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

International Standard Serial Number (ISSN)

0018-9375; 1558-187X

Document Type

Article - Journal

Document Version

Final Version

File Type





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