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

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

An efficient nonlinear circuit simulation technique

This paper proposes a novel method for the analysis and simulation of integrated circuits (ICs) with the potential to greatly shorten the IC design cycle. The circuits are assumed to be subjected to input signals that have widely separated rates of variation, e.g., in communication systems, an RF carrier modulated by a low-frequency information signal. The proposed technique involves two stages. Initially, a particular order result for the circuit response is obtained using a multiresolution collocation scheme involving cubic spline wavelet decomposition. A more accurate solution is then obtained by adding another layer to the wavelet series approximation. However, the novel technique presented here enables the reuse of results acquired in the first stage to obtain the second-stage result. Therefore, vast gains in efficiency are obtained. Furthermore, a nonlinear model-order reduction technique can readily be used in both stages making the calculations even more efficient. Results will highlight the efficacy of the proposed approac

A novel envelope simulation technique for high-frequency nonlinear circuits

The paper proposes a new approach for the analysis and simulation of circuits subject to input signals with widely separated rates of variation. Such signals arise in communication circuits when an RF carrier is modulated by a low-frequency information signal. The approach will involve converting the ordinary differential equation system that describes the circuit to a partial differential equation system and subsequently solving the resultant system using a multiresolution collocation approach involving a cubic spline wavelet-based decomposition

An efficient nonlinear circuit simulation technique

This paper proposes a new and efficient approach for the analysis and simulation of circuits subject to input signals with widely separated rates of variation. Such signals arise in communication circuits when an RF carrier is modulated by a low-frequency information signal. The proposed technique initially involves converting the ordinary differential equation system, that describes the nonlinear circuit, to a partial differential equation system. The resultant system is then semidiscretised using a multiresolution collocation scheme, involving cubic spline wavelet decomposition. A reduced equation system is subsequently formed, using a nonlinear model reduction strategy. This enables an efficient solution process using trapezoidal numerical integration. Results highlight the efficacy of the proposed approach

A new method for the determination of the locking range of oscillators

A time-domain method for the determination of the injection-locking range of oscillators is presented. The method involves three time dimensions: the first and the second are warped time scales used for the free-running frequency and the external excitation, respectively and the third is to account for slow transients to reach a steady-state regime. The locking range is determined by tuning the frequency of the external excitation until the oscillator locks. The locking condition is determined by analyzing the Jacobian matrix of the system. The method is advantageous in that the computational effort is independent of the presence of widely separated time constants in the oscillator. Numerical results for a Van Der Pol oscillator are presented

Hybrid Time-Frequency Numerical Simulation of Electronic Radio Frequency Systems

This chapter is devoted to the discussion of a hybrid frequency-time CAD tool especially designed for the efficient numerical simulation of nonlinear electronic radio frequency circuits operating in an aperiodic slow time scale and a periodic fast time scale. Circuits driven by envelope-modulated signals, in which the baseband signal (the information) is aperiodic and has a spectral content of much lower frequency than the periodic carrier, are typical examples of practical interest involving such time evolution rates. The discussed method is tailored to take advantage of the circuits and signals heterogeneity and so will benefit from the time-domain latency of some state variables in the circuits. Because the aperiodic slowly varying state variables are treated only in time domain, the proposed method can be seen as a hybrid scheme combining multitime envelope transient harmonic balance based on a multivariate formulation, with a purely time-step integration scheme

An effective method for the determination of the locking range of an injection-locked frequency divider

The paper proposes a methodology for the determination of the locking range of an Injection-Locked Frequency Divider. The technique involves the use of the Warped Multi-time scale model and is applicable to oscillators in general. The ability to determine, in an efficient manner, the locking ranges of Injection Locked Frequency Dividers is of great importance to design engineers as ILFDs are suitable for lower-power wireless applications

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

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