A COUPLED RESONATOR REFLEX KLYSTRON 735 



3.1.1 Variation of Input Impedance with Frequency j Fig. 6{a), Equation 

 3.2 may be written as 



G 



where 



^ g + jh, (3.3) 



and 



Hence 





\y\ _ 



G 

 and 



= VfTv 



It is seen that ^^ and 6^ involve even powers of (2Q5) only, so that G\ Z \ 

 is an even function, i.e., symmetrical about the vertical axis. For this 

 reason, one-half the normalized impedance plot only has been given in 

 Fig. 6(a). Inspection of this figure reveals that the effect of coupling to a 

 secondary resonator is to broaden the frequency range over which a 

 high impedance level can be maintained across the interaction gap. 

 Comparing the variation of input impedance with frequency for 

 {Qkf = (i.e., single cavity) with that for {Qkf = 0.3, we see that for 

 a frequency deviation of 2Qb = d=0.6 the former shows a drop of 14 per 

 cent while the latter only varies by ±0.58 per cent. In terms of two cou- 

 pled resonators having Q = 100 and operating at 4000 mc this means 

 a variation in impedance of only ±0.58 per cent or ±.052 db over a 

 frequency range of 24 mc. 



Another result clearly brought out by the family of curves of Fig. 

 6(a) is that the process of broadbanding by coupHng to a second resona- 

 tor results in a reduction in absolute impedance level. This reduction 

 in impedance level at midband is related to the tightness of coupling, 

 (Qk) , by the expression, 



