238 BELL S YSTEM TECHNICA L JOURNA L 



If the ami)lilu(les | Ei \ and | £2 | are equal, then 



(9) |£«| = (|£i|/2) V'2(l + cos.^) = |£i|cos(.^/2) 



(10) \En\ = ( I £1 1 /2) V2(l - cos.^) = I £1 1 sin (^/2) 

 (U) \Es\ — \ Ed\ = I £1 1 [cos (v?, '2) — sin (<^/'2)J 

 (12) |£,. |/|£,, I = cotan(v./2) 



When I £1 I 9^ I £2 I determination of (p by (11) or (12) is in error by A)^. 

 From (7) and (8) 



<^ + AiA _ /eJ' + 2 1 E1E2 I cos ^ 4- I £2 



(13) cotan '^L.^^ = i/ ^\L "^ ^ ' ^^^^ ' ^"' ^ "^ ' ^^ 



Hence 



Ei\^ — 2 I E1E2 1 cos v? + I £2 



£2 



£, 



, . 1 + cotan' [(^ + A^)/2] | £2 1 , . . 



+ ^ 1 - cotan^ [(^ + A^)/2] ^| ^°^ ^ + ^ ^ ^ 



(14) 



From trigonometry 

 ^j^^ 1 + cotan' [(<p + A^)/2] _ 1 



1 - cotan2 [{^ + Ai/')/2] cos (<^ + Ai^) 



(16) I £2 1 / I £1 1 = cos <^/cos (.^ + A^) + Vlcos <p/cos dp + A^f/)f - 1 



References 



1. "Electronic Instruments" (l)ook), MJ.T. Radiation Laboratory Series, Volume 21. 



McGraw Hill Book Compan\', First Edition, Page 342. 



2. "Automatic Freciuency Control Systems," A. F. Pomeroy, United States Patent 2,288,025. 



3. "The Carrier Stabilization of Frecjuencv Modulated Transmitters," Brown Boveri 



Revieic', Vol. 33, August 1946, Page 193. 



4. "Frequency Modulated Broadcast Transmitters for 88-108 Megacycles," Leonard 



Everett, Electrical Conimnnicalion, Vol. 24, March 1947, Pages 84-86. 



5. "Transconductance as a Criterion of Electron Tube Performance," T. Slonczewski : 



Bell Sys. Tech. Jour., Vol. XVIII, April 1949, Pages 315-328. 



