Mutual Inductor

Purpose

Ideal mutual inductor

Library

Electrical / Passive Components

Description

This component provides two or more coupled inductors. Electrically, it is equivalent with a vectorized Inductor. In contrast to the vectorized Inductor, this component displays the individual inductors in the schematic as separate windings.

In the symbol of the mutual inductor, the positive terminal of winding 1 is marked with a little circle. The positive terminals of all other windings are marked with dots.

Note

An inductor may not be connected in series with a current source. Doing so would create a dependency between an input variable (the source current) and a state variable (the inductor current) in the underlying state-space equations.

Example Model

• See the example model “Mutual Inductor”.

• Find it in PLECS under Help > PLECS Documentation > List of Example Models.

Parameters

Number of windings

The number of ideal inductors represented by the component.

Inductance

The inductance in henries \((\mathrm{H})\). All finite positive and negative values are accepted, including 0.

If the parameter is a scalar or a vector, no coupling exists between the windings. In order to model a magnetic coupling between the windings a square matrix must be entered. The size \(n\) of the matrix corresponds to the number of windings. \(L_i\) is the self inductance of the internal inductor and \(M_{i,j}\) the mutual inductance:

\[\begin{split}\begin{bmatrix} v_1 \\ v_2 \\ \vdots \\ v_n \end{bmatrix} = \begin{bmatrix} L_1 & M_{1,2} & \cdots & M_{1,n} \\ M_{2,1} & L_2 & \cdots & M_{2,n} \\ \vdots & \vdots & \ddots & \vdots \\ M_{n,1} & M_{n,2} & \cdots & L_n \end{bmatrix} \begin{bmatrix} \frac{di_1}{dt} \\ \frac{di_2}{dt} \\ \vdots \\ \frac{di_n}{dt} \end{bmatrix}\end{split}\]

The inductance matrix must be invertible, i.e. it may not be singular. A singular inductance matrix results for example when two or more inductors are ideally coupled. To model this, use an inductor in parallel with an Ideal Transformer.

The relationship between the coupling factor \(k_{i,j}\) and the mutual inductance \(M_{i,j}\) is:

\[M_{i,j} = M_{j,i} = k_{i,j} \cdot \sqrt{L_i \cdot L_j}\]

Initial current

The initial current in the windings at simulation start, in amperes \((\mathrm{A})\). This parameter may either be a scalar or a vector corresponding to the number of windings. The direction of the initial current inside the component is from the positive to the negative terminal. The default of the initial current is 0.

Probe Signals

Winding i current

The current flowing through winding i, in amperes \((\mathrm{A})\).

Winding i voltage

The voltage measured across winding i, in volts \((\mathrm{V})\).