Download The Fender Bassman 5F6-A Family of Preamplifier Circuits—A Wave Digital Filter Case Study 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.
Download Neural Net Tube Models for Wave Digital Filters Herein, we demonstrate the use of neural nets towards simulating multiport nonlinearities inside a wave digital filter. We introduce a resolved wave definition which allows us to extract features from a Kirchhoff domain dataset and train our neural networks directly in the wave domain. A hyperparameter search is performed to minimize error and runtime complexity. To illustrate the method, we model a tube amplifier circuit inspired by the preamplifier stage of the Fender Pro-Junior guitar amplifier. We analyze the performance of our neural nets models by comparing their distortion characteristics and transconductances. Our results suggest that activation function selection has a significant effect on the distortion characteristic created by the neural net.
Download Simulating guitar distortion circuits using wave digital and nonlinear state-space formulations This work extends previous research on numerical solution of nonlinear systems in musical acoustics to the realm of nonlinear musical circuits. Wave digital principles and nonlinear state-space simulators provide two alternative approaches explored in this work. These methods are used to simulate voltage amplification stages typically used in guitar distortion or amplifier circuits. Block level analysis of the entire circuit suggests a strategy based upon the nonlinear filter composition technique for connecting amplifier stages while accounting for the way these stages interact. Formulations are given for the bright switch, the diode clipper, a transistor amplifier, and a triode amplifier.
Download Aliasing Reduction in Neural Amp Modeling by Smoothing Activations The increasing demand for high-quality digital emulations of analog audio hardware, such as vintage tube guitar amplifiers, led
to numerous works on neural network-based black-box modeling,
with deep learning architectures like WaveNet showing promising
results. However, a key limitation in all of these models was the
aliasing artifacts stemming from nonlinear activation functions in
neural networks. In this paper, we investigated novel and modified activation functions aimed at mitigating aliasing within neural
amplifier models. Supporting this, we introduced a novel metric,
the Aliasing-to-Signal Ratio (ASR), which quantitatively assesses
the level of aliasing with high accuracy. Measuring also the conventional Error-to-Signal Ratio (ESR), we conducted studies on a
range of preexisting and modern activation functions with varying
stretch factors. Our findings confirmed that activation functions
with smoother curves tend to achieve lower ASR values, indicating a noticeable reduction in aliasing. Notably, this improvement
in aliasing reduction was achievable without a substantial increase
in ESR, demonstrating the potential for high modeling accuracy
with reduced aliasing in neural amp models.
Download Discretization of the '59 Fender Bassman Tone Stack The market for digital modeling guitar amplifiers requires that the digital models behave like the physical prototypes. A component of the iconic Fender Bassman guitar amplifier, the tone stack circuit, filters the sound of the electric guitar in a unique and complex way. The controls are not orthogonal, resulting in complicated filter coefficient trajectories as the controls are varied. Because of its electrical simplicity, the tone stack is analyzed symbolically in this work, and digital filter coefficients are derived in closed form. Adhering to the technique of virtual analog, this procedure results in a filter that responds to user controls in exactly the same way as the analog prototype. The general expressions for the continuous-time and discrete-time filter coefficients are given, and the frequency responses are compared for the component values of the Fender ’59 Bassman. These expressions are useful implementation and verification of implementations such as the wave digital filter.
Download Simplified, Physically-Informed Models of Distortion and Overdrive Guitar Effects Pedals This paper explores a computationally efficient, physically informed approach to design algorithms for emulating guitar distortion circuits. Two iconic effects pedals are studied: the “Distortion” pedal and the “Tube Screamer” or “Overdrive” pedal. The primary distortion mechanism in both pedals is a diode clipper with an embedded low-pass filter, and is shown to follow a nonlinear ordinary differential equation whose solution is computationally expensive for real-time use. In the proposed method, a simplified model, comprising the cascade of a conditioning filter, memoryless nonlinearity and equalization filter, is chosen for its computationally efficient, numerically robust properties. Often, the design of distortion algorithms involves tuning the parameters of this filter-distortion-filter model by ear to match the sound of a prototype circuit. Here, the filter transfer functions and memoryless nonlinearities are derived by analysis of the prototype circuit. Comparisons of the resulting algorithms to actual pedals show good agreement and demonstrate that the efficient algorithms presented reproduce the general character of the modeled pedals.
Download Resolving Grouped Nonlinearities in Wave Digital Filters using Iterative Techniques 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.
Download The Sounds of the Avian Syrinx - are they Really Flute-Like? This research presents a model of the avian vocal tract, implemented using classical waveguide synthesis and numerical methods. The vocal organ of the songbird, the syrinx, has a unique topography of acoustic tubes (a trachea with a bifurcation at its base) making it a rather unique subject for waveguide synthesis. In the upper region of the two bifid bronchi lies a nonlinear vibrating membrane – the primary resonator in sound production. Unlike most reed musical instruments, the more significant displacement of the membrane is perpendicular to the directions of airflow, due to the Bernoulli effect. The model of the membrane displacement, and the resulting pressure through the constriction created by the membrane motion, is therefore derived beginning with the Bernoulli equation.
Download RT-WDF — A Modular Wave Digital Filter Library with Support for Arbitrary Topologies and Multiple Nonlinearities 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
Download Simulation of the Diode Limiter in Guitar Distortion Circuits by Numerical Solution of Ordinary Differential Equations The diode clipper circuit with an embedded low-pass filter lies at the heart of both diode clipping “Distortion” and “Overdrive” or “Tube Screamer” effects pedals. An accurate simulation of this circuit requires the solution of a nonlinear ordinary differential equation (ODE). Numerical methods with stiff stability – Backward Euler, Trapezoidal Rule, and second-order Backward Difference Formula – allow the use of relatively low sampling rates at the cost of accuracy and aliasing. However, these methods require iteration at each time step to solve a nonlinear equation, and the tradeoff for this complexity must be evaluated against simple explicit methods such as Forward Euler and fourth order Runge-Kutta, which require very high sampling rates for stability. This paper surveys and compares the basic ODE solvers as they apply to simulating circuits for audio processing. These methods are compared to a static nonlinearity with a pre-filter. It is found that implicit or semiimplicit solvers are preferred and that the filter/static nonlinearity approximation is often perceptually adequate.