Simulation of Impedance Discontinuities Resulting from Degradation of Interconnections on Printed Circuit Boards

Numerical simulation of impedance discontinuities resulting from degradation of interconnections on printed circuit board

Combining LS-SVM and GP Regression for the Uncertainty Quantification of the EMI of Power Converters Affected by Several Uncertain Parameters

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

Bayesian Optimization of Hyperparameters in Kernel-Based Delay Rational Models

This paper presents an automatic procedure for the optimization of the hyperparameters of a delay rational model approximating the frequency-domain behavior of high-speed interconnects. The proposed model is built via a kernel-based regression, such as the Least-Square Support Vector Machine (LS-SVM), by considering an ad-hoc kernel with two hyperparameters related to the propagation delays introduced by the system. Such hyperparameters, along with the Tikhonov regularizer used by the LS-SVM regression, are carefully tuned via an automatic approach based on a k-fold cross-validation and Bayesian optimization. The feasibility of the effectiveness of the proposed modeling approach are investigated on a high-speed link

Machine Learning Applied to the Blind Identification of Multiple Delays in Distributed Systems

This paper focuses on the application of the Least-Square Support Vector Machine (LS-SVM) regression for the modeling of frequency responses of complex interconnect structures. The goal is to obtain a delayed-rational model (DRM) for the structure accounting for multiple time-delays generated by wave propagation and reflections along the channel. A novel approach for the time-delays estimation based on the LS-SVM regression is introduced. The delays are estimated using the dual space formulation of the LS-SVM with an ad-hoc kernel that considers a possible delay interval. The results highlight the lower order of DRMs obtained using the delays identified through this method when comparing to the vector fitting approach by applying it to a high-speed cable link

Bridging the Gap Between Artificial Neural Networks and Kernel Regressions for Vector-Valued Problems in Microwave Applications

Thanks to their convex formulation, kernel regressions have shown an improved accuracy with respect to artificial neural network (ANN) structures in regression problems where a reduced set of training samples are available. However, despite the above interesting features, kernel regressions are inherently less flexible than ANN structures since their implementations are usually limited to scalar-output regression problems. This article presents a vector-valued (multioutput) formulation of the kernel ridge regression (KRR) aimed at bridging the gap between multioutput ANN structures and scalar kernel-based approaches. The proposed vector-valued KRR relies on a generalized definition of the reproducing kernel Hilbert space (RKHS) and on a new multioutput kernel structure. The mathematical background of the proposed vector-valued formulation is extensively discussed together with different matrix kernel functions and training schemes. Moreover, a compression strategy based on the Nystrom approximation is presented to reduce the computational complexity of the model training. The effectiveness and the performance of the proposed vector-valued KRR are discussed on an illustrative example consisting of a high-speed link and on the optimization of a Doherty amplifier

Parametric Macromodels of Drivers for SSN Simulations

This paper addresses the modeling of output and power supply ports of digital drivers for accurate and efficient SSN simulations. The proposed macromodels are defined by parametric relations, whose parameters are estimated from measured or simulated port transient responses, and are implemented as SPICE subcircuits. The modeling technique is applied to commercial high-speed devices and a realistic simulation example is shown

Parametric Macromodels of Differential Drivers and Receivers

This paper addresses the modeling of differential drivers and receivers for the analog simulation of high-speed interconnection systems. The proposed models are based on mathematical expressions, whose parameters can be estimated from the transient responses of the modeled devices. The advantages of this macromodeling approach are: improved accuracy with respect to models based on simplified equivalent circuits of devices; improved numerical efficiency with respect to detailed transistor-level models of devices; hiding of the internal structure of devices; straightforward circuit interpretation; or implementations in analog mixed-signal simulators. The proposed methodology is demonstrated on example devices and is applied to the prediction of transient waveforms and eye diagrams of a typical low-voltage differential signaling (LVDS) data link

Enhanced Time-Invariant Linear Model for the EMI Prediction of Switching Circuits

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

EMI Prediction of Switching Converters

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