The ac winding resistance and leakage inductance of a transformer can have important effects on the operation of the connected circuit, particularly at high frequencies where these properties are frequency-dependent. Circuit simulation can be a useful tool for investigating the behavior of a new circuit design, but for transformers with more than two windings, existing circuit models have been inadequate. New models are presented here that can accurately represent ac winding resistance and leakage inductance in transformers having any number of windings. The parameter values for these models are calculated from leakage impedances, which can be measured for an existing transformer, or calculated from the layout and dimensions of a transformer not yet built.; For transformers with concentric, cylindrical winding layers, an analysis of the ac magnetic fields in the winding space is carried out to obtain equations by which the frequency-dependent short-circuit impedances can be predicted from the transformer's geometry. The accuracy of these predictions is demonstrated by a comparison with measured short-circuit impedances over a wide range of frequencies, and the limitations of this method are analyzed.; Various lumped-element equivalent-circuit models for multiple-winding transformers are derived, beginning with the frequency-dependent-element cross-coupled-secondaries (CCS) model. The accuracy of this model is demonstrated by its ability to predict steady-state output-voltage regulation, the change in all output voltages due to a change in one load. The mathematically equivalent link model is presented also, which is simpler but perhaps less convenient to use. Finally, the frequency-independent-element cross-coupled-secondaries (FIE CCS) model is derived, in which the frequency dependence of each CCS-model impedance is represented accurately over a wide frequency range by a network of elements with fixed values. The resulting model is suitable for simulating multiple-winding transformers under conditions of nonsinusoidal excitation and nonlinear loads.
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