Scanning Our Past Origins of the Equivalent Circuit Concept: The Voltage-Source Equivalent

The theoretical foundations of linear circuit theory rest on Maxwell’s theory of electromagnetism. In its more applied form, circuit theory rests on the key concepts of Kirchoff’s Laws, impedance, Ohm’s Law (in its most general sense by encompassing impedances), and the Principle of Superposition. From this foundation, any linear circuit can be solved: given a specification of all sources in the circuit, a set of linear equations can be found and solved to yield any voltage and current in the circuit. One of the most surprising concepts to arise from linear circuit theory is the equivalent circuit: no matter how complex the circuit, from the viewpoint of any pair of terminals, the circuit behaves as if it consisted only of a source and an impedance. From a narrow view, the equivalent circuit concept simplifies calculations in circuit theory, and brings to fore the ideas of input and output impedances. More broadly, the equivalent circuit notion means that a simpler but functionally equivalent form for complicated systems might exist. For example, this notion arises in queueing theory: The Chandy–Herzog–Woo theorem [1], sometimes known as Norton’s Theorem, states that a complicated queueing system has an equivalent form in interesting situations. Two equivalent circuit structures predominate: the Thévenin equivalent circuit and the Norton equivalent circuit (as they are known in the United States). As shown in Fig. 1, these circuits differ only in which kind of source—voltage source for the Thévenin equivalent and current source for the Norton. The development of these equivalents spans almost 75 years, with others than the eponymous people assuming equally important roles. Because priority will be an issue, I use the terms “voltage-source” and “current-source” equivalents to describe them. This paper describes the development of the voltage-source equivalent circuit. A subsequent paper [2] concerns the current-source equivalent and summarizes the story. The formal roots of equivalent circuits are Ohm’s Law, Kirchoff’s Laws, and the Principle of Superposition. Georg Simon Ohm (1789–1854) described his theory of conductors in his 1827 book [3]. Gustav Robert Kirchoff (1824–1887) described what have since become known