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This article presents a new noniterative inverse modeling technique based on machine learning regression and its applications to microwave design optimization. The proposed inverse model accepts the high-dimensional S-parameters computed at many frequency points as the input and estimates the optimal geometrical/physical parameters of the microwave component as its output. The least-squares support vector machine regression is combined with the principal component analysis to simultaneously overcome both the high-dimensional input space and ill-posed challenges of the inverse modeling. We also propose a new empirical method to find the optimum number of principal components (i.e., the compression level) for each example in an automated way. This makes our proposed model general and easy to use compared with the existing data-driven inverse modeling techniques. The inverse model is trained by a set of scattering parameters computed via a 2-D/3-D solver for few configurations of the geometrical parameters. The feasibility and the accuracy of the proposed optimization scheme are investigated by comparing its predictions with the corresponding optimal configuration estimated via a commercial solver. [ABSTRACT FROM AUTHOR]

Nonlinear phenomena in electrical contacts deteriorate the quality of communication systems with the production of passive intermodulation (PIM). The theoretical evaluation of PIM as a function of the physical parameters of the contact is rather complicated. Standard linear and macroscopic contact models do not take into account all microscopic aspects of the contact responsible for its nonlinear behavior. For the above reason, an accurate analysis of the PIM should be carried out by using microscopic contact models, defined by dozens of parameters, some of which cannot be precisely measured or estimated. This article presents a statistical analysis of the PIM level by taking into account a possible uncertain interval for the physical parameters of the contact. Such statistical interpretation is then used in order to identify the most relevant physical parameters for the PIM generation via a sensitivity analysis, through the use of a surrogate model that speeds up the huge amount of PIM computations. The results of the sensitivity analysis allow us to build a simpler model depending only on few dominant parameters. [ABSTRACT FROM AUTHOR]

This article deals with the application of the partial least-squares (PLS) regression to the uncertainty quantification of an integrated wireless power transfer with 30 random variables. It considers the development of surrogate models using a limited set of training samples in order to estimate statistical quantities of the converter efficiency with a relatively low computational cost compared with the standard brute-force Monte Carlo (MC) simulation. The strength, the performance, and the features of the proposed modeling approach are then compared with the ones of an advanced probabilistic surrogate model combining the least-squares support vector machine (LS-SVM) and the Gaussian process regression (GPR). The MC simulation is considered as a reference. [ABSTRACT FROM AUTHOR]

This article deals with the development of a probabilistic surrogate model for the uncertainty quantification of the voltage output spectral envelope of a power converter with several stochastic parameters. The proposed approach relies on the combination of the least-squares support vector machine (LS-SVM) regression with the Gaussian process regression (GPR), but it can suitably be applied to any deterministic regression techniques. As a first step, the LS-SVM regression is used to build an accurate and fast-to-evaluate deterministic model of the system responses starting from a limited set of training samples provided by the full-computational model. Then the GPR is used to provide a probabilistic model of the regression error. The resulting LS-SVM+GPR probabilistic model not only approximates the system responses for any configuration of its input parameters, but also provides an estimation of its prediction uncertainty, such as the confidence intervals (CIs). The above technique has been applied to qualify the uncertainty of the spectral envelope of the output voltage of a buck converter with 17 independent Gaussian parameters. The feasibility and the accuracy of the resulting model have been investigated by comparing its predictions and CI with the ones obtained by five different surrogate models based on state-of-the-art techniques and by the reference Monte Carlo results. [ABSTRACT FROM AUTHOR]

This article presents an innovative technique for the black-box modeling of the conductive emissions of switching circuits from external observations. The proposed methodology relies on the robust and elegant theory of periodically switched linear systems, providing the user with a tool for the generation of frequency-domain augmented linear time-invariant equivalents. The obtained models offer both a remarkable accuracy for different supply conditions and a deep understanding of the inherent switching mechanisms of this class of devices. The proposed framework also enables the derivation of a simplified enhanced Norton representation which outperforms the classical state-of-the-art models based on linear time-invariant approximations. Model parameters are computed via a blind procedure based only on two measurements. The feasibility and strength of the proposed approach are demonstrated on a dc–dc boost power converter and on a dc electrical motor via the prediction of their conducted disturbances. [ABSTRACT FROM AUTHOR]

