A COUPLED RESONATOR REFLEX KLYSTRON 733 



The above equation* essentially contains three variables: 



(a) The dependent variable, F/G, i.e. input admittance normalized 

 with respect to the shunt conductance, 



(b) the independent variable, (2Q5), which is a factor proportional 

 to the frequency deviation from resonance, and 



(c) parameter, (Qk), a measure of the tightness of coupling between 

 the two cavities. 



Compared mth the input admittance for a single resonator which 

 was given earlier, [equation (2.3),] as, Y/G = 1 + j2Q8, it is seen that 

 the conductance component has been changed by a factor 



L ^ 1 + (2Qsyj 



and the susceptance by 



L 1 + (2Q8yj • 



Also, by setting k = 0, i.e., completely decoupling the secondary resona- 

 tor, equation (3.2) reduces to equation (2.3) as, indeed, it should. 



The information contained in equation (3.2) may be presented graph- 

 ically in a number of ways. We can plot the magnitude of the normahzed 

 input impedance, GJ Z |, as a function of 2Q8 with (Qk)^ as parameter 

 as shown in Fig. 6(a).t Or we can plot the input admittance given by 

 equation (3.2) directly in the g-h plane as in Fig. 7. Finally, we may show 

 the variation of input phase angle with normalized frequency for differ- 

 ent degrees of coupling as in Fig. 6(b). Each of these graphical represen- 

 tations has an important bearing on the performance of the coupled 

 resonator klystron. Thus, the curves of Fig. 6(a) will have the same 

 general shape as the RF power output vs. frequency plot of the reflex 

 oscillator, the family of curves of Fig. 7, when superimposed on the 

 electronic admittance spiral, can be used for a detailed analysis of mode 

 shapes, and Fig. 6(b) determines the modulation characteristics obtain- 

 able with coupled resonators. 



Having briefly touched upon the significance of the families of curves 

 given in Figs. 6(a), 7, and 6(b), we can now proceed to discuss them in 

 greater detail and to establish further valuable results. 



* To check the accuracy of this equation, the curve for (Qky = 1 in Fig. 6(a) 

 was replotted using the full expression given by equation 3.1 and assuniing Q 

 = 100. The agreement was found to be essentially perfect as far as its use in this 

 investigation is concerned. 



t For a similar presentation of the transfer characteristics of coupled tuned 

 circuits see reference (6), 



