726 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1953 



frequency of oscillation determined by the location of point D on the 

 load line. By an argument similar to the one used before, we have 



OD _ ^\-2W) 



OC ' (^V^\ ^ ^ 



and once more, the plot of Fig. 2 will yield the value of 



(2-7-0)^^^ °'- (2T;)^^^'- 



It is apparent that /3/2Fo is a factor common to all these determinations 

 and may be neglected if we are only interested in the mode shape, i.e. 

 the relative variation of gap voltage or output power with the repeller 

 drift angle, 6. For modes higher than A/' = 2, the electronic admittance 

 spiral approximates a number of semi-circles with their centers close to 

 the origin. Hence 



OA^OC and -M_ > £^ . 



OC OA 



Figure 2, then indicates that 



ViOi > V^2 or Fi^i > KV^i 



and since K does not vary greatly from unity V\ > V2. This is as it 

 should be since we know that a change in repeller voltage from its mid- 

 mode value causes a decrease in power output and, hence, in gap volt- 

 age. The latter will decrease to zero when 6 has been adjusted to a 

 value such that the Ye, vector terminates at the intersections of the 

 electronic admittance spiral and the load line. 



Another result which becomes apparent from an inspection of Fig. 4 

 is this. For the condition of stable oscillation the phase angle of the 

 electronic admittance equals that of the passive circuit except for an 

 additive constant of 180 degrees which, however, may be disregarded 

 in this argument. The frequency of oscillation may be determined from 

 the input-phase-angle vs. frequency plot of the passive circuit by looking 

 up the frequency corresponding to the particular value of phase angle 

 to which the electronic admittance has been adjusted (by means of 

 repeller voltage). Thus, the curve relating repeller-drift-angle to fre- 

 quency is identical with the plot of input-phase-angle vs. frequency 

 for the passive circuit. Moreover, if repeller voltage is linearly related 



