Ideal Transformer

Purpose

Ideally coupled windings with or without magnetizing inductance

Library

Electrical / Transformers

Description

This component represents a transformer with two or more ideally coupled windings. At all windings \(w\), the voltage \(v_w\) across the winding divided by the corresponding number of turns \(n_w\) is the same:

\[\frac{v_1}{n_1} = \frac{v_2}{n_2} = \frac{v_3}{n_3} = \ldots\]

If the transformer does not have a finite magnetizing inductance (i.e. the inductance value is set to inf), the currents \(i_w\) of all windings multiplied with the corresponding number of turns add up to zero:

\[0 = i_1 \cdot n_1 + i_2 \cdot n_2 + i_3 \cdot n_3 + \ldots\]

If the transformer does have a finite magnetizing inductance, the currents \(i_w\) of all windings multiplied with the corresponding number of turns add up to the magnetizing current multiplied with the number of turns in the first winding:

\[i_{\mathrm{m}} \cdot n_1 = i_1 \cdot n_1 + i_2 \cdot n_2 + i_3 \cdot n_3 + \ldots\]

In the transformer symbol, the first primary side winding is marked with a little circle. The orientation of the other windings is indicated by a dot. Currents entering a terminal marked with the circle or a dot are considered positive.

Use the Polarity parameter to change the orientation of a specific winding. This is equivalent to making the corresponding number of turns \(n_w\) negative.

Parameters

Number of windings

A two-element vector \([w_1\; w_2]\) containing the number of windings on the primary side \(w_1\) and on the secondary side \(w_2\). The default is [1 1], which represents a two-winding transformer with opposite windings.

Number of turns

A row vector specifying the number of turns for each winding. The vector length must match the total number of primary and secondary side windings. First, all primary side windings are specified, followed by the specifications for all secondary side windings.

Polarity

A string consisting of one + or - per winding specifying the winding polarity. A single + or - is applied to all windings.

Magnetizing inductance

A non-zero scalar specifying the magnetizing inductance referred to the first winding, in henries \((\mathrm{H})\).

Initial magnetizing current

A scalar specifying the initial current through the magnetizing inductance at simulation start, in amperes \((\mathrm{A})\). Must be zero if the magnetizing inductance is infinite inf.