Stability considerations in lossless varactor frequency multipliers

A general analysis of stability conditions of pumped nonlinear systems is presented in this paper. The type of instability investigated for these systems is that which causes spurious tones to appear at any point in the system in the vicinity of an appropriate harmonic carrier. A set of stability criteria that assure stability for the system has been given in terms of scattering parameters of the system. These criteria have then been applied to investigate the stability of lossless varactor harmonic generators that have been shown in this paper to be potentially unstable systems. It is then investigated for these multipliers how instability arises, and how it can be avoided by proper terminations. For some simple terminations, which are usually used in practice, sufficient conditions, that assure total stability of the multipliers, are explicitly given.