Simulation of Electrical Circuits Using Conjugate Gradient Algorithm

Abstract

Problems of electrical circuits’ simulation are known for a long time. However, the simulation quality and speed are far from perfect, especially when it comes to non-linear circuits. The method offered is based on table form of electrical circuits’ equations. Differential-algebraic equations of electrical circuits are converted to the systems of linear algebraic equations (SLAE) with finite differences method. It is important that SLAE are solved with Conjugate Gradient Algorithm (CGA) that is well adapted to systems with sparse matrixes. The solution of the SLAE at previous time step is a good initial approximation of the solution at present time step. That is why CGA reduces calculations to 20-40% of the full algorithm typically. The possibility of using CGA for solving SLAE with matrixes that have no specific sign is proved by numerical experiments. A method for acceleration of solving electrical circuits’ SLAE is proposed. It differs from the Nodal Voltages Method as no apparent avatar of circuit SLAE is formed. A comparison of program “Electroscope” based on proposed method with programs “PSIM” and “Fastmean” is presented. “Electroscope” is leading in terms of quality and speed of test circuits’ simulations.