22 BELL SYSTEM TECHNICAL JOURNAL 



with respect to level is high. Similarly the frequency stability is favored if 

 the rate of change of phase with respect to frequency is high. 



If a circuit is to function well as a self-modulated oscillator, the above 

 conditions must be met and in addition the Nyquist diagram for the envelope 

 must meet similar requirements. That is, there must be a limiter and tilter 

 in addition to the effective amplifier in the envelope system. 



A circuit which meets these requirements is shown in Fig. 27. It is seen 

 to be similar to that of Fig. 6 but to have a more complicated low-frequency 

 path. The operation is best explained in terms of the relative size of the 

 various elements. The by-pass condensers Cx and d are comparatively 

 small. The blocking condensers Cz and d are quite large. The choke Li 

 is large. Thus these elements ser\'e as open or short circuits but do not 

 enter into the setting of either of the frequencies. 



The stability tests are carried out by opening the mesh at the plate of the 

 tube. At the operating frequency, as defined by the plate coil and condenser 

 the loop gain is high at low levels. Thus the fundamental conditions for 

 oscillation exist. 



The next step in the analysis is to supply a signal of suitable magnitude 

 and frequency to reduce the loop transmission to (1,0). A small modula- 

 tion of very low frequency is returned magnified and reversed in phase, as 

 with previous systems. The phase of the envelope transmission changes 

 with increase of modulating frequency until it is zero at the resonant fre- 

 quency of Lf, and C5. At this frequency a considerable gain exists so that 

 the Nyquist diagram for the envelope also loops the point (1,0). 



The tungsten lamp in conjunction with the other impedances of the bridge 

 serves to limit the degree of self-modulation. The operating frequency may 

 be set by means of Ce in conjunction with a suitable value of Le. The 

 operating amplitude may be controlled by adjustment of the bias battery B. 

 The frequency of the self-modulation is set by means of C5 in conjunction 

 with 1,5. 



XI\'. Conclusions 



A method of applying known feedback theory to the problem of self- 

 modulation in oscillators has been presented. Although the discussion has 

 been limited to electrical circuits it is clear that the analysis is applicable 

 .to other systems, such as electromechanical or mechanical oscillators. 



The analysis has been applied to several familiar oscillators to illustrate 

 the method and to clarify some details of their operation. A sample design 

 of a bias controlled oscillator is presented to show application to new designs. 



The application of bias control to thermistor stabilized oscillators is 

 described. The design of a self-modulated oscillator is undertaken to show 

 how intentional modulation mav be introduced and controlled. 



