Preservation of passivity during RLC network reduction via split congruence transformations

Resistance-inductance-capacitance (RLC) network reduction refers to the formulation of small networks whose port behavior is similar to that of large RLC networks. Several network reduction algorithms have been developed in the last few years, but none exist for RLC networks which preserve passivity, The loss of passivity can be a serious problem because simulations of the reduced networks may encounter artificial oscillations or "time step too small" errors which render the simulations useless. This paper presents a set of well-conditioned transformations called "split congruence transformations" (SCT's) which can be used to preserve specified moments and resonances for RLC network reduction, and these transformations are proven to preserve passivity. Network reduction examples are provided to demonstrate the utility of SCT's.