  contacts.  <  273 0.02  Si  z u  2*2  Henry  0.11 Oiooa 0.041 rafd. 0.57 0.75 Kenry 15.700 30 Henrys 5 ooo Ohjss 700,000 Cans 9  100 a  3 10-6  10  cmfd. tanfd.  miafd* Henry  P r a c t i c a l l y constant 25.0. r e s i a t a n c e K l e s condenser Conputed f r o m resonance P r a c t i c a l l y constant XuCo r e s i s t a n c e E f f e c t i v e r e s i s t a n c e a t 5500 cycles V a l u e a t 5500 c y c l e s AO s p a r k p l u g 01eo s p a r k p l u g Computed a p p r o x i m a t e l y  i i s t h e magneto a r o a t u r e l i n k i n g t h o w i r i n g s changes and  thera. the  I f t h e v a l u e s o f t h e maf  r o t a t e s , the nagnetic fins: induces  rotational safe  o f t h e p e r o a n e a t taaguets, and  r e l u c t a n c e s o f t h e v a r i o u s p a t h s ho known» e q u a t i o n s  he w r i t t e n g i v i n g t h e f l u x d i s t r i b u t i o n a n d  duced by i t s change w i t h r o t a t i o n . i n t o s a v e forrao a s i n f i g u r e ?.  I n t h e a c t u a l magneto  dotted curves.  As may  srf.ll r e s e o b l e  modified  bo n o t e d t h e v o l t a g e  considerations,  la©  short tiae necessary c i r c u i t e d primary, function.  r o t a t i o n a l emf  by  f r o a the  cycle fh©  i s required only f o r  a f t e r w h i c h i t perform® no  &esi~  fcllowing  to e s t a b l i s h a c u r r e n t 1 i n t h e  A g a i n , when t h e  how-  s  induced i n the  r e a c h e s - a l a r g e v a l u e o v e r a.-very s h o r t p e r i o d ,  r a b i l i t y o f each a *?ave foa-ri i s a p p a r e n t  plot  s o r e c l o s e l y the  c o i l s i s p r a c t i c a l l y scro f o r the g r e a t e r p a r t of the and  can  the v o l t a g e s i n -  'fhese e q u a t i o n s w i l l  e v e r , t h e s e wave f o r e s w i l l be c o n s i d e r a b l y  f r i n g i n g a n d l e a k a g e , and  in  the  short  farther useful  timing contacts close,  i f there i s  an a p p r e c i a b l e o a f i n the c i r c u i t , the r e s u l t i n g t r a n s i e n t  may  p o s s i b l y p r o d u c e a s p a r k a t the p l u g a t a n i m p r o p e r t l c i s .  The  a c t u a l s h a p e o f the  r o t a t i o n a l v o l t a g e safe i s immaterial  so  long as i t i s able t o e s t a b l i s h the r e q u i s i t e c u r r e n t I preced i n g the  o p e n i n g o f the  tiding  a s n o o t h wave s h a p e i s t o be OPTSXIIG OF  c o n t a c t s , but  i t i s obvious t h a t  preferred.  SIT, TlI'-nHG CQVZAG?:!. uhen  a spark  i s d e s i r e d a t the p l u g , t h e  timing  c o n t a c t s a r e s e p a r a t e d b y t h e c a n , t h u s c r e a k i n g t h e prietary Glrcait*' Tight  K e f e r r i n g - t o f i g u r e 2, (mad o m i t t i n g a l l t o t h e  o f TI) i t i s s e e n t h a t o p e n i n g t h e t i m i n g c o n t a c t s A i s  the .same" a s suddenly i n s e r t i n g t h e condenser cuit*  i n t o the c i r -  S h i s nay be t r e a t e d -so. i f t h e c i r c u i t v/ere p r e v i o u s l y  dead ana a r e v e r s e c u r r e n t 1 were s u d d e n l y a p p l i e d a t t h e s w i t c h A, i n w h i c h case t h e c u r r e n t I w i l l d i v i d e between t h e condenser 0^ and t h e t r a n s f o r m e r i n t h e r a t i o o f t h e i r tances.  admit-  L e t t h e c u r r e n t through t h e c o n d e n s e r 0^ and t h e r e -  fore the inductance  B  a t a n y t i n e a f t e r t = 0, be i • §  C a l c u l u s i s need* . See A p g e M i s I I a ^ I  admittance, of- condenser adm'iTtanceof  Trans-farmer  -  an**  Candcwsef"  U s i n g H e a v i s i d e ' s n o t a t i o n and l e t t i n g t h e o p e r a t o r d/dt be denoted by p„ t h e ad&itt&nee  o p e r a t o r o f t h e condenser  C?2 i o i c i s e d i a t e l y seen t o be C^P, end t h a t o r t h e t r a n s f o r m e r . is  i  .  =  impeda nte. where  2^  /  .  2T/ — Z-^/z.^  i s t h e p r i i a a r y irapekl&nce s % -* L j P i s t h e m u t u a l impedance  S  i s t h e secondary  2  s H P^ 2  inpedaaee s Eg *' LgF' + l / o ^ l -  She t r a n s f o r m e r a d n i t t a n o e thus becomes on s u b s t i t u t i o n (_R, + L,P)(R± + UP -t '/cp)  -M P Z  Z  S u b s t i t u t i n g these a d m i t t a n c e s t7o have,  =  ^  i n the r e l a t i o n ^  c,p(R,i-L,p)(R^ft,p-hy c p)~c,M p i-r^i-upi-^ ) r  l  where  y = C,P(R, +LIP)(R^-fUP  asd  z  xP  +tf*p)  p  P  - C,P(R,+L,PX^  •  J  l  z  P  -C,M P* Z  tup*  '/Z^-aM^+Cfo-H-^p+'/w)  "She ©filiation 2. s 0 i s o f t h e f o u r t h o r d e r i n p , hence t h e r e w i l l  he two p a i r s o f r o o t s , which s a y h e both  bo t i i c o D p l e z , o r one r e a l and one c o m p l e x . th© q u a n t i t i e s i n v o l v e d i t i s a p p a r e n t all  tho r o o t s s r i i i b e n e g a t i v e .  real,  From t h e n a t u r e o f  that the real  parts o f  I f t h e r o o t s o f ?^ s 0 a r e  , there w i l l  be, i n general, three  possible general solutions according as the roots a r c real o r coiaplex.  Case 1 , wiiere  Case 2  S  shore  ft  a n d f^^- a r e r e a l :  a n d fi>-  are imaginary;  C a s e - 3 * "shore ^h, i s r e a l and 'i'he s e c o n d a r y  i s issgin&rys  i n d u c e d v o l t a g e , e=, c o r r e s p o n d i n g t o  a n y o f t h e a b o v e e q u a t i o n s raay be o b t a i n e d from, t h e r e l a t i o n e^ s -K d i ^ / d t a n d w i l l h a v e e s s e n t i a l l y t h e same wave f o r a a s the prinary c u r r e n t .  That p o r t i o n o f t h i s v o l t a g e  appears  a c r o s s the secondary  circuit  wave 'form o f t h e magneto  which  d i s t r i b u t e d c a p a c i t y i s t h o open a n d stay be e v a l u a t e d i f t h e  .magneto, c o n s t a n t s a r e known. Fron equation  c a n be o b t a i n e d t w o f r e q u e n c i e s o f  o s o i l 1 s t ion., £j. s /#,/2 7r s i n g l e frequency %  a m i f ? s / I /a 7t, ©ad from 2 » a  falZKm '2'm h y p e r b o l i c f u n c t i o n s o b v i -  s  ously g i v e u n i d i r e c t i o n a l • irapolses* If the c o e f f i c i e n t of c o u p l i n g i s p r a c t i c a l l y unity, 2 then  Ljt-g s II a n d the e q u a t i o n  x  0 beeoces a cubic i n p  8  which w i l l have on©, real root and one p a i r of roots v?iiioh say be either real or oonp£©3s:» 2 f the f o l l o w i n g uaaerlcal values f o r t h e circuit c o n s t a n t s are inserted i s e q u a t i o n ( 1 ) l  E  %  - 58  s 0.11  %  s i s  r 0*041 at  'Cg s 100 X l o " ^  s 0»02  %  2  •0  1  ,  K s 0-75 10  5  1  when s i m p l i f i e d , the e q u a t i o n S~ s O becomes„  T h i s factors^® i n t o th© f o l l o w i n g terss  • fp^Z.7 W^(p+teO lo+) P+0-9*l^ f  7  r  which g i v e s the f o l l o w i n g r o o t s f o r p P(  1-7  /0-7 iio*  P -  .9 y.10*-j I-7 x IO* •  3  ? = -1-7 y-10^ -f. 10.7^/0^ L  P  * = - 0 -9 * io*-tj  Sbsse roots isay be s u b s 1 1 1 u t e d  /v*  i n the . a p p r o p r i a t e  s o l u t i o n , n a o e l y ( 2 c ) . i n v/hleh c a s e we h a v e , s  •(, = 6-.  l^toih 10-7 uo*t-tB, sink. I0-7+10^1-t-a  fhe- constants J.^, 3 ^ ,  I * 7  IC}t  +B1S1* !-7i toHl  and B^,-are a m p l i t u d e c o n s t a n t s a n d  nay be e v a l u a t e d by H e a v i s i d e s E&panalon T h e o r e E , i f r e q u i r e d . This s o l u t i o n gives o n l y t h e one frequency o f oscillationj second.  f  2  =  ftiiZ 7? s 1.7 x  1 0 / 2 K - 2700 c y c l e s per 4  Shis f r e q u e n c y , though n o t i n v e r y c l o s e agreement  -15-  w i t h the o b s e r v e d v a l u e o f 5500 c y c l e s p e r second  0  serves to  i n d i c a t e t h e approximate n u n e r i e a l v a l u e t o be e x p e c t e d *  She  d i s c r e p a n c y between t h e c a l c u l a t e d and o b s e r v e d v a l u e s i s p o s s i b l y due t o t h e a&gneto o p e r a t i n g a t a d i f f e r e n t a n g l e o f armature d i s p l a c e i a e n t t h a n t h a t f o r which t h e a s g n e t c  con-  s t a n t s >?ere laeasored. EF#3COTE EJKJISSAECE OF A 3PAK/C ETSGHAROE. An a p p r o x i m a t e e x p r e s s i o n f o r t h e e f f e c t i v e  resist-  ance o f an e l e c t r i c spark d i s c h a r g e can be o b t a i n e d by making c e r t a i n a a s o a p t i o n s r e g a r d i n g the maipsre o f the d i s c h a r g e and the mechanism by which t h e c u r r e n t i s c a r r i e d *  I t i s assumed  t h a t the d i s c h a r g e i s c a r r i e d by n d r i f t o f e l e c t r o n s produced by ionise.I,ion c f t h e gases between the e l e c t r o d e s .  