Parametric Macromodeling of Lossy and Dispersive Multiconductor Transmission Lines (original) (raw)
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Parameterized macromodels of multiconductor transmission lines
2009
We introduce a novel parametrization scheme for lossy and dispersive multiconductor transmission lines (MTLs) having a cross-section depending on geometrical and physical parameters, that is suitable to interconnect modeling. The proposed approach is based on the dyadic Green's function method for the analysis of lossy and dispersive MTLs which is parameterized by using the Multivariate Orthonormal Vector Fitting (MOVF) technique to build parametric macromodels in a rational form. Design parameters, such as substrate or geometrical layout features, in addition to frequency, can be easily handled. The rational form of the multi-port macromodel describing the MTL is a direct consequence of the MOVF technique and is especially suited to generate state-space macromodels or to be synthesized into equivalent circuits, which can be easily embedded into conventional SPICE-like solvers. A numerical example is presented providing evidence of the accuracy of the proposed approach in both frequency and time-domain.
Parameterized models for crosstalk analysis in high-speed interconnects
2009 IEEE International Symposium on Electromagnetic Compatibility, 2009
We present a new parametric macromodeling technique for lossy and dispersive multiconductor transmission lines (MTLs), that is suitable to interconnect modeling. It is based on a recently introduced spectral approach for the analysis of lossy and dispersive MTLs extended by utilizing the Multivariate Orthonormal Vector Fitting (MOVF) technique to build parametric macromodels in a rational form. They can handle design parameters, such as substrate or geometrical layout features, in addition to frequency. The presented technique is suited to generate state-space models and synthesize equivalent circuits, which can be easily embedded into conventional SPICE-like solvers. Parametric macromodels allow to carry out design space exploration, design optimization and crosstalk analysis efficiently. A numerical example validates the proposed approach in both frequency and time domain and is focused on the crosstalk analysis.
Generation of passive macromodels for lossy multiconductor transmission lines
2007 18th International Zurich Symposium on Electromagnetic Compatibility, 2007
This paper presents an algorithm for the enforcement of passivity in delay-based multiconductor transmission line macromodels based on the Generalized Method of Characteristics. The algorithm enforces passivity via an iterative procedure based on first-order perturbations. More precisely, the short-circuit admittance matrix of the macromodel is iteratively modified until it becomes positive real. This iterative perturbation is performed on the solutions of a nonlinear eigenvalue problem, whereas the passivity verification is performed using an adaptive frequency sampling process. The proposed technique results in passive, accurate, and efficient macromodels for arbitrary lossy multiconductor transmission lines, which can be synthesized in SPICE netlists for system-level analysis and design.
Systematic development of transmission-line models for interconnects with frequency-dependent losses
IEEE Transactions on Microwave Theory and Techniques, 2001
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.
Parametric modeling of integrated circuit interconnections
IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, 1992
This paper presents a parametric approach to the modeling and characterization of high frequency losses and dispersive propagation on integrated-circuit (IC) interconnections. An autoregressive movingaverage (ARMA) model is based on a lumped equivalent circuit of a lossy microstrip transmission line. Model parameters are estimated from on-wafer time-domain measurements using a weighted least squares OyU) algorithm and an Elmore delay approximation technique. It is shown that the effective microstrip permittivity can be evaluated from the estimated ARMA model parameters. Experimental results are compared with computer simulations of the lumped equivalent circuit and ARMA parametric models.
Passive closed-form transmission-line model for general-purpose circuit simulators
IEEE Transactions on Microwave Theory and Techniques, 1999
A passive closed-form model for multiconductor lossy transmission line analysis is presented in this paper. The proposed model is suitable for inclusion in general-purpose circuit simulators and overcomes the mixed frequency/time simulation difficulties encountered during the transient analysis. In addition, the model can handle frequency-dependent line parameters. This method offers an efficient means to discretize transmission lines compared to the conventional lumped discretization, while preserving the passivity of the discrete model. Coefficients describing the discrete model are computed a priori and analytically, using closed-form Padé approximants of exponential matrices. Numerical examples are presented to demonstrate the validity of the proposed model and to illustrate its application to a variety of interconnect structures.
Efficient Time-Domain Macromodeling of Complex Interconnection Structures
EUROCON 2007 - The International Conference on "Computer as a Tool", 2007
The Vector Fitting algorithm [1] is an iterative procedure to compute rational approximations of frequencydomain responses. It was shown that the robustness of this technique can be enhanced by using a set of orthonormal rational basis functions, leading to the Orthonormal Vector Fitting method [2]. In this paper, a time-domain implementation of this method is proposed for the macromodeling of transient port responses. It is shown that this method is more robust towards the initial pole specification, when compared to the classical time-domain Vector Fitting method [3].
Macromodeling of high-speed interconnects by positive interpolation of vertical segments
Applied Mathematical Modelling, 2013
In this paper a novel macromodeling scheme is presented to model the per unit of length (p.u.l.) parameters of uniform transmission lines. In particular, it is focused on single onchip interconnects, because their p.u.l. parameters are influenced by the presence of semiconductor (s) and as such exhibit a strong frequency-dependency, making the modeling process harder. Starting from a set of very accurate tabulated data samples, obtained by two-dimensional electromagnetic modeling, rational models for the four p.u.l. parameters are constructed. The novelty of the approach lies in the fact that the rational models are positive by construction and that a controllable accuracy is obtained. These models can then further be used to construct multivariate models, e.g., for variability analysis. Here, the novel scheme is applied to an on-chip inverted embedded microstrip line, of which the signal integrity behavior is assessed in both the frequency and the time domain, demonstrating the applicability of the macromodels.
IEEE Transactions on Components, Packaging and Manufacturing Technology, 2012
We present a new parametric macromodeling technique for lossy and dispersive multiconductor transmission lines. This technique can handle multiple design parameters, such as substrate or geometrical layout features, and provide timedomain sensitivity information for voltages and currents at the ports of the lines. It is derived from the dyadic Green's function of the 1-D wave propagation problem. The rational nature of the Green's function permits the generation of a timedomain macromodel for the computation of transient voltage and current sensitivities with respect to both electrical and physical parameters, completely avoiding similarity transformation, and it is suited to generate state-space models and synthesize equivalent circuits, which can be easily embedded into conventional SPICElike solvers. Parametric macromodels that provide sensitivity information are well suited for design space exploration, design optimization, and crosstalk analysis. Two numerical examples validate the proposed approach in both frequency and timedomain.
Efficient time-domain vector fitting for broadband interconnect modelling
… Compatibility (EMC), 2010 …, 2010
The time-domain vector fitting (TDVF) [1] was proven to be an extrapolation method which provides about a tenfold lengthening of a recorded time-domain response and reducing Gribbs phenomenon due to the limited length of the response and its abrupt discontinuity. TDVF is the counterpart of the vector fitting (VF) [2] in the time domain (TD), but it is not popular as VF due to the fact that a technique for estimating the order of the rational function fit for TDVF is not available even though the accuracy of the model built by TDVF strongly depends on the choice of the order of the rational function fit. This paper introduces a new methodology toward an efficient and robust whole channel simulation using the TDVF algorithm which is equipped with a sound estimate for the order of the rational function fit. This method significantly reduces the computational resource, while enhances the model accuracy. As a validation study, TDVF equipped with the order estimation method was applied for modelling a socket component in multi-Gbps interconnects.