Abstract:

To enhance students’ conceptual understanding and help them obtain a better overview of the electrical and electronic engineering subject, a sense of the applicability and limitations of the relevant theoretical tools is necessary.

To this aim, electrical engineering students were given a short questionnaire regarding the association between circuit analysis and electromagnetic theory, conventional circuits and transmission lines as well as electromagnetic propagation and ray optics. Students had already attended courses on electric circuits and electromagnetics and the questionnaire was given in the framework of the “Optical Communications” course, particularly the ray-optics consideration of optical fibers.

The great majority of students could see no association between circuit analysis and electromagnetics and had the impression that circuit theory only refers to electric circuits (that is, structures mainly including sources, resistors, inductors and capacitors) while electromagnetics regards electromagnetic fields and waves. This is mainly due to the fact that circuits and electromagnetics are addressed within different courses with little or no connection between each other. Regarding conventional circuits and transmission lines, most students could see a close relevance between them (in the sense that both structures involved similar concepts) however they could not find a way of transition between the transmission-line and the circuit “regime”. Regarding relevance between electromagnetics and ray-optics, the situation was better due to the fact that students had been already familiar with the applicability and the pros and cons of both approaches.

The paper proposes a teaching scenario for a 2-hour lesson regarding the applicability of the theories mentioned above. The expected learning outcome is the students to achieve a more unified consideration of electromagnetic phenomena and enhance their relevant conceptual understanding.

The issues addressed, together with the respective educational aims, are the following:
- Circuit analysis as a limiting case of electromagnetics (for static and low-frequency fields). The topic addresses issues such as voltage definition, Kirchhoff’s current law deduced from the continuity equation and Kirchhoff’s voltage law derived by means of field considerations. The aim is the students to see that circuit theory an approximation of electromagnetics (valid at the zero- or low-frequency limit) that enables the analysis of electric circuits without the complications of Maxwell equations.
- Conventional electric circuits as a limiting case of transmission lines when frequency is low enough so as the corresponding wavelength to be long compared to the circuit’s physical dimensions. The aim of the topic is the students to see (even in a qualitative manner) the connection between the transmission-line and electric-circuit regimes.
- Transmission line quantities (such as inductance and capacitance per unit length) derived by applying Maxwell equations. The aim is the students to see circuit quantities deduced by means of electromagnetic considerations and (in combination with topic 1) appreciate the relation between electromagnetics and circuit theory.
- A reference to the association between electromagnetic theory and ray optics (this particular issue is covered, in more detail, during the initial sessions of the “Optical Communications” course).

Keywords:

Engineering Education, Electrical Engineering Education, Circuit Analysis, Electromagnetic Waves.