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

Motivated by current interest in submillimeter and terahertz (THz) slow-wave vacuum electronic amplifiers, which employ miniature, difficult-to-manufacture slow-wave circuits, we evaluate the effects of small random fabrication errors on the small-signal characteristics of a traveling wave tube. The classical I-D small-signal theory of Pierce, generalized to allow axially varying circuit characteristics, is applied. Random, axially varying perturbations are introduced in the circuit phase velocity mismatch b, the gain parameter C, and the cold-tube circuit loss d, in Pierce notation. Results from a first-order perturbation analysis of the small-signal equations, which are confirmed by numerical analysis, 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. Our study confirms that the effects of perturbations in the circuit phase velocity dominate the effects of perturbations in C and d.