1,721,022 research outputs found
An effective modeling framework for the analysis of interconnects subject to line-edge roughness
Full text linkThis letter proposes a complete and efficient simulation framework to assess the effects of line-edge roughness appearing in on-chip lines. The modeling approach consists of three steps. First, a stochastic macromodel is created for the per-unit-length RLGC parameters of the line. Secondly, random conductor edge profiles are generated using randomized splines. These are combined with the stochastic macromodel to readily provide place-dependent RLGC parameters. Finally, the resulting nonuniform transmission line is analyzed by means of a fast and accurate perturbation technique. To validate the proposed approach, a statistical analysis of the response of a coupled inverted embedded microstrip line is carried out for different roughness parameters
Frequency- and time-domain stochastic analysis of lossy and dispersive interconnects in a SPICE-like environment
No full textThis paper presents an improvement of the state-of-the-art polynomial chaos (PC) modeling of high-speed interconnects with parameter uncertainties via SPICE-like tools. While the previous model, due to its mathematical formulation, was limited to lossless lines, the introduction of modified classes of polynomials yields a formulation that allows to account for lossess and dispersion as well. Thanks to this, the new implementation can also take full advantage of the combination of the PC technique with macromodels that accurately describe the interconnect properties. An application example, i.e. the stochastic analysis of an on-chip line, validates and demonstrates the improved method
On the relationship between the stochastic Galerkin method and the pseudo-spectral collocation method for linear differential algebraic equations
Full text linkPolynomial chaos-based methods have been extensively applied in electrical and other engineering problems for the stochastic simulation of systems with uncertain parameters. Most of the implementations are based on either the intrusive stochastic Galerkin method or on non-intrusive collocation approaches, of which a very common example is the pseudo-spectral method based on Gaussian quadrature rules. This paper shows that, for the important class of linear differential algebraic equations, the latter can be cast as an approximate factorization of the stochastic Galerkin approach, thus generalizing recent discussions in literature in this regard. Consistently with this literature, we show that the factorization turns out to be exact for first-order random inputs, and hence the two methods coincide under this assumption. Further, the presented results also generalize recent work in the field of electrical circuit simulation, in which a similar decomposition was derived ad hoc, via error minimization, for the case of Hermite chaos. We demonstrate that the factorization stems from the general properties of orthogonal polynomials and the error introduced by the approximation—or in other terms, the error of the stochastic collocation method in comparison with the stochastic Galerkin method—is carefully quantified and assessed. An illustrative example concerning the stochastic analysis of an RLC circuit is used to illustrate the main findings of this paper. In addition, a more complex and real-life example allows emphasizing the generality of the achieved results
On the Passivity of Polynomial Chaos-Based Augmented Models for Stochastic Circuits
No full textThis paper addresses for the first time the issue of passivity of the circuit models produced by means of the generalized polynomial chaos technique in combination with the stochastic Galerkin method. This approach has been used in literature to obtain statistical information through the simulation of an augmented but deterministic instance of a stochastic circuit, possibly including distributed transmission-line elements. However, transient simulations raise the critical question as to whether such an augmented network is passive or not. This paper discusses the general requirements for the augmented circuits to be passive and provides a sufficient condition for their passivity. Some numerical examples illustrate the theoretical results and conclude the paper
Improved polynomial chaos discretization schemes to integrate interconnects into design environments
No full textRecently, an efficient stochastic modeling method for interconnects with inherent variability in their physical parameters was proposed, based on applying the so-called polynomial chaos (PC) approach in conjunction with a Stochastic Galerkin Method (SGM) onto telegrapher's equations. Although this approach was already very successful from a numerical point of view, the novel technique could not be conveniently integrated into SPICE-like solvers, limiting the applicability of the method. In this letter, the PC-SGM scheme for telegrapher's equations is revisited, pinpointing the origin of this inconvenience and immediately allowing to mitigate the issue. By adapting the traditional discretization of the stochastic telegrapher's equations approach, an augmented, yet deterministic, set of ordinary differential equations is obtained that turns out to be of the same type as the telegrapher's equations, and hence, the physical property of reciprocity is preserved. Consequently, it can be directly and more efficiently handled using SPICE-like solvers, which usually assume matrix symmetries. As an application example, the variability analysis of a state-of-the-art on-chip line for millimeter-wave applications is performed in a SPICE solver
Analysis of nonuniform transmission lines with an iterative and adaptive perturbation technique
Full text linkThis 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
Uncertainty Assessment of Lossy and Dispersive Lines in SPICE-Type Environments
Full text linkThis paper presents an alternative modeling strategy for the stochastic analysis of high-speed interconnects. The proposed approach takes advantage of the polynomial chaos framework and a fully SPICE-compatible formulation to avoid repeated circuit simulations, thereby alleviating the computational burden associated with traditional sampling-based methods such as Monte Carlo. Nonetheless, the technique offers very good accuracy and the opportunity to easily simulate complex interconnect topologies which include lossy and dispersive transmission lines, thus overcoming the limitations of previous formulations. Application examples involving the stochastic analysis of on-chip and on-board interconnects validate the methodology propose
Parameterized Partial Element Equivalent Circuit Method for Sensitivity Analysis of Multiport Systems
No full text"\"This paper presents a new technique to perform parameterized sensitivity analyses of systems that depend on multiple design parameters, such as layout and substrate features. It uses the electromagnetic (EM) method called partial element equivalent circuit to compute state space matrices at a set of design space points. These EM matrices are interpolated as functions of the design parameters. The proposed interpolation scheme allows the computation of the derivatives of the matrices, which are needed to perform the sensitivity analysis. An extensive study of the required stability and passivity properties of the system involved in the parameterized sensitivity analysis is presented. Pertinent numerical results demonstrate the robustness, accuracy, and efficiency of the proposed methodology.\"
A micromagnetic study of the reversal mechanism in permalloy antidot arrays
No full textA numerical analysis is focused on the influence of patterning and finite-size effects on the hysteresis properties and magnetization reversal of permalloy antidot films with square lattice and square holes. Simulations are performed by solving the Landau-Lifshitz equation. The aim is to explain the relationships between the shape of the hysteresis loop and the different stages of the reversal process. In particular, the switching mechanism is characterized by the nucleation of domain chains that destroy the periodic symmetry in the magnetization present when infinite periodicity is considered. This behavior is strongly influenced by the demagnetizing effects arising both at the film boundaries and at the hole edges
A Calderon Multiplicative Preconditioner for the PMCHWT Equation for Scattering by Chiral Objects
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