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61
Passivity Enforcement via Perturbation of Hamiltonian Matrices
 IEEE TRANS. CASI
, 2004
"... This paper presents a new technique for the passivity enforcement of linear timeinvariant multiport systems in statespace form. This technique is based on a study of the spectral properties of related Hamiltonian matrices. The formulation is applicable in case the system inputoutput transfer func ..."
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Cited by 64 (18 self)
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This paper presents a new technique for the passivity enforcement of linear timeinvariant multiport systems in statespace form. This technique is based on a study of the spectral properties of related Hamiltonian matrices. The formulation is applicable in case the system inputoutput transfer function is in admittance, impedance, hybrid, or scattering form. A standard test for passivity is first performed by checking the existence of imaginary eigenvalues of the associated Hamiltonian matrix. In the presence of imaginary eigenvalues the system is not passive. In such a case, a new result based on firstorder perturbation theory is presented for the precise characterization of the frequency bands where passivity violations occur. This characterization is then used for the design of an iterative perturbation scheme of the state matrices, aimed at the displacement of the imaginary eigenvalues of the Hamiltonian matrix. The result is an effective algorithm leading to the compensation of the passivity violations. This procedure is very efficient when the passivity violations are small, so that firstorder perturbation is applicable. Several examples illustrate and validate the procedure.
Package Macromodeling via TimeDomain Vector Fitting
 IEEE Microwave and Wireless Components Letters
, 2003
"... Abstract—This paper addresses the construction of lumped macromodels for package structures. A technique named TimeDomain Vector Fitting (TDVF) is introduced for the identification of the dominant poles of the structure. This method uses as raw data transient excitations and responses at the ports ..."
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Cited by 28 (13 self)
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Abstract—This paper addresses the construction of lumped macromodels for package structures. A technique named TimeDomain Vector Fitting (TDVF) is introduced for the identification of the dominant poles of the structure. This method uses as raw data transient excitations and responses at the ports of the structure. These responses are easily obtained from transient fullwave electromagnetic solvers based, e.g., on Finite Differences. The rational approximation can be easily synthesized into a SPICEcompatible subcircuit providing a broadband approximation to the inputoutput behavior of the package. Index Terms—Circuit extraction, macromodeling, timedomain vector fitting, vector fitting.
A comparative study of passivity enforcement schemes for linear lumped macromodels
 IEEE Trans. Advanced Packaging
, 2008
"... Abstract—This paper presents a comparative study of several passivity enforcement schemes for linear lumped macromodels. We consider three main classes of algorithms. First class is represented by those methods based on a direct enforcement of Positive/Bounded Real Lemma constraints via convex opti ..."
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Cited by 19 (4 self)
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Abstract—This paper presents a comparative study of several passivity enforcement schemes for linear lumped macromodels. We consider three main classes of algorithms. First class is represented by those methods based on a direct enforcement of Positive/Bounded Real Lemma constraints via convex optimization. Second class includes those algorithms that enforce the passivity constraints at discrete frequency samples. These schemes are here formulated as Second Order Cone Programs in order to optimize performance. Finally, we consider algorithms based on Hamiltonian eigenvalue perturbation. These three classes are applied to a significant set of benchmark examples, essentially various kinds of highspeed interconnects and packages, with the aim of comparing their performance in terms of accuracy, efficiency, applicability, and robustness. These examples are specifically selected in order to be critical for one or more algorithms, in terms of excessive accuracy degradation, computational complexity, or even lack of convergence. One important result is that carefully designed weighting schemes may dramatically improve performance for all considered algorithm classes.
Enforcing Passivity of Macromodels via Spectral Perturbation of Hamiltonian Matrices
 7th IEEE Workshop on Signal Propagation on Interconnects (SPI
"... This paper presents a new technique for the enforcement of passivity of linear macromodels. The proposed algorithm is applicable to statespace realizations of the macromodels in case the inputoutput transfer function is in admittance, impedance, hybrid, or scattering form. The core of the algor ..."
