Turning Mesh Analysis Inside Out

Brian J. Skromme; Wendy M. Barnard

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Conference: 2020 ASEE Virtual Annual Conference Content Access
Location: Virtual On line
Publication Date: June 22, 2020
Start Date: June 22, 2020
End Date: June 26, 2021
Conference Session: Improvements in ECE Circuit Analysis
Tagged Division: Electrical and Computer
Page Count: 12
DOI: 10.18260/1-2--35403
Permanent URL: https://peer.asee.org/35403
Download Count: 824

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Paper Authors

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Brian J. Skromme Arizona State University

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Dr. Brian J. Skromme is a Professor in the School of Electrical, Computer, and Energy Engineering and was Assistant Dean of the Fulton Schools of Engineering at Arizona State University from 2011-19. He holds a Ph.D. in Electrical Engineering from the University of Illinois at Urbana-Champaign and was a member of technical staff at Bellcore from 1985 to 1989. His research interests are in engineering education, development of educational software, and compound semiconductor materials and devices.

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Wendy M. Barnard Arizona State University

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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.

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Abstract

Elementary linear circuit analysis is a core course and competency for electrical engineers and many other majors, and mesh analysis is one of the two major techniques taught in such courses. Here, we argue that the “standard” approach to teaching this subject is deficient in the sense that it obscures the fundamental duality and symmetry in circuit analysis between mesh analysis and nodal analysis, and may thereby impede the development of intuition as well as of understanding of the nature of “mesh currents.” We argue that the distinction between “inner” and “outer” meshes is meaningless, as is easily seen when drawing a planar circuit on the surface of a sphere. The conventional definition of a “mesh” should be altered to include the outer mesh. Any planar circuit can be re-drawn equivalently with any chosen mesh as the “outer” mesh. Further, it is illogical that the first step in nodal analysis is always to (arbitrarily) select a reference node, whose voltage is defined as some constant (normally zero), but that no such corresponding step exists in conventional mesh analysis. It is also inconsistent that every branch voltage is a difference of two node voltages, but that branch currents are said to be the difference of two mesh currents only if they are “interior” elements. Including the counter-clockwise outer mesh current (assuming clockwise direction for interior mesh currents), all branch currents are the difference of two mesh currents. The conventional approach implicitly selects the outer mesh as the reference mesh and sets its mesh current to zero (so it need not be shown), but there is no more requirement to do that than to select a particular node as the reference node in nodal analysis. We show that any mesh can be designated as the reference mesh, and that this freedom can avoid the use of supermeshes to solve many circuits that require them in the conventional approach. One simply needs to include the outer mesh current when writing KVL equations. This approach clarifies that mesh currents are no more absolute in nature than node voltages, and that choosing a different reference mesh merely shifts all mesh currents by the same amount, leaving all branch currents unaffected.

This revised approach has been used in two sections of a linear circuit analysis course in Fall 2019 and will be used in at least one section in Spring 2020. Informal student feedback to date has been very positive and appreciative of this approach. A formal survey will assess student opinions in more detail. We will also use this approach in a special session conducted as an adjunct to the normal class where an independent evaluator will collect detailed qualitative feedback on this approach, and the results will be reported. We are also analyzing student use of this freedom on examination problems to assess its impact. The approach will be presented to other circuits faculty at our institution in a special seminar and their subsequent adoption or non-adoption of this method will be assessed.

Citation
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Skromme, B. J., & Barnard, W. M. (2020, June), Turning Mesh Analysis Inside Out Paper presented at 2020 ASEE Virtual Annual Conference Content Access, Virtual On line . 10.18260/1-2--35403

TY - CPAPER
AB - Elementary linear circuit analysis is a core course and competency for electrical engineers and many other majors, and mesh analysis is one of the two major techniques taught in such courses. Here, we argue that the “standard” approach to teaching this subject is deficient in the sense that it obscures the fundamental duality and symmetry in circuit analysis between mesh analysis and nodal analysis, and may thereby impede the development of intuition as well as of understanding of the nature of “mesh currents.” We argue that the distinction between “inner” and “outer” meshes is meaningless, as is easily seen when drawing a planar circuit on the surface of a sphere. The conventional definition of a “mesh” should be altered to include the outer mesh. Any planar circuit can be re-drawn equivalently with any chosen mesh as the “outer” mesh. Further, it is illogical that the first step in nodal analysis is always to (arbitrarily) select a reference node, whose voltage is defined as some constant (normally zero), but that no such corresponding step exists in conventional mesh analysis. It is also inconsistent that every branch voltage is a difference of two node voltages, but that branch currents are said to be the difference of two mesh currents only if they are “interior” elements. Including the counter-clockwise outer mesh current (assuming clockwise direction for interior mesh currents), all branch currents are the difference of two mesh currents. The conventional approach implicitly selects the outer mesh as the reference mesh and sets its mesh current to zero (so it need not be shown), but there is no more requirement to do that than to select a particular node as the reference node in nodal analysis. We show that any mesh can be designated as the reference mesh, and that this freedom can avoid the use of supermeshes to solve many circuits that require them in the conventional approach. One simply needs to include the outer mesh current when writing KVL equations. This approach clarifies that mesh currents are no more absolute in nature than node voltages, and that choosing a different reference mesh merely shifts all mesh currents by the same amount, leaving all branch currents unaffected.

This revised approach has been used in two sections of a linear circuit analysis course in Fall 2019 and will be used in at least one section in Spring 2020. Informal student feedback to date has been very positive and appreciative of this approach. A formal survey will assess student opinions in more detail. We will also use this approach in a special session conducted as an adjunct to the normal class where an independent evaluator will collect detailed qualitative feedback on this approach, and the results will be reported. We are also analyzing student use of this freedom on examination problems to assess its impact. The approach will be presented to other circuits faculty at our institution in a special seminar and their subsequent adoption or non-adoption of this method will be assessed.
AU - Brian J. Skromme
AU - Wendy M. Barnard
CY - Virtual On line
DA - 2020/06/22
PB - ASEE Conferences
TI - Turning Mesh Analysis Inside Out
UR - https://peer.asee.org/35403
DO - 10.18260/1-2--35403
ER -