Cables, printed circuit boards, and VLSI interconnects are commonly modeled as multiconductor transmission lines. Models of electrically long transmission lines are memory and time consuming. In this paper, a robust and efficient algorithm for the generation of a delay-based model is presented. The impedance representation via the open-end matrix Z is analyzed. In particular, the rational formulation of Z in terms of poles and residues is exploited for both lossless and lossy cases. The delays of the lines are identified, and explicitly incorporated into the model. A model order reduction of the system is automatically performed, since only a limited number of poles and residues are included in the rational part of the model, whereas the high-frequency behavior is captured by means of closed expressions that account for the delays. The proposed method is applied to two relevant examples and validated through the comparison with reference methods. The time-domain solver is found to be more accurate and significantly faster than the one obtained from a pure-rational model.
The partial element equivalent circuit (PEEC) method provides an electromagnetic model of interconnections and packaging structures in terms of standard circuit elements. The surface-based PEEC (S-PEEC) formulation can reduce the number of unknowns compared to the standard volume-based PEEC (V-PEEC) method. This reduction is of particular use in the case of high-speed circuits and high-switching power electronics, where the bandwidth extends from low frequencies to the GHz range. In this article, the S-PEEC formulation is revised and cast in a matrix form. The main novelty is that the interaction integrals involving the curl of the magnetic and electric vector potentials are computed through the Taylor series expansion of the full-wave Green's function, leading to analytical forms that are rigorously derived. Therefore, the numerical integration is avoided, with a consequent reduction of the computation time. The proposed formulas are studied in terms of the frequency, size of the mesh, and distance between the basis function domains. Three examples are presented, confirming the accuracy of the proposed method compared to the V-PEEC method and surface-based numerical methods from literature.
In this paper, the transient analysis of lossy and dispersive multiconductor transmission lines is considered. The existing Green's function-based method is extended to explicitly include delays extraction, thus leading to a significant compressed time-domain state-space model. The proposed method is mainly based on poles and residues asymptotic analysis and lossless delays extraction. The resulting hybrid state-space model incorporates Dirac-combs in the input and results into a reduced number of state variables. A test case has been considered in order to clearly demonstrate the effectiveness of the proposed methodology. The results are compared with the original rational Green's function method, and with the standard inverse fast Fourier transform technique.
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