This i o n i -  z a t i o n aay be produoed i n i t i a l l y by t h e a p p l i c a t i o n o f a h i g h p o t e n t i a l g r a d i e n t o r by soise o t h e r mesas  f  but i s maintained  by c o l l i s i o n s o f the r a p i d l y moving e l e c t r o n s w i t h t h e g a s molecules*  She m i g r a t i o n c f the p o s i t i v e i o n s i s n e g l e c t e d *  She d i f f e r e n c e between a spark and a r c d i s c h a r g e i s t h a t i n the f o r m e r t h e d i s c h a r g e i s assumed t o be c a r r i e d n s i n l y by e l e c t r o n s l i b e r a t e d from the g a s e s between t h e e l e c t r o d e s , i v h i l e i n the l a t t e r the d i s c h a r g e i s c a r r i e d by e l e c t r o n s l i b e r a t e d f r o n the i n c a n d e s c e n t s u r f a c e s o f t h e e l e c t r o d e s . There i s however, c o n s i d e r a b l e o v e r l a p p i n g o f the phenomena 9  but f o r the sc>e o f s i m p l i c i t y t h i s i s n e g l e c t e d * #  e s charge on o i e l e c t r o n fa r mass o f an e l e c t r o n I* = number o f e l e c t r o n s p e r u n i t volume  d s s e e n f r e e path o f a n e l e c t r o n i n t h e d i r e c t i o n o f t h e . field v s average v e l o c i t y o f t h e e l e c t r o n i n the d i r e c t i o n o f the f i e l d 12 s v o l t a g e between t h e e l e c t r o d e s s s d i s t a n c e he t i r e e a t h e e l e c t r o d e s R * f i e l d strength o r p o t e n t i a l gradient & s c r o s s s e c t i o n a r e a o f t h e a pari: 2 s- c u r r e n t through t h e s p a r l : E a c h e l e c t r o n i n t h e f i e l d R i s a c c e l e r a t e d fey a n amount  a » Be * ms  P r o s m e c h a n i c s , t h e a v e r a g e v e l o c i t y v s</a£d  S u b s t i t u t i n g f o r a , v s / 5 e d i'  _  _  (1)  The c u r r e n t through t h e sparfc i s g i v e n by IsI'oAi?  ______________  I f i t i s assumed t h a t e a c h c o l l i s i o n o f a n e l e c t r o n  u n i o n i s e d aoleeule  'results i n the production  o f sore  ,  w i t h an  electrons,  i t raay b e shov;n t h a t t o a c l o s e a p p r o x i m a t i o n B ss 1 v  Substitution, i n (2) g i v e s J s I A e v  -ftft,e  2  g  d s g  I'he r e s i s t a n c e o f t h e spark t h e r e f o r e becomes V  St  S » T  The { j u a n t i t i e e e  ?  —  El 0  tn, a n d K a r e c o n s t a n t s a n d e i s  f i x e d b y t h e g e o m e t r y o f t h e s p a r k gap* an e l e c t r o n ,  C3)  She mean f r e e p a t h o f  d, vri 11, h o n e v e r , d e p e n d o n t h e d e n s i t y a n d com-  p o s i t i o n o f the gases involved.  I'or-j i t i s f o u n d b y e x p e r i m e n t  t h a t f o r a g i v e n s e t o f c o n d i t i o n s t h e v o l t a . e e 13 a c r o s s t h e gap i s c o n s t a n t  r e g a r d l e s s ' o f c u r r e n t changes s o l o n g a s s u c h  changes a r e s l o w as c o s p a r e d with the i o n i z a t i o n tic;e o f the gap*  this then leads to the c o n c l u s i o n , that the current den-  sity i n a n electric  spark i s constant f o r a g i v e n set o f .  conditions or e x p r e s s e d mathematically t  i s I  s  A  or  X»  where K  ?  s 2, IC E d e  2  . • - • - - (4)  I f the current through the s p a r k changes faster than the i o n i z a t i o n time o f the gap, the sectional area A does not have time to change and the q u a n t i t y  m s  becomes  c o n s t a n t s and the s p a r k acta as s pure r e s i s t a n c e .  If,, how-  e v e r t h e c u r r e n t changes a r e e x t r e m e l y r a p i d t h e nuraber of s  e l e c t r o n s p e r u n i t volume cannot change appreciably  8  that i s ,  H remains f o r the moaent approximately constants and the e x p r e s s i o n f o r t h e c u r r e n t becoaes I M H e A  a e &... #  _ _ „ _ * • . . . « . ( 5)  A closer study o f ( 5 ) leads t o a very i n t e r e s t i n g result,  A sudden s n a i l increase i n S w i l l result i n a large  increase i n 1* T h i s a b n o r a a l i n c r e a s e i n c u r r e n t w i l l i n t u r n produce a n abnormal i n c r e a s e i n Is w h i c h w i l l i a h e p l a c e much Gore s l o w l y depending  on t h e i o n i s a t i o n ticse o f the s p a r k .  Mm  I i s l a r g e a n d II i s l a r g e so i n o r d e r t h a t (jj) be s a t i s f i e d t h e r e sust b e a large decrease i n B w i t h i t s c o r r e s p o n d i n g decrease i n current»  Hence i t way r e a d i l y be a p p r e c i a t e d t h a t  en o s c i l l a t o r y d i s c h a r g e w i l l take p l a c e t h r o u g h t h e spark„ t h e f r e q u e n c y a n d wave f o r s b e i n g cone co-apples f u n c t i o n o f t h e q u a n t i t i e s i n v o l v e d , including the i o n i z a t i o n t i n e o f t h e  s p a r k and the n a t u r e o f t h e g a s e s b a t e o o n t h e e l e c t r o d e s * l a 1 . 7 e l l Jrnovrn that t h e v o l t a g e r e q u i r e d  It  cown a Eparfc g a p i s s u c h h i g h e r  t o break  thmi t h a t r e p a i r e d t o a a i n t a i i i  a d i s c h a r g e through i t . I n v i e w o f t h i s f a c t and t h o a b o v e doveiopstrnt  i t follows t h a t t h e r e i s considerable  tion f o rt a k i n g the voltage drop across  .lustlfica-  a epork t o be {n -f b i }  where' a and b a r e c o n s t a n t s depending o n t h e c o n d i t i o n s under t h i o l s t h e ®pwfk fc&fccs p l a c e wa& t h o p r o b a b l e f r e q u e n c y o f t h o discbai»ge. The constant® a a n d b % i l x not n o o ^ s s s r i l y r a s a i n  c o n s t a n t t h r o u g h o u t tfec entir© d u r a t i c - s o f t h e s p a M : v a r y as t h e c h a r a c t e r o f t h o s p a r k c h a n g e s .  e  b u t may  2hafc i s * t h e  valaes f o r a and © which h o l d f o r tho i n i t i a l  broaftdocm o f t h e  gap may bo d i f f e r e n t froja t h o v a l u e s w h i c h h o l d * f o r i n s t a n c e , for  t-n o s c i l l a t o r y discharge©  iiowevor, i t i s f o u n d  oxperiasn*-  t r . l l y t h a t a and b a r e p r a c t i c a l l y c o n s t a n t d u r i n g each separate ported o f the discharge.  Hence„ f o r a n a l y t i c a l par*,  pooos one taasfc bo c a r e f u l t o choose v a l u e s o f a a n d b w h i c h a r e a p p l i c a b l e * t o t h e p r o b l e m 5a bench* H?SA£DG*?J: OP I S S  us.  Ebon t h o v o l t a g e  across  the sparking  t i p s has b u i l t  up t o a s u f f i c i e n t v a l u e a , tho g a p b r e a k s down and She s t r a y c a p a c i t i e s o f tho secondary c i r c u i t d i s c h a r g e t h r o a g h Beferring  t h o gap*  t o f i g u r e 2, brasltdoKn o f t h e gap i s tho see© a s  c l o s i n g switch  B, w h i c h  i n g a negative  v o l t a g e a t t h o s w i t c h E o f v?-iue e q u a l t o t h a t  tsfcieh o s i s t c d  i c t a r n i s t h e asms a s sudd o n l y  a c r o s s t h o s p i t eh p r i o r t o i t s c l o s i n g .  fcjjply-  9  •-17How,  In taach greater than  and £g Is jsuch  g r a n t o r thou C, 'hones tvs a r e justified i n c o n s i d e r i n g t h e component c i r c u i t s separately, s i s t i n g ef r , C, H  t  and  Consider f i r s t the c i r c u i t conthat i s , ifasgln© YY  t o be shorted,,  Assuming t h e s e c o n d a r y voltage S t o regain c o n s t a n t , and taking, the drop a c r o s s the a park a s a -t b l , we have, by e q u a t i n g v o l t a g e s aronnd the. c i r c u i t , E=  a--rt?s€  —:  -+- I—7—'  ry  J A  whence /  =  (£'-«)  ( / '1 CR  F -g /- C P )  ^  z  CR-t-b)-f(bRC-tl-)P-i-bLCp^  1  •P  J&at t h e  roots of  s  -  ^bLC  o  y  be  — <=<-  (Z£>LC)  Z  bLC  I f /3 i s i m a g i n a r y , tho general solution i s •& darspod o s c i l l a tion o f f r e q u e n c y f ^ ~  ,  . I n order to g«tt sone 1ft es of- tte frequency e £ f,'Xat us s u b s t i t u t e  nu?3srieal  hot us tafco C  :  5 x  10  vsiu.es in the above eseprosBion f o r /3.. , i  s  10  , H - 10, and b - 5. x I t r .  These v a l u e s , though o n l y a p p r o x i m a t e ,  a r e of t h o o r d e r o f  magnitude to bo found i n m a c t u a l installation® Substituting these v a l u e s in t h e e q u a t i o n /3  /  (ZbLC) 7  bi-c  iso have —/z  -18whieh r e d u c e s t o  from w h i c h we o b t a i n f ^ -  /Sfzic - 7 x 10* c y c l e s p e r second,  which c o r r e s p o n d s t o a wave length o f about 4 factors » C o n s i d e r nest t h e c i r c u i t  consisting o f r , K  C , t h a t i s , n e g l e c t i n g c and a l l t o t h e l e f t o l 3 » 2  t  L, safi  flie  o p e r a t i o n a l solution in t h i s c a s e i s  and  t h o general solutions, i f /3 i s Ss&gftHU^r, l e  where  * =  &afl  ~ «c l / ^  ^  ^ ^  are aa bo fere the roots c f  -  t h i s also i s a de taped o s c i l l a t i o n  - -0  o f frequency f  4  -  /5f27\.  A g a i n l e t us s u b s t i t u t e s u i t a b l e n u m e r i c a l v a l u e s i n the e x p r e s s i o n 10, end b  . £ot I B tefc« Cp - 10"*^°, j,  for  5 x 10^*  :  10**^ E -  s  »hen t h esc v a l u e s e r e s u b s t i t u t e d i n t h e  eonation. ••.  have  /  6  / (so/oy~ J (z  =  which s i m p l i f i e s  to ^  = \T^hZfx  /d'  6  =  j/-/x/a  a  7 ana we o b t a i a f  4  fro a the re l e t ion  c y c l e s p e r second,  - ^ / 2 7T - 1*8  JC 10  fhia f r e q u o n c y eoi«responaa t o a v?av©  l e n g t h o f about 16 ssetero. Prom t h o above i t sppours t h a t f ^ and f high  radio  frequency,  4  are o f quite  Since t h e f r e q u e n c y o f the so o s c i l l a -  t i o n s depends to s o {treat a n extent o n t h e s t r a y i n d u c t a n c e  r.nd c a p a c i t y o f t h e ; ; y s t e s ty h  and t h e soGiesfhat u n c e r t a i n q u a n t i -  e  i t I s apparent t h a t • t h e s e f r e q u e n c i e s s a y he found  0  almost e a r n e r s  i n t h e s h o r t ??ave b a n c s , d e p e n d i n g on t h e  installation,,  particular  iJov?, w h e n to the a b o v e ,  tho  g a p b r o c k s <IOT;n t h e r e i s i n a d d i t i o n  t r a n s i e n t s cue t o a v o l t r » g e  taken m  B  E c o s vtt„  applied a t t h e s w i t c h B t o tho c i r c u i t c o n s i s t i n g o f r i n s e r i e s i-^ith Cg S D 5 E i n p a r a l l e l , c l i e r e 2 i s t h e c c u i v o X e n t  .