In this paper, we present a novel and unified small-signal modeling technique for Pulse-Width Modulated (PWM) DC-DC Buck converters with Ripple-Based Constant On-Time (RBCOT) control. In fact, despite the spread of RBCOT-based converters in several applications requiring tight dynamic performances and a low architectural complexity, their description through small-signal models is not always as reliable as that of fixed-frequency PWM control architectures, and a general and exact modeling framework is not well established. The proposed methodology is grounded on the DC-DC converter state-space representation and thus, differently from other modeling techniques, it permits to fully characterize the dynamic behavior of generic RBCOT converter topologies with arbitrary complex power stage and ripple injection networks. As a case study, we derive the small-signal model for a Buck converter embedding a widely used ripple injection network in industrial applications. The validity of the theoretical results is confirmed through direct comparison with SIMetrix/SIMPLIS simulations and experimental measurements in practical application scenarios, confirming the accuracy of the model even well beyond the converter switching frequency.

We present an algorithm for passivity verification and enforcement of multivariate macromodels whose state-space matrices depend in closed form on a set of external or design parameters. Uniform passivity throughout the parameter space is a fundamental requirement of parameterized macromodels of physically passive structures, that must be guaranteed during model generation. Otherwise, numerical instabilities may occur, due to the ability of nonpassive models to generate energy. In this paper, we propose the first available algorithm that, starting from a generic parameter-dependent state-space model, identifies the regions in the frequency-parameter space where the model behaves locally as a nonpassive system. The approach we pursue is based on an adaptive sampling scheme in the parameter space, which iteratively constructs and perturbs the eigenvalue spectrum of suitable skew-Hamiltonian/Hamiltonian pencils, with the objective of identifying the regions where some of these eigenvalues become purely imaginary, thus pinpointing local passivity violations. The proposed scheme is able to detect all relevant violations. An outer iterative perturbation method is then applied to the model coefficients in order to remove such violations and achieve uniform passivity. Although a formal proof of global convergence is not available, the effectiveness of the proposed implementation of the passivity verification and enforcement schemes is demonstrated on several examples.

The electrical performance of Power Distribution Networks (PDNs) is usually assessed by computing frequency responses through quasi-static or full-wave electromagnetic solvers. Such responses, often available in the scattering form, are then fed to suitable macromodeling algorithms for the extraction of compact reduced-order behavioral models that can be seemlessly simulated in the time domain by standard circuit solvers. Such algorithms perform a rational fitting of the raw scattering responses, followed by a passivity check and enforcement step. The resulting macromodel is typically very accurate when compared to the raw scattering responses. It may however happen that the responses of the PDN macromodel exhibit significant deviation from the true system responses under realistic loading conditions, which include appropriate models for active device blocks, decoupling capacitors, voltage regulators, etc. We highlight the source of this accuracy loss, and we propose a sensitivity-based weighting strategy that is able to optimize and tune the macromodel accuracy based on its specific nominal termination network. The particular focus of this paper is the definition and the inclusion of optimal weigths in the passivity enforcement loop, which is recognized as the most challenging step. The result is a reliable macromodeling flow, which is able to produce passive, accurate and efficient reduced-order models of general PDN structures for power integrity analysis and verification.

This paper describes a novel approach for passivity enforcement of compact dynamical models of electrical interconnects. The proposed approach is based on a parameterization of general state-space scattering models with fixed poles. We formulate the passivity constraints as a unitary boundedness condition on the H∞norm of the system transfer function. When this condition is not verified, we use it as an explicit constraint within an iterative perturbation loop of the system state-space matrices. Since the resulting optimization framework is convex but nonsmooth, we solve it via localization based algorithms, such as the ellipsoid and the cutting plane methods. The proposed technique solves two critical bottleneck issues of the existing approaches for passivity enforcement of linear macromodels. Compared to quasi-optimal schemes based on singular value or Hamiltonian eigenvalue perturbation, we are able to guarantee convergence to the optimal solution. Compared to convex formulations based on direct Bounded Real Lemma constraints, we are able to reduce both memory and time requirements by orders of magnitude. We demonstrate the effectiveness of our approach on a number of cases for which existing algorithms either fail or exhibit very slow convergence.

