Determination of copper losses from measurement and simulation in planar windings

This paper presents a new approach in order to determine copper losses from measurements or simulations of planar inductors. Copper losses are modeled with a series resistance r(f) that depends on the frequency. Measured or simulated admittances of the inductors are used to determine the model parameters of the inductors. The resistance r(f) is determined in 3 frequency domains: i) at very low frequencies (or DC) ii) at low frequencies (capacitive couplings are negligible) iii) at resonant frequencies i.e. high frequencies. The presented approach is different as those encountered in literature and allows the series resistance from measured or simulated Sij parameters to be determined.