Minimum loss operation of high-frequency inductors

Abstract

This paper investigates the losses of a power inductor employed in a 2kW, 400V input DC-DC converter, in dependency of key operating parameters, i.e. switching frequency and current ripple. Based on detailed high-frequency winding and core loss models, including the implications of DC-bias, temperature and frequency on the core losses, and an analytic thermal model, a minimum loss inductor is designed for each combination of switching frequency, f, and current ripple, r. In the course of the optimization, the core (E55, N87) and the winding (litz wire, 100 μm) are considered given. Surprisingly, the evaluation of the losses calculated in the f-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. Further detailed investigations of the calculated inductor losses reveal a decrease of the losses for increasing frequencies up to a very high frequency of 500 kHz. In this regard, at f = 100kHz, minimum total losses of 4.0W result for r = 45%, which can be reduced to 1.8W at f = 500 kHz for r = 10%. Finally, the sensitivities of the losses with regard to different litz wires (71 μm, 200 μm) and a different core (E42, N87) are examined and a design guidance is extracted that summarizes the main findings of the detailed investigation. A calorimetric measurement set-up is used to measure the losses of a realized inductor at different operating points in order to confirm the theoretical considerations.