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BELL SYSTEM TECHNICAL JOURNAL 



This is an approximation for the conditions for oscillation and relative 

 amplitude. 



The frequency equation (12.39) becomes 



where 



G =Cl 



U 



"111m 



^ + ~ + ^ + • 



Co C4 C^ K^g 



u \cx "^ Co ~ gJ 



(12.42) 



1 + i?p I — coo C2 J 



\CO0 iv2 / 



and coq is a fixed value written in place of co„ . Figure 12.16 shows the fre- 

 quency and amplitude changes as a function of C2 for the crystal connected 

 between grid and plate. 



Fig. 12.17 — Generalized oscillator circuit in the form of a filter network 



12.25 Condition miS = 1 for Circuits in General 



It is convenient to apply the rule m/^ = 1 as the condition for sustained 

 oscillations to more complex oscillator circuits. The circuits may be drawn 

 as shown in Figure 12.17 and the characteristics of the filter network between 

 transmitting and receiving end may be analyzed by conventional filter 

 theory to determine the conditions which fulfill the oscillation requirements. 

 An example of this is the oscillator shown in Figure 12.18A. The equiva- 

 lent configuration, Figure 12.18B, indicates that the crystal is part of a low 

 pass filter and the frequency of operation is that at which the total phase 

 shift is 180°. 



Oscillators involving more than one tube may also be inspected in this 

 manner. Figure 12.19 is a two tube oscillator designed to operate at a 

 frequency close to the resonant frequency of the crystal. The proper phase 

 shift is obtained by a two-stage amplifier and, therefore, no phase shift is 

 required through the crystal network. The crystal thus must operate as a 

 resistance which it can only do at its resonant or antiresonant frequency. 

 Since the transmission through the crystal branch is very low at the anti- 

 resonant frequency of the crystal, it will oscillate only at the resonant 



