STABILIZED FEEDBACK OSCILLATORS 



469 



The necessary condition for self-oscillation stated in equation (15) 

 is satisfied in the attenuation band between fz and fi. The overall 

 phase shift in the feedback path will follow the image phase shift 

 characteristic approximately and will be equal to 180 degrees at some 

 frequency in this range depending upon the values of the terminal 

 resistances provided by the tube space paths. Oscillations may result 

 but their frequency will be unstable. By reducing the width of the 

 attenuation band stability is increased and becomes theoretically 

 complete when the band is reduced to zero. Proportioning the circuit 

 in accordance with equation (27) to give stability makes the two upper 

 pass-bands of the network confluent. If the whole network be propor- 

 tioned as a one-and-a-half-section constant-^ filter all three pass-bands 

 become confluent. 



Since the stabilization requirement 



XqXz = XiXi 



need hold only at the oscillation frequency, various possible modifica- 

 tions of the circuit of Fig. 4 become readily apparent. For example, 

 the inductance Lt may be replaced by a series resonant combination 

 which has the same reactance at the oscillation frequency coq. This 



10 ^WS^ 



LO 



20- 



1 



"-2 r' 



-03 



Fig. 6 — Modification of the feedback network of the stabilized Colpitts oscillator by 

 the introduction of an extra element. 



gives the circuit shown in Fig. 6, in which Li is replaced by the com- 

 bination L^ , C2 such that 



W = L2 + -4r-, ' (32) 



Wo C2 



A further possible modification is shown in Fig. 7 in which L2 is re- 

 placed by a three-element combination comprising a series resonant 



'o n^^^ f 



I — "^^J^h 



20 



c' 



C3 



-03 



-04. 



Fig. 7 — Further modification of the feedback network of the stabilized Colpitts 



oscillator. 