-impedoaco o p e r a t o r o f a l l t o t h e l e f t o f JSC „ f i g a r s 2« E - (Ri+LipjK.+UP  + '/ctP) ~  B o a s t i n g v o l t a g e s , we  f  rf?  r  o  n  the  relation z  -  ZzZ  '  have  froir. ?;Meh C =  (Ct-PZ dp  i>Z  cosast •+- b -f-Z-  -a)  j  Zl p I n o r d e r t o obfcnln the g e n e r a l s o l u t i o n f o r t h e abevg o p e r a t i o n a l . g e l a t i o n no G u & t f i a d t h e r o o t s o f £ where Z  It we  ~  tt?ko  GgbZl>  b •+ 2 ,  2 havS.Bg t h e v a l u e a s s i g n e d  b d i f f e r e n t frore sero  a f o u r t h d e g r e e ©quittioa i n p  p e i r s o f r o o t s which assy be rod  and  one c o r . p i o x .  B  i t i s apparent that  - 0 above•  » ois  "  aue- a c c o r d i n g l y T?XI1 h a v e  both  r e a l , both  In s e d i t i o n  f j t ? which a p p l y t o  there  eosqsiOK,  w i l l  roots  involving  5 c o s trfe b u t n e t t o t h a t i n v o l v i n g e.«  the  port  o r ono  be a p a i r  imaginary  of  tea  of  the s o l u t i o n Since  these  r o o t s .t $w c o n t r i b u t e not his*? cf' I n t e r e s t t o our s o l u t i o n vo may die-eard the® and  consider  only t h e -solution  involving  &„  •-20-  I f tho roots o f z  - o a r e —<*-< ± A mat -<**. * / ? 2 , .  Ti  the g e n e r a l - s o l u t i o n t r i l l c o n t a i n i f /$, a n d ^6/ a r e i E s s g i c a r y  tortus o f t h o f o l l o t T i n c for©  e  T h i s ^ i v e s t s o mors p o s s i b l e f r e q u e n c i e s o f o c c i l l n t i o n , f  5  s / ^ / / 2 7r  nnfl f  G  -  fap.n*  • Proa m i inspection c i r c u i t co l i s t c u t s i n v o l v e s *  o f the r e l a t i v e s o g n S t u f i e s c f tho i t my  ho s e e n t h a t s n y p o s s i b l e  o s c i l l a t i o n s w i l l p r o b o h l y he o f a u d i o frequency,, t h a t io„ r«n^ c u r r e n t chfrnges w i l l he r e l a t i v e l y nlov.- n f t e r t h e i n i t i a l i m p u l s e a t t - 0*  Sow, i t i o na e x p e r i e e n t s l f a c t t h s t the  voltage across e spark i o j y o e t l c a l l ^ cosstmfc f o r r e l a t i v e l y c l e w c u r r e n t elvmgQS*  S h l a gay bo c o i i f i r r > 3 u b y r e f e r e n c e t o  the o a c i l l o ^ r a p b i e r e c o r d s tsftavn on p l a t e 8,„ Xomos t r a c e , s u a p l a t e 13* l e t t e r t r o e e , t?bieh s r e o f the s p a r k c u r r e n t *n£ v o l t sg© r e s p e c t i v e l y *  ^ h o s e t r e c c s a r e -explained n o r e f u l l y i n t h o  s e c t i o n ©s o s c i l l o g r a p h a n a l y s i s * ,  itrom t h e a b o v e i t t o l l e r s a t  o n c e t h o t b must be garo s i n c e a  b i l a c o n s t a n t witis r a s p c a t  to  current*  I f warn wo- put. h - 0 i n t h e agnation S p - 0, t h e l a t t e r r o f i a c o s t o "A - 0, w h i c h ishen m u l t i p l i e d o u t mil  oimpli-  f i e u y i e l f l s t h e ©quaties (c>LiLi. - Cr M ) ? ~t (CIRT. L/ -f Ci R\< h z ) P -f (Lz z  3  z  -fR R,C,)P t  -+ H z  T h i s i s a c u b i c .in p which w i l l have r o o t s —e< „ sna — - K j shore  fa  ~0  ,  m?y be e i t i i a r r e a l o r i r s s f t i n & r y * I f fa i s I s r ^ d o ^ r y  os c i H o t Sons % * i l l o c c u r o f f r e q u e n c y %  - fal?. 7T, <ai£ i f r e n l ,  t h e r e u i l l be pro cert o n l y u n i S i r e c t ! o n n l i a r u l s e s .  i&% lis taho th© eano r/ho r a b - O and m s b a t i t u t o n u m e r i c a l values for the fsogncto c o n s t a n t s In tho above c u b i c i a pm  have the follow lug m a s o n e d s  h  «*02  C  - 50  2  x  vaXuas  - G*C41  if - 0*15  E  X  Z  0,11  Eg * f x 1 0  5  r h i c h v?hen s u b s t i t u t e d i n tho above a q u a t i o n and simplified  T h i s aquation f a c t o r ! s e a into t h o following t e r m s  tthich  gives tho f o l l o w i n g roots for p  P, = - 3 -2S- x / a  Pz. = - z •Ss'x. SO *-h jz  r  -6 X/d*  Eonco the gassrsl solution c o s t G i n s the following terrsn  Tm frequency of the ahove o s c i l l a t i o n i s f8j/2 7r . 2„6 x 10 /2 7T s 4200 c y c l e s p e r second* 4  cuency  ~  T h i s £ro-  arrived at by t s f c i n g for Jig the value f?fciefc i t has  a t 3500 cycles p o r s e c o n d *  By o x t r c p o l & t l n g frois the graph  shotm i n figure 6, i t is x o o f i i l y soon t h a t t h o actual v a l u e of Sg should he soaowhst ahove this v a l u e , of tho order o f 10^ ohms  0  lit this c a s e , i t in gaits p o s s i b l e t h a t the Sacrament  of the c i r c u i t w i l l bo above the c r i t i c a l value and o s c i l i a t i e n s cannot take p l a c e *  T h i s conclusion i s oonfirissS  e x p e r i m e n t a l l y by tho oscillograms snotm on plates 16 sad 1 ? , 7,'hieb arc of tho v o l t a g e across tho s p e r h fitting- this p e r i o d * These traces f a i l to she© any o s c i l l a t i o n s of tho above s o r t , but do shot? c o r r e s p o n d i n g e x p o n e n t i a l t e r s e •  s h e a the voltage a e r o c a She a p a r t p l u g h a s decreased to t h o c r i t i c a l v a l u a a , ( n o t n e c e s s a r i l y the Q S K C v a l u e of a so at hreaMown) the a p a r h i s osrsiugai ished ana a f u r t b o r a c t o f t r a a s i e n t o s a y he s e t u p .  I f t h e c u r r e n t f l o w i n g lr» t h e  aparh J u a t b e f o r e e x t i n c t i o n i a i  9  tho m t h e n s t i c a l  develop-  ment i s i d e n t i c a l a i t h t h a t g i v e n i n s e c t i o n .2 c n t h o o p e n i n g o f the- t i m i n g c o n t a c t s , K i t h t h o e x c e p t i o n o f c o u r s e of the i n t e r c h a n g e o f the p r i a s r y and eocoudsry c o n s t a n t s *  -5?hus the  operational solation for t h o s e c e n d o r y c u r r e n t Is ' C.P(fo±L±P)(R -tL P-fi/ )- ^ Lf>3 _ - . -l £ l  fmm  l  ClP  C  M  i  Ri  i LlPi  /  1  ip  w h i c h , i f th© r o o t s of f»  ps  and ' /3, and  0 a r e — oo t-/ ,  and -«*,. ±/5 ,  2  z  a r e is^gtxiary^ the f o l l o w i n g : general e o l a t i o n  i s oMaiiiet  t = A<  s/'n(/*.t-0 ) -r Az 6 f  1  s/n(/3_t-0^  The froauaneSaa of these o s c i l l a t i o n s a r e  »  /3,iZ~K  and  It wae found o o r X t s e n t a l l y that at tho e x t i n c t i o n cf the eparli the c u r r e n t d i e d away g r a d u a l l y , rather than s u d d e n l y as v:ae assessed i a this development*  In this c a e e ,  s i n c e tho c u r r e n t at o:€tiiietloxi i a s«ro» i t f o i l OK-a a t once t b r t t b a o o c l l l o t i o t i s of irecu.oncisa £^ and f.^ s i l l be entirely ahacut*  cay,, hesever^ esy-ect a voltage rS.an to-  vrards e x t i n c t i o n of tho aparlc due to t h e removal of tho l o a d fro® the nngnetc*.  0M)$mG  OF  ms muxm o o m c f a ,  It £ Q poaeihlo that ihm .timing' contacts cjsy elose  while tiers f a . s t i l l as-.-sppyaslahle voltage stress- them* i n efatch c a s e this auMmi change of c i r c u i t constants, amy result  I n farther trossionto*  I f the total voltage osSeting* serosa  the t l s i i B g contacts a t the i s a t n n % of ©losing ho B„ the effect i s tho sa«so m  applying -3 to tho switch A astf emitting,  ftom. the o i y c a i t , figsro 2*  conSossor  tho  Sifa^llfleatletj eaa  he -mate by neglecting 7, sua C am! tho constant tors a of the spark' crop i n case the l a t t e r i s s t i l l i n pro^reaso  From the relation  can bo obtniaoQ tho operational solution for tha ceoouaary current i l  s  3  Q-h  =  (R -t/-,P)(H -f-b l  CzbP)  MPES  •__  -t ftzCz bP-tLzP  z  i-1-2.  c_  b P )-(n-ubp)  , MP  z  Z  2  She vol tags appearing acrossfetess-eeoisdsry i s e , t'm operations! solution being  e = (R^-tUp) s  _  i  s  (RL+LzP)(l+CzbP) (R +i-,p)(R^-tb t  -f  fi G 2  MPE bP-f  1  LzP-i-  If the roots o f this cubic i n p, Z  =  LzC^bP ) 2  s/n  MP  2  c are -o< end — °c. i/^/  the gonef-sl s o l u t i o n t r i l l bo a£ tho 'fern. I f /l<f  - (1+CzbP)  Z  ta isaglsary*  fp3,t~-•<?,)  The froouaucy of this o s c i l l a t i o n w i l l bo  s  (3,lz~K»  In tha COB©, of the aagaeto usefi i n theae invssfei--  gstlsas  e  i t isss not p e s s i M s b y S B J sorosl sfl.fustssnt o r apoefi  vsristio&« t o cmioo t h o tising eesifcnefce to e l o c e  vh$K  th&re  rsss s u f f i c i e n t wltsgo across fcfcoe t o prefiaco O K otjssgmiolo fc2?w5o£cmt« Hoscnror, s?e !iave mt p l a t o 7 n n oscillographic f o& o e o i Z l a t j i o s ^ b i i f c c l o o s l y rooc&fcloo £ « 0ael.21«ti&i5 i c 81m t o « 2 C i « £ at the timing eo&fecctc  last prler  to their o p e n i n g , ane i s o f f y o q a o n c y nbout 2.6 si 20^ c y c l e 0 per soe-OBfi*  How, if??© o^rtrspola t o f r a r , t h e grspfe i s flftorc 6  f o r 3 l st 16 2t 20** c y c l e s vrc t r i l l obtain on enortioiia vnl"ao« ?  A c c o r d i n g l y •«© ctsy e c u s i d o r t h e s o c o s d s z y c i r c u i t es ©pea c i r c u i t e d * ( i n r e a l i t y t h e r e i o s t i l l ci p o r t i o n of Cp asaroas t h e 33oona*ypy Sua t o t o o i n t e r n a l  filstslbstafi  capacity) ihe r  o s c i l l a t o r c i r c u i t thus fceeOESfJ the pri&iij^ c i r c u i t ot3l$«. e e s d a t i n g of roBistS3CQ#.  C j * Ej.. © B 4 SB. a&k&o%& t o r n tes to fins ere s  S£ an insp^eflcta o f tho. s a ^ B i t s f i o ©f the q&*mt£«.  