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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 — Wo ^ ^4 \C 



/. 



0)0 



(4) 



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

 equal, 



/ — /o . Xi Xi 



U 



2coL 2QRi 



(5) 



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

 tions,^ we obtain 



^ 



E ~ MRi +jNXi' 



(6) 



^hich 



A = R,{R,Rz - RiRa), 



B = RiRiRi,, 



M = (Ri + R2){R2R^ + RM + (Rs + Ra){RiR2 + RM 



-f (i?5 + R,){RiRa + R2R:i) + 7?5(i?li?3 + R2Ra) [ (7) 



and 



iV = Ri{Ri + i?3 + i^5)(i?2 + i^e) + RiRa{R, + ^5). 



The condition for oscillation, as mentioned previously, is ;u/3 = 1|0. 

 Putting M = Ml + JM2, we may write 



(mi + iM2) 



^i?4 - jBXi 



MRi + JW.Y4 



which gives the pair of equations 



fiiARi + ix2BXi - Afi?4 = 

 and 



HiARi - (fXiB + N)Xi = 0. 



(8) 



(9) 

 (10) 



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

 these become 



Ml = -T = ImI (llj 



and 



Xi = 0. 



(12) 



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

 284-5. D. Van Nostrand Company, 