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Cited by 14 (11 self)
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This paper presents a new technique for the enforcement of passivity of linear macromodels. The proposed algorithm is applicable to statespace realizations of the macromodels in case the inputoutput transfer function is in admittance, impedance, hybrid, or scattering form. The core of the algorithm is the application of firstorder perturbation theory to the eigenvalues of an associated Hamiltonian matrix. This allows both a precise definition of the frequency bands where passivity violations occur, and the determination of a new set of state matrices leading to passivity compensation. The main algorithm is very efficient in the case of small passivity violations, so that firstorder perturbation is feasible. An application to passive macromodeling of a package structure is presented.
On the Generation of Large Passive Macromodels for Complex Interconnect Structures
, 2006
"... This paper addresses some issues related to the passivity of interconnect macromodels computed from measured or simulated port responses. The generation of such macromodels is usually performed via suitable least squares fitting algorithms. When the number of ports and the dynamic order of the macr ..."
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Cited by 12 (8 self)
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This paper addresses some issues related to the passivity of interconnect macromodels computed from measured or simulated port responses. The generation of such macromodels is usually performed via suitable least squares fitting algorithms. When the number of ports and the dynamic order of the macromodel is large, the inclusion of passivity constraints in the fitting process is cumbersome and results in excessive computational and storage requirements. Therefore, we consider in this work a postprocessing approach for passivity enforcement, aimed at the detection and compensation of passivity violations without compromising the model accuracy. Two complementary issues are addressed. First, we consider the enforcement of asymptotic passivity at high frequencies based on the perturbation of the direct coupling term in the transfer matrix. We show how potential problems may arise when offband poles are present in the model. Second, the enforcement of uniform passivity throughout the entire frequency axis is performed via an iterative perturbation scheme on the purely imaginary eigenvalues of associated Hamiltonian matrices. A special formulation of this spectral perturbation using possibly large but sparse matrices allows the passivity compensation to be performed at a cost which scales only linearly with the order of the system. This formulation involves a restarted Arnoldi iteration combined with a complex frequency hopping algorithm for the selective computation of the imaginary eigenvalues to be perturbed. Some examples of interconnect models are used to illustrate the performance of the proposed techniques.
Improving the Convergence of Vector Fitting for Equivalent Circuit Extraction from Noisy Frequency Responses
 IEEE Transactions on Electromagnetic Compatibility
, 2006
"... Abstract—The vector fitting (VF) algorithm has become a common tool in electromagnetic compatibility and signal integrity studies. This algorithm allows the derivation of a rational approximation to the transfer matrix of a given linear structure starting from measured or simulated frequency resp ..."
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Cited by 9 (1 self)
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Abstract—The vector fitting (VF) algorithm has become a common tool in electromagnetic compatibility and signal integrity studies. This algorithm allows the derivation of a rational approximation to the transfer matrix of a given linear structure starting from measured or simulated frequency responses. This paper addresses the convergence properties of a VF when the frequency samples are affected by noise. We show that small amounts of noise can seriously impair or destroy convergence. This is due to the presence of spurious poles that appear during the iterations. To overcome this problem we suggest a simple modification of the basic VF algorithm, based on the identification and removal of the spurious poles. Also, an incremental pole addition and relocation process is proposed in order to provide automatic order estimation even in the presence of significant noise. We denote the resulting algorithm as vector fitting with adding and skimming (VFAS). A thorough validation of the VFAS algorithm is presented using a Monte Carlo analysis on synthetic noisy frequency responses. The results show excellent convergence and significant improvements with respect to the basic VF iteration scheme. Finally, we apply the new VFAS algorithm to measured scattering responses of interconnect structures and networks typical of highspeed digital systems. Index Terms—Circuit extraction, linear macromodeling, noise, rational approximation, vector fitting. I.
PassivityPreserving InterpolationBased Parameterized Macromodeling of Scattered SData
"... Abstract—A new technique to build parametric macromodels based on scattered Sdata samples in the design space is presented. Stability and passivity are guaranteed by construction over the entire design space by a robust and efficient twostep algorithm. In the first step, a set of univariate stable ..."
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Cited by 5 (5 self)
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Abstract—A new technique to build parametric macromodels based on scattered Sdata samples in the design space is presented. Stability and passivity are guaranteed by construction over the entire design space by a robust and efficient twostep algorithm. In the first step, a set of univariate stable and passive macromodels is built. In the second step, a geometrical structure that determines the connections between the scattered data points in the design space is built to perform multivariate positive interpolation. Index Terms—Interpolation, parametric macromodeling, passivity, rational approximation, scattered data. I.