ti-es i n v s l ^ s a , . © o far  -jsassiolo^ eiii. all.0f?i«g. £©?• t h e  i u t e r a s l saomito*? csp&ci%  #  i t i s ecsm thet feis e i r e a i t w i H .  g i v e s s e i l l a t i o s s c f t h e eesrsroet srSaa* o f aftgi&tttfie, BitaeXi^ / . 5 a b o u t 16 5 : 10 c y c l o G p o r &eoon£«  fhs p r e c e d i n g aas&ye/ia  hm nhovm.  tbet t h e r e ©re  9  possible fraq&oacte© o f o e e i l l o t i o a comjoefcsS srlfeh the couplet© osgssto ignition s y s t e m .  O f theses,,, o s l g twe.  l i f e It? te ba o f *®8io £$QqmnB$*  B  f ^ an3  ©re  fhs- resninlBgr e«rven srfces fcfeoy  «xl&t; ero t o b a fstisafi i n tbs asMs f r e c p t aey rang©.*  Xn th©  aeta&l m g s e t o only © vsr^r f e w of those frequencies a r e founfi, the others baing. e n t i r e l y a b s e n t O E r e p l o e o f i b ^ h y p e r b o l i c o r  &sg?anost£&l SiwGtiom*  Of coarse,, u 3?mtrler i m ^ X r i i i e ray ]>c^m-Q f e r c s ^ i s t?hich esse s l a r g e jamoor  c&o'e &f ssy of tt&BG  of harmtmte fregseaeiss m*? %@ o»§ei»s£# Ii0wa¥or of l i t t l e e  TO&US  £sch em ssalj-sla i e ,  cissec It i s v a l i d o n l ^ f o r the porioe  co^oroa I'-*? fcbe f i r e t half G$Q1Q of tho fttjaaaca?atol* In c&Sition to tho eT»TO 9 pure oscSllofcloMQ, there is a possible oscillation of the apsrJ: i t s e l f ^ trhich we ca;? fros the vex-f smtitre o f t h i s o s o i l l a t i o a i t i s  •call  sppsroist that the mm  tax®  s i l l hertll^" 1® sintteoiojaX* hosee i t  is reaeo&stoXe to espsot a eosS es of BarsofiSc o s o S l l f c t i O B B e-f this frequency? a l s o . It i s quite* gpparoat that  th© forenoiug? analysis i s  of raeh «<s?a us© i n i n t o r p r e t o D e o r v o o " osoSilntlcsjic thare i s p r e d i c t i n g them*  Is on*? csso tfc® n m l r s i e holds r S g i e i ^ o s l ^  f c r trriiii5S«r»ts o f an o s o i l i n t o r ^ stature* tiinm tmat o f tho c i r c u i t constants ser© &©$«rc&ne$ fos g*e?r£o£ic forces n » 6 not iiEpalsce*  Ale©, unless the r-etis&ttng trass isat-iJ oars J a w s , i t  thecomas - e s t r o n e ! ; ?  filffiealt  values f o r etiijstitatios*  t o pi 6? cttt saifesMo' nttfaericsl .  ffcs. c h i e f 5us£i£ie&tio& for «ai«g  .this saothoc* of .analysie i s the s c l o t i v o l ^ dimply cgaatioao which r e s u l t *  An tmclycl©  :  tretiM c o m i t of a complete  sixniertcsl eolutioa Bsr a l l possible t r e m i c R t s , involves the ueo ©f so6oi© a a i heco-acs co eeiaplicatei se to he uoll^nigh ?  Issclnole*  s  So&eve?* sines this thesis l a coiicerDctf chle£l>  t-?itb ©acillotcrjr transients, the acre sisjjip sss&lrsis i s e,cito auQimf.te*  en P4  m:m  niacin?  ECJMIOBAL  P i s t e 3 i s an .ooeXllogaroBfcalien a s a o b o c h f a r t h o c a r v e s chews, i n f i g u r e 7» a  50  "^ha t o p t r a c e i s t h a t o b t a i n e d from  t a r n c o i l ©ound o i v o o t l y o n t h e pcaaaancn* a a g s e t g *  2ho  s i e c l e t r a c e i a o f t h o v o l S a g o g e n e r a t e a i n t h e 10 t a r n c o i l mntkti m t h o c o r e t i l t h the s a i n c o i l e *  s e c o n d a r y r o t a t i o n a l v o l t a g e Trove f t i c a i ;vi th t h i s t r a c e *  OTKE  scorch  Tn& p y t o r y and  s e r e found  t o ho i a o n -  S h e peak v a l u e on t h i s irravo form  a o r r e s p s i i i a t o a aasissu© p r i m a r y volfeag© o f a b o u t  volts*  The lot7er t r a c e i© a 60 c y c l e ticl»g isav©» OOm: I?ICO?J 01? OP>X QXBC9Z?. t l h e s t h e as&gnot© i s o p e r a t i n g ' •©» e p o s c i r c u i t 8 J ©  o p c a i n p o f t h a timing contact© cuusa© a v e r y h i g h w i t age t o  00 i a f i u c e t ! i n t h o s e c o n d a r y s d n n i u g e  She-isarlaua value o f  t h i s v o l t a g e trae s s a s r s r a f l b y a s p a r k ga-p sno* foufitl t o ho  apprcTTin-ately  9,000 v o l t s *  P i s t e 4 shews fchs r e l a t i v e  timing  o f t h a v a r i o u s phsnofasnu ©eourriag wx apesi c i r c u i t y a s w o l l  m  t h e aan-sral shape o f t h e lc?;ar f r e q u e n c y c o v e n a n t s o f tho wave f o r m *  S»c t o p t r a c e was o b t a i n e d b y a m p l i f y i n g a a s s a i l  voltage f r o s s voltogs Siviaor  eDimsotefi a c r o s s  the s e c t a r y  B  v?Ith t h e t w o s t a g e a m p l i f i e r p r e v i o u s l y <?. e s c r i b e d * a no" a t o p p i n g cio^ii t h o r o s a l b i n g v o l t a g e , w I t h a 2 0 s i p o t e n t i a l traxts*  fcrraor*  'xho n i f i f i l e t r a c e l a o£ t h e a r i n a r y c u r r a n t , t h a v a l u e  | a o t a t h r o o h b e i n g s t o a t 0»6 apposes.  S h e l o s e r t r a c e so o f  the prienry v o l t a i c . JFlate 5 i s an e n l a r g e s  t r a c e o f t h e a o c o n c a r y opsn  PLATE 6 .  -27-  o i x e a i t volts-pe t o k o s % a c s p l i f y i r - t wltage  fil-Jiaox  elocsnfc  ttiareetly  o f Ite  Toltegs  tho tcoe  T?T50  BO  o u s s l l nreltnge f r o c i «  c i t f c s VK 24$. m e m t n taoo s ^ t h i a t h e plofco c i r c u i t * fiitrMer  the ^ S t e t o r  t o t a l resistance  t?ns o f t h o c r f i o r of 12 s: 10^ cheo onS  biasofl o n ! operated" t h o t t o o s a t i r e x^svo f o r ©  • t?oo ^ o l l V3ltlil« the r ® g o o f l l m s r o p e r a t i o n *  An i & e p o e t i o t i  o f t h i s t r a c e . ©feows e t t h e feogimjinr? o f  •  t S a n c f f r e q u e n c y 2160 c y c l e s per  Jte t h i s i s t h e  ascetic*  en o e c i l l a -  .  r e c o i i i i n t f r e q a e a c y o f tho o s c i l l o g r a m e l e m e n t , .St la d i f f i c u l t t o s a j ^ a e t h e r o r .net t e i o f r e e « e n e y tseloags t o fcftie cev© fona., Hos?evor  p  e « i n v e s t i g a t i o n tsy ,«seors o f the  cothefie r a y  oscillo-  g r a p h e s t o o l i o h e S fcfce exlotoace o f oaeii a n o B o i - H a t i o s i M t o f f r - e t a s a e y B%m%  ^ I t i t e 6 ..sne^s a csti3«  J^OQ- c y c l e s p a r ooecaa..  oSe ray s & c i l l o c r s n o f t h e  tjgg-iiitiisg o f the  af&ova vmvo  s  p l a t e 7 5o tlAQ e a » e t?5tii t h e a a i s i ^ e c t i o s a l c o ^ p f j i i o s t g p e o t l y re£sco6 t<y c » e x t r e r ^ e l y a s w l X c o n c e n t e r i s ««rlo3 w i t h t h e v o l t e s ^ f!S¥icIai%  /© -may fee s e e n , t h e r e i s  initially  m  o o c i l l r i t i o u o f l a r g e nG-plitaSc?^ &*oojaonoy 5500 c y c l e a p e r eeeoofi w&  &&umm&t.  Q*#2 se X 0 *  #  «M>ch i s folletiaa* o y s asji-»  ' f i i r o c t S o f i s l c G c p o n s n t n f e i c h S e e r e f i s o s mmh  p r e c e d i n g Use 358® o y e l o o o c i l l s t i o n m another o s c i l l a t i o n  1*2 2-: 1G^«  eore. slowly*  laet  p i n t o f tfeere e p F ^ a ? ®  o f £recjK.escy 16 s 1 0 ^ c y c l e s crafi Hecreoent  f M s o s c i l l a t i o n i s flue t o e r c i s i g e t the  c o n t a c t s ana s p p e s r e o;a s e v e r a l o f the no p r e v i s i o n aoac i n t e e s t t t h c y s t i c a !  oscillogram* a ^ o l y i d e for  ti©lng £hore  is  fchie  o s c i l l a t i o n "but i t i s a p p a r e n t t h a t i t w i l l ©c v e r y n e a r l y idoafcieel w i t h  tee  freq&eney e x i o i a g : o n c l e a l j i g t h o timing  -26CO?i'tSGtC  a  . •  € 0 2 B J f I 0 " 3 UK£3H LOAD. f h e p r i a o r y a s d secoufioi-y c u r r e n t s uhen the eapnoto i s s u p p l y i n g e n e r g y fee t h e a p o r h plug- a r e  The  en p l a t e  to  t o p t r a e o i s o f t h o p r i n a r y c u r r e n t t h e r.asinuia v a l u e  1>s i n g , a a b e f o r e , age  shGVua  oboat G.C atapcro*  n o r a t e a i n t h e 10 t u r n mtwch  I s o f t h e c u r r e n t tlovizt® t h r o u ^  tho cdaole i s o f the v o l t coiX  and th© b o t t o m  e  t h e apuzk p l u g ,  Shis  trace  letter  t r a c e uao o b t a i n e d b y c e p l i f y i a g t h e v o l t a g e drop a c r o s s a 60 ohm r o s i s t a i c o w i t h the two s t a g e a m p l i f i e r &»S a t o p p i a g <iows the* r o c u l t i o g v o l t a g e w i t h t h e 20s 1 p o t e n t i a l  fcraasfornsr  Tha wQ7rSa.ua v a l u e o f the car r e n t i a a b o u t 6*>  reilliajspcrea*  An e x t e n s i v e v i s u a l s t u d y  o f t h e above o p a r h  a  plug  c u r r e n t t?avo v?aa ciaae v.*S t h t h e cat ho tic r a y o s c i l l o s c o p e * S B S tho  i b H o n i n g - p o i n t s Botocl©  She g e n e r a l  tha eat-B a s t h a t sliowa on p l a t o 8  a  s h a p e o f t h e wave i^ae  f h o c u r r e n t r o s e audctciiiy  t o a b o u t j?Q o i H i i i s p a r o s when a n c a c i l l a t i o n o f f r e q u e n c y g r e a t e r t h a n 50 k i l o c y c l e a , ( t h e r e s o l v i n g powor o f t h e i n a t r u -  cioat) took p l a c e  0  ?he b e h a v i o u r  e r r a t i c t h a t i t urns i s p o a a i b l c  i n g i t s - aaturo»  J a i l e r l u g this  o f t o l a o©dilation titm eo  t o f o r i a s u y c o n c l u . n o u a ro{jart)»»  a s e i l l a t i o n tho o u r r a a t e l o t s l y  i a e r o a s a f i t o a s i a s i i a u a o f a b o u t 6 5 a i H i rape-res a f t e r w h i c h i t  doers&seti r a t h e r r a p i d l y t o s e r e *  £hero v;as no o b s e r v a b l e  d i s c o n t i n u i t y o r o e c i l l e t i o e irhou th© c u r r e n t coo-sou* S e v e r a l t r a c o o t?ers takers o» tho  cathoco r a y o a e i l -  l o e r a p h o f t h e o s c i l l a t i o n s o c c u r r i n g ; a t the he$?:amivij o f tho a b o v e c u r r e n t wave*  "hose a r e ahetm o n p l a t e a 9 t o l i e  Plato  •  1  I  o  (  1  I 2  3  I'  _j_  I  * Microseconds  6  f  | 7  '  |  [  8  9  PLtfOE $+  tit/ntired M'lctvstreoneli  —•  1  1  —  1  Micro ietanc/s  FLATS 1 0 ,  .  ^_  i_ "  FLA?H  12.  *8$u 9 ebot?a fee traces of tha v o l t a j p drop across- a 50*000 ohr-i r c a i c tar,eo i n a o i l o a K i t h the spark pluav  i l a t e 10 shot: a the  v o l t a g e drop a c r o s s a oO ohm r e s i s t a n c e i n series sdtb t h o spark p l u c  f  a m p l i f l a d vd t h t h e two s t a g e a m p l i f i e r *  f h e time  axis for the lowsr trace i s o r e fourth o f that for the upper trace«  *?his oscillation i s apparently w i t h o u t decrement e*iu  la certainly far froei a i i m c o i d a l , thus liici catiugr t h a t i t i s most p r o b a b l y duo to o e e i i l e t i o u a o f t h o a p a r h i t s e l f *  Tho  fuBdaeeataX f r e q u e n c y i s about 160 k i l o c y c l e s but ss e:>ny ho SOSB,  mii'im  by so isuch as loo^U  l*X&£e 11 shags s coapttiriaoa  bettcaoa an d e e  aviation plug am  Tlw  latter plug mc  observed feo g i v e those i r r e g u l a r oseilletSejis  as AG automobile p l i t f v  e o a t S m i o a a i y s r h i l e t h e forssr gmro tlism only oceaEioi3talljpf» el though both wore used unci o r identical c o n d i M 02 a» •Elate IS ehetis th© v o l t a g e a c r o s s the aprirk plug c o r r e s p o n d i n g ts t h e c u r r e n t o s c i l l a t i o n appear 5 r*£ on plate 10« uiifortauatsly the i u d i T i s u a l oscillations are isssstcofl b y the w i d t h u£ the l i n e aria the d o t t e d  offset*  P l a t e s 15 t o 15 are IOT: f r e q u e n c y traces of tho v o l tog© appear lag- aerea© tfcs aparls plug  flaring  operation  Those  t r a c e a vr-erc t a k e n by d r i v i n g a Irsl 245 vacuoo tabe frorv; a voltage divider scrota tho plug  eemliag the p l u t o car r e s t  of tho tub© directly through the o s c i l l o g r a p h element*  By  s u l t a b l y r e g u l a t i n g the £L l a c oat c u v r o a t tho p l a t e essrresit WSB not alloived to excaea 150 r . i i i l i a a p 0 r o a  B  thus f t vim p o a a i b l o  to boost up the lower part of tho c u r v e without drainer to tho ' oscillograph element*  She traces on plate 13 vrora tejcea irlth  m  m  i>  PJU?^ 14.  PLATIi 15.  -30-  the e>:ci£etio» ao rsdueed t h a t t h e o p e r a t i o n o f t h e t o h a v:?3 linear,  An i n s p e c t i o n o f the l e x e r t r a c e s h c e a t h a t t h e v o l t -  age -aerobe the opark i s p r a e t i e a l l y c o n s t a n t f o r the g r e a t e r part o f t h e period*  " h e r e i s hcv?evnr 6  e  c slight increase i n  v o l t o g e ao tho c u r r e n t ait?pa t o v e r y Itre v a l u e s l u o t t  the  e x t i n c t i o n o f t h e apar£*  preceding  F o l l o w i n g - t h e e x t i n c t i o n o f the  sperfe t h e r e i s a s a a l l modest I n c r e a s e i n v o l t a g e a f t e r » M c h the c a r v e f o l l o w s c X u t o l y t h o c o r r e s p o n d i n g p o r t i o n e f t h o ?!aftos l i a m i 3.5 a r e the l o w e r t r a c e o n  open c i r c u i t c u r v e ,  up c c t h a t t h e w a l l e r v o l t a g e s f e l i m - i n g t h e  13 H o t f t o d  She upper t r u c e on  esrfcinetS on o f t h e *ipnr£ eseewe v i e ! h i e ,  p l a t s ' 13 i l l u s t r a t e s t'm e f f e c t , o f a r c i n g a t t h e t i c i n g c o n tacts*  Shew t h i s a r c i s e x t i n g u i s h e d " n e r v a l o p e r a t i o n i s  r-;:£ur:;o« b a t owing- t o t h e l i s t i t e o " eiiorgy ncsr a v a i l a b l e , tho 6  a p j r h no est d i e s o u t *  Tmiz n r d :*£ a t the t i d i n g c o n t a c t s n o t  e n i y prod^cee h a r n i n g c f th& e c u t a c t s hut r o h s tho aparh. o f c o u s i o e r s o l s aueafcgr* H a t e s Ife ssM. 11 Skew the esrfeeefaely • - s h a r p %mvs f o r m t h e lre<&6oc?a o f the gape  occurring  J?late Id i s o f t h e  v o l t a g e a c r o s s t L o sp&^k plug eoa p l a c e 17 i s tns so^tj r l t h t h e a a i o i s e c t i o n o l cooponoate g r e a t l y r e d u c e s * b e f o r e T&o&M&m vaa s h o u t 3*koo v o l t s ,  3bo v o l t a g e  jnat  'fhefcse o s c i l l o g r a m s do  not shoe a n y r a d i o f r e q u e n c y o s c i l l a t i o n s f a l l e g i n g t h o g a p t r e a k a o s i i h a tfieshow a n e x p o n e n t i a l , tor© c f .spproj&asifcoly 10QO cue  & *" ^ 1<5  x  a  0  J f l i o aosence o f o s c i l l a t i o n s s a y fcavo hoe a  to t h e ikB.ap.im a c t i o n o f tho v o l t a g e d i v i d e r r e s i s t a n c e *  heeaaao c s e i H s t i o n a w e r e observed i n tho corresponds n# c a r r o n t  PLAT:-; 18  MU3S3 OF I : J T X B F ^ U ? 5 C E . f h e r e a r c t h r e e way© i n tshieh- a cug&oto i f u i i t i o n s y a t e s i ssi^ht cause r a d i o i n t e r f e r e n c e *  Firsts  oscillations  and tiuvo f o r e s o f aaflio f r e q u e n c y s a y a f f e c t t h e r a d i o s o t fey i 2 i d a c t i o n or ceudactiou,  Second,, o s c i l l a t i o n s o f r a d i o f r o -  c m o c c y c a y . . r a d i a t e tm£tialm.t.enevgp  f r o cadency c i r c u i t s o f v.a-n a c t *  radio  rhirfi„ oxtrer«ely aherp travo  forms .T&y r a d i a t e p u i s G O e h i o h m y quency c i r c u i t s *  t o a f f e c t tho  a l s o a f f e c t tho r a d i o  fre-  Qt tbeaOg the l a t t e r two oro the r;oot  S r r o r taint s i B c c t h e r a d i o e a t i s u s u a l l y - i c o n t o d m  f a r frosi  the 5 c a t i o n uystOK t h a t i n d u c t i o n i s n e g l i g i b l e and p a t h s  of  -conduct! on a r e u s u a l l y stbaisiit* C o n s i d e r i n g t f e r a d i o f r e q u e n c y o s c l l l f t l i o K S , i t ©as s h o r n i n t h e tsat h e c t i c a l m s l y e i e t h a t t h e r e wore two f r o cueneiee*  f x and f ^  ©altitude,, aud  om  t  wM eh r.'ould p r o b a b l y ha o f t M e  i n d a t a r s i i n a t Q f r e q u e n c y #, ^%Q*  &  M  order o f t  0  the  c s o i l i n t i o n o f tho spari:, a l s o p r o b a b l y i n t h i s range®  The  n u m e r i c a l v a l u e s o f these* o a c i l l s t l o m s do,pp,D.d t o s u c h a s ejrtonfc u p o n e t r a y i n d u c t a n c e s  c a p a o i feies o f tho c i r c u i t  and  condition© i n t h s eparfe, t h a t any a t t e m p t t o e v a l u a t e thorn i s p r a c t i c a l l y hopelosa,  r  iha h o s t wo  can aaconplish i s to fl«e  H a l t i n g condition© f o r tbe. o c c u r r e u e e o f th0.se  os0illn.tl.oua  s?n thrt. i f I t *s Sees r o d t o e3.iETl.PGte t h e n tr© c a n a d j u s t  tbe  c i r c u i t c o n s t a n t s co t h a t t h e y cannot o c c u r * Sharp vav« f o r n s o c c u r vbemovor t h e r e I s c oufidsn cheapo o f e i t h e r c u r r e n t o r v o l t a g e , each a s a t th©  broaMovrn -  o f the QpQfk gap . e  t r o c i i h e e l e c t r o m a g n e t i c t h e o r y i t e s s ho  iihoita t h a t a change o'Z c u r r e n t ca-aaoe t h e r a d i i * t i e n o£ e isngr ; c t i c p o i s e , o r v e c t o r , the c&cnitu<!o o f t?hich i s p r o p o r t i o n s ! t o the r a t e of change c i * c u r r e n t  upon r a d i a t i o n t h i s osgne-  c  • t i e v e c t o r i c a s s d i & t s l y eeaceiefces i t o e l f ^ i f c h a n r e c t o r st r i g h t angles to i t  e l e c t r o - m a g n e t i c trr.vc«  t'rdi  electric  t h e tt;o becocs© a p o l o r i s e d  3 i s i l a r l y a change o f v o l t e g e p r c d u c o e  on e l e e t r i e v e c t o r t?hieh i s p r o p o r t i o n a l t o i t s r a t e o f ch&ngo, one z h i e h , when r & d i s t e d prodncse- e. perpend S e a l e r segno t i c v e c t o r and  "becomes e l s e a p o l a r i s e d ©leotree&gnetie t?avo*  •These v;sve& hove a var;? i n tie f i n i t e  s  freqaencjr  ?  hut  provided  t h a i * have e n o u g h energy e r e quite, c a p a b l e o f a r - t s o t l s g t t h e r a d i o frequency  c i r e a l e n c f a r a d i o ueb*  -The i d e a l  ronody  radio interference i s of  for  c o i i r c s t o e l i m i n a t e t h e tjcuree*  In t h e e a s e o f c s e i i l n f c i cue  doe t o a t r a v i n t e e t s n o e e . end c e p o e i t i e s t h i s , i s sfitita f o m e i h i e , , hut o s c i l l a t i o n s o f t h o aparh and e&arp %mm  ferns  nrecont  c c n s i . d e r s h l y s e r e . . d i f f i c u l t y i n t h a t s e have no a o a & t i o n s f o r  t h o s e phenomena froes r b i e h conditions*  may  compote p o s s i b l e l i m i t i n g  •  In section 4 of th~  rasthssiafcieel  a n a l y s i s ! -ore-  developed e e u c t i o n n f a r two p e s s l o l s f r o q a e n c i e s o f o s c i l l a tion,  C o n s i d e r 'chs 'Xre-qr.o 120.7  in o r d e r th 't c. s c i 11ac  t i m i s «sy t*:I:c p l a c e , t h e q u a n t i t y under t h e r o o t e a s t lie i m e y i n e r y , hone? f o r n c n - o s c i l i e t i c n t h i s q u a n t i t y s u a t bo e i t h e r r a o l o r e a r o , c r e E p r s c a s a nn£hesiat;i c u l l y ( Z-bLC) 2  '  bLC  frc-s vrliSeh tre g o t the r e l a t i o n  A p p l y i n g t h e oar.® r a c s o n i n g t o f,, r.