AC Winding Loss of Phase-Shifted Coupled Windings

In circuits where there is an inherent phase shift angle between coupled winding currents such as in coupled inductors, it is important to accurately calculate the ac winding loss at the correct phase shift and frequency. Phase shift between winding currents can cause the ac winding loss to vary significantly due to changes in the magnetic field distribution. This paper presents an analysis of winding loss for the general case of coupled windings with arbitrary phase-shifted currents and its effect in a number of practical devices. A detailed approach to analytically calculate ac winding loss in microfabricated-coupled stripline inductors is presented along with a derivation of the resistance matrix for the device. The analysis and methodology are then validated using finite element analysis and experimental results.