A Study of Symbolic Analysis of Electrical Circuits on the Example of a Radio Frequency Filter

Abstract

The year 2022 marks the 175th anniversary of Kirchhoff's theorem on finding a symbolic expression of the current of an electric circuit branch from its contour determinant in the form of a fraction with a denominator and numerator. The first part of Kirchhoff's theorem concerning finding the contour determinant (fraction denominator) marked the beginning of graph theory, while the second part of the theorem on finding the numerator of a fraction remains unused to date. A symbolic circuit analysis calculation of transient processes in the radio frequency filter is carried out at the operator's stepwise and harmonic influences. The computer-aided calculation program developed by the authors is based on the modified Kirchhoff rule for finding the symbolic expression of the current of a branch of an electrical circuit from its contour determinant and it can be useful for researchers, engineers and students of mathematical and technical specialties. The program console is written in the Delphi package and opens in the Windows environment under the name "TINS" and it has an intuitive interface. The expressions for the branch currents can be copied without modification to the Maple computer algebra package, and to the Mathcad package – with the replacement of mathematical symbols. The reliability of the calculations was checked by initial and final conditions by comparing the Laplace transform table with the originals found by the “invlaplace” operation built into the Mathcad package. The presented computer program and calculation methodology allow you to quickly understand certain sections of mathematics and radio electronics and easily choose another object as a study. Computer-aided calculation of electromagnetic processes in radio engineering devices using the "TINS" program reduces the analysis time by obtaining results in symbolic form.
Copyright © 2022 Praise Worthy Prize - All rights reserved.