Efficient analysis of oscillators with multiple time dimensions

Abstract

Harmonic Balance (H B ) analysis is an established technique for the analysis of nonlinear circuits. In this thesis, we present a method to find the transient and steady-state behavior of oscillators based on a harmonic balance implementation which proves to be faster than traditional time domain simulations. It is derived from the warped multi-time partial differential equation (WaMPDE) approach developed in recent years. This approach efficiently separates the frequency modulation (FM) and amplitude modulation (AM) in oscillators. A review of Multi-time Partial Differential Equation (MPDE) and WaMPDE is presented along with the motivation and interest in warped multiple time axes. The first proposed method shows how to obtain initial boundary conditions for a WaMPDE system consistently with arbitrary physical initia l conditions in the system of ordinary differential equations in transient analysis. The second proposed method improves steady-state analysis since it does not require a good initial guess of the oscillation frequency and exploits the frequency-domain latency of circuits by using a different number of harmonics in each state variable. The WaMPDE approach is used to simultaneously bring the circuit state to the region of convergence of the HB analysis and determine the optimum number of harmonics required at each node in the circuit. In both transient and steady-state, an adaptive time step control technique is employed in one of the time axes and this considerably reduces the computational effort. Simulation results of different applications are described to demonstrate the performance of the proposed method. Finally, the proposed methods are validated with experimental results.