Equivalent circuit

Winding joule losses and leakage reactances are represented by the following series loop impedances of the model:

• Primary winding: R_P, X_P
• Secondary winding: R_S, X_S.

In normal course of circuit equivalence transformation, R_S and X_S are in practice usually referred to the primary side by multiplying these impedances by the turns ratio squared, (N_P/N_S) ² = a².

Real transformer equivalent circuit

Core loss and reactance is represented by the following shunt leg impedances of the model:

• Core or iron losses: R_C
• Magnetizing reactance: X_M.

R_C and X_M are collectively termed the magnetizing branch of the model.
Core losses are caused mostly by hysteresis and eddy current effects in the core and are proportional to the square of the core flux for operation at a given frequency.^[31] The finite permeability core requires a magnetizing current I_M to maintain mutual flux in the core. Magnetizing current is in phase  with the flux, the relationship between the two being non-linear due to saturation effects. However, all impedances of the equivalent circuit shown are by definition linear and such non-linearity effects are not typically reflected in transformer equivalent circuits.^[31] With sinusoidal supply, core flux lags the induced EMF by 90°. With open-circuited secondary winding, magnetizing branch current I₀ equals transformer no-load current.^[30]
The resulting model, though sometimes termed 'exact' equivalent circuit based on linearity assumptions, retains a number of approximations.^[30] Analysis may be simplified by assuming that magnetizing branch impedance is relatively high and relocating the branch to the left of the primary impedances. This introduces error but allows combination of primary and referred secondary resistances and reactances by simple summation as two series impedances.
Transformer equivalent circuit impedance and transformer ratio parameters can be derived from the following tests: open-circuit test,^[m] short-circuit test, winding resistance test, and transformer ratio test.