Steady-State Response of Periodically Switched Linear Circuits via Augmented Time-Invariant Nodal Analysis

This paper focuses on the simulation of periodically switched linear circuits. The basic notation and theoretical framework is 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 to create, via circuit inspection, a timeinvariant 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

Steady-State Analysis of Switching Power Converters via Augmented Time-Invariant Equivalents

This letter addresses the simulation of the steadystate 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 timeinvariant 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 converte

Steady-state analysis of switching converters via frequency-domain circuit equivalents

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

EMI Analysis and Modeling of Switching Circuits

Nowadays, switching power converters are massively used in almost any electrical and electronic equipment and appliances. This class of circuits are inherently time-varying systems that are characterized by the periodic activity of their internal switches which leads to discontinuous absorbed currents. The above currents, that play the role of high frequency noisy disturbances feeding the power distribution system, become a serious concern for designers that need to comply with the electromagnetic compatibility (EMC) regulation for the conducted emission (CE). In this frame- work, modeling and simulation tools for switching circuits are key resources in the early design phase for the prediction of the conducted emission and for the assessment of alternative design scenarios. The classical approach to CE prediction is via physical-based models and time-domain simulations. This solution, however, requires intimate knowledge of the internal device structure. Also, large simulation times are in general needed to avoid integration errors and to achieve accurate results (the CE are in fact computed by applying the Fourier transform on the steady-state portion of the current response of the circuit). As an alternative, frequency-domain behavioral approaches are available in literature. In the latter case, the proposed models are small-signal time-invariant approximations computed from the external observation of the circuit behavior. These approaches, that are based on simplified equivalents, do not take into account the internal time-varying nature of the circuit and in many cases unavoidably lead to a model accuracy that strongly depends on the operating condition of devices. To overcome the above limitations, this thesis proposes an alternative approach to CE assessment based on the mathematical framework developed for time-varying circuits and systems. The proposed method allows for the steady-state prediction of circuit responses directly in the frequency-domain. A topological approach is used, where the original time-varying circuit is suitably replaced by an augmented time-invariant equivalent solved via standard tools for circuit analysis. The new augmented variables in the above equivalent turn out to be the harmonic coefficients of the Fourier series expansion of the corresponding voltage and current variables in the original circuit. A second important contribution in this work is the application of the pro- posed mathematical tool to the modeling of a switching converter and of its CE disturbances from measured data. The converter is seen as a black-box element that is characterized via a limited set of port voltage and current observations, leading to an equivalent augmented admittance fully describing the time-varying nature of the system. Summarizing, this thesis provides a comprehensive theoretical discussion together with several tutorial examples. What is more important, it proposes a novel approach to CE prediction with improvements with respect to state-of-the-art approaches and linear time-invariant surrogates. A real application test case involving a dc-dc boost converter and real measured data is also used to validate the method and stress its features for both numerical simulation and black-box modeling

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

Augmented Thevenin Model for the Harmonic Analysis of Switching Circuits

This article addresses the use of the Thevenin equivalent model in the case of switching circuits. An augmented Thevenin model is proposed, based on a well-established augmented equivalent approach for the analysis of periodically switched linear networks. It can profitably be used to provide a time-invariant equivalent description of a switching network and to investigate on the harmonics behavior at any of its ports even upon the varying of one of its internal parameters. This makes the article interesting for harmonic analysis purposes as, for instance, in the analysis and troubleshooting of electromagnetic interference or in the monitoring of a system behavior through the assessment and analysis of some of its spectral components. The model has also the advantage to be simple in its implementation. The feasibility and potentiality of the method are verified via simulations and comparisons with the results obtained by applying the augmented equivalent approach to the case of a dc\u2013dc Buck converter

TMsim : an algorithmic tool for the parametric and worst-case simulation of systems with uncertainties

