Electrically connected and magnetically coupled inductors: Aiding or opposing fluxes?

Abstract

Representing components combined in series or parallel as a single equivalent component is a powerful tool for simplifying systems, both in mechanics and in electrical circuits. When combining inductors, the effect of mutual inductance decreases or increases the total inductance of the system, depending on the coupling factor between the inductors and on how they are connected. The analysis of mutually coupled inductors can be complex and is often avoided, obscuring the underlying physics. Here, we discuss the dependence of the equivalent inductance on the coupling factor for two parallel-connected inductors with linear magnetic core and negligible resistance. By analyzing the current distribution in each coil, we show that the so-called aiding and opposing arrangements are more complicated than is frequently assumed. We recommend avoiding these terms and calling them instead aligned and anti-aligned arrangements.