228 



BELL SYSTEM TECHNICAL JOURNAL 



in connection with the curve for the forced sinusoidal field, then the two 

 ordinates are both {E?/0^Pyi^ {v/cY'^ and the curve for the sheet is higher 

 than that for the forced field because, for the helicallv conducting sheet 



(a) (b) 



Fig. 5.4 — Pillbox and rectangular resonators. When a number of resonators are coupled 

 one to the next, a filter-type circuit is formed. 



T 



Q: 

 a 

 a 



I 



^^ 



® 



b> 



Vg < V for small values of -ya. Curve C shows {v/vgY-'^ 

 for the sheet vs. ^a. Aside from the influence of group 

 velocity, we might have expected the curve for the 

 sheet to be a little lower than that for the forced field 

 because of the energy associated with the transverse 

 electric field component of the sheet. This, however, 

 becomes small in comparison with the transverse mag- 

 netic component when v « r, as we have assumed. 



Various other circuits will be compared, using 

 the impressed sinusoidal field as a sort of standard 

 of reference. 



One of the circuits which will be considered is a 

 series of fiat resonators coupled together to make a 

 filter. Figure 5.4a shows a series of very thin pill- 

 boxes with walls of negligible thickness. A small cen- 

 tral hole is provided for the electron stream, and the 

 field E is to be measured at the edge of this hole. 

 The diameter is chosen to obtain resonance at a 

 wavelength Xo . Figure 5.4b shows a similar series 

 of flat square resonators. 

 For the round resonators it is found that* 



Fig. 5.5 — Resonators 

 with the opposing paral- 

 lel surfaces reduced to 

 lower stored energ\- and 

 increase impedance. 



(E^/lS^Py = 5.36 (v/cyi' {v/vgY'^ 

 for the square resonators* 



{E^/^H^yi-' = 5.33 {v/cyi^ {v/v„yi^ 



For practical purposes these are negligibly diiTerent. 

 * See Appendix Til. 



(5.24) 



