Steady state analysis of oscillators

Abstract

A common method used for steady-state analysis of oscillators is called Harmonic Balance. Harmonic balance finds the steady-state solution directly in frequency-domain. However, Harmonic Balance is very sensitive to the initial guess and may not converge if the oscillation frequency is not known a priori. Sometimes it may converge to the unstable DC operating point of the oscillator. Moreover, it is usually difficult to have such good initial guess. In this thesis, a fast approach is developed to improve the initial guess for Harmonic Balance (HB). This approach is derived from Minimal Polynomial Extrapolation (MPE) and Warped Multi- time Partial Differential Equation (WaMPDE). The WaMPDE works by separating the fast and slow variations in the response of oscillators, thus minimizing time and CPU consumption. The role of MPE is to accelerate the work of WaMPDE. The advantage of the MPE method is that it saves Jacobian matrix decomposition and it is easy to implement. Simulation results of different oscillators (Colpitts and LC-tuned bipolar) are presented to evaluate the performance of the proposed method.