STABILIZED FEEDBACK OSCILLATORS 



473 



as in equation (34). When the phase constant \p has the value ± 90 

 degrees, equation (40) becomes 



± aR2^K,K, 



^^ (KiK. + R1R2) sinh A + (R,K2 + R2K,) cosh A 



(41) 



When the feedback network is purely reactive, stabilization of the 

 frequency requires that the phase shift component of the image trans- 

 fer constant have a value ± 90 degrees within a transmission band. 

 Under this condition the attenuation component of the transfer con- 

 stant is zero and equation (41) is simplified by the reduction of sinh A to 

 zero and cosh A to unity. 



A simple example of an oscillator stabilized in the above manner is 

 shown in Fig. 8. The two vacuum tubes are coupled by a simple shunt 



Fig. 8 — Stabilized two-stage oscillator. 



inductance of relatively low magnitude and low dissipation. With the 

 high resistance of the screen-grid tube in the first stage this shunt re- 

 actance coupling provides a substantially constant phase shift of 90 

 degrees. A low-impedance transformer might also be used for coupling 

 the stages or, if desired, a four- terminal dissipative network designed 

 to provide the required phase shift in a moderately wide frequency 

 range. 



The feedback network is required to produce a phase shift of only 90 

 degrees and may therefore have a relatively simple configuration. The 

 direction of the phase shift should, of course, be opposite to that of the 

 amplifier. In the example illustrated the feedback network corre- 

 sponds to that of a simple Colpitts oscillator. The condition for 

 stabilization is that the two shunt capacitances be equal and the 

 oscillation frequency is that of the resonance of the inductance with 

 one of the two equal condensers. 



