472 BELL SYSTEM TECHNICAL JOURNAL 



If cycles drift at the maximum or hump of the curve. This means that 

 the circuit impedance for the dissipation cur\'e shown is such as to result in 

 maximum production of power for If cycles drift. For 2f cycles drift and 

 for longer drifts, the power dissipation curve crosses the power production 

 curves to the right of the maximum and hence the particular circuit loading 

 shown does not result in maximum power production for these longer drift 

 times. This is an example of operation with lighter than optimum load. 

 The power dissipation curve might cross the power production curve to 

 the left of the maximum, representing a condition of too heavy loading for 

 production of maximum power output. The power dissipation curve in 

 Fig. 6 lies always above the power production curve for a drift of f cycles. 

 This means that the oscillator for which the curves are drawn, if loaded to 

 give the power dissipation curve shown, would not oscillate with the short 

 drift time of f cycles, corresponding to a very negative repeller voltage. 



In general, the conclusions reached by examining Fig. 6 are borne out in 

 practice. The longer the drift time, that is, the less negative the repeller, 

 the lower is the power output. For very negative repeller voltages, how- 

 ever, corresponding to very short drift times, the power either falls off. 

 which means that most of the available power is dissipated in circuit losses, 

 or the oscillator fails to operate at all because, for all gap voltages, the power 

 dissipated in circuit losses is greater than the power produced by the elec- 

 tron stream. 



Having examined the situation qualitatively, we want to make a some- 

 what more quantitative investigation, and to take some account of circuit 

 losses. In the course of this we will find two parameters are very important. 

 One is the parameter X previously defined by equation (2.9), which ex- 

 presses the amount of bunching the beam has undergone. In considering a 

 given tube with a given drift time, the important thing to remember about 

 X is that it is proportional to the r-J gap voltage V . For 6 = 6,, expression 

 (2.2) is a pure conductance and we can express the power produced by the 

 electron stream as one half the square of the peak r-f voltage times the cir- 

 cuit conductance which for stable oscillation is equal to the negative of the 

 electronic conductance given by (2.2). This may be written with the aid 

 of (2.9) as 



. P = 2(hVo/en)XJ,(X). (3.1) 



Suppose we take into account the resonator losses but not the power lost 

 in the output circuit, which in a well designed oscillator should be small. 

 If the resonator has a shunt resonant conductance (including electronic 

 loading) of Gr , the power dissipated in the resonator is 



P, = V'Gr/2. (3.2) 



