THE BRIDGE STABILIZED OSCILLATOR 



581 



The latter equation indicates that the frequency is then independent 

 of changes in any of the circuit parameters except the crystal, which 

 must operate exactly at resonance. 



If the phase of ix differs only slightly from zero, so that jU2 is very 

 small, then it may be inferred from continuity considerations that the 

 frequency is still very nearly independent of all circuit parameters, 

 except of course variations in d, the phase of y.. When Q is limited to 

 values for which ^2^X4 < < iiiARi, (11) still applies closely. Substi- 

 tution into (10) gives 



X4 = 



MR A 



B,xr + N 





MRS 



B 



M 



+ iV 



(13) 



and finally from (5) and (13) we obtain the frequency deviation in the 

 form 



/ - /o . Md 



/o 



2Q{B\tx\ +N) 



(14) 



As noted above, this expression applies accurately only when 6 is 

 small, as it should be in a well designed bridge oscillator. 



The effect of variations in the amplifier may be examined by dif- 

 ferentiating (14). For changes in d only, 



and for those of | /x | , 



dd, 



d\ 



(15) 



(16) 



Equations (15) and (16) have been found to be closely in accord with 

 experiment, although the differentiation is not rigorously allowable 

 (B, M and N being only approximately constant). 



In the special case where all the fixed bridge resistances (R2 to Re 

 Inclusive) are equal, and |m| is large enough so that Ri has nearly the 

 same value, (14), (15) and (16) reduce to the following: 



/-/o 

 /o 



<2(ImI +8) 



8 



e <2(|m|+8) 



dd, 



<2(|mI +8)^ 



dU\ 



(17) 

 (18) 

 (19) 



