A Foster-Type Field-to-Transmission Line Coupling Model for Broadband Simulation

Abstract

A passive and inherently stable multiport equivalent circuit for lossy transmission lines is presented. The convergence of the infinite modal representation is accelerated by appropriate inductances, for which an exact closed-form expression is developed. The order number of the truncated modal circuit is estimated by a simple relation, according to the required signal bandwidth. The coupling of arbitrary external electromagnetic fields is incorporated by a limited number of corresponding modal sources. The accuracy and versatility of the suggested SPICE-compatible equivalent circuit is demonstrated by examples in frequency and time-domain, including nonlinear terminations.

SPICE‐compatible admittance equivalent circuit for stochastic transmission line under external field illumination

“…Recently, Leone et al have presented a SPICE-compatible Foster equivalent circuit for two-dimensional planar interconnections of rectangular shape [25,26] and arbitrary shape [27], which provide a generalised, rapidly convergent and physical interpretation clear circuit model. It is then extended to the TL structure, for which the impedance model based on TL theory [28][29][30] and the admittance model based on the method of moments (MOM) [31] are derived. In this paper, in combination with the PC theory and stochastic Galerkin method (SGM), an alternative random admittance equivalent circuit model derived from the TL equation instead of the MOM-eigenvalue method [31] is presented to describe the stochastic TL under plane wave illumination.…”

Broadband field coupling model of transmission lines based on Foster-type equivalent-circuit

“…Another group of methods solves the problem via numerical methods such as the Finite-Difference Time-Domain Method (FDTD) [9] or the Time-Domain Finite-Element Method (TDFE) [10]. In this contribution an approach is used, which has been recently developed for parallel-plane structures [13] and is and , respectively adopted for TL's in [15]. The model is extended for the first time to account for the coupling of incident external electromagnetic fields, using voltage and modal equivalent current sources.…”

“…Introducing the static inductance [15], allows decomposing (3) in the following, rapidly converging form:…”

“…Rearranging (10) with the closed form expression assuming ≥ [15], we finally obtain the equivalent-circuit impedance solution:…”

“…To avoid a complicated implementation of the frequency-dependent zeroorder conductance 0 (9), we use a fixed value at the intermediate frequency 1 /2 = 1/(4 √ ′ ′ ) below the 1 modal resonance at 1 , as given by (8). The validity of the proposed circuit is shown in [15].…”