This article presents a time-domain macromodeling algorithm for buried transmission lines subject to coupling of an incident field and terminated with linear and nonlinear loads. Different from overhead lines, the determination of the transient ground admittance is of great importance due to the complexity of the analytical expressions and the necessity of assuring a good approximation over a wide frequency range. The proposed macromodel adopts the analog behavioral modeling (ABM) library of Spice solvers to model frequency-dependent transmission line parameters directly, and calculate convolution in time domain, making it simple and convenient to treat time-domain field-to-line coupling equations without the need of time and spatial discretization and curve fitting used in other time-domain numerical algorithms. Besides, the model complexity is not limited by the line length. Hence, the proposed algorithm can significantly simplify the modeling process and improve simulation efficiency, especially for long multiconductor transmission lines. Furthermore, an effective and simplified expression for self and mutual ground impedance and admittance of underground lines is proposed in this article. With the proposed expression, the time-consuming numerical integration can be avoided, leading to a saving of 98% of the computational time. Finally, several validation examples of field coupling to buried power cables terminated with linear and nonlinear devices are investigated. The comparison of calculated waveshapes and CPU times shows the accuracy and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

This letter presents a black-box modeling approach for the prediction of the spectrum of the maximum currents induced on a generic linear load in an automotive radiated immunity test. The proposed approach relies on a parametric Thévenin-based circuit equivalent built from a limited set of measured or simulated data. The frequency-domain behavior of the equivalent voltage source is provided via a metamodel by combining the support vector machine (SVM) regression with a regularized Fourier kernel with a simple adaptive algorithm. The latter allows defining the minimum number of training samples needed to accurately predict the maximum values of the currents induced on a generic linear load for different azimuth directions of the excitation field. The accuracy and the strength of the proposed approach are demonstrated for an example, by comparing the model predictions with the results of a parametric full-wave electromagnetic simulation. [ABSTRACT FROM AUTHOR]

An accurate and efficient time-domain macromodeling algorithm based on the analog behavioral modeling (ABM) and generalized method of characteristics is proposed to calculate current and voltage responses of multiconductor transmission lines (MTLs) to incident field coupling. The proposed macromodel adopts the frequency response table of Laplace-domain elements in ABM library of Spice solvers to model the characteristic impedance (or admittance) and propagation operator of transmission lines and calculate the convolution in the time domain. Time-domain convolution is implemented by the solver, without the need of delay extraction and rational approximation for the MTLs solution. Compared with the existing algorithms for calculating the responses of incident field coupling to MTLs, the proposed algorithm largely simplifies the modeling and simulation process while ensuring stable responses, especially for long MTLs. Besides, it is also applicable and efficient to solve the case of nonlinear terminal elements, directly in the time domain. Several numerical examples of single conductor, two conductors, and three-phase 35 kV power transmission lines loaded with nonlinear metal oxide arresters are studied. The calculation results and CPU times are compared with those of other existing algorithms to validate the accuracy and efficiency of the method proposed in this paper. [ABSTRACT FROM AUTHOR]

This paper investigates the application of support vector machine to the modeling of high-speed interconnects with largely varying and/or highly uncertain design parameters. The proposed method relies on a robust and well-established mathematical framework, yielding accurate surrogates of complex dynamical systems. An identification procedure based on the observation of a small set of system responses allows generating compact parametric relations, which can be used for design optimization and/or stochastic analysis. The feasibility and strength of the method are demonstrated based on a benchmark function and on the statistical assessment of a realistic printed circuit board interconnect, highlighting the main features and benefits of this technique over state-of-the-art solutions. Emphasis is given to the effects of the initial sample size and of input noise on the model estimation. [ABSTRACT FROM AUTHOR]

This paper deals with uncertainty propagation applied to the analysis of crosstalk in printed circuit board microstrip traces. Complex interconnection networks generally are affected by many uncertain parameters and their point-to-point transfer functions are computationally expensive, thus making Monte-Carlo analyses rather inefficient. To overcome this situation, a metamodel is highly desirable. This paper presents a sparse and accelerated polynomial chaos approach, which proves to be well adapted for high-dimensional uncertainty quantification and well suited for the sensitivity analysis of crosstalk effects. We highlight the significant advantage of the advocated approach for the design of microstrip line networks of complex topology. In fact, we demonstrate how a small number of system simulations can help to quantify the statistics of the output variability and identify a reduced set of high-impact parameters. [ABSTRACT FROM AUTHOR]

In this paper, we adopt the so-called sparse polynomial chaos metamodel for the uncertainty quantification in the framework of high-dimensional problems. This metamodel is used to model a realistic electronic bus structure with a large number of uncertain input parameters such as those related to microstrip line geometries. It aims at estimating quantities of interest, such as statistical moments, probability density functions, and provides sensitivity analysis of a response. It drastically reduces the model computational cost with regard to brute force Monte Carlo (MC) simulation. The method presents a good performance and is validated in comparison with MC simulation. [ABSTRACT FROM AUTHOR]

