Symbolic analysis of linear electric circuits with MIT Julia Symbolics.jl package

Abstract

This paper presents novel free open-source software JuliaCAP for symbolic analysis of linear time-invariant electric circuits in the complex domain of the Unilateral Laplace Transform or Phasor Transform. Modified Nodal Analysis (MNA) has been chosen for formulation of circuit equations in JuliaCAP. JuliaCAP has been developed by Kristina Rajković, Glorija Došlo, Nikola Radojević, Tamara Petković and Ivana Stanojević, at the University of Belgrade - School of Electrical Engineering, Belgrade, Serbia. JuliaCAP is written in Julia, a free open-source (MIT licensed) programming language. Whereas Julia is a relatively new language, there will be some words about it. As a free opensource software package, the underlining algorithm is revealed in full detail, so anybody can get a better understanding of the used methods. We offer JuliaCAP as a useful tool for solving linear time-invariant electric circuits. The future directives should be the improvement of simplifying expressions and the absence of the possibility to solve electric circuits in the complex domain of the Unilateral Laplace Transform. Also, it is shown through examples how this software operates. Electric circuits that are used in examples are Riordan gyrator network, 3rd order Butterworth Low-pass Filter, Subtractor and Adder.

Keywords

• symbolic analysis
• linear time-invariant electric circuit
• julia programming language
• symbolic simulation
• modified nodal analysis (mna)
• unilateral laplace transform