Matrix Formulation of the Cauer Ladder Network Method for Efficient Eddy-Current Analysis

Abstract

Advanced power control often requires detailed eddy-current analyses of electric machines handling thin skin depth due to high frequency switching. The Cauer circuit [1], [2] is a very efficient and exact representation of the eddy-current field in magnetic sheets and cylinders for wide frequency range, where magnetic and electric fields are optimally expanded by orthogonal polynomials. Recently, the Cauer circuit representation is extended to describe general eddy-current fields powered by the finite element method (FEM). This method is called Cauer ladder network (CLN) method [3], [4] and still retains clear physical meaning based on the orthogonal function expansion. The generality of CLN method has a similarity to model order reduction (MOR) methods [5], [6]. The relation between the CLN method and other MOR methods has not been clear yet because of the physics-based derivation of CLN method. This article derives a matrix formulation of CLN method for clear understanding of mathematical aspects of the CLN method.