Minimum Loss Operation and Optimal Design of High-Frequency Inductors for Defined Core and Litz Wire

Abstract

This paper studies the loss-optimal design of a power inductor employed in a 2 kW, 400 V input DC-DC converter. The design of an inductor is subject to a large number of design parameters and the implications of the different design parameters on the losses are often not clearly traceable in a full optimization, e.g., different current ripple amplitudes can lead to designs with similar losses, as larger ripple amplitudes lead to increased AC core and winding losses but lower DC losses in the winding due to lower inductance values and/or numbers of turns. In an effort to achieve a comprehensible description of the implications of the key design parameters (switching frequency, f_\text{s} , current ripple, r, number of turns, N) on the losses, the remaining parameters, e.g., core (E55/28/21 N87) and type of conductor (litz wire), are considered to be given. In a first step, the investigation is based on a simplified analytical model, which is refined in a step-by-step manner, e.g., to consider core saturation. In a second step, the implications of further critical aspects on the losses, e.g., temperatures of core and coil, are examined using a comprehensive semi-numerical model. Surprisingly, the evaluation of the losses calculated in the f_\text{s}-r domain reveals that nearly minimum inductor losses are obtained for a current ripple that is inversely proportional to the frequency, i.e., for a constant inductance, within a wide frequency range, from 200 kHz to 1 MHz. Furthermore, the investigation reveals a decrease of the losses for increasing frequencies up to 375 kHz, e.g., from 4.32 W at 80 kHz (r = 110 %) to 2.37 W at 375 kHz (r = 18 %). The detailed analysis related to these results enables the compilation of a simple two-equation guide for the design of an inductor that achieves close to minimum losses. In a next step, interesting trade-offs are identified based on a study of the design space diversity, e.g., with respect to low cost and increased partial-load efficiency. The findings of this work are experimentally verified, i.e., the losses of three different inductors are measured with an accurate calorimetric method and at four different frequencies, ranging from 150 kHz to 700 kHz.