Time-Varying Volterra Analysis of Nonlinear Circuits

Today’s advances in communication systems and VLSI circuits increases the performance requirements and complexity of circuits. The performance of RF and mixed-signal circuits is normally limited by the nonlinear behavior of the transistors used in the design. This makes simulation of nonlinear circuits more important. Volterra series is a method used for simulation of mildly nonlinear circuits. Using Volterra series the response of the nonlinear circuit is converted into a sum of multiple linear circuit responses. Thus, using Volterra series, simulation of nonlinear circuits in frequency-domain analysis becomes possible. However, Volterra series is not able to simulate strongly nonlinear circuits such as saturated Power Amplifiers. In this thesis, a new time-varying Volterra analysis is presented. The time-varying Volterra analysis is the generalization of conventional Volterra analysis where instead of using a DC expansion point a time-varying waveform has been used. Employing a time-varying expansion waveform for Volterra analysis, time-varying Volterra achieves better accuracy than conventional Volterra. The time-varying expansion waveforms are derived using a fast pre-analysis of the circuit. Using numerical examples, it has been shown that the time-varying Volterra is capable of simulating nonlinear circuits with better accuracy than conventional Volterra analysis. The time-varying Volterra analysis in both time and frequency domains are discussed in this thesis. The time-varying Volterra analysis has been used to simulate a saturated Class-F Power Amplifier in frequency-domain. The simulation results show good agreement with ELDO® steady-state and Harmonic Balance simulation results. The proposed method manages to simulate nonlinear circuits, such as saturated Power Amplifier, mixers and nonlinear microwave circuits, with good accuracy. Also, this method can be used to simulate circuit with large number of nonlinear elements without the convergence issues of Harmonic Balance

Simulation, and Overload and Stability Analysis of Continuous Time Sigma Delta Modulator

The ever increasing demand for faster and more powerful digital applications requires high speed, high resolution ADCs. Currently, sigma delta modulators ADCs are extensively used in broadband telecommunication systems because they are an effective solution for high data-rate wireless communication systems that require low power consumption, high speed, high resolution, and large signal bandwidths. Because mixed-signal integrated circuits such as Continuous Time sigma delta modulators contain both analog and digital circuits, mixed signal circuits are not as simple to model and simulate as all discrete or all analog systems. In this dissertation, the delta transform is used to simulate CT sigma delta modulators, and its speed and accuracy are compared to the other methods. The delta transform method is shown to be a very simple and effective method to get accurate results at reasonable speeds when compared with several existing simulation methods. When a CT sigma delta modulator is overloaded, sigma delta modulator\u27s output signal to quantization noise ratio (SQNR) decreases when the sigma delta modulator\u27s input is increased over a certain value. In this dissertation, the range of quantizer gains that cause overload are determined and the values ware used to determine the input signal power that prevents overload and the CT sigma delta modulator\u27s maximum SQNR. The CT sigma delta modulators from 2nd to 5th order are simulated to validate the predicted maximum input power that prevents overload and the maximum SQNR. Determining the stability criteria for CT sigma delta modulators is more difficult than it is for Discrete time sigma delta modulators (DT sigma delta modulators) because CT sigma delta modulators include delays which are modeled mathematically by exponential functions for CT systems. In this dissertation an analytical root locus method is used to determine the stability criteria for CT sigma delta modulators. This root locus method determines the range of quantizer gains for which a CT sigma delta modulator is stable. These values can then be used to determine input signal and internal signal powers that prevent sigma delta modulators from becoming unstable. Also, the maximum input power that keeps the CT sigma delta modulators stable for CT sigma delta modulators operating in overload can be determined. The CT sigma delta modulators from 2nd to 5th order are simulated to validate the predicted maximum input power that keeps the CT sigma delta modulators stable