-o .f;ot t h e r o l o t i o n s r  R)  _  z  TUB fcaneoi,  /  above r e l a t i o n s i u a t i f y the u s e o f o o r l o o r o ^ S e -  eorauoreially  2OJOV;U  aa *"i5Uppro«3ora . s i * a e o a n s o f  reaucinj* radio intorferoncs*  ?  B  'rho o n e s e r i o u s orawfesefc t o t h i s  p r a c t i c e i s t h a t f o r s a t i s f a c t o r y o p o r s t i o n t h o vela© o f thouo cupyi'oa^oro  i s <if n e c e s s i t y  about 50,000 ohca, a m i t h o I n s e r -  ts en o f t f c i i i auch r o e i o t e n e o i n e o r i o a w i t h che £>pnr*: cansou a carious, r a duct Son gop  i n tho cvxima  c u r r a n t florin.« tbrottffc tho  ar?& h e n c e o d e c r e a s e i n e f f i c i e n c y o f tho- e n t i r e i g n i t i o n  .'u r o i p i r d a fcho s h a r p iv&vo £01« n* v o r y l i t t l e s con ho dons f r o m a t h o o r a t i c u l j t u n c p o i i J t .  Sharp c u r r o a t nctvoc c o u l d  bo smoothed" o u t by i m i a r f c l r v ; i n d u c t a n c e i n t o tho c i r c u i t , t h n t I s i a e r a a a i a c 1,  b u t t h . » i n t u r n v o u l d n.eccas:i t u t o iat-roaaizip :  E w h i c h i s a l r e a d y t o o lnri?o f o r pood o p e r a t i o n * tsaves c o u l d  3harp  voltvm  c o s t "00 dool t - ; i t h by c u r o f w l o h i n i c i n r - c f o i l  o."Ulr-;:.o-it o u l v G e t c d to i;];son c-i;rf?6a  e  r.uch Ohio Id in**  -3*-— . i n c i d e n t a l l y s c u l d a l s o provo a a e f u l i n r e d u c i n g r a d i a t i o n -fro::: any o t h e r d i s t u r b a n c e s w h i c h c i d i b bo p r o n o n t * o i n e e t h o o s c i l l a t i o n o f the apart; i t s o l f i s duo o n l y to  c o n d i t i o n s i n t h o s p a r k , I t i s e v i d e n t t h a t r o c a n e 15rrali-  n t o t h i s o s c i l l a t i o n o n l y b y a l t o r i n n thaaa c o n f i i t i o n s o f o r t u n a t e l y , tho o n l y c o n d i t i o n s o v e r tsliich v.'o have  Un-  enroot  c o n t r o l a r e , t h o c u r r e n t f l o w i n g and t h o dirsonoSona o f t h o gap, tho o t h e r s boli)£t e i t h o r dependent on these o r f i n e d by t h o conditions o f operation*  J u s t ivhat e f f e c t these q u a n t i t i e s  h a v e upon tha o s c i J l n t i o n o f tho anar2c s u n t bo determined by cjrpoi'lr>3ont s i n e o a t h e o r e t i c a l i uvea t i {rat i o n  i a o a t o f the  CjtlGStiOSe'  TOT tho p n r p o s e o f m o n i t o r i n g  the r a d i o i n t e r f e r e n c e  a throe tube r a d i o eat r a a i n a t a i l e d approximately fro*" tho I g n i t i o n o j / s t c o under t e s t e  6 f o o t away  5?his n o t eonaiafcod  of a  regenerate v o d e t e c t o r v?5th pluft i n o o i l o c o v e r i n g a servo l e n g t h xrmm  Stotn  .-;tG{ro O K p l i f i o r . t  fipijsrosifcatciy  50 t o 500 wo t o r s , w i t h a tr,*o  IHfro c o r l & l c sroro p r o v i f i o d , a 3 f o o t l o o p and  r r?5 f o o t o u t o i d o vij:o«  She a c t i t a e i f z:as c o m p l e t e l y un-  a h l d d e d and i f a s ©nrthod o n l y t h r c n y h t h o l a b o r a t o r y b a t t e r y f r o o t?h J ch the p l a t o c u r r a n t vm  drawn.  «>hon t h o I g n i t i o n aye to..< r w ? f u n c t i o n i n g n o r n n i l y tha i n t e r f e r e n c e wsa uo bad t h a t l o c a l broadcaatia,{.r a t u t i o n s IToro  completely  drowned e u t  s  TUB  intensity o f this  interfer-  ence r a s n e a r l y c o n s t a n t o v e r t h y e n t i r e rau^o o f the s o t ,  beir.p  o n l y s l i g h t l y g r e a t e r o n tho s h o r t e r v,*aveOo  xhoro sreus  ~35~ no a p p r e c i a b l e i n t e r f e r e n c e r.hoii vim s p o r k p l a ^ m e t3d and t h o wDg-nfito o p e r a t e d  on opon c i r c u i t , ,  h i ceonnoc-  dnbntitutien o f  E .-inhere (*ap f o r the s p n r k plug- r e s u l t e d i n t h o i n t e r f e r e n c e l e i u r ai>r.-ar;hfit l o e c l i r.ad i n t o d i s t i n c t x-mve l e n g t h h n n d s , hut t h s o c tvoro o t 3 c r v o d t o c h i f t about i n a var;j e r r a t i c ^ n u i i a r , A v a r i a b l e r e s i s t a n c e WBG connected  i n eorioo rrith  tho s p a r i c p l u g end i t s v a l u e v a r i e d f r e t s a c r e t o 50,000 ehsae* The - i n t e r f o r o n e e woe observed  to de creese a t e n d i l j e s the  r e s i s t a n c e isns i n c r e a s e d u n t i l i t n e a r l y vanloft*A ufc s v t l u e o l ' 40,000 o h a j  c  Jfetcreaeinjr the r e u i o t n n e e f u r t h e r hod n c  n e U c e e b l c e f f e c t , u n t i l each a v a l u e was reached  t h . t R oporfc n  as l e n d e r o c e a r r s d , i?hen tho I n t e r f e r e n c e dropped euddenl:.- t o & n e g l i g i b l e vslno*  M t h no r e s i s t a n c e i n s e r i e s t h o sp&rh  •rsts b r i l l i e n t l y w h i t e h a t 2 3 r e s i s t a n c e ?res I n o e r t e e i t become b l u e "aid l e e s b r i l l i a n t u n t i l a t 50,000 ©tow i t v-«os n f o e h l o blue  line*' A eoneontrS e a M o l d e d c a b l e t?a- t r i e d e.a e l o r d  free  the s-.<?£noto t o tho a p a r h p l u g 2i:d t h i s a f f e c t a a «, e e n s i d o r o b l o r o c u e t i o n i n the i n t e r f e r e n c e , but duo t o the u u s b i o i c e d p o r t i o n s ofc t h e ondu aorse e n e r g y «ee s t i l l r a d i a t e d , *  i t ©as  found t h a t s o l i t t l e a s an i n c h e f a n s h i e l d e d l o a d van e u f f i cic?".t t o c a u s e o b ' o c t i c n - u c l o i n t e r f e r e n c e o  Koivovar, *ehoii t h i o  i c e d u o o need t ? l t h a 50,000 elm s u p p r e s s o r nfc t h e p l t t f , th© interfere*.ice r n.: i i c i r c o l ; ; i ; o t i c n n b l o oven thourrh & poa t i o n o f the c a b l e r e g a i n e d  unuhiolded,  F l s t o 1G jhou-n the e f f e c t o f s h e 50,000 ohis s a p e r e e s o r on t h o /»0 p l u g c u r r e n t *  -2he l o w e r t r a c e i s o f the  a w n l i f l e f i v o l t a g e drop neross e 60 ohn r e s i s t a n c e w i t h o u t tho  . suppressor  In circuit*  tion olsilcr rrest p r o b a b l y  i s s a y he n o t e d t h e r e it- a n o s o i noon p i c t c a i O and 11  t o those e p r o s r i  duo t o o s c i l l a t i o n o f t h o sporh:*  and i s  The s p p e r  tre.ee i s o f t h o s a n e v o l t s g e c r o p h u t K i t h t h e 50„ 000 ohm . suppro~ucr i n series* p i o t o i ^ eliminated  *s G C J he a e o n the - s u p p r e s s o r  the o e e i l l e t i c n appearing  truce, hot there i s s t i l l  present  f r e q u e n c y a b o u t 45 k i l o c y c l e s ,  on t h e lot;or  a vsrv m a i l o s c i l l a t i o n o f  A v i s u a l i n s p e c t i o n £&va  p r e c i s e l y tho saae r e s u l t s f o r the Olco 13ES1SH OF 2l£h S F B C l A h i S P J m  ime etxj-  ping*  P3£S,-  I t a p p e a r s free* t h e p r e c e d i n g  osrperi&entol  invooU-  •gsfcions t h a t t h e r a d i o i n t e r f e r e n c e a r i s i n g f r o a t h e s p a r k plugspark  isev h s r e d u c e d t o a s a t i s f a c t o r y l e v e l i f n o t o f e 50,000. o h a s e r i e s r e s -  i i l i f a i n a t o d e o c a p l c t e l r , b y t h o mm  i & t a u o o o r »sappre»eor , eoraVineS v s i t h r-. c o m p l e t e o y s t e r o f f  shielding".  However t h e r e  i s n s e r i o u s o b j e c t i o n t o t h o us© o f  v lerpro s e r i e s r e s i s t a n c e i n t h a t t h o e f f i c i e n c y o f t h o opnrh i s .thorefcj- r e d u c e d * onslyeic  I t wag p o i n t e d o u t i n . t h e l a s t h e c a f c i e e l  t h a t t h e c r o s s s e c t i o n e r e n o f t h e spar!: i s p r o p o r -  t i o n a l -to t h e ©arrant f l o w i n g t h r o u g h I t , h e n c e a r e d u e t i o n i n current ^perfc*  causes a p r o p o r t i o n a l r e d u c t i o n i n t h e siste o f the :  .Viih t h e s u p p r e s s o r  i n tho c i r c u i t  i s n e v e r e a c h gsfo&ter t h e n t h e m e n SXES  tho nsxiratis  current  c u r r e n t a n d t h e r e f o r e t h o ..  o f t h e s p ^ r f c i s i s o r e o r l e s s d.etextiSned' b y t h i s me&n  current*  Zi t h o u t  tho suppressor  c u r r e n t due t o t h e d i s c h a r g e w h i c h i o many eiscos t h e v a l u e  t h e r e i s on i n S t i u l r a s h o f  of the secondary s t r u y c a p a c i t i e s , o f t h e fcoan c u r r e n t ,  T h i s r.sy be  -37SC-CJS  by r c f a r a n e o  t o p l a t e s 9 iniu 22.  