EQUIVALENT CIRCUIT OF TRANSFORMERLecture No. 5

By: Sajid Hussain Qazi

Equivalent Circuit of Ideal Transformer

Equivalent Circuit of Practical Transformer

For the non ideal or practical iron-core transformer, the equivalent circuit appears as in figure below:

Equivalent Circuit of Practical Transformer

As indicated, part of this equivalent circuit

includes an ideal transformer.

The remaining elements of Figure are those

elements that contribute to the non ideal

characteristics of the device.

The resistances Rp and Rs are simply the dc

resistance of the primary and secondary

windings, respectively.

Equivalent Circuit of Practical Transformer

For the primary and secondary coils of a transformer, there is a small amount of flux that links each coil but does not pass through the core, as shown in Figure below for the primary winding.

Equivalent Circuit of Practical Transformer

This leakage flux, representing a definite loss in the system, is represented by an inductance Lp in the primary circuit and an inductance Ls in the secondary.

The resistance Rc represents the hysteresis and eddy current losses (core losses) within the core due to an ac flux through the core.

The inductance Lm (magnetizing inductance) is the inductance associated with the magnetization of the core, that is, the establishing of the flux Φm in the core.

Equivalent Circuit of Practical Transformer

The capacitances Cp and Cs are the lumped capacitances of the primary and secondary circuits, respectively, and Cw represents the equivalent lumped capacitances between the windings of the transformer.

The capacitances Cp, Cw, and Cs do not appear in the equivalent circuit, since their reactance at typical operating frequencies will not appreciably affect the transfer characteristics of the transformer.

Equivalent Circuit of Practical Transformer

Since i′p is normally considerably larger than iΦm (the magnetizing current), we will ignore iΦm for the moment (set it equal to zero), resulting in the absence of Rc and Lm in the reduced equivalent circuit of Figure.

Reduced equivalent circuit of transformer