In this paper, we present a reduced order modeling methodology, based on the utilization of optimal non-uniform grids generated by Gaussian spectral rules, for the direct passive synthesis of SPICE-compatible modeling of multi-conductor interconnect structures. The algorithm is based on a Padé-Chebyshev approximation of the frequency-dependent input impedance matrix of the passive interconnect system. The synthesized circuit is represented as the concatenation of a number of non-uniform sections of passive lumped coupled circuits. However, contrary to the popular uniform segmentation-based distributed circuit models for interconnects, where 10 to 15 segments per minimum wavelength are needed for multi-GHz accuracy, the proposed model is "optimal" in the sense that highly-accurate responses can be obtained with a number of segments per minimum wavelength barely exceeding the Nyquist limit of 2. This high accuracy stems from the super-exponential convergence of the Padé-Chebyshev approximation of the input impedance of the transmission-line model of the interconnect, and results in the synthesis of MNA stamps for the interconnect structure with five to ten times reduction in the number of state variables compared to uniform grids.Moreover, the passivity of the generated SPICEcompatible multi-port models is guaranteed through the use of passive equivalent circuits for the representation of the frequencydependent, per-unit-length series impedance and shunt admittance matrices of the interconnect.
A methodology is presented for the rational function approximation of a passive network function from sampled values of its real part over the bandwidth of interest. The accuracy and validity of the proposed methodology are demonstrated through its application to the fitting of several broadband, multiport transfer functions.
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