Abstract
An avalanche diode is one of the most important devices for microwave oscillation. Its operation is modeled by the basic system which is described by two-dimensional ordinary differential equations. The basic system with no perturbation which is caused by the velocity modulation has already been analyzed. The system has periodic orbits, but they are structurally unstable.
The object of this paper is to analyze the extended basic system with the perturbation. At first, we linearize the system in the neighborhood of a singular point, and classify the solution characteristics on the parametric space. Next, applying Hopf bifurcation theorem in R2, the existence of a stable limit cycle is proved. The existence conditions of periodic orbits correspond to the oscillation conditions on real silicon avalanche diode. Further, the numerical simulation is used to confirm the local characteristics of the system obtaind by the linearization method and Hopf bifurcation theorem. The simulation also shows the global properties of the system such as an emergence and a collapse of a limit cycle and phase portraits of trajectories.
Finally, by use of above results, we discuss 1) the case in normal bias, 2) the operation during start-up and 3) the limitation on DC current required for oscillation. It is shown that the extended system describes the physical phenomena more accurately than the known system with no perturbation.
