Frequency-domain transient analysis of multitime partial differential equation systems

Multitime partial differential equations (MPDEs) provide an efficient method to simulate circuits with widely separated rates of inputs. This paper proposes a fast and accurate frequency-domain multitime transient analysis method for MPDE systems, which fills in the gap for the lack of general frequency-domain solver for MPDE systems. A block-pulse function-based multidimensional inverse Laplace transform strategy is adopted. The method can be applied to discrete input systems. Numerical examples then confirm its superior accuracy, under similar efficiency, over time-domain solvers. © 2011 IEEE.published_or_final_versionThe 2011 IEEE/IFIP 19th International Conference on VLSI and System-on-Chip (VLSI-SoC), Hong Kong, 3-5 October 2011. In IFIP International Conference on Very Large Scale Integration Proceedings, 2011, p. 160-16

Analysis, simulation and design of nonlinear RF circuits

The PhD project consists of two parts. The first part concerns the development of Computer Aided Design (CAD) algorithms for high-frequency circuits. Novel Padébased algorithms for numerical integration of ODEs as arise in high-frequency circuits are proposed. Both single- and multi-step methods are introduced. A large part of this section of the research is concerned with the application of Filon-type integration techniques to circuits subject to modulated signals. Such methods are tested with analog and digital modulated signals and are seen to be very effective. The results confirm that these methods are more accurate than the traditional trapezoidal rule and Runge-Kutta methods. The second part of the research is concerned with the analysis, simulation and design of RF circuits with emphasis on injection-locked frequency dividers (ILFD) and digital delta-sigma modulators (DDSM). Both of these circuits are employed in fractional-N frequency synthesizers. Several simulation methods are proposed to capture the locking range of an ILFD, such as the Warped Multi-time Partial Differential Equation (WaMPDE) and the Multiple-Phase-Condition Envelope Following (MPCENV) methods. The MPCENV method is the more efficient and accurate simulation technique and it is recommended to obviate the need for expensive experiments. The Multi-stAge noise Shaping (MASH) digital delta-sigma modulator (DDSM) is simulated in MATLAB and analysed mathematically. A novel structure employing multimoduli, termed the MM-MASH, is proposed. The goal in this design work is to reduce the noise level in the useful frequency band of the modulator. The success of the novel structure in achieving this aim is confirmed with simulations

Frequency-Domain Transient Analysis of Multitime Partial Differential Equation Systems

Abstract-Multitime partial differential equations (MPDEs) provide an efficient method to simulate circuits with widely separated rates of inputs. This paper proposes a fast and accurate frequency-domain multitime transient analysis method for MPDE systems, which fills in the gap for the lack of general frequency-domain solver for MPDE systems. A blockpulse function-based multidimensional inverse Laplace transform strategy is adopted. The method can be applied to discrete input systems. Numerical examples then confirm its superior accuracy, under similar efficiency, over time-domain solvers

Analysis of multirate behavior in electronic systems

Doutoramento em Engenharia ElectrotécnicaEsta tese insere-se na área da simulação de circuitos de RF e microondas, e visa o estudo de ferramentas computacionais inovadoras que consigam simular, de forma eficiente, circuitos não lineares e muito heterogéneos, contendo uma estrutura combinada de blocos analógicos de RF e de banda base e blocos digitais, a operar em múltiplas escalas de tempo. Os métodos numéricos propostos nesta tese baseiam-se em estratégias multi-dimensionais, as quais usam múltiplas variáveis temporais definidas em domínios de tempo deformados e não deformados, para lidar, de forma eficaz, com as disparidades existentes entre as diversas escalas de tempo. De modo a poder tirar proveito dos diferentes ritmos de evolução temporal existentes entre correntes e tensões com variação muito rápida (variáveis de estado activas) e correntes e tensões com variação lenta (variáveis de estado latentes), são utilizadas algumas técnicas numéricas avançadas para operar dentro dos espaços multi-dimensionais, como, por exemplo, os algoritmos multi-ritmo de Runge-Kutta, ou o método das linhas. São também apresentadas algumas estratégias de partição dos circuitos, as quais permitem dividir um circuito em sub-circuitos de uma forma completamente automática, em função dos ritmos de evolução das suas variáveis de estado. Para problemas acentuadamente não lineares, são propostos vários métodos inovadores de simulação a operar estritamente no domínio do tempo. Para problemas com não linearidades moderadas é proposto um novo método híbrido frequência-tempo, baseado numa combinação entre a integração passo a passo unidimensional e o método seguidor de envolvente com balanço harmónico. O desempenho dos métodos é testado na simulação de alguns exemplos ilustrativos, com resultados bastante promissores. Uma análise comparativa entre os métodos agora propostos e os métodos actualmente existentes para simulação RF, revela ganhos consideráveis em termos de rapidez de computação.This thesis belongs to the field of RF and microwave circuit simulation, and is intended to discuss some innovative computer-aided design tools especially conceived for the efficient numerical simulation of highly heterogeneous nonlinear wireless communication circuits, combining RF and baseband analog and digital circuitry, operating in multiple time scales. The numerical methods proposed in this thesis are based on multivariate strategies, which use multiple time variables defined in warped and unwarped time domains, for efficiently dealing with the time-scale disparities. In order to benefit from the different rates of variation of slowly varying (latent) and fast-varying (active) currents and voltages (circuits’ state variables), several advanced numerical techniques, such as modern multirate Runge-Kutta algorithms, or the mathematical method of lines, are proposed to operate within the multivariate frameworks. Diverse partitioning strategies are also introduced, which allow the simulator to automatically split the circuits into sub-circuits according to the different time rates of change of their state variables. Novel purely time-domain techniques are addressed for the numerical simulation of circuits presenting strong nonlinearities, while a mixed frequency-time engine, based on a combination of univariate time-step integration with multitime envelope transient harmonic balance, is discussed for circuits operating under moderately nonlinear regimes. Tests performed in illustrative circuit examples with the newly proposed methods revealed very promising results. Indeed, compared to previously available RF tools, significant gains in simulation speed are reported