This paper addresses the behavioural modelling of digital integrated circuit buffers for performance assessment of high‐speed data links. A new modelling technique, with several important advantages is described. All the requirements of black‐box identification are met: the approach relies exclusively on the observation of the external port voltages and currents, thus allowing the extraction of models that mimic the operation of real devices without insight on their internal structure. Furthermore, unlike the standard algorithms currently used in EDA tools, the method described in this study provides a straightforward solution to modelling the input–output behaviour. Good model performance in overclocking conditions is an important advantage. This study also investigates the possibility of accounting for power‐supply voltage variations and provides a simple solution. [ABSTRACT FROM AUTHOR]

This brief presents a frequency-domain approach for the steady-state analysis of pulsewidth-modulated converters and switched circuits with nonideal switching behavior. The proposed strategy generalizes recent methodologies based on the Fourier expansion of the steady-state responses of a periodically switching circuit and on the simulation of an augmented linear-time-invariant system. This system is now also given an interpretation in terms of an equivalent circuit, which is simulated at a single frequency point to solve for all the harmonics. The method offers a modular topological approach that is combined with standard tools for circuit analysis and enables the simulation of networks with an arbitrary number of switches and driving mechanisms. Single, multiple, and possibly nonideal commutation events within the switching period are handled in the same framework, without additional complexity. The technique allows for the full frequency-domain characterization of both the functional and the noisy behavior of the circuit responses. The feasibility and strength are demonstrated via comparisons with simulations and measurements on two application examples, i.e., a full-bridge single-phase inverter and a dc–dc boost converter. [ABSTRACT FROM AUTHOR]

The vulnerability of microcontroller system against high-altitude electromagnetic pulse (HEMP) is taken as an illustration to demonstrate the assessment methodology based on Bayesian networks (BN). The complete procedure is performed by two steps: the qualitative and the quantitative. The first step focuses on the analysis of three classes of properties, the electromagnetic environment, system function/structure, and their interactions. The primary BN model is built at the end of the first step. The second step investigates the BN nodes and branches one by one, which further implemented through two stages, i.e., the data acquisition and data fusion. The susceptibilities of devises are examined with the pulsed current injection. The responses of the transmission lines to HEMP are computed using the field-line coupling model. Comparing the probability density functions of the electromagnetic stresses and strengths produces the failure probabilities of the interface components. Through two-step analysis, the critical elements and coupling paths are identified and highlighted. After neglecting those unimportant factors, many BN nodes and branches are deleted. Thus, the complexity of assessment is reduced. By assigning the probability values to the simplified BN model, the system failure probability is calculated, which characterizes the system vulnerability against HEMP environment. The illustration validates the rationality and flexibility of the BN assessment methodology. [ABSTRACT FROM AUTHOR]

This paper addresses the simulation of the conducted electromagnetic interference produced by circuits with periodically switching elements. The proposed method allows for the computation of their steady-state responses by means of augmented linear time-invariant equivalents built from circuit inspection only, and standard tools for circuit analysis. The approach is demonstrated on a real dc–dc boost converter by comparing simulation results with real measurements. [ABSTRACT FROM AUTHOR]

The ever-increasing impact of uncertainties in electronic circuits and systems is requiring the development of robust design tools capable of taking this inherent variability into account. Due to the computational inefficiency of repeated design trials, there has been a growing demand for smart simulation tools that can inherently and effectively capture the results of parameter variations on the system responses. To improve product performance, improve yield and reduce design cost, it is particularly relevant for the designer to be able to estimate worst-case responses. Within this framework, the article addresses the worst-case simulation of lumped and distributed electrical circuits. The application of interval-based methods, like interval analysis, Taylor models and affine arithmetic, is discussed and compared. The article reviews in particular the application of the affine arithmetic to complex algebra and fundamental matrix operations for the numerical frequency-domain simulation. A comprehensive and unambiguous discussion appears in fact to be missing in the available literature. The affine arithmetic turns out to be accurate and more efficient than traditional solutions based on Monte Carlo analysis. A selection of relevant examples, ranging from linear lumped circuits to distributed transmission-line structures, is used to illustrate this technique. [ABSTRACT FROM PUBLISHER]