STJii-s l a r g o  c u r r e n t w i l l r e s u l t i n c n a c r b o t h o f two t h i n g s ? tho  initial tho r r o c o f  s p a r k t ? i l l be i s i t i a l l y larcto o r t h o t o n p o r a t o r e  w i l l ho  hiphe e i t h e r e f f e c t asking, f o r a g r e a t e r e f f i c i e n c y o f t h e spark. I f now a c o n d e n s e r o f v a l u e  equal t o the s t r a y  s e e e n & e r y e u p n e i t i a a be p l n c e a a o r o a a t h o aparh: p i n ; ; hctu'aesx the  u r . p p r e a a o r ant! t h o gap, S t 3a a p p a r e n t t h a t t h o i n i t i a l  coT.'tlit! o-:s - 1 1 1 be . n s s r l y t h o a a r o a s w i t h o u t  t h a auppsmasor*  That I s  tho auppreiinor  f  thic  roo5 *taacp tho  e o n d o u a o r i v i l l a & r g o u p ihhrouyn  untij  pups r l n n  t h o v o l t n / t e *roco^oii M y h  i t will  diacharya  e?iou£h t o brawl:  t h r o u g h , t h e a-ap r i t h c  corn  n current  c-l 7 o a s t a,a f r a a t a a t h a t d"o t o t h a d i a c h a r r - e o f t h o s e c o n d a r y G«racItie3o usy-l  ana 11  *hia i n i t i a l  c!5schr?rao  r i l l  bo f c l l o r a d  by t h o  c u r r e n t ifnloh t h a auppreaaor p e m i t s t o ftor;,  rith  t h o a b o v e earslAoratf ons i s s t u d  abotru J u section §r» f i f y r r o f r a n c o n s t r a o t m i ,  the span: p l u r The i a a t i r  por-  t i o n i s tho - r e g u l a t i o n nparlc p l i a r baeo *?ith t h e e x c e p t i o n the  uph^ro r a p o l o c t r o d o a ,  b u i l t * * i n eoauenss£ large  0  vhe n p p o r p o r t i o n c o n t a i n - : t h e  2hla c o n s i s t s of a stack o f a l t e r n a t e l y  cud s c u l l a l i M i n n a r r s s l i a r s s s p s r & t o a  ^hc* .M'.nll c r a s h e r s  by Ki-ea ca.sk eves*  c o n n e c t t o t h a c o n t r o l r o d VMC t h a I r i r o 1 B o f isles, and. l a h e l d  eonnact t o tho o b e l i *  2ao c o r e  hy  o n t o she c e n t r a l r o d *  'the c o l l a r  of  threaded  cues  together  3h& capaalt;.. o f  tJio c o n d e n s e r a a r-osaurea b y a c o a d o r a o r b r i d g e r a n fount, t o bo S5 r-; c r o r , i e r o f a r a d s , u l i f r h t i y l o s a t h a n t h o s t r a y s e c o n d a r y c-ip -'C11;.o  i t v.'ii-u a o o i r l c c t"; \iz,c- job-: r l ^ c l ^ p n r J r i n y a l o c t r o d o a  P t n e e i t r a a found t h a t o s c i l l a t i o n s o f the spark  aoldom  o c c u r r e d tri'sh s l i i a t y p e o f e l e c t r o d e «?hoi3 the c u r r e n t  v-as  rol'.-:15 v e l y o a a l l * P l a t o .19 shows t r a c e s o f the c u r r e n t through t h i s s r a c i a l p l u g , tho Upper t r a c e h^in^, o f t h o a o p l i f i e e drop across a l o s e r ooo  ths  voltage  ofesj r e s i s t e u c e w i t h o u t a s u p p r e s s o r , SOD©  e«d  h a t v - i t h o 50,000 ohr< s u p p r e s s o r in s e r i e s *  £s a s p be c e e n , t h e r e i s a t no t i m e .on  o s c i l l a t i o n o f the  spar!: u ; K i the t r a n s i e n t u h i c h c o o s appear o n t h e u p p e r i s g r e a t l y reduced on the l o r c r t r a c e v. hen i n t^s c i r c u i t *  rue c u r r a s t trove f o r s i *?as nuver o&servod. t o  v o l t a g e s a c r o s s the  w i t h t h o ^0,000 ohm  traces  plats*  s p e c i s i l p l u g and  the /.0  plug  s u p p r e s s o r i n a e r i e s , a t the hroahdovca o f  t h e ffap„ a r e s h o w o n p i s t e u 20 and 'those  trace  tho s u p p r e s s o r i s  •deviate t o any e x t e a t f r o m t h a t shewn o n t h i s fhe  the  <?1 r e s p e c t i v e l y *  i t a p p e a r s t h a t b r e a k d o w n o f the gap  trot; -  is reletivo~  l y l a t e r i n the e s s e o f t h o s p e c i a l p l u g by a b o u t ,$G u j i c r o eecoods, o t h e r w i s e ohsorvatiens  i t was  the t r a c e s are v e r y s i m i l a r *  Txat* v i s u a l  f o u n d t h a t o s c i l l a t i o n s s i m i l a r to t h o s e  s p p o a r i ^ g on p l a t e IS o c c a s i o n a l l y appeared I n the volfearo 'oeroos t h e AC p l u g even P i t h t h e s u p p r e s s o r i n s e r i e s but ouch o s c i l l a t i o n s 'g-oro c o v e r oboarved In t h e case o f the plug*  special  P l a t e 22 shows a ceesporXsoji o f the c u r r e n t s f l o u i n y i n  the th.roo plugs used 'in chose i n v e s t i g a t i o n s * -...'hose t r a c e s a r e a l l o f the v o l t a g e drop a c r o s s a j?0,000 ohia u a r i e s r e s i s t a n c e * the t o p t r a c e being- from the .AO plu£, tho n i a d l e *ron tho Oleo plur- S'jc the bot t o n f r o o the e r . o e i o i .plug* not represent  irhoao. t r a c e r do  say p a r t i c u l a r c o u c i t l o c u o e c o r r i a - * i n o p e r a t i o n  s i n e s tho p l a c i n g : o f th©  oscillograph dofloetion plates  across  the j > 0 0 0 0 ohm r e s i s t a n c e i n t r o d u c e d c o n s i d e r a b l e 0  c a p a c i t y i n t o t h e circuit« large  initial  current  at the  fhey ec»  extraneous  however, i l l u s t r a t e  breakdown o f t h e gap  the  as w e l l  as  the tisao tahen t o charge the condenser o f the s p e c i u l p l u g t o n sufficient voltage•  Ine o s c i l l a t i o n s shown on t h e s e t r a c e s  did  n o t t a k e p l a c e nhen the o s c i l l o g r a p h p l a t e s w e r e d i s c o n n e c -  ted  frcrri the c i r c u i t , a s wag a s c e r t a i n e d hy aeans o f the r a d i o  EC  to  Bis  the  spar]: p r o v i d e d  hy t h e s p e c i a l p l u g was  typical  diocharging o f a c o n d e n s e r , being b r i l l i a n t l y white  accompanied, hy  the u s u a l  snap*,' f h a r e was  circuit a  and  only a slight  c r e a s e i n h r i l l l a n c y v/hen t h e s u p p r e s s o r was  of  de-  inserted into  the  She r a d i o i n t e r f e r e n c e frons t h i s p l u g rras a l m o s t a s  bad a s f r o m t h e o t h e r p l u g s , w i t h o u t t h e s u p p r e s s o r , h u t w i t h it the  the  i n t e r f e r e n c e d r o p p e d t o a n e g l i g i b l e v a l u e , and. when  s h i e l d e d c a h l e was  In  used* a l s o , v a n i s h e d  entirely,.  t h e E n t h c a a t i c a l a n a l y s i s i t v;as shown t h a t  w e r e i n a l l 10 p o s s i b l e f r e q u e n c i e s o f o s c i l l a t i o n f o r  c o m p l e t e oagneto i g n i t i o n system. w e r e o b s e r v e d , cone v/ere p r e s e n t  cone \7ere e n t i r e l y 'absent* summary o f  these  Sane o f these but  inposcible  the  frequencies to l o c a t e ,  The f o l l o w i n g t a b l e (jiven a  oscillations*  there  and  iYbsent a o a n o s c i l l a t i o n b a t a p p e a r s o a p l a t e 6 a s a n exponential# A p p e a r s o a p l a t e s 6 a n d 7 , t r e o u e n e y a b o u t 3500 c y c l e s . Cno  o r b o t h were p r e s e n t "out c o u l d n o t be l o c a t e d , d e f i n Italy t h e f r e q u e n c i e s were p r o b a b l y b e t w e e n l o V and 10© c y c l e s * t  Could n o t b e observed a s o s c i l l a t i o n c b u t e q u i v a l e n t e x p o n e n t i a l terras a p p e a r o n p l a t e a 1 6 and 17*  Entirely absent. • E n t i r e l y absent but a s i m i l a r frequency appears o n p l a t e A p p e a r s on p l a t e s 10 , 1 1 ,  ana 1*2, a b o u t 1 8 0 k i l o c y c l e s *  Radio i n t e r f e r e n c e fro a the i g n i t i o n  system w i t h o u t  s h i e l d i n g o r s u p p r e s s o r r c a i s t a n c e c r m s f o u n d t o be e x t r e m e l y bad  Such, s h i e l d i n g no w a s t r i e d p r o v e d t o b e q u i t e i n a d e -  0  quate , b u t t h e i n t e r f e r e n c e c o u l d be v e r y n e a r l y e l i m i n a t e d b y the  use of a  plug.  5 0 , 0 0 0  ohm r e s i s t a n c e i n s e r i e s w i t h  the s p a r k  T h i s r e s i s t a n c e had* H o o v e r , a v e r y d e l e t e r i o u s e f f e c t  u p o n t h e s p o r l ; , w h i c h c o u l d i n a measure be eonpensatefc f o r b y t h e u s e o f a s p e c i a l s p a r k p l u g i n >.?hioh t h e e l e c t r o s t a t i c • c a p a c i t y h a d been-increased, b y a b u i l t - i n c o n d e n s e r . plug  t  together  w i t h a J50,000 oho s u p p r e s s o r a n d r e a s o n a b l e  shielding„ r e d u c e d t h e i n t e r f e r e n c e t o s u c h a lent l e v e l r e a d e r i t inaudible« w i t h o u t a n a p p r e c i a b l e brilliancy  Shis  o f the  spirit*  as to  reduction i n the  In c o n c l u s i o n t h e w r i t e r w i s b e s t o thank B r * SI* Tickers  s  E e a d o f th©  the U n i v e r s i t y  Bepartsent  o f E l e c t r i c a l Jlngiiaeerins a t  o f B r i t i s h C o l u m b i a , f o r h i s many h e l p f u l  s a g c e s t i o n s and c o n s t r u c t i v e criticise©; P r o f e s s o r V.'.B« C o o l t h a r d , a l s o o f the Separfcnenv o f E l e c t r i c a l T i i g i n e e r i u r ; , f o r his  h i n d a s s i s t a n c e i n t h e l a b o r a t o r y ; a n d I3r« &«!£• Shram, o f  the  a e p a r t r a e n t o f Physio©  t  f o r .the l o a n o f t h e C a t h o d e  OacS 11 e s c a p e w i t h wfeiea a v i s u a l s t u d y ot  Ray  t h e v a r i o u s wave  f a r r a s v?as aade*  BXBL10GMHIT. FsBc 3 i l a b e e  *»  i!ath6i?mtieal Sheory o f I n d u c e d V o l t a g e High-tension Ilagneto* UeGo B u r e a u o f S t a n d a r d s  IIo.  424.  i n the  Scientific  lapora  KeGrswIlili,  191?*  ~  E l e c t r i c a l Yoaaurononts-o  Tciylor-Jones  -  Theory o f i l i e I n d u c t i o n C o i l *  S.J*  -  ileaviaide s Operational l i C G r a ^ - i l i l l " , 1929"  -  C o n d u c t i o n of E l e c t r i c i t y t h r o u g h Gases.  Berg  J * J * Thomson  f  Pitnan,  Calculus.  C a m b r i d g e U n i v e r s i t y P r e s s , 2$0p<,  193%*  0  42»  The f o l l o v / l n g I s a p r o o f o f t h e r e l a t i o n used i n determining the c o e f f i c i e n t o f coupling  secondary o f t h e nagneto, secondary resonant  n^ /n^ 2  2  b e t w e e n the p r i n a r y a n d  « 1 » K , s h o r e 21-. i s t h e 2  frecu.en.cy w i t h t h e p r i m a r y open, n ^ i s t h e  secondary r e s o n a n t f r e q u e n c y v?ith t h e p r i m a r y s h o r t e d  and K i s  the c o e f f i c i e n t o f coupling* i s t h e secondary s e l f  inductance  i s the• ©eeoMary c a p a c i t y EP ^  the secondary r e s i s t a n c e  B  I>2 i s t h e p r i m a r y  self  inductance  Hi i s t h e primary r e s i s t a n c e V/hsa the primary i s o p e n c i r c u i t e d t h e r e s o n a n t f r e 2 oft^  c u e n e y i s £iven b y  where  s  1  since at  /ZTcT rescnanco t h e power f a c t o r o f t h e c i r c u i t i s u n i t y t h a t i s 9  CO< L z —  , ! ^ CO 1 Oz  l e t u s aaow w r i t e t h e g e n e r a l d i f f e r e n t i a !  