I 



A COUPLED RESONATOR REFLEX KLYSTRON 737 



showing that the size of the loop is a sensitive function of the degree of 

 coupUng. The conductance value for the first and third crossover points 

 is obtained by substituting 



2Q5 = ±V{QkY - 1 



into equation (3.4) and results in gr = 2, i.e., a value of g independent of 

 the coupling coefficient. 



The dashed lines shown in Fig. 7 connect points of equal frequencies. 

 It is of interest to note that these loci are straight lines crossing the 

 conductance axis at g = 2. To prove this, eliminate (Qk)^ between equa- 

 tions (3.4) and (3.5). This yields, 



whence 



h = i'2Q8){g - 2). (3.8) 



For a particular and constant value of 2Q8, equation (3.8) describes a 

 straight line of slope equal to ( — 2Q5) intersecting the g-a,xis Sit g = 2. 

 3.1.3 Variation of Input Phase Angle with Frequency, Fig. 6(h). The 

 last driving point property of interest to this study is the dependence 

 upon frequency of the input phase angle, 0. Referring to equation (3.2), 

 this quantity is obtained as. 



The graphical representation of this function is given in Fig. 6(b). It 

 shows the gradual transition from a simple S-shaped curve for (Qk) = 0, 

 having its only point of inflection at the origin, to the type of curve 

 corresponding to (Qk)'^ > 1 which intersects the frequency axis three 

 times. The special case of {Qkf = 1, considered earlier and found to 

 result in the formation of a cusp in the complex admittance plane, now 

 gives rise to a plot of input phase which is tangent to the horizontal 

 axis at the origin. 



To investigate the condition for greatest linearity between phase 

 angle and frequency, which, when applied to the coupled resonator 

 reflex klystron, would be the condition for optimum modulation linearity, 

 one could simply apply a straight edge to the curves of Fig. 6(b) and 

 pick the best value of (Qk)^ in this manner. A much more sensitive 

 criterion of linearity, however, is the variation with frequency of the 

 slope of these curves. An analytical expression for this slope has been 



