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

Weakly nonlinear circuit analysis based on fast multidimensional inverse Laplace transform

There have been continuing thrusts in developing efficient modeling techniques for circuit simulation. However, most circuit simulation methods are time-domain solvers. In this paper we propose a frequency-domain simulation method based on Laguerre function expansion. The proposed method handles both linear and nonlinear circuits. The Laguerre method can invert multidimensional Laplace transform efficiently with a high accuracy, which is a key step of the proposed method. Besides, an adaptive mesh refinement (AMR) technique is developed and its parallel implementation is introduced to speed up the computation. Numerical examples show that our proposed method can accurately simulate large circuits while enjoying low computation complexity. © 2012 IEEE.published_or_final_versio

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

Volterra Series-Based Time-Domain Macromodeling of Nonlinear Circuits

Volterra series (VS) representation is a powerful mathematical model for nonlinear circuits. However, the difficulties in determining higher order Volterra kernels limited its broader applications. In this paper, a systematic approach that enables a convenient extraction of Volterra kernels from X-parameters is presented. A concise and general representation of the output response due to arbitrary number of input tones is given. The relationship between Volterra kernels and X-parameters is explicitly formulated. An efficient frequency sweep scheme and an output frequency indexing scheme are provided. The least square linear regression method is employed to separate different orders of Volterra kernels at the same frequency, which leads to the obtained Volterra kernels complete. The proposed VS representation based on X-parameters is further validated for time-domain verification. The proposed method is systematic and general-purpose. It paves the way for time-domain simulation with X-parameters and constitutes a powerful supplement to the existing blackbox macromodeling methods for nonlinear circuits.postprin

Variable domain transformation for linear PAC analysis of mixed-signal systems

This paper describes a method to perform linear AC analysis on mixed-signal systems which appear strongly nonlinear in the voltage domain but are linear in other variable domains. Common circuits like phase/delay-locked loops and duty-cycle correctors fall into this category, since they are designed to be linear with respect to phases, delays, and duty-cycles of the input and output clocks, respectively. The method uses variable domain translators to change the variables to which the AC perturbation is applied and from which the AC response is measured. By utilizing the efficient periodic AC (PAC) analysis available in commercial RF simulators, the circuit’s linear transfer function in the desired variable domain can be characterized without relying on extensive transient simulations. Furthermore, the variable domain translators enable the circuits to be macromodeled as weakly-nonlinear systems in the chosen domain and then converted to voltage-domain models, instead of being modeled as strongly-nonlinear systems directly

Time-domain analysis of RF and microwave autonomous circuits by vector fitting-based approach

This work presents a new method for the analysis of RF and microwave autonomous circuits directly in the time-domain, which is the most effective approach at simulation level to evaluate nonlinear phenomena. For RF and microwave autonomous circuits, time-domain simulations usually experiment convergence problems or numerical inaccuracies due to the presence of distributed elements, preventing de-facto their use. The proposed solution is based on the Vector Fitting algorithm applied directly at circuit level. A case study relative to a RF hybrid oscillator is presented for practical demonstration and evaluation of performance reliability of the proposed method

A new nonlinear time-domain op-amp macromodel using threshold functions and digitally controlled network elements

A general-purpose nonlinear macromodel for the time-domain simulation of integrated circuit operational amplifiers (op amps), either bipolar or MOS, is presented. Three main differences exist between the macromodel and those previously reported in the literature for the time domain. First, all the op-amp nonlinearities are simulated using threshold elements and digital components, thus making them well suited for a mixed electrical/logical simulator. Secondly, the macromodel exhibits a superior performance in those cases where the op amp is driven by a large signal. Finally, the macromodel is advantageous in terms of CPU time. Several examples are included illustrating all of these advantages. The main application of this macromodel is for the accurate simulation of the analog part of a combined analog/digital integrated circui

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