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Loss Minimization for Coupled Inductors with Significant Ac Flux

Fig1. (a) Prototype of coupled inductors and (b) definition of MLT, WA, le and Ac for toroid core used in the analysis.
In this paper, a design methodology (Kgac) for coupled inductors (and one-winding inductor) with dominant core loss is described to identify the core volume that yields the lowest total loss. The excitation frequency is assumed as sufficiently low so that eddy-current effects in the winding can be neglected. Compared to conventional methods, the core loss density of the coupled inductor designed by the Kgac method can be 9.3 times smaller with the same core volume, which is demonstrated for coupled inductors of a 30-W flyback converter switched at 200 kHz. The total loss of the coupled inductors has also been evaluated by experiments, which is matched with the theoretical analysis.

The procedure of core selection is demonstrated for the coupled inductors shown in Fig. 1 (a). The definition of mean length per turn MLT, window area WA, effective length le, and effective area Ac for the toroid core used in the analysis are shown in Fig. 1 (b). The Kgac method is an extension of the Kg method. With the "Kgac" method, a designer can select the magnetic flux density based on the thermal constraint. An empirical relationship among the effective area (Ac), the mean length per turn (MLT), the window area (WA), and the volume (Ve) is suggested for the derivation of the core volume that minimizes the total loss. Under the constraints of ac flux density, inductance and window area utilization, the optimal core volume is derived by



where



Fig. 2. shows the comparison of losses and volumes for Kgac, Ap and Kg methods based on the 30-W flyback converter at 200 kHz. If core loss is neglected in the Ap and Kg methods, the core loss density of the Ap and Kg methods are 9.3 times as high when compared to the Kgac method, which means the temperature of the core will be unacceptably high at the normal cooling condition. The measurement results are consistent with the theoretical calculations shown in Fig. 3.
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