Moore's Law has driven the semiconductor revolution enabling over four decades of scaling in frequency, size, complexity, and power. However, the limits of physics are preventing further scaling of speed, forcing a paradigm shift towards multicore computing and parallelization. In effect, the system is taking over the role that the single CPU was playing: high-speed signals running through chips but also packages and boards connect ever more complex systems. High-speed signals making their way through the entire system cause new challenges in the design of computing hardware. Inductance, phase shifts and velocity of light effects, material resonances, and wave behavior become not only prevalent but need to be calculated accurately and rapidly to enable short design cycle times. In essence, to continue scaling with Moore's Law requires the incorporation of Maxwell's equations in the design process. Incorporating Maxwell's equations into the design flow is only possible through the combined power that new algorithms, parallelization and high-speed computing provide. At the same time, incorporation of Maxwell-based models into circuit and system-level simulation presents a massive accuracy, passivity, and scalability challenge. In this tutorial, we navigate through the often confusing terminology and concepts behind field solvers, show how advances in field solvers enable integration into EDA flows, present novel methods for model generation and passivity assurance in large systems, and demonstrate the power of cloud computing in enabling the next generation of scalable Maxwell solvers and the next generation of Moore's Law scaling of systems. We intend to show the truly symbiotic growing relationship between Maxwell and Moore!

The passivity characterization and enforcement of linear interconnect macromodels has received much attention in the recent literature. It is now widely recognized that the Hamiltonian eigensolution is a very reliable technique for such characterization. However, most available algorithms for the determination of the required Hamiltonian eigenvalues still require excessive comoputational resources for large-size macromodels with thousands of states. This work intends to break this complexity by introducing the first parallel implementation of a specialized Hamiltonian eigensolver, designed and optimized for shared memory multicore architectures. Our starting point is a multi-shift restarted and deflated Arnoldi process. Excellent parallel efficiency is obtained by running different Arnoldi iterations concurrently on different threads. The numerical results show that macromodels with several thousands states are characterized in few seconds on a 16-core machine, with close to ideal speedup factors.

This paper describes a robust and accurate black-box macromodeling technique, in which the constitutive equations combine both closed-form delay operators and low-order rational coefficients. These models describe efficiently electrically long interconnect links. The algorithm is based on an iterative weighted least-squares process and can be interpreted as a generalization of the well-known Vector Fitting. The paper is focused, in particular, on the passivity enforcement of these models. We present two perturbation methods and we show how the accuracy of the models is well-preserved during the passivity enforcement process.

This paper presents a wavelet-based algorithm for the detection, identification, and extraction of gravity waves from atmospheric pressure traces. The main data processing tool is a nonlinear adaptive filter based on the selective reconstruction of a waveform from its wavelet coefficients. The time-frequency localization of the wavelet transform provides an ideal framework for the decomposition of long-period gravity waves (30 min-6 h), which are characterized by a generally broad spectrum and few oscillation cycles. The procedure is iterative and allows the exhaustive processing of all the events present in a fixed time period. The waveform of each disturbance is reconstructed with high accuracy. This minimizes the influence of the data-processing technique on the estimate of horizontal speed and direction of propagation, obtained by maximization of the cross-correlation functions between the reconstructed waveforms at the different stations. The introduction of coherency criteria through the network of seven stations allows the authors to separate the events into two classes. The first includes the events that propagate with very small distortion through the network, while the second includes less coherent but still highly energetic events. The size of the network and the algorithm developed for the analysis is well suited for the identification and the extraction of those mesoscale disturbances that have a particularly strong influence on the weather as well as on the forecast.