Designing Coupled Inductors

Apr 1, 2006 12:00 PM
By John Gallagher, Field Applications Engineer, Pulse, San Diego

Equating Reluctance and Circuit Models

One approach to relate reluctances R and R_C to the circuit elements L_M and L_K is to look at how one would actually measure the circuit elements (Fig. 3a), and how this measurement equates back to the reluctance model. The first and most obvious measurement to take on the inductor component is to measure the open-circuit inductance on each of the two windings. Fig. 3b makes it clear that the measured open-circuit inductance equals:

In regards to the reluctance model (Fig. 3c), the open circuit inductance measurement on only one winding is equivalent to removing or shorting the other source such that the equivalent circuit reduces to that shown in Fig. 3d. It is clear from this figure that the equivalent reluctance is equal to:

The second measurement on the inductor component could be to measure the short-circuit inductance by measuring the inductance on one winding with the other winding shorted. Assuming a perfect short, the short-circuit inductance equals:

This measurement is often used to measure the leakage inductance (L_K) in transformer applications because it is assumed that L_M >> L_K. However, for the coupled inductor, this is not the case, and as such L_SHORT does not lead to a clear or direct measurement of the leakage inductance. A better measurement is the reverse-series inductance, in which the windings of the inductor are tied in series but out of phase (Fig. 3e). In this measurement, the opposing polarity of the windings effectively cancels the magnetizing inductance (L_M) and the series inductance equals:

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