TY - JOUR
T1 - Turning mesh analysis inside out
AU - Skromme, Brian J.
AU - Barnard, Wendy M.
N1 - Funding Information:
This work was supported by the National Science Foundation through the Improving Undergraduate STEM Education Program under Grant No. 1821628. The first author thanks Don Fowley of Wiley for his support.
Funding Information:
Wendy Barnard is an Assistant Research Professor and Director of the College Research and Evaluation Services Team (CREST) at Arizona State University. Dr. Barnard received her Ph.D. from the University of Wisconsin-Madison, where she focused on the impact of early education experiences and parent involvement on long-term academic achievement. Her research interests include evaluation methodology, longitudinal research design, STEM educational efforts, and the impact of professional development on teacher performance. Currently, she works on evaluation efforts for grants funded by National Science Foundation, US Department of Education, local foundation, and state grants.
Publisher Copyright:
© American Society for Engineering Education 2020.
PY - 2020/6/22
Y1 - 2020/6/22
N2 - Elementary linear circuit analysis is a core competency for electrical and many other engineers. Two of the standard approaches to systematic analysis of linear circuits are nodal and mesh analysis, the latter being limited to planar circuits. Nodal and mesh analysis are related by duality and should therefore be fully symmetrical with each other. Here, the usual textbook approach to mesh analysis is argued to be deficient in that it obscures this fundamental duality and symmetry, and may thereby impede the development of intuition and the understanding of the nature of mesh currents. In particular, the usual distinction between inner and outer meshes (if the latter is even recognized) is argued to be meaningless, as can be seen when drawing a planar circuit on the surface of a sphere. A generalized definition of a mesh is proposed that includes both inner and outer meshes on the same footing. Selection of a reference node in nodal analysis should be paralleled by the selection of any mesh to be the reference mesh in mesh analysis, which is always selected to be the outer mesh by default in the usual approach. All branch currents are shown to the difference of two mesh currents, and the zero of all mesh currents is now arbitrary just as it is for node voltages. Use of supermeshes is sometimes obviated by the new approach, and the analysis is sometimes simplified. This new approach has been used in two sections of a linear circuit analysis course in Fall 2019, and student survey data is presented to show preference for the new method over the usual textbook method. An interactive multiple-choice tutorial describing the new method has been integrated into a step-based tutoring system for linear circuit analysis.
AB - Elementary linear circuit analysis is a core competency for electrical and many other engineers. Two of the standard approaches to systematic analysis of linear circuits are nodal and mesh analysis, the latter being limited to planar circuits. Nodal and mesh analysis are related by duality and should therefore be fully symmetrical with each other. Here, the usual textbook approach to mesh analysis is argued to be deficient in that it obscures this fundamental duality and symmetry, and may thereby impede the development of intuition and the understanding of the nature of mesh currents. In particular, the usual distinction between inner and outer meshes (if the latter is even recognized) is argued to be meaningless, as can be seen when drawing a planar circuit on the surface of a sphere. A generalized definition of a mesh is proposed that includes both inner and outer meshes on the same footing. Selection of a reference node in nodal analysis should be paralleled by the selection of any mesh to be the reference mesh in mesh analysis, which is always selected to be the outer mesh by default in the usual approach. All branch currents are shown to the difference of two mesh currents, and the zero of all mesh currents is now arbitrary just as it is for node voltages. Use of supermeshes is sometimes obviated by the new approach, and the analysis is sometimes simplified. This new approach has been used in two sections of a linear circuit analysis course in Fall 2019, and student survey data is presented to show preference for the new method over the usual textbook method. An interactive multiple-choice tutorial describing the new method has been integrated into a step-based tutoring system for linear circuit analysis.
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M3 - Conference article
AN - SCOPUS:85095756788
SN - 2153-5965
VL - 2020-June
JO - ASEE Annual Conference and Exposition, Conference Proceedings
JF - ASEE Annual Conference and Exposition, Conference Proceedings
M1 - 1446
T2 - 2020 ASEE Virtual Annual Conference, ASEE 2020
Y2 - 22 June 2020 through 26 June 2020
ER -