496 BELL SYSTFAf TECHNICAL JOURNAL 



wliere 



Ve = G.0 + jBrO (8.5) 



is the admittance for vanishing; amplitude, wliicli is taken as a reference 

 value. The foregoing facts are familiar to an}' one who has worked with 

 oscillators. 



Now-, condition (8.,\) ma}- be satisfied although (8.2) is not. Then an 

 oscillator will not be self-starting, although once started at a sulTiciently 

 large amplitude its operation will become stable. An example in common 

 experience is a triode Class C oscillator with fixed grid bias. In such a case 



■ F{Vi) > /<(()) (8.6) 



holds for some Fi . 



As an example of normal behavior, let us assume that F(V) is a continu- 

 ous monotonically decreasing function of increasing V, with the reference 

 value of V taken as zero. Then the conductance, G> = G(oF{V) will vary 

 with V as shown in Fig. 21. Stable oscillation will occur when the ampli- 

 tude Vi has built up to a value such that the electronic conductance curve 

 intersects the horizontal line representing the load conductance, Gi . G,o 

 is a function of one or more of the operating parameters such as the elec- 

 tron current in the vacuum tube. If w-e vary any one of these parameters 

 indicated as X„ the principal effect will be to shrink the vertical ordinates 

 as show-n in Fig. 21 and the amplitude of oscillation will assume a series 

 of stable values corresponding to the intercepts of the electronic conductance 

 curves with the load conductance. If, as we have assumed, F{V) is a 

 monotonically decreasing function of F, the amplitude will decrease con- 

 tinuously to zero as we uniformly vary the parameter in such a direction as 

 to decrease Geo . Zero amplitude will, of course, occur when the curve has 

 shrunk to the case where Gco = Gl . Under these conditions the power 

 output, ^GlV-, will be a single value function of the parameter as shown in 

 Fig. 22 and no hysteresis will occur. 



Suppose, however, that F{V) is not a monotonically decreasing function of 

 V but instead has a maximum so that G,qF{V) appears as shown in Fig. 23. 

 In this case, if we start with the condition indicated by the solid line and 

 vary our parameter A' in such a direction as to shrink the curve, the ampli- 

 tude will decrease smoothly until the parameter arrives at a value of A'5 

 corresponding to amplitude Fsat which the load line is tangent to the maxi- 

 mum of the conductance curve. Further variation of A' in the same direc- 

 tion will cause the amplitude to jump to zero. Upon reversing the direction 

 of the variation of the parameter, oscillation cannot restart until X arrives 

 at a value A'4 such that the zero amplitude conductance is equal to the load 

 conductance. When this occurs the amplitude will suddenly jump to the 



