Editing Transformer (section)

====Equivalent circuit====
{{See also|Induction motor#Steinmetz equivalent circuit|l1=Steinmetz equivalent circuit}}

Referring to the diagram, a practical transformer's physical behavior may be represented by an [[equivalent circuit]] model, which can incorporate an ideal transformer.<ref name="daniels1985-47">{{harvnb|Daniels|1985|pp=47–49}}</ref>

Winding joule losses and leakage reactance are represented by the following series loop impedances of the model:
* Primary winding: ''R''<sub>P</sub>, ''X''<sub>P</sub>
* Secondary winding: ''R''<sub>S</sub>, ''X''<sub>S</sub>.
In normal course of circuit equivalence transformation, ''R''<sub>S</sub> and ''X''<sub>S</sub> are in practice usually referred to the primary side by multiplying these impedances by the turns ratio squared, (''N''<sub>P</sub>/''N''<sub>S</sub>)<sup>&nbsp;2</sup>&nbsp;=&nbsp;a<sup>2</sup>.

{{anchor|Real transformer equivalent circuit figure}}
[[Image:Transformer equivalent circuit.svg|thumb|upright=2|Real transformer equivalent circuit]]
Core loss and reactance is represented by the following shunt leg impedances of the model:
* Core or iron losses: ''R''<sub>C</sub>
* Magnetizing reactance: ''X''<sub>M</sub>.
''R''<sub>C</sub> and ''X''<sub>M</sub> 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.<ref name="Say1983">{{cite book | last = Say | first = M. G. | title = Alternating Current Machines| edition = 5th| publisher = Pitman| year = 1983| location = London | isbn = 978-0-273-01969-5}}</ref>{{rp|142–143}} The finite permeability core requires a magnetizing current ''I''<sub>M</sub> 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.<ref name="Say1983"/>{{rp|142}} With [[sinusoidal]] supply, core flux lags the induced EMF by&nbsp;90°. With open-circuited secondary winding, magnetizing branch current ''I''<sub>0</sub> equals transformer no-load current.<ref name="daniels1985-47"/>
[[File:Instrument Transformer_LV_terminals.jpg|thumb|Instrument transformer, with [[Polarity (mutual inductance)|polarity dot]] and X1 markings on low-voltage ("LV") side terminal]]
The resulting model, though sometimes termed 'exact' equivalent circuit based on [[linearity]] assumptions, retains a number of approximations.<ref name="daniels1985-47"/> 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 reactance 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]], [[short-circuit test]], winding resistance test, and transformer ratio test.