FILTER-TYPE CIRCUITS 



211 



We obtain vs w by adding — tt to the phase angle from 4.48, using (4.55) 

 and (4.57) in obtaining Bt and B^ . The phase angle vs. frequency is shown 

 in Fig. 4.27. As the irises are made larger, the bandwidth, co/, — cor , becomes 

 larger, largely by a decrease in w/. . 



The voltage of interest is that across C2 , that is, that across the gap. 

 I-rom (4.37), (4.44), (4.45), (4.55) and (4.57) we obtain 



V'/P = l/i-BrBi^y-' (4.58) 



V'/P = (V2/CMo:l - a;)(co - cor))'''' (4.59) 



This goes to infinity at both co = wl and w = coy • In Fig. 4.28, 

 (rV^)C2\/co/.ajr is plotted vs w. This curve represents the performance of 

 all narrow band structures of the type shown in Fig. 4.11. 



Fig. 4.28 — A quantity proportional to {E?/^'^P) for the circuit of Fig. 4.11, plotted vs 

 radian frequency w. 



In a structure such as that shown in Fig. 4.11, there is little coupling 

 between sections which are not adjacent, and hence the lumped-circuit 

 representation used is probably quite accurate, and is certainly more ac- 

 curate than in structures such as that shown in Fig. 4.10. 



Other structures could be analyzed, but it is believed that the examples 

 given above adequately illustrate the general procedures which can be 

 employed. 



4.4 Traveling Field Components 



Filter-type circuits produce fields which are certainly not sinusoidal with 

 distance. Indeed, with a structure such as that shown in Fig. 4.11, the elec- 



