Evaluation of the constitutive parameters of a multiconductor transmission line model aimed at the representation of inductor windings at high frequencies

This paper is the first part of a work dedicated to the analysis and computation of the electric and magnetic behavior of inductor windings (e.g., power transformer windings) operating at high-frequency regimes; a recognized key issue for very fast transient overvoltage studies. Here, the inductor winding, containing a total number of N turns, is modeled as a system of N-coupled parallel conductors resembling a uniform inhomogeneous multiconductor transmission-line structure (MTL) where proximity effects cannot be neglected. The characterization of the winding's equivalent MTL structure requires the specification and evaluation of its constitutive parameters, namely, the per-unit-length (PUL) capacitance and inductance matrices, and also the PUL resistance and conductance matrices, the latter two associated with losses. Close proximity between inductor turns together with the consideration of dielectric-coated turns prevents the utilization of closed-form expressions for the evaluation of most of the inductor constitutive parameters. Here we employ a harmonic expansion method (HEM) primarily aimed at the construction of the capacitance matrix from where the inductance and conductance matrices can be derived. A new theory based on Dubanton's approach but taking into account proximity effects related to eddy currents in the inductor core is also proposed and developed. This research paper provides, in a tutorial fashion, a comprehensive explanation of the details and approximations involved in the evaluation of the constitutive parameters of the MTL structure under analysis-an aspect that unfortunately is lightly tackled or even ill-treated in the literature of winding models. Copyright (C) 2007 John Wiley & Sons, Ltd.