Analysis of crosstalk and field coupling to lossy MTL's in a SPICE environment

This paper proposes a circuit model for lossy multiconductor transmission lines (MTLs) suitable for implementation in modern SPICE simulators, as well as in any simulator supporting differential operators. The model includes the effects of a uniform or nonuniform disturbing field illuminating the line and is especially devised for the transient simulation of electrically long wideband interconnects with frequency dependent per-unit-length parameters. The MTL is characterized by its transient matched scattering responses, which are computed including both dc and skin losses by means of a specific algorithm for the inversion of the Laplace transform. The line characteristics are then represented in terms of differential operators and ideal delays to improve the numerical efficiency and to simplify the coding of the model in existing simulators. The model can be successfully applied to many kinds of interconnects ranging from micrometric high-resistivity metallizations to low-loss PCBs and cables, and can be considered a practical extension of the widely appreciated lossless MTL SPICE model, which maintains the simplicity and efficienc

Transient simulation of lossy multiconductor interconnects

The transient simulation of electrically-long low-loss multiconductor interconnects is considered from a practical point of view. The importance of frequency dependent losses in these interconnects is discussed and a simple transmission line characterization procedure allowing for such losses is proposed. The characterization obtained yields simple and efficient interconnect models, that the user can include, without programming, in any simulator accepting differential operator

A perturbative approach to predict eye diagram degradation in differential interconnects subject to asymmetry and nonuniformity

This paper proposes a novel framework for the signal integrity (SI) analysis of differential interconnects affected by nonuniformity and geometrical asymmetry. The pertinent nonuniform transmission-line (TL) equations are solved in the frequency domain by means of a perturbation technique, which allows interpreting the resulting response degradation as a perturbation with respect to the response of a reference uniform differential line (DL) with averaged per-unit-length (p.u.l.) parameters. Following this interpretation, the problem is recast as a standard TL equation for the reference uniform line with additional equivalent distributed sources that account for the perturbative effect of asymmetric nonuniformity. This equivalent perturbation problem is solved iteratively in the frequency domain, and the corresponding time-domain behavior is obtained via inverse Fourier transform. Moreover, upon consideration that local perturbations negligibly impact on far-end differential mode (DM) quantities, the uniform DL model with averaged p.u.l. parameters is used for the SI performance evaluation of transmitted DM voltages in SPICE, showing that comparable results can be obtained while avoiding the cumbersome implementation of a nonuniform transmission line topology. The methodology is applied to the prediction of the eye diagram degradation for a 20 Gbps transmission through a microstrip DL subject to geometrical asymmetry and nonuniformity

Analysis of nonuniform transmission lines with an iterative and adaptive perturbation technique

This paper presents an iterative and adaptive perturbation technique for the analysis of nonuniform transmission lines. Place-dependent variations of the per-unit-length parameters are interpreted as perturbations with respect to their average values along the line. This allows casting the governing equations for the corresponding perturbations of the voltages and currents as those of a uniform transmission line with distributed sources. Therefore, standard transmission line theory is used to calculate these perturbation terms. Specifically, perturbations of increasing order are computed iteratively starting from the solution of the unperturbed line. The accuracy is adaptively adjusted by setting a threshold on the convergence of the solution. The algorithm turns out to be simple to implement and very accurate, yet faster than traditional approaches based on the discretization of the line into uniform sections. The technique is validated through the analysis of several nonuniform transmission line structures of relevance in EMC applications, namely uniformly and nonuniformly twisted wire pairs as well as a cable bundle with lacing cords

A Framework for Robust Assessment of Power Grid Stability and Resiliency

Security assessment of large-scale, strongly nonlinear power grids containing thousands to millions of interacting components is a computationally expensive task. Targeting at reducing the computational cost, this paper introduces a framework for constructing a robust assessment toolbox that can provide mathematically rigorous certificates for the grids' stability in the presence of variations in power injections, and for the grids' ability to withstand a bunch sources of faults. By this toolbox we can "off-line" screen a wide range of contingencies or power injection profiles, without reassessing the system stability on a regular basis. In particular, we formulate and solve two novel robust stability and resiliency assessment problems of power grids subject to the uncertainty in equilibrium points and uncertainty in fault-on dynamics. Furthermore, we bring in the quadratic Lyapunov functions approach to transient stability assessment, offering real-time construction of stability/resiliency certificates and real-time stability assessment. The effectiveness of the proposed techniques is numerically illustrated on a number of IEEE test cases