224 BELL SYSTEM TECHNICAL JOURNAL 



width. We have discussed the impedance and phase or velocity curves in 

 Chapters III and W . Field' has compared a coiled waveguide structure with 

 a series of apertured disks of comparable dimensions. Both of these struc- 

 tures must have about the same stored energy for a given field strength. 

 He found the coiled waveguide to have a low gain and broad bandwidth 

 as compared with the apertured disks. We explain this by saying that the 

 particular coiled waveguide he considered had a higher group velocity than 

 did the apertured disk structure. Further, if the coiled waveguide could be 

 altered in some way so as to have the same group velocity as the apertured 

 disk structure it would necessarily have substantially the same gain and 

 bandwidth. 



In another instance, Mr. O. J. Zobel of these Laboratories evaluated the 

 efifect of broad-banding a filter-type circuit for a traveling-wave tube by 

 w-derivation. He found the same gain for any combination of m and band- 

 width which made v = Vg(dv/do: = 0). We see this is just a particular 

 instance of a general rule. The same thing holds for any type of broad- 

 banding, as, by harmonic operation. 



5.3 A Comparison of Circuits 



The group velocity, the phase velocity and the ratio of the two are param- 

 eters which are often easily controlled, as, by varying the coupling between 

 resonators in a filter composed of a series of resonators. Moreover, these 

 parameters can often be controlled without much affecting the stored energy 

 per unit length. For instance, in a series of resonators coupled by loops or 

 irises, such as the circuit of Fig. 4.11, the stored energy is not much affected 

 by the loops or irises unless these are very large, but the phase and group 

 velocities are greatly changed by small changes in coupling. 



Let us, then, think of circuits in terms of stored energy, and regard the 

 phase and group velocities and their ratio as adjustable parameters. We 

 find that, when we do this, there are not many essentially different configura- 

 tions which promise to be of much use in traveling-wave tubes, and it is 

 easy to make comparisons between extreme examples of these configura- 

 tions. 



5.3a L niform Currenl Density throughout Field 



Suppose we have a uniform current density /q wherever there is longi- 

 tudinal electric field. We might approximate this case by flooding a helix 

 of very fine wire with current inside and outside, or by passing current 

 through a series of flat resonators whose walls were grids of fine wire. 



' Lester M. Field, "Some Slo\v-\V;ive Structures for Traveling-Wave Tuijes," Proc. 

 I.R.E., Vol. 37, J)]). 34-40, January 1949. 



