Analysis of helical waveguide

The dispersion characteristics of the large-diameter helical waveguide are calculated using Pierce´s small-signal theory. The backward wave oscillation poses a serious problem for the development of this circuit as a broad-band high-gain amplifier. The gain of the backward waves is in general higher than the gain of the forward waves. For the first space harmonic (m = 1) mode, the forward and the backward wave gains are, respectively, 2.17 and 2.24 dB/cm. The bandwidth is 40 percent for a total gain of 30 dB if the backward waves are ignored. The onset of the backward wave oscillation limits the bandwidth to 5 percent for such high gain. The threshold interaction length for the onset of oscillation is also calculated. If the oscillations are not suppressed, the total gain of the circuit is limited to about 12 dB. At this low gain, the bandwidth can be as high as 57 percent. The device performs better with the low-order space-harmonic modes. Not only are the gain and the bandwidth larger for the low-order modes, but the ratio of the backward to forward wave gains and the number of backward waves excited are also smaller.