Characterization of time-dependent quantum phenomena

Basierend auf einer mehrzeitlichen Verallgemeinerung der P Funktion, dem P Funktional, wird eine Technik entwickelt, um Nichtklassizität im Hinblick auf mehrere Zeitpunkte aufzuzeigen. In diesem Mehrzeitszenario treten Effekte auf, die im einzeitlichen Fall nicht vorhanden sind. Des Weiteren wird das verstimmte nichtlineare Jaynes-Cummings Modell betrachtet. Es wird gezeigt, dass die entsprechende Dynamik exakt gelöst werden kann wenn der Hilbertraum erweitert wird. Es zeigt sich, dass das Modell für die Untersuchung von nichtgleichzeitigen Kommutatoren des Hamiltonoperators geeignet ist.Based on a multi-time-dependent generalization of the P function, the so-called P functional, a technique is developed to reveal nonclassicality with respect to multiple points in time. In this multi-time scenario novel effects occur, which are not present in the single-time case. Furthermore the detuned nonlinear Jaynes-Cummings model is considered. It is shown that its dynamics can be solved exactly if the Hilbert space is extended. It turns out that the model is especially suitable to study non-equal-time commutators of the corresponding Hamiltonian

Steady state analysis of oscillators

A common method used for steady-state analysis of oscillators is called Harmonic Balance. Harmonic balance finds the steady-state solution directly in frequency-domain. However, Harmonic Balance is very sensitive to the initial guess and may not converge if the oscillation frequency is not known a priori. Sometimes it may converge to the unstable DC operating point of the oscillator. Moreover, it is usually difficult to have such good initial guess. In this thesis, a fast approach is developed to improve the initial guess for Harmonic Balance (HB). This approach is derived from Minimal Polynomial Extrapolation (MPE) and Warped Multi- time Partial Differential Equation (WaMPDE). The WaMPDE works by separating the fast and slow variations in the response of oscillators, thus minimizing time and CPU consumption. The role of MPE is to accelerate the work of WaMPDE. The advantage of the MPE method is that it saves Jacobian matrix decomposition and it is easy to implement. Simulation results of different oscillators (Colpitts and LC-tuned bipolar) are presented to evaluate the performance of the proposed method

Concepts of quantum non-Markovianity: a hierarchy

Markovian approximation is a widely-employed idea in descriptions of the dynamics of open quantum systems (OQSs). Although it is usually claimed to be a concept inspired by classical Markovianity, the term quantum Markovianity is used inconsistently and often unrigorously in the literature. In this report we compare the descriptions of classical stochastic processes and quantum stochastic processes (as arising in OQSs), and show that there are inherent differences that lead to the non-trivial problem of characterizing quantum non-Markovianity. Rather than proposing a single definition of quantum Markovianity, we study a host of Markov-related concepts in the quantum regime. Some of these concepts have long been used in quantum theory, such as quantum white noise, factorization approximation, divisibility, Lindblad master equation, etc.. Others are first proposed in this report, including those we call past-future independence, no (quantum) information backflow, and composability. All of these concepts are defined under a unified framework, which allows us to rigorously build hierarchy relations among them. With various examples, we argue that the current most often used definitions of quantum Markovianity in the literature do not fully capture the memoryless property of OQSs. In fact, quantum non-Markovianity is highly context-dependent. The results in this report, summarized as a hierarchy figure, bring clarity to the nature of quantum non-Markovianity.Comment: Clarifications and references added; discussion of the related classical hierarchy significantly improved. To appear in Physics Report

Nonequilibrium Langevin Approach to Quantum Optics in Semiconductor Microcavities

Recently the possibility of generating nonclassical polariton states by means of parametric scattering has been demonstrated. Excitonic polaritons propagate in a complex interacting environment and contain real electronic excitations subject to scattering events and noise affecting quantum coherence and entanglement. Here we present a general theoretical framework for the realistic investigation of polariton quantum correlations in the presence of coherent and incoherent interaction processes. The proposed theoretical approach is based on the {\em nonequilibrium quantum Langevin approach for open systems} applied to interacting-electron complexes described within the dynamics controlled truncation scheme. It provides an easy recipe to calculate multi-time correlation functions which are key-quantities in quantum optics. As a first application, we analyze the build-up of polariton parametric emission in semiconductor microcavities including the influence of noise originating from phonon induced scattering.Comment: some corrections in the presentation mad

The Road to Stueckelberg's Covariant Perturbation Theory as Illustrated by Successive Treatments of Compton Scattering

We review the history of the road to a manifestly covariant perturbative calculus within quantum electrodynamics from the early semi-classical results of the mid-twenties to the complete formalism of Stueckelberg in 1934. We chose as our case study the calculation of the cross-section of the Compton effect. We analyse Stueckelberg's paper extensively. This is our first contribution to a study of his fundamental contributions to the theoretical physics of twentieth century.Comment: This paper is a "working-physicist" version of a paper to be published in Studies in History and Philosophy of Modern Physic