Effects of multiple internal reflections on the small signal gain and phase of a TWT

We formulate and solve a set of equations that model the effects of reflections from an arbitrary number of circuit discontinuities in a traveling wave tube operating under small signal conditions. Applying this model to a case in which the discontinuities represent a series of small random pitch variations due to fabrication errors in a helix TWT, we find that reflections may significantly increase the statistical effects on gain and output phase first reported in reference [1].