Equivalent circuit of X'mer

Equivalent circuit of X'mer



The physical limitations of the practical transformer may be brought together as an equivalent circuit model built around an ideal lossless transformer.[20] Power loss in the windings is current-dependent and is easily represented as in-series resistances RP and RS. Flux leakage results in a fraction of the applied voltage dropped without contributing to the mutual coupling, and thus can be modeled as self-inductances XP and XS in series with the perfectly-coupled region. Iron losses are caused mostly by hysteresis and eddy current effects in the core, and tend to be proportional to the square of the core flux for operation at a given frequency.[21] Since the core flux is proportional to the applied voltage, the iron loss can be represented by a resistance RC in parallel with the ideal transformer.

A core with finite permeability requires a magnetizing current IM to maintain the mutual flux in the core. The magnetizing current is in phase with the flux; saturation effects cause the relationship between the two to be non-linear, but for simplicity this effect tends to be ignored in most circuit equivalents.[21] With a sinusoidal supply, the core flux lags the induced EMF by 90° and this effect can be modeled as a magnetising reactance XM in parallel with the core loss component. RC and XM are sometimes together termed the magnetising branch of the model. If the secondary winding is made open-circuit, the current I0 taken by the magnetising branch represents the transformer's no-load current.[20]

The secondary impedance RS and XS is frequently moved (or "referred") to the primary side after multiplying the components by the impedance scaling factor.

The resulting model is sometimes termed the "exact equivalent circuit", though it retains a number of approximations, such as an assumption of linearity.[20] Analysis may be simplified by moving the magnetising branch to the left of the primary impedance, an implicit assumption that the magnetising current is low, and then summing primary and referred secondary impedances.