Solution of a set of nonlinear algebraic equations for general-purpose CAD programs

Abstract

In this paper, we describe a method for solving sets of nonlinear alge braic equations that arise in computer-aided circuit (CAD) programs in the steady-state mode of analysis. The method discriminates among differ ent circuit elements in their contribution to the circuit equations. A loga rithmic mapping is used on a subset of the correction vector involved in updating nonlinear current and voltage elements and their partial deriva tive contribution to the circuit equations. The values of nonlinear resis tors, conductors, inductors, and capacitors are updated at every iterative step and then treated as though they were linear elements. However, in the steady-state mode, the values of capacitors and inductors are trans formed into conductors and resistors, respectively. The values of these ele ments are made functions of the Newton iteration. The functional relation depends upon the convergence behavior of the solution vector.We will also derive the element stamps of different nonlinear elements and generalize the stamps of arbitrary nonlinear functions.

Numerical electronic device modeling for circuit simulators

“…The variations on tlie iutrinsic terminal charges and branch voltages are checked to avoid slow convergence of tlie P\Te\vton-Raphson algorit.hm due to charge nonconservation. Logarithmic Ne\rton-Raphson iteration step size control [5] is implemented to adjust step size variations on device nonlinearities.…”