Circuit modelling by difference equation: Pedagogical advantages and perspectives

Salehizadeh, Mohammad Reza; Nouri, Hassan

Abstract

Circuit theory is a cornerstone course in electrical engineering and control majors in ordinary universities and colleges throughout the world. This course covers fundamental principles and analysis methods of basic circuits commonly employed in the forthcoming courses. In most electrical programs after the introduction of basic elements of Ohm's and Kirchhoff's current and voltage laws, the dynamic response of the circuits containing capacitors and inductors will be studied. Customarily to solve these circuits, advanced mathematical approaches such as differential equations are used. Under such circumstances, the students are faced with two challenges, solving the differential equations, and understanding the dynamic response of circuits. In order to improve students' understanding, an analysis tool with less mathematical prerequisites should be used for the solutions before embarking on the use of conventional differential equation techniques such as Laplace transform. Hence, we propose a novel approach for these circuit analyses through the application of a discretized version of differential equations which is used in discrete control systems. Although this approach has a well-established background, its exploration uses in the circuit theory course as yet has not been reported. The novelty of the proposed approach not only lies in its intuitive simplicity but also in its contribution to the understanding and visualization of students in the real-time response of linear and non-linear circuits to any desirable input without any mathematical burden. The analysis can be performed by hand or this is also helpful for those who prefer modern education aided by computers. This, in turn, may attract more students to the program. In this paper, the effectiveness of the proposed approach is demonstrated through a set of illustrative examples.

Citation

Salehizadeh, M. R., & Nouri, H. (2020). Circuit modelling by difference equation: Pedagogical advantages and perspectives. Mathematical Modelling of Engineering Problems, 7(1), 26-30. https://doi.org/10.18280/mmep.070104

• Journal Article Type: Article
• Acceptance Date: Jan 26, 2020
• Online Publication Date: Mar 31, 2020
• Publication Date: Mar 31, 2020
• Deposit Date: Apr 29, 2020
• Publicly Available Date: May 4, 2020
• Journal: Mathematical Modelling of Engineering Problems
• Print ISSN: 2369-0739
• Electronic ISSN: 2369-0747
• Peer Reviewed: Peer Reviewed
• Volume: 7
• Issue: 1
• Pages: 26-30
• Series ISSN: 2369-0747
• DOI: https://doi.org/10.18280/mmep.070104
• Keywords: circuit; modelling; difference equation; dynamic response; non-linear circuits
• Public URL: https://uwe-repository.worktribe.com/output/5872819
• Publisher URL: http://iieta.org/journals/mmep