74 BELL SYSTEM TECHNICAL JOURNAL 



equal to (/x — !)• Thus, in the simplest kind of vacuum tube circuit, 

 it is seen that Vg is apt to be appreciably smaller than r^,, and by no 

 means negligible in its effect. 



To return to (8), which expresses the relation between Xn, X5 and 

 other circuit reactances which are necessary to cause the frequency to 

 be independent of battery voltages, we note that, although (8) is still 

 in generalized form, and is yet to be applied to the particular case 

 shown in Fig. 2, the very significant fact that the oscillation frequency 

 for this type of stability must be the series resonant frequency of 

 the tuned circuit is a direct consequence of the requirements of the 

 equation. 



For application to the Hartley type of oscillator, the various terms 

 of (8) have the following significance: 



X\ = coLj, 



X2 == ^-1^2, 



Xm = wM, 



where co = lir X frequency and Xa or A^s are to be determined. In 

 the case of Fig. 2, where stabilization is accomplished on the plate side, 

 we put ^"4 equal to zero. Then solving (8) for X5, we find: 



X, = 2coM i / ^ ,, ) - wLs ( r T ^r ] - ^Li. 



X5 is thus required to be negative, so that a capacitive reactance is 

 necessary for plate stabilization of a Hartley-type oscillator. Thus 

 putting 



X - --1- 



C0C5 



and remembering that since A'o = 0, the angular frequency is given by 



(02 = \/C,{U + U + 2M), 

 finally we get 



C -c Lr + U + 2M 



^'^^'\u + m) ^^^\L2 + m) 



which is the value of capacity which should be inserted between the 

 plate and the tuned circuit of a Hartley-type oscillator in order to 

 cause the frequency to remain constant when the battery voltages are 

 varied, and there is no reactance between the grid and tuned circuit. 



