A pair of magnetically coupled coils - equivalent circuits

Prepared by Dr. Aaron Scher
[email protected]

Back to Aaron's home page.

Introduction

Two magnetically coupled inductors have many alternative circuit representations that are useful for impedance matching and transformations. This page presents some of my favorites. Here we assume "ideal" components, meaning we ignore the resistance of the coils and any stray capacitance that may exist. Figure 1 shows a schematic diagram of the coupled inductors along with their current-voltage relationships. Figure 2 shows how the magnetically coupled inductors transforms the impedance of a real load. Note that, in these figures, the coupling coefficient k is positive if both currents (i₁ and i₂) enter or both leaving through a dotted terminal. The coupling coefficient is negative if one current enters through a dotted terminal, while the other leaves through a dotted terminal.

Figure 1. Schematic diagram of magnetically coupled inductors.

Figure 2. Magnetically coupled inductors transforms the impedance of a real load.

Equivalent circuits

Transformer model

Impedance inverter model

Figure 4. Equivalent circuit with impedance inverter (also called the "K-inverter").