Turning mesh analysis inside out

Abstract

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.