Effects of random circuit fabrication errors on small signal gain and phase in traveling wave tubes

We evaluate the effects of small random fabrication errors on the small signal characteristics of a traveling wave tube.The classical ID small signal theory of Pierce, is applied. Random, axially varying perturbations are introduced in the circuit phase velocity mismatch the gain parameter and cold tube circuit loss in Pierce notation. First order perturbation analysis of the small signal equations show that the standard deviations in the output phase and in the small signal gain are linearly proportional to the standard deviations of the individual perturbations in b, C, and d. The study confirms effects of perturbations in the circuit phase velocity dominate the effects of perturbations in C and d.