A method to determine winding losses in integrated inductors and separate skin and proximity effects

Abstract

This paper presents a method to determine winding losses from scattering matrix parameters in planar inductors. Winding losses are taken into account by a dependent frequency resistance. This method allows losses to be separated in two parts for coreless inductors: skin effect and proximity effect. In high frequencies both software, like High Frequency Structure Simulator, and equipment, like Vector Network Analyzer, provide scattering parameters that allow both impedance or admittance matrices to be calculated. Then, parameters of an electric equivalent circuit can be calculated. The resistance value taking into account both skin and proximity effects is determined in three frequency domains. The first domain is at very low frequencies or at direct current. The second domain is at low-medium frequencies where the capacitive couplings are negligible. The last domain is at the resonant frequencies of the admittance matrix parameters, so at high frequencies. The presented approach is different from those encountered in literature and allows the series resistance from measured or simulated scattering matrix parameters to be determined.