Thevenin's theorem approach to mutually coupled elements

The aim of this paper is to apply Thevenin's theorem to mutually coupled elements. Mutual coupling between elements exist due to proximity of elements in electric circuits. The determination of the current in a new added element to an existing circuit is usually done through Thevenin's theorem when the new element is not mutually coupled with any other element in the circuit. However, when the element is mutually coupled with other elements in the circuit, then application of Thevenin's theorem is not straightforward. Thevenin's voltages and impedances have to be modified to include the effect of mutual coupling between the new element and the existing elements of the circuit. A systematic approach to modify Thevenin's voltages and impedances is presented in this paper. Two examples are presented to demonstrate the procedure. The first example considers only single coupling while the second considers multiple coupling. In single coupling, the new element is coupled only with a single element of the circuit. In multiple coupling, the element is coupled with several elements of the circuit.