An algorithm for numerical analysis of oscillator including the shifting bias of active element

The problem of numerical analysis of oscillators has been extensively studied in the literature, O.L. Chua and P.M. Lin (1975). However the proposed iterative methods which include the effect of shifting bias of the active element are not effective enough. Problems occur with computing time when stiff problems are included in the circuit, or the oscillator is DC unstable (relaxation oscillations occur) and when a high quality factor resonant circuit is simulated. In this paper an algorithm which allows one to separate the dynamical simulation process from the shifting bias of active element, is presented. This effect as a slow time phenomenon, which appears at least after one period of oscillation time, is transformed into a suitable static problem. This approach rapidly reduces computation time, can demonstrate DC relaxations and also gives more accurate information for oscillator design