Wideband passive multiport model order reduction and realization of RLCM circuits

This paper presents a novel compact passive modeling technique for high-performance RF passive and interconnect circuits modeled as high-order resistor-inductor-capacitor-mutual inductance circuits. The new method is based on a recently proposed general s-domain hierarchical modeling and analysis method and vector potential equivalent circuit model for self and mutual inductances. Theoretically, this paper shows that s-domain hierarchical reduction is equivalent to implicit moment matching at around s=0 and that the existing hierarchical reduction method by one-point expansion is numerically stable for general tree-structured circuits. It is also shown that hierarchical reduction preserves the reciprocity of passive circuit matrices. Practically, a hierarchical multipoint reduction scheme to obtain accurate-order reduced admittance matrices of general passive circuits is proposed. A novel explicit waveform-matching algorithm is proposed for searching dominant poles and residues from different expansion points based on the unique hierarchical reduction framework. To enforce passivity, state-space-based optimization is applied to the model order reduced admittance matrix. Then, a general multiport network realization method to realize the passivity-enforced reduced admittance based on the relaxed one-port network synthesis technique using Foster's canonical form is proposed. The resulting modeling algorithm can generate the multiport passive SPICE-compatible model for any linear passive network with easily controlled model accuracy and complexity. Experimental results on an RF spiral inductor and a number of high-speed transmission line circuits are presented. In comparison with other approaches, the proposed reduction is as accurate as passive reduced-order interconnect macromodeling algorithm in the high-frequency domain due to the enhanced multipoint expansion, but leads to smaller realized circuit models. In addition, under the same reduction ratio, realized models by the new method have less error compared with reduced circuits by time-constant-based reduction techniques in time domain.