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BELL SYSTEM TECHNICAL JOURNAL 



wave wires C . In all cases, it is assumed that the coupling is so adjusted as 

 to make (r„ z') = 1 (broad-band condition). 



What sort of information can we get from the curves of Fig. 5.8? Con- 

 sider the curves for 1,000 volts. Suppose we want to cut down the opposed 

 areas of resonators, as indicated in Fig. 5.5, so as to make them as good as 

 half-wave wires (curve C). The edge capacitance in Fig. 5.5 will be about 

 equal to that for quarter-wave wires (curve C). Curve C is about 3.7 times 

 as high as curve B, and hence represents only about (1/3.7)'^ = .02 as much 

 capacitance. If we make the opposed area in Fig. 5.5 about .01 that in Fig. 

 5.4a or b, the capacitance* between opposed surfaces will equal the edge 



>!? 



Q. 8 



rvj 



6 



/3a 



4 



fla 



fla 



Fig. 5.8 — Coni]5arisons in terms of impedance parameter of an im|)ressed sinusoidal 

 field (.'1 ), circular resonators (B), half-wave wires (C) andquarter-wave wires (C) assuming 

 the group and phase velocities to equal the electron velocity. The radius of the impressed 

 sinusoidal field is a. 



capacitance and the total stored energy will be twice that for quarter-wave 

 wires, or equal to that for half-wave wires. This area is shown appro.xi- 

 mately to scale relative to Fig. 5.4 in Fig. 5.5. Thus, at 1,000 volts the 

 resonant strips of Fig. 5.5 are about as good as fine, closely spaced half- 

 wave wires. 



Suppose again thai we wish at 1,000 volts to make the gain of the reso- 

 nators of Fig. 5.4 (or of a coiled waveguide) as good as that for a helix with 

 (ia — 3. For /3a = 3 the helix curve .1 is about 3.2 limes as high as ihc resona- 



* This takes into account a difference in field distriljution — thai in I'Ik. 5.4h. 



