Low-dimensional model of a microwave resonator with p-n junction varactor diode

In many microwave devices there are units involving a length of transmission line and a semiconductor element with p-n junction. These systems can operate separately (for example, as a resonant filter returned by a varactor) or be a part of a circuit (in some generators a section of the line is inserted between the transistor base and collector). In general such units can be considered as distributed systems with the lumped nonlinearity. The experiments with various transmission lines with silicon varactor diodes have shown, that at high power of external periodic excitation these systems demonstrate a hierarchy of periodic, quasiperiodic and chaotic oscillations. Various scenarios of transition to chaos are observed, and namely via a cascade of period doubling bifurcations, intermittency and collapse of torus. A low-dimensional model has been constructed, qualitatively representing the parameter space structure of the distributed system. The purpose of the present paper is to investigate the influence of the varactor diode location on the dynamics of a driven microwave resonator and to model this situation with nonautonomous circuits.