Systematic development of transmission-line models for interconnects with frequency-dependent losses

Karen M. Coperich, Jason Morsey, Vladimir I. Okhmatovski, Andreas C. Cangellaris, Albert E. Ruehli

Research output: Contribution to journalArticlepeer-review


This paper presents a new method for the extraction of the frequency-dependent, per-unit-length (p.u.l.) resistance, and inductance parameters of multiconductor interconnects. The proposed extraction methodology is based on a new formulation of the magneto-quasi-static problem that allows lossy ground planes of finite thickness to be modeled rigorously. The formulation is such that the p.u.l. impedance matrix for the multiconductor interconnect is extracted directly at a prescribed frequency. Once the matrix has been calculated over the bandwidth of interest, rational function representations of its elements are generated through a robust matrix curve-fitting process. Such a formulation enables subsequent transient analysis of interconnects through a variety of approaches. Direct incorporation of the rational function model into a general-purpose circuit simulator and a standalone multiconductor-transmission-line simulator is demonstrated.

Original languageEnglish (US)
Pages (from-to)1677-1685
Number of pages9
JournalIEEE Transactions on Microwave Theory and Techniques
Issue number10
StatePublished - Oct 2001


  • Broad-band transmission-line model
  • Closed-form electromagnetic Green's functions
  • Dispersion
  • Dispersive multiconductor interconnect model
  • Equivalent circuit
  • Finite-difference time-domain simulation
  • Frequency-dependent losses
  • Frequency-dependent per-unit-length impedance matrix
  • Frequency-dependent per-unit-length inductance parameters
  • Frequency-dependent per-unit-length resistance parameters
  • High-speed electrical interconnections
  • Lossy ground planes
  • Magneto-quasi-static problem
  • Method of moments
  • Multiconductor transmission lines
  • Ohmic losses
  • Parameter-extraction methodology
  • Planar inhomogeneous media
  • Proximity effect
  • Rational function representations
  • SPICE-compatible models
  • Skin effect
  • Telegrapher’s equations
  • Time-domain simulation
  • Transmission line
  • Vector curve fitting

ASJC Scopus subject areas

  • Radiation
  • Condensed Matter Physics
  • Electrical and Electronic Engineering


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