The Cauer ladder network (CLN) method provides an efficient representation of eddy-current fields. This paper proposes a reformulation of the CLN method that considers expansion points using the magnetic/current vector potential. To cover a wide range of frequencies, the expansion point may be changed at a later stage of the network. Only a few stages of the ladder network are required for the eddy-current field to be reconstructed accurately around the target frequency using the expansion points.

To achieve efficient multi-port model order reduction, a multi-port Cauer ladder network (CLN) method is formulated that directly yields resistance and inductance matrices that consist of the network elements in the matrix Cauer form. The eddy current field driven by multiple power sources is accurately reconstructed using a small number of network elements. The matrix Cauer form achieves faster convergence of the transfer function than a single-port CLN method and almost the same convergence as a block PVL method.

Multiple expansion points are introduced to the multi-port Cauer ladder network method to realize an efficient model order reduction of an eddy-current field. The proposed method can set multiple target frequencies to cover a wide frequency range with a small number of multi-port electric network elements. A time-dependent response to pulse-width-modulation (PWM) excitation is accurately reconstructed by setting the target frequencies at both fundamental and carrier frequencies.