String Diagrammatic Electrical Circuit Theory

06/14/2021

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by   Guillaume Boisseau, et al.

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We develop a comprehensive string diagrammatic treatment of electrical circuits. Building on previous, limited case studies, we introduce controlled sources and meters as elements, and the impedance calculus, a powerful toolbox for diagrammatic reasoning on circuit diagrams. We demonstrate the power of our approach by giving comprehensive proofs of several textbook results, including the superposition theorem and Thévenin's theorem.