Truncation Error Formula for Multi-Port Cauer Ladder Networks

Frequency responses of multiple-input multiple-output (MIMO) systems involving eddy current fields are efficiently approximated as matrix-valued continued fractions via the multi-port Cauer ladder network (CLN) method. This study investigates the truncation error of matrix-valued continued fractions in multi-port RL networks by generalizing the result of ordinary (scalar-valued) continued fractions. The network-theoretic interpretation of matrix-valued continued fractions obviates a complicated mathematical framework and enables the derivation of an explicit formula for truncation errors. Numerical examples, including its application to an inductor model, validated our approach.