Steady-State Analysis of Circuits with Multiple Adaptive Grids

This paper explores an effective adaptive algorithm to obtain the steady-state response of circuits with periodic excitation. This algorithm offers an alternative to conventional steady-state simulation techniques such as harmonic balance or shooting method. One of the contributions of this paper is the generic formulation of nonlinear circuit equations in terms of transformation matrices. This algorithm is especially advantageous to circuits showing high nonlinearity. In the proposed method, each circuit variable is represented by a linear combination of a set of adaptive basis functions (ABF). Waveform samples are obtained by multiplying a vector of coefficients times a transformation matrix. Furthermore, in order to improve the output resolution, the positions of the basis functions for each variable are adaptively controlled. In other words, we start the analysis with a uniform grid and increase the resolution where needed by adjusting the position of the grid points independently for each variable. The least squares method is used to find the set of coefficients that minimizes the error function defined by the formulation. We present for the first time simulation results with different grids in each state variable.