This paper presents a general purpose, algebraic tool—named TMsim—for the combined parametric and worst-case analysis of systems with bounded uncertain parameters.The tool is based on the theory of Taylor models and represents uncertain variables on a bounded domain in terms of a Taylor polynomial plus an interval remainder accounting for truncation and round-off errors.This representation is propagated from inputs to outputs by means of a suitable redefinition of the involved calculations, in both scalar and matrix form. The polynomial provides a parametric approximation of the variable, while the remainder gives a conservative bound of the associated error. The combination between the bound of the polynomial and the interval remainder provides an estimation of the overall (worst-case) bound of the variable. After a preliminary theoretical background, the tool (freely available online) is introduced step by step along with the necessary theoretical notions. As a validation, it is applied to illustrative examples as well as to real-life problems of relevance in electrical engineering applications, specifically a quarter-car model and a continuous time linear equalizer

Worst-Case Analysis of Electrical and Electronic Equipment via Affine Arithmetic

In the design and fabrication process of electronic equipment, there are many unkown parameters which significantly affect the product performance. Some uncertainties are due to manufacturing process fluctuations, while others due to the environment such as operating temperature, voltage, and various ambient aging stressors. It is desirable to consider these uncertainties to ensure product performance, improve yield, and reduce design cost. Since direct electromagnetic compatibility measurements impact on both cost and time-to-market, there has been a growing demand for the availability of tools enabling the simulation of electrical and electronic equipment with the inclusion of the effects of system uncertainties. In this framework, the assessment of device response is no longer regarded as deterministic but as a random process. It is traditionally analyzed using the Monte Carlo or other sampling-based methods. The drawback of the above methods is large number of required samples to converge, which are time-consuming for practical applications. As an alternative, the inherent worst-case approaches such as interval analysis directly provide an estimation of the true bounds of the responses. However, such approaches might provide unnecessarily strict margins, which are very unlikely to occur. A recent technique, affine arithmetic, advances the interval based methods by means of handling correlated intervals. However, it still leads to over-conservatism due to the inability of considering probability information. The objective of this thesis is to improve the accuracy of the affine arithmetic and broaden its application in frequency-domain analysis. We first extend the existing literature results to the efficient time-domain analysis of lumped circuits considering the uncertainties. Then we provide an extension of the basic affine arithmetic to the frequency-domain simulation of circuits. Classical tools for circuit analysis are used within a modified affine framework accounting for complex algebra and uncertainty interval partitioning for the accurate and efficient computation of the worst case bounds of the responses of both lumped and distributed circuits. The performance of the proposed approach is investigated through extensive simulations in several case studies. The simulation results are compared with the Monte Carlo method in terms of both simulation time and accuracy

Reduced-order modeling of power electronics components and systems

This dissertation addresses the seemingly inevitable compromise between modeling fidelity and simulation speed in power electronics. Higher-order effects are considered at the component and system levels. Order-reduction techniques are applied to provide insight into accurate, computationally efficient component-level (via reduced-order physics-based model) and system-level simulations (via multiresolution simulation). Proposed high-order models, verified with hardware measurements, are, in turn, used to verify the accuracy of final reduced-order models for both small- and large-signal excitations. At the component level, dynamic high-fidelity magnetic equivalent circuits are introduced for laminated and solid magnetic cores. Automated linear and nonlinear order-reduction techniques are introduced for linear magnetic systems, saturated systems, systems with relative motion, and multiple-winding systems, to extract the desired essential system dynamics. Finite-element models of magnetic components incorporating relative motion are set forth and then reduced. At the system level, a framework for multiresolution simulation of switching converters is developed. Multiresolution simulation provides an alternative method to analyze power converters by providing an appropriate amount of detail based on the time scale and phenomenon being considered. A detailed full-order converter model is built based upon high-order component models and accurate switching transitions. Efficient order-reduction techniques are used to extract several lower-order models for the desired resolution of the simulation. This simulation framework is extended to higher-order converters, converters with nonlinear elements, and closed-loop systems. The resulting rapid-to-integrate component models and flexible simulation frameworks could form the computational core of future virtual prototyping design and analysis environments for energy processing units