578 



BELL SYSTEM TECHNICAL JOURNAL 



In this discussion the input and output impedances of the amplifier, 

 Ri and R&, are assumed to be constant pure resistances. Actually, 

 changes in the tube parameters or in certain circuit elements are likely 

 to afifect both the magnitude and the phase of these impedances. It 

 may be shown, however, that such changes have the same effect upon 

 the bridge and upon the frequency as do changes of about the same 



UZz 



I3R3 



I2R2 



I1R1 



il-sR^-i- 





LOCUS OF TAIL OF 

 VECTOR e FOR 

 VARYING FREQUENCY 



Fig. 2 — ^Vector diagrams illustrating operation of bridge oscillator, with simplify- 

 ing assumptions that i?6 is large and that E and E' are strictly in phase. 



A — At resonance 



Z4 = Ri+jO 



e = 



Ri K Ri = R3 = Ri 

 B — Above resonance 



Z4 = i?4 + jXi 



Xt Inductive 



e = +45° 



Ri< R. = R, = i?4« Ri 



percentage in 1ju| or ^; therefore all variations in the driving circuit 

 external to the bridge may be assumed for convenience to be repre- 

 sented by variations in its gain and phase. 



This leniency with regard to R5 and Re does not apply to the other 

 bridge resistances, however. Ru R2 and R3 are directly responsible 

 for the crystal's operating phase and amplitude; they should be made 

 as stable and as free from stray reactance as possible. 



