Fast transient analysis of oscillators using multiple time scales with accurate initial conditions

A fast and robust method to analyze the transient response of free-running oscillators is proposed. It is based on the harmonic balance technique derived from the warped multi-time partial differential equation approach. We show for the first time how to precisely obtain initial boundary conditions that are consistent with arbitrary physical initial conditions in the system of ordinary differential equations at any setting time. An adaptive time step technique also reduces the computational effort. The analysis of a LC-tuned bipolar oscillator demonstrates the excellent performance of the proposed method