String Diagrammatic Electrical Circuit Theory

TL;DR

This paper introduces a string diagrammatic framework for electrical circuit theory, incorporating controlled sources and meters, and provides diagrammatic proofs of fundamental theorems like superposition and Thevenin's.

Contribution

It extends previous limited case studies by developing a comprehensive diagrammatic approach with new elements and impedance calculus for electrical circuits.

Findings

Diagrammatic proofs of superposition theorem

Diagrammatic proofs of Thevenin's theorem

Enhanced toolbox for circuit reasoning

Abstract

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 idiomatic proofs of several textbook results, including the superposition theorem and Thevenin's theorem.