transformation, RS and XS are in practice usually referred to the primary side by multiplying these impedances by the turns ratio squared, (NP/NS) 2 = a2. Core loss and reactance is represented by the following shunt leg impedances of the model: Core or iron losses: RC Magnetizing reactance: XM. RC and XM 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. The finite permeability core requires a magnetizing current IM 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. 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. The resulting model, though sometimes termed 'exact' equivalent circuit based on linearity assumptions, retains a number of approximations. 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, short-circuit test, winding resistance test, and transformer ratio test. Transformer EMF equation If the flux in the core is purely sinusoidal, the relationship for either winding between its rms voltage Erms of the winding, and the supply frequency f, number of turns N, core cross-sectional area A in m2 and peak magnetic flux density Bpeak in Wb/m2 or T (tesla) is given by the universal EMF equation: Polarity A dot convention is often used in transformer circuit diagrams, nameplates or terminal markings to define the relative polarity of transformer windings. Positively increasing instantaneous current entering the primary winding's ‘dot’ end induces positive polarity voltage exiting the secondary winding's ‘dot’ end. Three-phase transformers used in electric power systems will have a nameplate that indicate the phase relationships between their terminals. This may be in the form of a phasor diagram, or using an alpha-numeric code to show the