Paper Archive

The Fender Bassman model 5F6-A was released in 1958 and has become one of the most revered guitar amplifiers of all time. It is the progenitor of a long line of related Fender designs in addition to inspiring Marshall’s first amplifier design. This paper presents a Wave Digital Filter study of the preamplifier circuit of 5F6-Abased amplifiers, utilizing recent theoretical advances to enable the simultaneous simulation of its four nonlinear vacuum tube triodes. The Dempwolf triode model is applied along with an iterative Newton solver to calculate the scattering at the 25 port R-type adapter at the root of the WDF tree. Simulation results are compared to “ground truth” SPICE data showing excellent agreement.

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The sound of a vacuum tube guitar amplifier may be significantly influenced by the non-linear behavior of its output transformer, which therefore should also be considered in digital simulations. In this work, we develop a model for inductors and transformers with the magnetization following the model of Jiles and Atherton. For this purpose, the original magnetization model is rewritten to a differential equation with respect to time which can then easily be integrated into a previously developed circuit simulation framework. The model thus derived is then exercised in the simulation of three simple circuits where it shows the expected behavior.

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This paper describes black-box modeling of distortion circuits. The analyzed distortion circuits all originate from guitar effect pedals, which are widely used to enrich the sound of an electric guitar with harmonics. The proposed method employs a blockoriented model which consists of a linear block (filter) and a nonlinear block. In this study the nonlinear block is represented by an extended parametric input/output mapping function. Three distortion circuits with different nonlinear elements are analyzed and modeled. The linear and nonlinear parts of the circuit are analyzed and modeled separately. The Levenberg–Marquardt algorithm is used for iterative optimization of the nonlinear parts of the circuits. Some circuits could not be modeled with high accuracy, but the proposed model has shown to be a versatile and flexible tool when modeling distortion circuits.

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In the present contribution we present the preliminary results of a black box nonlinear system (NLS) modeling. The NLS is composed by a nonlinear sigmoid-type input-output relationship (NLTF) followed by a linear system (LTI), as in a Hammerstein nonlinear system. Here, the used NLTF is derived from a deformation of the Hyperbolic Tangent power expansion. The advantage of using the hyperbolic tangent function is that nonlinearity depends on the linear and cubic terms that measure curvature (and thus nonlinearity) of the transfer function. The hyperbolic tangent model is extended to other types of nonlinear systems by expanding the nonlinear system in linear and increasingly nonlinear contributions, where the expansion parameters are deformed to enhance or suppress specific nonlinear modes of the expansion. Simulations were performed using Matlab 2012a. The preliminary results show fairly good agreement between the system obtained by parametric inference and a reference system, with mean square error (MSE)=0.035.

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In this paper, iterative zero-finding techniques are proposed to resolve groups of nonlinearities occurring in Wave Digital Filters. Two variants of Newton’s method are proposed and their suitability towards solving the grouped nonlinearities is analyzed. The feasibility of the approach with implications for WDFs containing multiple nonlinearities is demonstrated via case studies investigating the mathematical properties and numerical performance of reference circuits containing diodes and transistors; asymmetric and symmetric diode clippers and a common emitter amplifier.

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This paper deals with simulation of BBD circuit based analog flanger effects. The famous Electro-Harmonix Deluxe Electric Mistress flanger effect was used as a case study in this paper. The main attention of this paper is paid to the analysis and simulation of the LFO circuit, the BBD clock generator circuit and BBD circuit simulation of this effect. However, in order to compare the simulation results with measured data, the signal path simulation using the DK-method has been introduced as well.

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Wave Digital Filters (WDF) [1] are a popular approach for virtual analog modeling [2]. They provide a computationally efficient way to simulate lumped physical systems with well-studied numerical properties. Recent work by Werner et al. [3, 4] enables the use of WDFs to model systems with complicated topologies and multiple/multiport nonlinearities, to a degree not previously known. We present an efficient, portable, modular, and open-source C++ library for real time Wave Digital Filter modeling: RT-WDF [5]. The library allows a WDF to be specified in an object-oriented tree with the same structure as a WDF tree and implements the most recent advances in the field. We give an architectural overview and introduce the main concepts of operation on three separate case studies: a switchable attenuator, the Bassman tone stack, and a common-cathode triode amplifier. It is further shown how to expand the existent set of non-linear models to encourage custom extensions. Index Terms— wave digital filter, software, real time, virtual analog modeling, multiple nonlinearities

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Nonlinear waveshaping is a common technique in musical signal processing, both in a static memoryless context and within feedback systems. Such waveshaping is usually applied directly to a sampled signal, generating harmonics that exceed the Nyquist frequency and cause aliasing distortion. This problem is traditionally tackled by oversampling the system. In this paper, we present a novel method for reducing this aliasing by constructing a continuous-time approximation of the discrete-time signal, applying the nonlinearity to it, and filtering in continuous-time using analytically applied convolution. The presented technique markedly reduces aliasing distortion, especially in combination with low order oversampling. The approach is also extended to allow it to be used within a feedback system.

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We present a computational model of the Hammond tonewheel organ vibrato/chorus, a musical audio effect comprising an LC ladder circuit and an electromechanical scanner. We model the LC ladder using the Wave Digital Filter (WDF) formalism, and introduce a new approach to resolving multiple nonadaptable linear elements at the root of a WDF tree. Additionally we formalize how to apply the well-known warped Bilinear Transform to WDF discretization of capacitors and inductors and review WDF polarity inverters. To model the scanner we propose a simplified and physically-informed approach. We discuss the time- and frequency-domain behavior of the model, emphasizing the spectral properties of interpolation between the taps of the LC ladder.

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A method to measure the response of a linear time-variant (LTV) audio system is presented. The proposed method uses a series of short chirps generated as the impulse response of several cascaded allpass filters. This test signal can measure the characteristics of an LTV system as a function of time. Results obtained from testing of this method on a guitar phaser pedal are presented. A proof of concept gray-box model of the measured system is produced based on partial knowledge about the internal structure of the pedal and on the spectral analysis of the measured responses. The temporal behavior of the digital model is shown to be very similar to that of the measured device. This demonstrates that it is possible to measure LTV analog audio systems and produce approximate virtual analog models based on these results.

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