Passive Synthesis of Compact Frequency-Dependent Interconnect Models via Quadrature Spectral Rules

Authors:
Traianos Yioultsis;Anne Woo;Andreas C. Cangellaris
Affiliations:
Aristotle University of Thessaloniki, Greece;University of Illinois, Urbana;University of Illinois, Urbana
Venue:
Proceedings of the 2003 IEEE/ACM international conference on Computer-aided design
Year:
2003

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Abstract

In this paper, we present a reduced order modeling methodology,based on the utilization of optimal non-uniform grids generatedby Gaussian spectral rules, for the direct passive synthesis ofSPICE-compatible modeling of multi-conductor interconnectstructures. The algorithm is based on a Padé-Chebyshevapproximation of the frequency-dependent input impedancematrix of the passive interconnect system. The synthesized circuitis represented as the concatenation of a number of non-uniformsections of passive lumped coupled circuits. However, contrary tothe popular uniform segmentation-based distributed circuitmodels for interconnects, where 10 to 15 segments per minimumwavelength are needed for multi-GHz accuracy, the proposedmodel is "optimal" in the sense that highly-accurate responses canbe obtained with a number of segments per minimum wavelengthbarely exceeding the Nyquist limit of 2. This high accuracy stemsfrom the super-exponential convergence of the Padé-Chebyshevapproximation of the input impedance of the transmission-linemodel of the interconnect, and results in the synthesis of MNAstamps for the interconnect structure with five to ten timesreduction in the number of state variables compared to uniformgrids. Moreover, the passivity of the generated SPICE-compatiblemulti-port models is guaranteed through the use ofpassive equivalent circuits for the representation of the frequency-dependent,per-unit-length series impedance and shunt admittancematrices of the interconnect.