This paper addresses an integrated circuit (IC) modeling procedure for mixed-signal immunity simulations of communication networks. The procedure is based on a gray-box approach, modeling (IC) ports with a physical circuit and the internal links with a behavioral block. The parameters are estimated from time and frequency domain measurements, allowing accurate and efficient reproduction of nonlinear device switching behaviors. The effectiveness of the modeling process is verified by applying the proposed technique to a controller area network (CAN) transceiver, involved in a direct power injection (DPI) immunity test on a data communication link. The obtained model is successfully implemented in a VHDL-analog mixed-signal (AMS) solver to predict both the functional signals and the RF noise immunity at component level. [ABSTRACT FROM PUBLISHER]

This paper delivers a considerable improvement in the framework of the statistical simulation of highly nonlinear devices via polynomial chaos-based circuit equivalents. Specifically, a far more efficient and “black-box” approach is proposed that reduces the model complexity for nonlinear components. Based on recent literature, the “stochastic testing” method is used in place of a Galerkin approach to find the pertinent circuit equivalents. The technique is demonstrated via the statistical analysis of a low-noise power amplifier and its features in terms of accuracy and efficiency are highlighted. [ABSTRACT FROM AUTHOR]

This paper proposes a distributed analytical representation and Gauss–Seidel iterative technique (Seidel-DARIT-field), which has a faster convergence rate than the Jacobi-DARIT-field method in the simulation of electromagnetic pulse (EMP) radiated field coupling to multiconductor transmission lines (MTLs) and is more valid and accurate. The process of the first iteration in this method is similar to that in the Jacobi-DARIT-field method. At the second iteration and after, every line will be updated based on the present iteration state of other lines. [ABSTRACT FROM AUTHOR]

This letter addresses the simulation of the steady-state response of switching power converters. The proposed approach is based on the interpretation of the voltage and current variables of a periodically switched linear circuit in terms of a series expansion and on the generation of augmented time-invariant constitutive relations of the circuit elements. The circuit solution is obtained from an augmented time-invariant nodal equation generated from topological information and circuit inspection only. The feasibility and strength of the approach are demonstrated on a dc-dc boost converter. [ABSTRACT FROM AUTHOR]

This letter addresses the stochastic analysis of nonlinear switching power converters via an augmented circuit equivalent and a single deterministic SPICE simulation. The proposed approach is based on the expansion of the constitutive relations of the circuit elements in terms of orthonormal polynomials within the well-established framework of polynomial chaos. The feasibility and strength of the method are demonstrated on a dc-dc boost converter described by either detailed nonlinear components or via its averaged linear circuit. Excellent modeling accuracy as well as remarkable speed-ups compared to traditional sampling-based approaches are achieved. [ABSTRACT FROM AUTHOR]

This paper presents a numerical procedure for the calculation of the polynomial chaos (PC)-expansion coefficients for the per-unit-length capacitance and inductance matrices of wire structures affected by random parameter variability. According to the recent literature results, these coefficients in turn allow the generation of electrical circuit models for stochastic cables. The procedure is based on the twofold expansion of the nonuniform and stochastic charge distributions on the wire boundaries in terms of both Fourier and PC expansions. A stochastic Galerkin method allows to cast the problem in terms of a deterministic system of equations, whose solution provides the unknown coefficients. The proposed methodology is validated via the generation of statistical models for wire structures with random parameters, whose probabilistic responses are compared against the results of Monte Carlo simulations. [ABSTRACT FROM PUBLISHER]

We focus on the simulation of periodically switched linear circuits. The basic notation and theoretical framework are presented, with emphasis on the differences between the linear time-invariant and the time-varying cases. For this important class of circuits and sources defined by periodic signals, the computation of their steady-state response is carried out via the solution of an augmented time-invariant MNA equation in the frequency-domain. The proposed method is based on the expansion of the unknown voltages and currents in terms of Fourier series and on the automatic generation of augmented equivalents of the circuit components. The above equivalents along with the information on circuit topology allow creating, via circuit inspection, a time-invariant MNA equation, the solution of which provides the coefficients of both the time- and the frequency-domain responses of the circuit. Analytical and numerical examples are used to stress the generality and benefits of the proposed approach. [ABSTRACT FROM AUTHOR]

This 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 proposed. [ABSTRACT FROM AUTHOR]

