CONSTANT FREQUENCY OSCILLATORS 73 



In order to complete the general demonstration, it remains to show 

 that the values imposed on (7) by the condition of (8) do not require 

 physically impossible values of Vp, r„, and yu in order to satisfy (6) and 

 thus maintain oscillation. To do this, assume that (8) is solved for 

 either A'4 or A'5 and substitute in (6), remembering that .Yo is zero. 

 The result is: 



r„ ^\x,^XmJ \X, + X^I' ^^^ 



Inspection of this expression shows that the conditions required are 

 physically possible, and it follows that the amplitude of oscillation 

 increases or decreases until the effective values of Vp and of rg, which 

 are measures of the dissipation of energy on the plate and on the grid 

 sides, take up the values specified by the conditions of (9). Thus, for 

 instance, if Xi and X2 were approximately equal, then Tp would have 

 to be (yu — 1) times as large as Tg before the oscillation amplitude set- 

 tled down to a steady state value. To many who are accustomed to 

 neglect the losses occurring on the grid side of a vacuum tube when 

 dealing with oscillator problems, this low value of Tg wall appear as 

 somewhat unusual. In this connection, it may be pointed out that the 

 low value of Vg is not in any way a special requirement imposed by the 

 stabilizing reactances, X4 and X5, but is inherent in vacuum tube os- 

 cillators in general, unless particular conditions are arranged to render 

 it otherwise. For instance, it is a well-known experimental fact that 

 resistances of the order of 4000 ohms may be placed across the grid- 

 filament terminals of an oscillator employing any of the more common 

 types of three-element receiving amplifier tubes without stopping the 

 oscillations, when a good low-loss tuned circuit is employed. In view 

 of the fact that the amplitude of the oscillations is commonly limited 

 by Yg, this is evidence that stable oscillations may be secured with 

 values of Tg which are of the order of 2000 or 3000 ohms. 



The demonstration may be made more rigid by the use of (6) and 

 for the special case where A'l = Xo and X4 = Xr, = Xm = 0, in which 

 the stabilizing reactances have been omitted. For such a simplified 

 circuit, it is found by elimination of Xq between (6) and (7) that: 



Vp 

 To 



rpVg — Xi^ 

 r^rg + A'i2 



- 1. 



Now, Xi is of the order of 500 or 600 ohms at the most, while both r^ 

 and Tg are at least enough larger than this in the case of the more 

 commonly used vacuum tubes so that the expression for rp/vg is roughly 



