746 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1953 



3.4 Mode Shapes Obtainable with Two Coupled Resonators of Unequal 



The complex admittance plane representation for the case of the 

 secondary Q equal to half the primary Q is shown in Fig. 13(a) and the 

 resulting mode shapes for the 3 + % repeller mode in Figs. 13(b), (c), 

 (d), and (e). Again we notice that the coupUng coefficient required for 

 best modulation linearity is considerably smaller than that which re- 

 sults in a flat topped power curve. From Fig. 13(c) the most linear 

 frequency-repeller voltage curve is associated with (Qfc)^ = 0.8 while 

 from Fig. 13(d) a flat power mode may be obtained with a value of 

 (Qk)^ somewhat less than 1.6. In cases where neither modulation linearity 

 nor constant power output are of importance but where the application 

 requires a wide electronic tuning range. Fig. 13(e) shows the advantage 

 to be gained from coupled cavities. Here, power output has been nor- 

 malized with respect to its peak value within the particular mode under 

 consideration and plotted against Q8. The ratio of half -power band- 

 widths for the curve corresponding to (Qk) = 2 A to the single resonator 

 case, i.e., (Qk)^ = 0, is seen to equal 1.73. 



A phenomenon which may be encountered in the operation of the 

 coupled resonator reflex klystron is illustrated by the (Qk)^ = 4.0 curve 

 of Fig. 13(b). Here we are dealing with a split mode in which the powder, 

 though everywhere a single valued function of repeller voltage, drops 

 to zero over a range of repeller voltages centered about the middle of 

 the mode. The reason for this behavior may be readily understood from 

 an inspection of the complex admittance plane representation of Fig. 

 13(a). It is caused by the Fcs-locus for the 3 -|- % repeller mode crossing 

 the appropriate load line and thereby resulting in a frequency band over 

 which the condition for oscillation cannot be met. 



4.0 AN EXPERIMENTAL COUPLED-RESONATOR REFLEX KLYSTRON 



The reduction to practice of the theoretical results obtained in the 

 above study raises these requirements: 



(1) An arrangement must be found which allows the coupling between 

 primary and secondary cavities as well as between primary cavity and 

 waveguide output line to be varied continuously and independently. 



(2) Either primary or secondary resonators (or both) must be tunable 

 to allow frequency adjustments for synchronous operation. 



(3) Secondary resonator Q should be continuously variable. 



(4) The secondary resonator should be detachable for independent 

 determination of Q. 