In this paper, a stochastic modeling method is presented for the analysis of variability effects, induced by the manufacturing process, on interconnect structures terminated by general nonlinear loads. The technique is based on the solution of the pertinent stochastic Telegrapher's equations in time domain by means of the well-established stochastic Galerkin method, but now allows, for the first time in the literature, the inclusion of loads with arbitrary I-V characteristics at the terminals of the lines. The transient solution is obtained by combining the stochastic Galerkin method with a finite-difference time-domain scheme. The proposed technique is validated and illustrated with a meaningful application example, demonstrating its accuracy and efficiency. [ABSTRACT FROM AUTHOR]

This paper provides an efficient iterative solution in the frequency domain for electromagnetic pulse (EMP) radiated field coupling to multiconductor transmission lines (MTLs) based on distributed analytical representation of the exciting sources and iterative technique originated from waveform relaxation. The method consists of two kinds of iterations, the first is that the incoming EMP wave couples to each conductor while the effects of neighboring conductors were neglected; the second is that each conductor will be not only subject to the illumination of the EMP wave, but also influenced by the virtual sources which are the induced voltages and currents of the neighboring conductors at the previous iteration. The key highlights of the proposed method are that the induced voltage and current at each iteration are considered as the virtual distributed exciting sources for next iteration, and the integrals were solved analytically by the Baum–Liu–Tesche equation, leading to a pretty good efficiency and quick convergence for most real cases. The validation results over a wide range show that the proposed method could efficiently handle EMP coupling to MTLs with a large number of conductors and the accuracy of the solutions is closely related to the number of iterations allowing the flexibility to choose between the accuracy and the time cost. [ABSTRACT FROM AUTHOR]

This paper addresses the generation of an enhanced stochastic model of a carbon nanotube interconnect including the effects of process variation. The proposed approach is based on the expansion of the constitutive relations of state-of-the-art deterministic models of nanointerconnects with uncertain parameters in terms of orthogonal polynomials. The method offers comparable accuracy and improved efficiency with respect to conventional methods like Monte Carlo in predicting the statistical behavior of the electrical performance of next-generation data links. An application example involving both the frequency- and time-domain analysis of a realistic nanointerconnect concludes this paper. [ABSTRACT FROM AUTHOR]

This paper addresses the generation of behavioral models of digital integrated circuits (ICs) for signal and power integrity simulations. The proposed models are obtained by external measurements carried out at the device ports only and by the combined application of specialized state-of-the-art modeling techniques. The present approach exploits a behavioral formulation, leading to models reproducing all the behavior of the IC ports as the input/output buffers and the core power delivery network. The modeling procedure is demonstrated for a commercial nor Flash memory in 90-nm technology housed by a specifically designed test fixture. [ABSTRACT FROM PUBLISHER]

The growing importance of signal integrity (SI) analysis in integrated circuits (ICs), revealed by modern system-in-package methods, is demanding for new models for the IC sub-systems which are both accurate, efficient and extractable by simple measurement procedures. This paper presents the contribution for the establishment of an integrated IC modeling approach whose performance is assessed by direct comparison with the signals measured in laboratory of two distinct memory IC devices. Based on the identification of the main blocks of a typical IC device, the modeling approach consists of a network of system-level sub-models, some of which with already demonstrated accuracy, which simulated the IC interfacing behavior. Emphasis is given to the procedures that were developed to validate by means of laboratory measurements (and not by comparison with circuit-level simulations) the model performance, which is a novel and important aspect that should be considered in the design of IC models that are useful for SI analysis. [ABSTRACT FROM PUBLISHER]

This paper focuses on the derivation of an enhanced transmission-line model allowing the stochastic analysis of a realistic multiconductor interconnect. The proposed model, which is based on the expansion of the well-known telegraph equations in terms of orthogonal polynomials, includes the variability of geometrical or material properties of the interconnect due to uncertainties like fabrication process or temperature. A real application example involving the frequency-domain analysis of a coupled microstrip and the computation of the parameters variability effects on the transmission-line response concludes this paper. [ABSTRACT FROM PUBLISHER]

This paper presents novel theoretical probability density functions (PDFs) for the magnitude and phase of electromagnetic fields inside reverberation chambers (RC) operating in a “good-but-imperfect” regime. The derivation is based on considering two Gaussian random variables with mean values, variances, and correlation that are departed from the ideal assumptions. A bivariate approach using a complete joint Gaussian distribution of these variables is defined. Marginal distributions obtained by integration of a 2-D joint PDF are compared with theoretical PDFs for ideal situations, and significantly lower rejection rates are experienced for field data measured in real RCs. Additionally, these novel marginal PDFs are highly general since they are able to describe both ideal and nonideal stirred fields and reproduce other findings. [ABSTRACT FROM PUBLISHER]