Canonical Piecewise-Linear Representation of Curves in the Wave Digital Domain

Global, explicit representations of nonlinearities are desirable when implementing nonlinear Wave Digital (WD) structures, as they free us from the burden of managing look-up tables, performing data interpolation and/or using iterative solvers. In this paper we present a method that, starting from certain parameterized PieceWise-Linear (PWL) curves in the Kirchhoff domain, allows us to express them in the WD domain using a global and explicit representation. We will show how some curves (multi-valued functions in the Kirchhoff domain) can be represented as functions in canonical PWL form in the WD domain. In particular, we will present a procedure, which, in the most general case, also returns the conditions on the reference port resistance under which it is possible to find explicit mappings in the WD domain

Adaptive transient solution of nonuniform multiconductor transmission lines using wavelets

Abstract—This paper presents a highly adaptive algorithm for the transient simulation of nonuniform interconnects loaded with arbitrary nonlinear and dynamic terminations. The discretization of the governing equations is obtained through a weak formula-tion using biorthogonal wavelet bases as trial and test functions. It is shown how the multiresolution properties of wavelets lead to very sparse approximations of the voltages and currents in typical transient analyzes. A simple yet effective time–space adaptive al-gorithm capable of selecting the minimal number of unknowns at each time iteration is described. Numerical results show the high degree of adaptivity of the proposed scheme. Index Terms—Electromagnetic (EM) transient analysis, multi-conductor transmission lines (TLs), wavelet transforms. I

CMOS design of chaotic oscillators using state variables: a monolithic Chua's circuit

This paper presents design considerations for monolithic implementation of piecewise-linear (PWL) dynamic systems in CMOS technology. Starting from a review of available CMOS circuit primitives and their respective merits and drawbacks, the paper proposes a synthesis approach for PWL dynamic systems, based on state-variable methods, and identifies the associated analog operators. The GmC approach, combining quasi-linear VCCS's, PWL VCCS's, and capacitors is then explored regarding the implementation of these operators. CMOS basic building blocks for the realization of the quasi-linear VCCS's and PWL VCCS's are presented and applied to design a Chua's circuit IC. The influence of GmC parasitics on the performance of dynamic PWL systems is illustrated through this example. Measured chaotic attractors from a Chua's circuit prototype are given. The prototype has been fabricated in a 2.4- mu m double-poly n-well CMOS technology, and occupies 0.35 mm/sup 2/, with a power consumption of 1.6 mW for a +or-2.5-V symmetric supply. Measurements show bifurcation toward a double-scroll Chua's attractor by changing a bias current

Deep Learning-Based Wave Digital Modeling of Rate-Dependent Hysteretic Nonlinearities for Virtual Analog Applications

Electromagnetic components greatly contribute to the peculiar timbre of analog audio gear. Indeed, distortion effects due to the nonlinear behavior of magnetic materials are known to play an important role in enriching the harmonic content of an audio signal. However, despite the abundant research that has been devoted to the characterization of nonlinearities in the context of virtual analog modeling over the years, the discrete-time simulation of circuits exhibiting rate-dependent hysteretic phenomena remains an open challenge. In this article, we present a novel data-driven approach for the wave digital modeling of rate-dependent hysteresis using recurrent neural networks (RNNs). Thanks to the modularity of wave digital filters, we are able to locally characterize the wave scattering relations of a hysteretic reluctance by encapsulating an RNN-based model into a single one-port wave digital block. Hence, we successfully apply the proposed methodology to the emulation of the output stage of a vacuum-tube guitar amplifier featuring a nonlinear transformer

Efficient computation of transient responses of frequency-dependent nonlinearly loaded transmission lines

The authors address the combined time and frequency domain analysis of nonlinearly loaded low-loss transmission lines. They show that a variety of interconnects are characterized by transfer functions, whose impulse responses have a fast initial-time structure and a slow long-time component. A piecewise linear approximation of the transient functions with nonuniform sampling is proposed as an effective method to obtain high accuracy with low computational cost

Glosarium Matematika

273 p.; 24 cm

Propagation modeling and path loss prediction tools for high frequency surface wave radars

Propagation modeling and simulation approaches for the use of High Frequency Surface Wave Radar (HFSWR) are discussed. HFSWR uses vertically polarized surface waves along multi-mixed paths in the lower HF band (3 MHz - 15 MHz). Various numerical propagators are reviewed with an early analytical model. Split Step Fast Fourier Transformation, finite- difference, and finite-element solutions of the well-known one-way, forward propagation Parabolic Equation (PE) model are presented. MATLAB-based numerical propagation prediction tools based on these models are listed. Tests and comparisons among these analytical and numerical tools are given for some canonical surface wave propagation scenarios. The Millington effect for both smooth and irregular terrain paths, which contain land-sea and sea-land transitions, is also discussed

Modeling nonlinear power amplifiers in OFDM systems from subsampled data: a comparative study using real measurements

A comparative study among several nonlinear high-power amplifier (HPA) models using real measurements is carried out. The analysis is focused on specific models for wideband OFDM signals, which are known to be very sensitive to nonlinear distortion. Moreover, unlike conventional techniques, which typically use a single-tone test signal and power measurements, in this study the models are fitted using subsampled time-domain data. The in-band and out-of-band (spectral regrowth) performances of the following models are evaluated and compared: Saleh’s model, envelope polynomial model (EPM), Volterra model, the multilayer perceptron (MLP) model, and the smoothed piecewise-linear (SPWL) model. The study shows that the SPWL model provides the best in-band characterization of the HPA. On the other hand, the Volterra model provides a good trade-off between model complexity (number of parameters) and performance