INTERMITTENT BEHAVIOR IN OSCILLATORS 7 



The conditions of absolute and conditional stability and instability are 

 exactly the same as those already given. 



It must be appreciated that Nyquist's criterion supplies no information as 

 to the type or frequency of oscillations which will be generated by an unstable 

 system. This is true because the analysis is limited to linear systems. The 

 only information imparted is that a very small oscillation of some frequency 

 will increase exponentially with time until the amplitude is limited by the 

 action of some non-linear device. A small or relatively large shift of fre- 

 quency may occur and the oscillation may be regular or intermittent. The 

 present work extends the usefulness of Nyquist's criterion by using it in 

 modified form to determine whether or not a particular unstable system 

 (oscillator) has or lacks stability as to self-modulation. There is no apparent 

 reason why a system lacking in both fundamental and envelope sta- 

 bility might not be analyzed a third time for the stability of the 

 self-modulation. 



VI. Analysis of an Oscillator having Automatic Output Control 



Figure 6 presents a simple form of feedback oscillator having a separate 

 rectifier as limiter. For small ampUtudes of oscillation the tube operates 

 in a linear fashion with cathode self-bias. No bias is produced by the diode 

 rectifier until the peak voltage in the coil L3 exceeds that of the bias battery 



B. All voltage in excess of this value is rectified, smoothed by the condenser 



C, and applied to the resistor ;• as bias. It is seen that a small percentage 

 change in the output level may result in a large change in the bias. Accord- 

 ingly an output which is quite stable with respect to the tube condition and 

 applied voltages, except that of B, is to be expected. 



The stability of this circuit with respect to self modulation is mosu con- 

 veniently tested by opening the oscillatory loop at the plate of the tube. 

 In so far as the plate resistance of the tube is high with respect to that of the 

 associated circuit it is not necessary to control the impedances of the test 

 generator and detector extremely accurately. A block diagram equivalent 

 to Fig. 6 is presented in Fig. 7. The conditions which must exist for the 

 test of stability are shown in Fig. 8. In both those figures it should be noted 

 that the gain control is actuated by the input, not the output, of the ampli- 

 fier. It is therefore possible for a marked decrease of output voltage to 

 result from a small increase of input voltage. This behavior is very different 

 from that of the conventional, back-acting, automatic-volume-control 

 amplifier in which the output change is in the same direction as the input 

 change but of reduced magnitude. It is this difference which is the basis 

 of most difficulty with amplitude controlled oscillators. 