f o r the t r a n s f o r m e r a l o n e w i t h t h e p r i i s a r y s h o r t e d ,  equations  letting  T,g r e p r e s e n t t h e v o l t a g e a c r o s s t h e s e c o n d a r y .  Peso a r»-vr s i v j i n s  equation 2, we have  MJ = -(±L<%-  + f3iii )  ^  N  Substitute t h i s v a l u e o f  A  i n equation 1 . Git  E  z  = R,C  2  t  U±±  at  - J f i # Li  d-t  -  R, Li  L-+  -43' R e a r r f i s g i s g s a n a t i o n j5, s?e'-.'bav& \  *~< J  ait  ?ro» e q u a t i o n 4 i t i s seen t h a t t h e secondary 'inductance  i  s  ueereased hy t h e introduction o f t h e s h o r t e d  p r i m a r y h y an unount H / l ^ . c  Kll^t*  He a l s o have t h e r e l a t i o n  s  -"^aing t h i s , -m o b t a i n f o r t h e new s e c o n d a r y i n d u c t a n c e  '•••Q  a r e now a b l e t o g e t a n e x p r e s s i o n f o r the  r e s o n a n t f r e q u e n c y o f the secondary v?ith t h e p r i a a r y s h o r t e d * We h a v e Z 7 T  where  I f sow'we a c i n a r s cO, mmi u>  > /(v  co  Z  z  z  z  a n d t a k e 'the r a t i o of.  we o b t a i n a t o n c e th© d e s i r e d r e l a t i o n m 8  follows.  -44  K e & v i s i d e ' s o p e r a t i o n s ! c a l c u l u s i s b a a e d on t h e o f the . o p e r a t o r d / d t ,  w h i c h i s w r i t t e n *p*,  use  a s an. a l g e b r a i c  Quantity operating on u n i t f u n c t i o n , w r i t t e n  "be u n i t  f u n c t i o n i s a f u n c t i o n a h i c h baa t h e v a l u e sero f o r a i l t i n e s b e f o r e t s 0 , and At  t s 0 the  v a l u e u n i t y f o r a l l t i m e s a f t e r t » 0*.  f u n c t i o n r i s e s suddenly from s e r o t o  I f we a  the  series circuit  consider  the  unity.  s u d d e n a p p l i c a t i o n o f an essf IS t o  c o n t a i n i n g - r e s i s t a n c e It and  o b t a i n t h e w e l l knovm d i f f e r e n t i a l  i n d u c t a n c e 1,  ®e  equation  In Kenviside s n o t a t i o n this i s written v  It we  now  t r e a t the v a r i o u s Q u a n t i t i e s  a s a l g e b r a i c symbols ere  raay s o l v e f o r 1  T h i s i s c a l l e d the o p e r a t i o n a l  solution.  I f t h e r e i s a condenser G i n s e r i e s s r i t h oar hypot h e t i c a l c i r c u i t , the d i f f e r e n t i a l e q u a t i o n  jf'Ueft  E1 - RI ~t l~ | f rt limi K e a y i e i d e d e f i n e s  Jdt  a s i d e n t i c a l eritfa the  when t h e y b o t h o p e r a t e o n u n i t f u n c t i o n *  above d i f f e r e n t i a l a g n a t i o n  -  bocoiaes  becoses  L.r-'c'p) 1  operator l/p  Using this fact,  the  f r o a w h i c h ;ve o b t a i n t h e o p e r a t i o n a l s o l u t i o n  7  1  /  -f-Rcp-f-LCpZ-  A n abbreviated, sray o f w r i t i n g t h e above o p e r a t i o n a l s o l u t i o n  ^hers  i n c a l l e d t h e admittance  t h e i m p e d a n c e operator,,  Y  P  and  = CP  Z  =  P  o p e r a t o r and. Z  P  i s called  I n t h i n c a s e these a r e r e s p e c t i v e l y  / -P RC P  -f-  LC  P^  S h i e a a t i i o d , s a y be e x t e n d e d , t o a n y c i r c u i t  h o e o m p l e s g p r o v i d e d we a l w a y s r e c c n b e r  no matter  s  t h a t t h e opera t o r p'  must e v e n t u a l l y o p e r a t e o n u n i t f u n c t i o n * 2n o r d e r t o o b t a i n t h e g e n e r a l s o l u t i o n f ror-i t h e  o p e r a t i o n a l e o l a t i o n sre m y a s s K e a v i s i d e ' s E&paneien 2heoret&  She  a c t u a l procedure i s a s f o l l o w s t  (!)  t ? r i t e mwx t h e v a l u e o f Z  (<c)  3 c t Sp s 0 a n d s o l v e f o r p , w h i c h g i v e s a s r o o t s ,  n  from the o p e r a t i o n a l  solution*  r^,  etc*  (3) CO  :  llfferentiatc  w i t h r e s p e c t t o p; l*e« f i n d d2 /dp»  - r i t e out P-lf*  and — j / l y -  p  (5)  S u b s t i t u t e i n (4) t h e values o f p found I n ( 2 ) ,  (6)  Vrite  and s u b s t i t u t e p s G„  f h i o £ives t h o c o n s t a n t  t e r n o f t n e expansion., i i  (7)  V:"rite o u t t h e r e m a i n d e r o f t h e s o l u t i o n by p u t t i n g f o r e a c h c f t h e stunts t i o n t e r e s t h e v a l u e s f o u n d I n (>)» t h u s , E  X I  —  So  2ZP\  ^_  -+ ~  /  6  -t-  -46I f v,'s a r e n o t i n t e r e s t e d i n t h e a m p l i t u d e o f t h e t r a n s i e n t s h a t v/isU o n l y t o hue?/ t h e i r c h a r a c t e r pense w i t h s t e p s p  %  4  >  s  sasy d i s -  and 7, s i n c e those s t e p s serve o n l y  s  t o f i n d the c o n s t a n t c o e f f i c i e n t s o f € ~ Pn1  «  I f we knov? the  r o o t s o f the e q u a t i o n 2 . s 0, we may w r i t e i n n e c l i n t e l y t h e general s o l u t i o n a s , p.t  X = Aa -h A,6  e  HQVJ e  ' =  -fit  ?  -i- A? £  jt  -(-••-•  p,t  s a y he w r i t t e n , i f cosh  or i f £  p*_t-  -t- Az€  -t Sihh\  Pit  i s positive  9  P,t  i s negative,  =.  • ,  coshr,t  or i f Jar £ -  -s/.nhPxt  i s imaginary . / ^ t -t s/n Pit 8  Also i f  and  A,e -t  a r e c o n j u g a t e s , nay c( i J /  A , 6 * = € ~- (A,£ -tA,e' )  p,t  P  t  r  m  J/3t  3  r;e have,  e ^ArtKicaspt  ^A^As/n/3t)  where $ i s a phase angle determined" f r o a t h e • c o n s t a n t s Aj_ t .and -Af..--I n a c t u a l problems i t i s u s u a l l y p o s s i b l e t o group terms so t h a t the g e n e r a l s o l u t i o n aay he e x p r e s s e s i n one o r nore o f t h e f o l l o w i n g I  =  A*  €• -f P,t  AL£  -t-  Pztr  Ac -/- e^'^A'Cash/S-t-p  1= j =  + A,  forms,  -p £ (A>cos/Z,T-+B, K,t  A  a  B,sthh/3,t^ -p 6 *' (AiCosh/3 tf  BzSmh^ij-t--  L  s/n{5,t)  -f £ ^\Atcc>s/3zt  i- /k/5 t) S  I f we a r c i n t e r e s t e d o n l y i n t h e c h a r a c t e r o f t h e t r a n s i e n t s p r e s e n t , uinee t h e q u a n t i t i e s A« 3 , and. 0 a r c  z  P•  merely aaplit&de  c o n s t a n t s , we s e y writ© one o f t h e above  g e n e r a l g e l a t i o n s a s soon a s we Kiio?? t h e va2a.es o f t h e r o o t s of Z  v  s 0»  A l s o we may change f r o m o n e s o l u t i o n t o a n o t h e r by  use o f e i s p l e t r i g o n o a e t r i c o r h y p e r b o l i c r e l a t i o n s a n d t h e operator  * y, l a case  the a p p l i e d v o l t a g e i e n o t o f u n i t f u n c t i o n  s h a p e , i t o a s t be c o n v e r t e d i n t o i t s e q u i v a l e n t o p e r a t o r bef o r e the g e n e r a l s o l u t i o n c a n be obtained* o f some eomaon e q u i v a l e n t  s,»(cut±0)7~  Ptoa  .following i s a l i s t  operators  *fc£' <t  co*C«**<t)f  h  s  ^ % \ % l '  h  ±  1  k c o r e complete l i s t o f e q u i v a l e n t o p e r a t o r s a o w e l l a n c a n y o t h e r o p e r a t i o n a l r e l a t i o n s a n d s o l u t i o n s , and a p r o o f  for  t h e E x p a n s i o n Sfaeoren, a r e t o be f o u n d i n ' R c a v i c l f i e ' s  C/peratioiial (lul c u i u s * by  E.t?«  Berc, !rcfrra a-;iill !  0  -48-  ivpP3I2Jl£ I I I .  I n a r o a t h c a a t i e a l s i a l y e i s o f coupled o f t e n n e c e s s a r y t o have expressions  circuits i t i s  f o r the equivalent  donce a n d t h e t r a n s f e r i n pe dance o f t h e c i r c u i t u n d e r aticn.  If all  prirsary q u a n t i t i e s be denoted b y t h e  U , a l l secondary r  q u a n t i t i e s b y the s u b s c r i p t 2 ?  ? B  inpecousider-  subscript and a l l  ctatual q u a n t i t i e s by.no s u b s c r i p t s t h e d e s i r e d r e l a t i o n s  are  as follows, E q u i v a l e n t Impedance s Z = -p- =  Z  / Z  e  ? r a a o f e r Impedance  s  Z  =  r  =  z  ~ —  ^  z  z  ^  where t h e " - t e r n s a r e i ope canoe o p e r a t o r s ^ t h a t i s * t h e y a r e  f u n c t i o n s o f th© c i r c u i t c o n s t a n t s a n d t h e o p e r a t o r She  ?  p  p r o o f o f these r e l a t i o n s i s a s f o l l o c / S o  b o t h primary a n d secondary t o c o n t a i n  B  in aeries  8  f  »(&/dt}* Suppose  resistance,  induetance and c a p a c i t y , (the proof i s e q u a l l y v a l i d f o r any c i r c u i t c o n s t a n t a p r o v i d e d the c o r r e c t impedance o p e r a t o r s a r e  tahen)•  B y equating eefe a r o u n d b o t h p r i e e r y and  c i r c u i t s t?e o b t a i n t h e f o l l o w i n g d i f f e r e n t i a l  E.-X.Z+t.g  +J.yW  -Mg*  secondary  equations,  *  ,  Ifow, e q u a t i o n s ( 1 ) e n d ( 2 ) c a n a l s o b e w r i t t e n a s  O = (Rz.-f-L-.P -From ( 2 a ) we g e t t h e r e l a t i o n -r Z /Jt _  X -MPl, t  ^Zt-Xi-Zml,  -<  A.  -49-  Sufestitate t h i s iralne o f X  2  i s (la)  f l i e e q u i v a l e n t i o p s d e m e o f o l l o w s a t once  zz  IA g a i n , f r o m ( 2 a ) *re h a v e  tiiat  z  Zfr,  S u b s t i t u t e t h i s v a l u e o f X* i n ( l a ) r^- -7 LZi I ~  -Z/ Z *—2-i  —  -T~ r-  -7-  -~7~ 7  iz  —Z-fn-t-i.  T  _  /'2"/Z  —  ,  fixe t r a n s f e r imps fiance t h u s become*  z  —  -2" / -I'M  

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