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High-speed interconnects are increasingly becoming susceptible to electromagnetic interference (EMI). Hence, there is a growing need for fast simulation of interconnect lines in the presence of incident field coupling using circuit simulators such as SPICE. However, the presence of a large number of coupled lines in modern interconnect structures is a serious limiting factor in these simulations. In order to simultaneously address these difficulties, a new algorithm is presented in this paper for EMI analysis of large number of coupled interconnects. The new method exploits the recently developed waveform relaxation (WR) and transverse partitioning algorithms for fast EMI analysis. The same WR sources that are computed for multiconductor transmission line analysis are also employed for EMI analysis. The computational complexity of the proposed EMI analysis grows only linearly with the number of lines. In addition, the algorithm lends itself to parallel implementation leading to further reduction in CPU time. Index Terms--Electromagnetic interference (EMI), high-speed interconnects, incident fields, multiconductor transmission lines (MTLs), waveform relaxation (WR).

Circuit modeling of high-frequency devices described by tabulated multiport parameters has generated immense interest during recent years. In most cases, equivalent circuit models (ECMs) are available to the designers, which correlate well with the measured parameters at lower frequencies, however, deviate at higher frequencies. Traditional efforts to improve ECMs are device specific, laborious, and ad-hoc in nature. In order to address these difficulties, this paper presents an efficient and automated algorithm to identify appropriate frequency-dependent elements for adding to the ECM at arbitrary locations so as to correct for high-frequency errors. The new method enables the designers to retain their existing physical models while providing a means to capture the high-frequency effects accurately, Index Terms--Large-scale augmentation, linear device modeling, multiport parameters, passive macromodels.

Electromagnetic compatibility (EMC) analysis of high-speed designs has become imperative due to rapidly increasing radio-frequency interference and emerging technological trends such as higher operating frequencies, denser layouts, and multifunction convergent products. In this paper, a simplified macromodel of multiconductor transmission lines (MTLs) exposed to incident fields is presented. The proposed formulation can also handle frequency dependence of resistance, capacitance, conductance, and inductance (RLGC) line parameters. The method employs the recently developed delay-extraction-based compact and passive MTL macromodel, while developing closed-form expressions for incident field analysis. An error bound for the proposed macromodel is also presented. The macromodel is simulation program with integrated circuit emphasis (SPICE) compatible and overcomes the mixed frequency/time simulation difficulties usually encountered during transient analysis, while guaranteeing the stability of the global transient simulation. The algorithm provides higher accuracy as well as significant speed gains for EMC analysis of transmission line networks as compared to the existing techniques. Index Terms--Circuit simulation, delay extraction, distributed interconnects, electromagnetic coupling, electromagnetic interference (EMI), high-speed modules, incident fields, method of characteristics (MoC), multiconductor transmission lines (MTLs), passive macromodels, printed circuit boards (PCBs), transient analysis.

This paper presents a new algorithm for computing the sensitivity of steady-state responses of nonlinear circuits with respect to an arbitrary network parameter. The proposed algorithm is based on circuit-reduction […]

An efficient approach is presented for time-domain sensitivity analysis of lossy multiconductor transmission lines with respect to electrical and/or physical parameters. The proposed method employs delay extraction prior to approximating the matrix exponential stamp of the line and guarantees macromodel passivity. A delay-extraction-based equivalent circuit for sensitivity analysis is derived in a closed form, leading to significant computational advantages. Index Terms--Delay extraction, matrix rational approximation, passive macromodels, sensitivity analysis, transmission lines.

This paper presents a new theory that addresses the issue of passivity in macromodels of electrical interconnects constructed based on the method of characteristics (MoC). The proposed approach develops a new algebraic test to check for passivity in macromodels generated using MoC. The theory behind the developed test is based on deriving the necessary and sufficient conditions for the loss of positive-realness in the admittance matrix of the developed macromodei. An algorithmic procedure is proposed to verify passivity of general macromodels derived from the MoC. The results presented in this paper can be employed to test for positive-realness in dynamical systems described by algebraic delay-differential equations with discrete commensurate delays. Index Terms--Delay systems, high-speed interconnects, method of characteristics (MoC), passivity, positive-real matrices.

With the increasing operating frequencies and functionality in modern designs, the resulting size of circuit equations of high-frequency interconnect and microwave subnetworks are becoming large. Model-order reduction-based algorithms were recently suggested to handle the solution complexity of such circuits. The major objectives in state-of-the-art model-reduction algorithms are: 1) achieving accurate and compact models; 2) numerically stable and efficient generation of models; and 3) preservation of system properties such as passivity. Algorithms such as PRIMA generate guaranteed passive reduced-order models for large interconnect circuits described by RLC type of circuits. However, with the diverse technologies and complex geometries, it is becoming prevalent to describe some of the embedded linear modules in terms of state-space equations. In this paper, we show how to extend the scope of PRIMA-type first-level reduction algorithms for simultaneous reduction of combined circuits containing both RLC interconnects and embedded modules described by general passive state-space equations, while preserving the passivity of the resulting reduced-order model. Necessary formulation, proof of macromodel passivity, and validation examples are given. Index Terms--Algebraic Ricatti equations, electromagnetic (EM), Hamiltonian matrices, Krylov subspace, measured subnetworks, model order reduction, passive macromodels, PRIMA, state-space systems, tabulated data, transmission lines.

Recently, several time-domain passive macromodeling algorithms were proposed for distributed transmission-line networks. Most of them employ some kind of approximation in the frequency domain to match the response up to a maximum frequency of interest and the behavior after the highest frequency is generally not considered. This can cause significant errors in transient responses (especially in the early-time period). In order to address this difficulty, we will present a new algorithm to reduce high-frequency errors in time-domain macromodels, while preserving passivity. The proposed algorithm is very useful in eliminating spurious ripples in the flat delay portion of transient responses of distributed transmission-line networks without needing to increase the order of approximation. Index Terms--Circuit simulation, distributed networks, high-speed interconnects, model-reduction, printed circuit boards, transient analysis, transmission lines.

An efficient approach for sensitivity analysis of lossy multiconductor transmission lines in the presence of nonlinear terminations is described. Sensitivity information is extracted using the recently developed closed-form matrix-rational approximation of distributed transmission-line model. The method enables sensitivity analysis of interconnect structures with respect to both electrical and physical parameters. An important advantage of the proposed approach is that the derivatives of the modified nodal admittance matrices with respect to per-unit-length parameters are obtained analytically. Index Terms--Interconnects, optimization, sensitivity analysis, transmission lines.

In this paper, an efficient time-domain macromodel for incident field coupling to lossy-multiconductor transmission lines is presented. The model takes the form of ordinary differential equations and can be easily included in SPICE like simulators for transient analysis. The model is based on the closed-form matrix-rational approximation of the exponential matrix describing Telegrapher's equations and semi-analytic rational approximation of forcing functions. Index Terms--Circuit simulation, electromagnetic coupling, EMI, interconnections, macromodeling, multiconductor transmission lines, PCB, transient simulation.

This paper presents an efficient technique for transient simulation of linear subnetworks characterized by S-parameters in the presence of nonlinear components. The proposed method is based on the recently developed model-reduction technique, complex frequency hopping. A new algorithm for computing the moments of S-parameter-based subnetworks is presented. The proposed method is suitable for simulating large number of S-parameter-based subnetworks in a general circuit environment consisting of lumped/distributed elements and nonlinear devices. Index Terms - Circuit simulation, complex frequency hopping, distributed networks, high-speed interconnects, model-order reduction, moment-matching techniques, RF circuits, scattering parameters.