Computer aided analysis of electric circuits using state-variable techniques.

Abson, Derek S.

Abstract

There are three main tasks that a computer program based on state-variable analysis must perform: 1) formulation of a degenerate system of equations; 2) processing of these equations until they eventually become the state equations; 3) the solution of the state equations. The first task requires the computation of a topological tree and its associated tie-set matrix. This can be done using either matrix or search methods. Degenerate variables can then be eliminated using Pottle's method or the Auxiliary Trees method, which is based on Bashkow's work. The solution of the state equations can be accomplished using: 1) an Adams-Bashforth-Moulton predictor corrector method; 2) a Runge-Kutta method (e.g. England's method); 3) Certaine's method of transition matrices; 4) methods suitable for use with systems containing equations with widely separated time constants, known as Stiff equations (e.g. Gear's method). It was found that the formulation of the degenerate system of equations was relatively easy to program, but the elimination of degenerate variables from the main system of equations proved more difficult to program. Additionally, the solution of the state equations gave rise to problems that were sometimes difficult to diagnose. Apart from one problem that could not be resolved using Certaine's method, all test networks containing capacitors, resistors, inductors and independent sources were solved. However, test circuits containing linearly-controlled sources failed without exception when a row of the augmented matrix contained all negative elements - this gave rise to transient responses of the right shape, but grossly distorted in magnitude. Program FOFSVM5 was based on Bashkow's topological formulation of the state equations and uses the Auxiliary Tree method of eliminating the degenerate variables from the main system of equations. It is hoped that FOFSVM5 can be used to investigate integrated circuits in future, subject to various improvements.

Citation

ABSON, D.S. 1976. Computer aided analysis of electric circuits using state-variable techniques. Robert Gordon's Institute of Technology, MPhil thesis. Hosted on OpenAIR [online]. Available from: https://doi.org/10.48526/rgu-wt-1993274

• Thesis Type: Thesis
• Deposit Date: Nov 8, 2024
• Publicly Available Date: Nov 8, 2024
• DOI: https://doi.org/10.48526/rgu-wt-1993274
• Public URL: https://rgu-repository.worktribe.com/output/1993274
• Award Date: Aug 31, 1976