Model

The equivalent circuit model for the non-ideal transformer is shown in Figure 1. An ideal transformer with resistors and inductors in parallel and series replaces the non-ideal transformer. This model is called the high side equivalent circuit model because all parameters have been moved to the primary side of the ideal transformer. The series resistance, R_eq, is the resistance of the copper winding. The series inductance, X_eq, accounts for the flux leakage. That is, a small amount of flux travels through the air outside the magnetic core path. The parallel resistance, R_m, represents the core loss of the magnetic core material due to hysteresis. The parallel inductance, X_m, called the magnetizing inductance, accounts for the finite permeability of the magnetic core.

Figure 1. High side transformer equivalent circuit model.

It is easy to see how each parameter of the equivalent circuit model could be adjusted by changing the transformer design. For example, increasing the diameter of the wire in the windings decreases the series resistance. Therefore, the equivalent circuit model parameters can be used as a way to evaluate a transformer, or compare transformers.

The parameters can be found in the same way that Thevenin equivalent circuit parameters are found: open circuit and short circuit tests. The parallel parameter values are found with no load connected to the secondary (open circuit) and the series parameter values are found with the secondary terminals shorted (short circuit). It is possible, for convenience in the lab, to make the tests on either the primary or the secondary. Figure 2 shows the equivalents circuits for the two tests. For the open circuit test, the series parameters are neglected for convenience. This is reasonable since the voltage drops are across R_eq and X_eq are normally small.

Figure 2. Equivalent circuits for tests. (a) Open circuit. (b) Short circuit.

Expressions for the non-ideal transformer parameters are derived from the equivalent circuits shown in Figure 2. The results are Equations (1), (2), (3), and (4). All parameters are expressed in terms of quantities measured in the open circuit and short circuit tests.

(1)

(2)

(3)

(4)