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BELL SYSTEM TECHNICAL JOURNAL 



tube for 0.625 cm wavelength, it was felt desirable to use a relatively large 

 helix diameter. Accordingly, a value of ya of 6.7 was chosen. We see that, 

 unless r/a is 0.9 or larger, this must result in an appreciable increase in gain 

 at some frequency lower than operating frequency. It was only by use of 

 great care in focusing the beam that gain was attained at 0.625 cm wave- 

 length, and there was a tendency toward oscillation, presumably at longer 

 wavelengths. This discussion of course neglects the effect of transmission 



0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 55 6.0 6.5 7.0 7.5 8.0 



Fig. 3.6 — The ordinate is yaF{ya) times the parameters from Fig. 3.5. For a fixed cur- 

 rent and voltage it is nearly proportional to gain per unit length, and hence the curves 

 give roughly the variation of gain with frequency. 



loss or gain. Usually the loss decreases when the frequency is decreased, 

 and this favors oscillation at low frequencies. 



3.1c Impedance of the Helix 



No impedance which can be assigned to the helically conducting sheet 

 can give full information for malching a heli.x to a waveguide or transmission 

 line. As in the case of transducers between a coaxial line and a waveguide or 

 between waveguides of different cross-section, the impedance is important, 



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