computer-aided transient simulation of switched power electronic circuits

Die Leistungselektronik zählt zu den sogenannten Schlüsseltechnologien. Sie findet überall dort Verwendung, wo elektrische Energie umgeformt werden muss. Sei es die Stromversorgung eines Prozessors, die Motorelektronik einer Waschmaschine, das Vorschaltgerät einer LED-Lampe, unzählige Steuergeräte im Automobil oder die Anbindung regenerativer Energiequellen an das Versorgungsnetz. Die Anwendungsbereiche sind äußerst vielfältig. Fortschritte im Gebiet der Leistungselektronik wirken sich dadurch direkt auf die Einsatzgebiete aus und erlauben noch effizientere, kleinere und kostengünstigere Gesamtlösungen. In den letzten Jahren prägt ein hoher Anteil an Modellbildung und Simulation zunehmend die Entwicklung moderner Leistungselektronik. Der große wirtschaftliche Druck auf die Hersteller sowie die zunehmende Komplexität der Schaltungen stellen den Schaltungsentwickler vor Herausforderungen, die er nur durch eine simulationsbasierte Vorgehensweise beherrschen kann. So helfen Simulationsergebnisse die Funktionsweise und Zusammenhänge besser und schneller zu verstehen sowie die Schaltungsparameter optimal an die Entwicklungsziele anzupassen. Ausgehend von einem Überblick über aktuelle Lösungsansätze zur Schaltungssimulation, beschäftigt sich die vorliegende Arbeit mit der Entwicklung eines neuen Programms zur transienten Simulation getakteter, leistungselektronischer Schaltungen. Die rechnerinterne Beschreibung geschieht, ausgehend von einer SPICE-Netzliste, mit Hilfe stückweise linearer Netzwerke im Zustandsraum. Durch eine Eingangsgrößenmodellierung, d. h. dem Ersetzen der unabhängigen Strom- und Spannungsquellen durch Ersatznetzwerke, gelingt die Reduktion auf ein homogenes Differentialgleichungssystem. Virtuelle Widerstände helfen unterbestimmte Netzwerke, wie sie im Zusammenhang mit idealen Schaltern auftreten können, zu beheben. Ebenfalls eine mögliche Folge der Verwendung idealer Schaltelemente sind inkonsistente Anfangswerte der dynamischen Schaltungselemente, die das Programm selbstständig mit Hilfe der Gesetze zur Ladungs- bzw. Flusserhaltung löst. Die dabei auftretenden Spannungs- und Stromimpulse werden mittels ihres Gewichts quantitativ erfasst und ermöglichen die automatische Auffindung des korrekten Zustands aller als stückweise linear modellierten, nichtlinearen Schaltungselemente. Maßgeblich für die benötigte Simulationsdauer ist unter anderem die Bestimmung des Zeitpunkts intern gesteuerter Unstetigkeiten, bspw. dem Ein- bzw. Ausschaltzeitpunkt idealer Dioden. Dieser wird mit Methoden der Intervallarithmetik abgeschätzt und durch iteratives Auswerten durch immer kleinere Zeitintervalle zuverlässig eingegrenzt. Eine Blockdiagonalisierung der Systemmatrix mit anschließender Eigenwertverschiebung liefert die für die Abschätzung nötige, analytische Lösung der Matrixexponentialfunktion. Die Kombination all dieser Methoden erlaubt eine hochgradige Ausnutzung des Potenzials der stückweise linearen Modellierung. Das im Rahmen dieser Arbeit entwickelte Simulationswerkzeug ermöglicht es dem Schaltungsentwickler, einzig auf Basis einer SPICE-Netzliste, zuverlässige und hochgenaue Ergebnisse mit geringem Rechenaufwand zu erhalten.Power electronics is a key enabling technology which can be found wherever electric power has to be controlled and converted. Its extremely wide application area ranges from power supplies for CPUs to motor electronics of washing machines to LED lamp ballasts to countless car control units and to grid integration of regenerative energy sources. Progress in power electronics, thus, has large implications on many other areas and enables more efficient, smaller and less expensive solutions. The design process of modern power electronics is characterised by a large amount of modeling and simulation. A simulation-based approach helps the circuit designer to master the conflict between the demand for shorter time to market and an ever increasing circuit complexity. Simulation results allow to understand a circuit's basic operation and let the designer optimize parameter values to reach specified design constraints. Based on an overview of the state of the art of circuit simulation this thesis develops a new computer simulation software aimed at switched power electronic circuits. Within computer memory, state-space matrices, derived from piece-wise linear networks, represent the circuit, which itself is defined by a SPICE-netlist. Replacing the networks' independent sources by equivalent circuits allows a formulation as an homogeneous differential equation system. Under-determined networks, which can occur with ideal switches, are fixed using virtual resistors. Networks with ideal switches may as well exhibit inconsistent initial conditions of energy storing circuit elements. The simulator uses the laws of charge and flux conservation to solve this issue. Accompanying impulses in voltage or current are quantified by their weight and allow the automatic state detection of all piece-wise linear elements. During the transient analysis some circuit components, e. g. diodes, cause breakpoints controlled by internal quantities. The detection of these events exhibits a large impact on simulation time. The corresponding time instants are bound iteratively by increasingly narrow intervals employing methods from interval analysis. Block diagonalisation of the system matrix in combination with eigenvalue shifting enables the analytical expressions required for the upper and lower bounds of the matrix exponential function. The combination of all these methods provides access to the full potential of piece-wise linearly modeled circuits. The proposed simulation tool allows circuit designers to get reliable and highly accurate simulation results in short time on the basis of a SPICE-netlist without the need for any further user input