Passive Synthesis of SPICE-Compatible, Optimal, Dispersive Transmission-Line Models for High-Speed Interconnects

A methodology is proposed and demonstrated for the direct passive synthesis of SPICE-compatible models of multi-conductor interconnect structures. The algorithm is based on a PadéChebyshev approximation of the frequency-dependent input impedance matrix of the passive interconnect system. Given the bandwidth of simulation, the length of the interconnect system, and its per-unit-length, frequency-dependent resistance, inductance, capacitance and conductance matrices, the proposed algorithm synthesizes a compact, multi-port, dispersive, SPICEcompatible model for the interconnect. The synthesized circuit is formed as the concatenation of a number of non-uniform segments and 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. Moreover, the passivity of the generated SPICE-compatible 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.