The low-signal-gain versus frequency slope is often a highly desirable property of traveling wave tube (TWT) used in a communication system. The gain ripple is usually caused by internal reflexions of forward and backward waves in the TWT. Random fabrication error may have a detrimental effect on the performance of TWT. The quartic equation including backward wave models the effect of reflection to analyze the effect of Gain ripple from many small circuit errors in a TWT operating under small-signal condition. We present a transfer matrix method (TMM) to correctly calculate the transmission and reflection of the wave incident respectively from left and right at a single isolated joint. The TMM, which links the input signal to output signal that includes the feedback signal from the reflections at multiple joints to the output end, can calculate the gain ripple of multiple internal reflections. Appling this method to several numerical examples, we look at how small signal gain is affected by a single isolated discontinuity and many small randomly distributed discontinuities. In particular, we investigate the effects of random perturbations of Pierce velocity detuning parameter b and Pierce gain parameter C on the small signal gain at different values of space charge 4QC . The computed result agrees with that from Chernin’s model. We find that reflections may significantly increase the statistical effects on the gain. A further conclusion is that the standard deviation of gain, σdgain, increases with σb gradually, but the ratio of the backward wave power to the forward wave power at x=0 decreases with σb when standard deviation of pierce velocity detuning parameter, σb, is more than 1.5. In another example, the effects of two discontinuities of pitch distribution and many small random pitch errors on gain ripple are reported for a G-band TWT. We find that larger pitch error and longer distance for the discontinuities may produce a larger ripple in the small-signal-gain versus frequency. Many small discontinuities may produce a large gain ripple, and the gain ripple grows as the level of pitch error increases. These effects of random fabrication errors become increasingly important for very high frequencies, such as 1 THz, at which TWTs are currently being designed and built.
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