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BELL SYSTEM TECHNICAL JOURNAL 



The frequency deviation from resonance, expressed as a fraction of 

 the resonant frequency /o, is thus 



/ — /o CO — COo , A'4 \C 



/o 



Wo 



(4) 



and in the region of interest, where coL and 1/wC are approximately 

 equal, 



f — fo . Xi -^4 



/o 



2coL 2QRi 



(5) 



Considering now the bridge circuit, and applying well-known equa- 

 tions,^ we obtain 



hRr, _ AR, - jBX, 



E ~ MRi + jNXi ' 



(6) 



^hich 



and 



A - R.iR^Rz - RiRa), 



B = RiRiRc,, 



M = {R, -f R2)(R,Ra + RM + (Rs + Ra){RiR2 + RM 



+ (i?5 + R6){RlRi + i?2i?3) + i?5(i?1^3 + R2Ri) 



+ 7?6(i?li^2 + RsRi), 



N = R,{Ri + R, + i?5)(i?2 + i^e) + RiRi{Rs + i^s). 



(7) 



The condition for oscillation, as mentioned previously, is jjl^ = 1|0. 

 Putting /x = Ml + iM2, we may write 



(mi + JM2) 



ARi - jBXi 



AIRi + JWX4 

 which gives the pair of equations 



fiiARi + ^2^X4 - MRi = 



HiARi - {fiiB + N)Xi = 0. 



1, 



and 



(8) 



(9) 

 (10) 



For the special case in which the amplifier phase shift is zero (m = 0), 

 these become 



Ml = ^ = IMI 



(ii: 



and 



X4 = 0. (12) 



3 "Transmission Circuits for Telephonic Communication," K. S. Johnson, pp. 

 284-5. D. Van Nostrand Company. 