An efficient reducedorder interconnect macromodel for timedomain simulation
 in Proc. Int. Circuits and Systems Symp
, 2003
"... Abstract—A typical integratedcircuit model consists of nonlinear transistor models and large linear RLC networks describing the interconnects. During the last decade, various modelreduction algorithms have been developed for replacing each RLC network with an approximately equivalent, but much sma ..."
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Cited by 5 (1 self)
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Abstract—A typical integratedcircuit model consists of nonlinear transistor models and large linear RLC networks describing the interconnects. During the last decade, various modelreduction algorithms have been developed for replacing each RLC network with an approximately equivalent, but much smaller, model. Since these reducedorder models are described in the frequency domain, they have to be linked to the transient analysis of the whole nonlinear circuit, which can be done by replacing these models with appropriate macromodels. In the interconnect literature, the actual macromodel realization, which has a great impact on the transientsimulation CPU time, is often overlooked. This paper presents a comprehensive comparison of nine reducedorder interconnect macromodels for timedomain simulation: the macromodels are reviewed, presented in a unified manner, and compared both theoretically and numerically. Since we have implemented all the nine macromodels into the APLAC circuit simulation and design tool, we are able to present a fair and meaningful CPU–time comparison. Index Terms—Interconnect simulation, macromodeling, modelorder reduction, transient analysis.
A coupled efficient and systematic fullwave timedomain macromodeling and circuit simulation method for signal integrity analysis of highspeed interconnects
 IEEE Trans. Adv. Packag
, 2004
"... Abstract—This paper presents an accurate and systematic approach for analysis of the signal integrity of the highspeed interconnects, which couples the fullwave finite difference time domain (FDTD) method with scattering ( ) parameter based macromodeling by using rational function approximation ..."
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Cited by 4 (0 self)
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Abstract—This paper presents an accurate and systematic approach for analysis of the signal integrity of the highspeed interconnects, which couples the fullwave finite difference time domain (FDTD) method with scattering ( ) parameter based macromodeling by using rational function approximation and the circuit simulator. Firstly, the fullwave FDTD method is applied to characterize the interconnect subsystems, which is dedicated to extract the parameters of the subnetwork consisting of interconnects with fairly complex geometry. Once the frequencydomain discrete data of the parameters of the interconnect subnetwork is constructed, the rational function approximation is carried out to establish the macromodel of the interconnect subnetwork by employing the vector fitting method, which provides a more robust and accurate solution for the overall problem. Finally, the analysis of the signal integrity of the hybrid circuit can be fulfilled by using the parameters based macromodel synthesis and simulation program with integrated circuits emphasis (SPICE) circuit simulator. Numerical experiments demonstrate that the proposed approach is accurate and efficient to address the hybrid electromagnetic (interconnect part) and circuit problems, in which the electromagnetic field effects are fully considered and the strength of SPICE circuit simulator is also exploited. Index Terms—FDTD method, highspeed interconnects, macromodeling, rational function approximation, signal integrity, parameter. I.
A general class of passive macromodels for lossy multiconductor transmission lines
 IEEE Trans. Microwave Theory and Techniques
"... The rapid increase in operating speeds, density and complexity of modern integrated circuits has made interconnect analysis a requirement for all stateoftheart circuit simulators. In this paper, a general class of passive macromodels for lossy multiconductor transmission lines with frequencydep ..."
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Cited by 4 (0 self)
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The rapid increase in operating speeds, density and complexity of modern integrated circuits has made interconnect analysis a requirement for all stateoftheart circuit simulators. In this paper, a general class of passive macromodels for lossy multiconductor transmission lines with frequencydependent parameters is presented. The proposed methodology is based on closedform matrixrational approximation of exponential functions describing Telegrapher’s equations and enables the development of the transmission line macromodel to be formulated analytically in terms of known (stored) constants and given perunitlength parameters. The proposed algorithm can be easily incorporated with conventional circuit simulators such as SPICE and also with the recently developed passive modelreduction techniques. I.