Use of Maple to Analytically Solve the Equations of an Electrical Circuit Containing a Resistor, Diodes and Voltage Generator

M�Hamed El Aydi,Mohammed Sbaa,Said Bounouar,Mohammed Barkatou,Rachid Bendaoud

doi:10.3844/jcssp.2020.1669.1683

Abstract

The role of technology and the use of software in the educational process are growing in recent times. The use of software is essential especially if the analytical method available is too complicated for the students. In this study, we used the Maple software to deal with two physics problems, in the first problem we consider an electrical circuit containing a resistor and two diodes powered by a sinusoidal voltage generator and in the second problem we consider an electrical circuit containing a resistor and a diode powered by a saw tooth voltage generator. For each problem we use Maple software to determine the exact analytical solutions for the current flowing in the different branches of the electronic circuit, we derive analytical expressions for the terminal voltages of all the elements of the circuit, we calculate the dynamic resistances diodes of the circuit and we animate graphic representations to study the influence of certain parameters on the current and the voltages at the terminals of all the elements of the circuit. The analytical solutions proposed are all expressed as functions of the Lambert W function.

Highlights

Maple is a proprietary computer algebra software allowing to manipulate mathematical expressions symbolically and to make exact calculations
The proposed analytical solutions are all expressed as functions of the Lambert W function In the second problem: Maple is used to determine exact analytical solution for the current flows through the Electrical circuit containing a resistor and diode powered by a saw tooth voltage generator presented in Fig. 2 and to study the influence of four parameters involved
Exact analytical solution in electronic circuit containing a resistor and two diodes powered by a sinusoidal voltage generator (Fig. 1)

Summary

Introduction

Maple is a proprietary computer algebra software allowing to manipulate mathematical expressions symbolically and to make exact calculations. Fjeldly et al (1991) exploited an approximate analytical resolution technique combined a test function with a series of expansion This method leads to a precise solution without requiring a lot of computing time. The authors (Pimbley et al, 1992) used Newton's method provides an accurate solution for negative values of normalized tension, but the precision of the solution is less acceptable for very large values of the normalized tension. This method induced a lot of computing time

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Results

Conclusion