Skip to main content
Causal RLGC( Ƒ ) Models for Transmission Lines from Measured S-Parameters
IEEE Transactions on Electromagnetic Compatibilty
  • Jianmin Zhang
  • James L. Drewniak, Missouri University of Science and Technology
  • David Pommerenke, Missouri University of Science and Technology
  • Marina Koledintseva, Missouri University of Science and Technology
  • Richard E. DuBroff, Missouri University of Science and Technology
  • Wheling Cheng
  • Zhiping Yang
  • Qinghua B. Chen
  • Antonio Orlandi

Frequency-dependent causal RLGC(f) models are proposed for single-ended and coupled transmission lines. Dielectric loss, dielectric dispersion, and skin-effect loss are taken into account. The dielectric substrate is described by the two-term Debye frequency dependence, and the transmission line conductors are of finite conductivity. In this paper, three frequency-dependent RLGC models are studied. One is the known frequency-dependent analytical RLGC model ( RLGC-I), the second is the RLGC(f) model (RLGC-II) proposed in this paper, and the third (RLGC-III) is same as the RLGC -II, but with causality enforced by the Hilbert transform in frequency domain. The causalities of the three RLGC models are corroborated in the time domain by examining the propagation of a well-defined pulse through three different transmission lines: a single-ended stripline, a single-ended microstrip line, and an edge-coupled differential stripline pair. A clear time-domain start point is shown on each received pulse for the RLGC-II model and the RLGC-III model, where their corresponding start points overlap. This indicates that the proposed RLGC(f) model (RLGC-II) is causal. Good agreement of simulated and measured S-parameters has also been achieved in the frequency domain for the three transmission lines by using the proposed frequency-dependent RLGC (f) model.

Electrical and Computer Engineering
Research Center/Lab(s)
Electromagnetic Compatibility (EMC) Laboratory
Keywords and Phrases
  • Causality,
  • Dielectric Materials,
  • Hilbert Transforms,
  • Scattering Parameters,
  • Transmission Line Modeling,
  • Transmission Line Measurements,
  • Power Transmission Lines,
  • Dielectric Losses,
  • Integrated Circuit Modeling,
  • Gallium,
  • Strip Lines,
  • Coupled Transmission Lines,
  • Permittivity,
  • Skin Effect,
  • S-Parameters,
  • Skin-Effect Loss,
  • RLGC(f) Models,
  • S-Parameters Measurement,
  • Frequency-Dependent Causal Models,
  • Hilbert Transform,
  • Single-Ended Microstrip Line,
  • Transmission Line Conductors,
  • Edge-Coupled Differential Stripline Pair,
  • Dielectric Dispersion
Document Type
Article - Journal
Document Version
Final Version
File Type
© 2010 Institute of Electrical and Electronics Engineers (IEEE), All rights reserved.
Publication Date
Citation Information
Jianmin Zhang, James L. Drewniak, David Pommerenke, Marina Koledintseva, et al.. "Causal RLGC( Ƒ ) Models for Transmission Lines from Measured S-Parameters" IEEE Transactions on Electromagnetic Compatibilty Vol. 52 Iss. 1 (2010) p. 189 - 198 ISSN: 0018-9375; 1558-187X
Available at: