218 BELL SYSTEM TECHNICAL JOURNAL 



CHAPTER V 

 GENERAL CIRCUIT CONSIDERATIONS 



Synopsis of Chapter 



TN CHAPTERS III AND IV, helices and filter-type circuits have been 

 ^ considered. Other slow-wave circuits have been proposed, as, for in- 

 stance, wave guides loaded continuously with dielectric material. One may 

 ask what the best type of circuit is, or, indeed, in just what way do bad cir- 

 cuits differ from good circuits. 



So far, we have as one criterion for a good circuit a high impedance, 

 that is, a high value of Er/^P. If we want a broad-band amplifier we must 

 have a constant phase velocity; that is, 13 must be proportional to frequency. 

 Thus, two desirable circuit properties are: high impedance and constancy 

 of phase velocity. 



Now, E^/l3~P can be written in the form 



Er-/(3'-P = E'/l3nVvg 



where W is the stored energy per unit length for a field strength E, and Vg 

 is the group velocity. 



One way of making E-/i3-P large is to make the stored energy for a given 

 field strength small. In an electromagnetic wave, half of the stored energy 

 is electric and half is magnetic. Thus, to make the total stored energy for a 

 given field strength small we must make the energy stored in the electric 

 field small. The energy stored in the electric field will be increased by the 

 presence of material of a high dielectric constant, or by the presence of large 

 opposed metallic surfaces, as in the circuits of Figs. 4.8 and 4.9. Thus, such 

 circuits are poor as regards circuit impedance, however good they may be in 

 other respects. 



If the stored energy for a given field strength is held constant, £"- J3'-P 

 may be increased by decreasing the group velocity. It is the phase velocity 

 V which should match the electron speed. The group velocity Vg is given in 

 terms of the phase velocity by (5.12). We see that the group velocity may 

 be much smaller than the phase velocity if —dv'dw is large. It is, for in- 

 stance, a low group velocity near cutoff that accounts for the high imped- 

 ance regions exhibited in Figs. 4.20 and 4.28. We remember, however, 

 that, if the phase velocity of the circuit of a travehng-wave tube changes 

 with frequency, the tube will have a narrow bandwidth, and thus the high 



