Extensions of Johnson’s Theory of Backward-Wave Oscillations in a Traveling-Wave Tube

This paper extends Johnson's classical theory [Johnson, Proc. IRE 43, 684 (1955)] for the threshold of backward-wave oscillation (BWO) in a traveling-wave tube by considering the effects of: 1) small random variations of the circuit phase velocity along the tube axis and 2) end reflections. We find that both the BWO threshold and BWO frequency are minimally affected by random variations of the phase velocity, but we find that the oscillation threshold depends sensitively on the magnitude and phase of the composite reflection coefficients.