Doctoral Dissertation

A contribution to algorithms in computer-aided symbolic analysis of linear electric circuits and systems

University of Belgrade, School of Electrical Engineering, Belgrade, Serbia, Yugoslavia, 1996

Advisor: Dr Branimir D. RELJIN, full professor


Summary

Matrix approach to the analysis of linear time-invariant electric circuits and systems reveals a unique final form of the circuit/system equations - the matrix system of linear equations. What is specific for certain circuits and systems is the algorithm of forming the required matrices and matrix equations, and identification of the circuit/system variables. This research presents a new and unique concept and formulation of general symbolic analysis of linear electric circuits and systems (CAS - Circuit And/or System).

The most general concept is proposed for

The package SALECAS (Symbolic Analysis of Linear Circuits and Systems) has been developed in Mathematica to implement this general concept of symbolic analysis.

At the highest level of abstraction, from the viewpoint of the automated computer-aided symbolic analysis, a linear circuit and system have identical representations in the form of a list

system = {"class", "label", components, knowledge}.

The elements of the list are

The following major CAS classes can be identified:

The CAS components represent ideal circuit elements, microwave network ports, functional blocks like integrators and differentiators, digital filter multipliers and delays, equivalent networks for modeling electronic devices, multiport networks whose matrix parameters are known, etc. A CAS component is described by a list:

component = {"type", "name", connection, parameters, energy}.

The list items are

The required knowledge to analyze a CAS is a list of the form

knowledge = {library, variables, matrices, rules, procedures, presentation}.

The corresponding items are

A CAS library is a list of types:

library = {type1, type2, type3, ...}.

Each type is a list of the form

type = {symbol, terminals, definition, stamp},

whose items are

Generally, symbolic analysis can be viewed as a scan of the CAS net-list, and systematic update of the CAS matrices according to the components' stamps.

Following the previously exposed system of abstractions, several symbolic simulators have been developed to analyze various classes of CASs. They constitute the package SALECAS. The simulators are:

Except the simulators, a set of specialized functions has been developed within SALECAS:

A novel framework for general symbolic analysis of linear time-invariant circuits and systems is presented. A detailed decomposition of the problem is offered. Linear circuits and systems are viewed as lists of items representing their identification, components and symbolic analysis knowledge.

A consequent system of abstractions is developed to specify linear CASs and to provide encapsulation mechanisms of analysis procedures and entities. It can serve as a starting point for object-oriented decomposition in symbolic analysis.

A unique conceptual engine is proposed for symbolic analysis of physically different systems. These systems are essentially different in appearance and physical background, but they have the same mathematical matrix formulation from the symbolic analysis viewpoint.


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Last updated 1998/10/27 16:00.