A COUPLED RESONATOR REFLEX KLYSTRON 



725 



negative electronic conductance exceeds the circuit conductance and 

 where the build-up of oscillations is possible, and the region to its right 

 where the condition for the build-up of oscillations is not met. Thus, 

 for the load line in the position indicated, the tube will not oscillate in 

 the A^ = mode, but will do so in the iV = 1, 2, 3 and higher order 

 modes. 



Still referring to Fig. 4, suppose 6 has been adjusted by means of the 

 repeller voltage to ^i = (3 + %)27r radians, i.e., the center of the 3 -f 

 % mode. The small signal-electronic-admittance vector will then be a 

 pure negative conductance terminating on the spiral at point A and 

 together with the passive circuit conductance yielding a net negative 

 conductance across the grids of value {OA-OB). Oscillations, therefore, 

 will build up until the equiUbrium condition. Ye = — F, has been satis- 

 fied. In terms of the admittance plane representation, the electronic- 

 admittance vector will shrink without change in its phase until it termi- 

 nates on the load line at point B. Since the electronic admittance for 

 the particular value of d chosen is a pure conductance, oscillations will 

 occur at the resonant frequency of the cavity, /o , which is also the fre- 

 quency corresponding to the intersection of the electronic-admittance 

 vector and the load line. 



From equation 2.1 we see that, 



OB _ V2Fo/ 



L V2F„; J 



\2Vo) 



(2.6a) 



v=o 



where Vi is the steady state RF gap voltage corresponding to drift 

 angle, ^i . Entering the graph of Fig. 2 with OB/OA as the ordinate, we 

 can read off the corresponding value of (i8/2Fo)7i^i . For a particular 

 tube structure and operating conditions, iS/2Fo will be a fixed constant 

 so that, in effect, we have determined the value of a quantity propor- 

 tional to the product of Fi^i . 



Next, consider the case where d has been changed from Si = 

 (3 -f M)27r to 02 = K(S -f M)27r radians. The electronic admittance 

 vector for F = will now terminate on the Fe«-plot at C Again a 

 build-up of oscillations will ensue and upon attainment of the steady 

 state condition the vector will have shrunk to the value OD, with the 



