On deciding stability of high frequency amplifiers

Hyper-frequency amplifiers are nonlinear because of active components (diodes…) and infinite-dimensional because of transmission lines, here modelled by telegrapher’s PDEs. Using a resolved form for the latter, one obtains delay difference and differential equations, strictly more general than "neutral type equations". CAD tools provide estimates of frequency responses, but nothing on their stability. We discuss the mathematical foundations of deducing stability from various frequency responses. After linearisation around periodic solutions, this involves spectral properties of the monodromy operator of time-periodic delay systems that are far from well known. We will outline these results, mostly relying on an appropriate example.