FILTER-TYPE CIRCUITS 



199 



Proceeding as before, we find 



= jSo h tan jSo h 



tanh {(d/h) yh) 

 We see that, in this case, for small values of yh we have 

 ^oh tanh ^oh = h/d 



(4.33) 



(4.33a) 



There is no transmission at all for frequencies below that specified by (4.33). 

 As the frequency is increased above this lower cutoff frequency, yh and 

 hence I3h increase, and approach infinity at fSoh = x/2. Actually, of course, 

 the upper cutoff occurs at /3^ = x. In Fig. 4.7 I3h is plotted vs jSoh for h/d — 0, 



20 



/3h 



/3oh 

 Fig. 4.7 — The variation of /3 with frequency (proportional to /3o//) for the longitudinal 

 mode of the circuit of Fig. 4.3. This mode has a band pass characteristic; the band narrows 

 as the opening of width 2d is made small compared with the iin height. Again, the curves 

 are in error near the upper cutoff at 0( = tt. 



10, 100. This illustrates how the band is narrowed as the opening between 

 the slots is decreased. 



By the means used before we obtain 



E'/^'P ^ i2/MV){y/^y 



cosh yd 



sinh yd cosh yd — yd 



)v. 



fJi/e (4.34) 



We see that this goes to infinity at 7 J = 0. For large values of yd it be- 

 comes the same as (4.30). 



4.2 Practical Circuits 



Circuits have been proposed or used in traveling-wave tubes which bear 

 a close resemblance to those of Figs. 4.1, 4.3, 4.5 and which have very similar 



