Download Physical Modeling of the MXR Phase 90 Guitar Effect Pedal In this study, a famous boxed effect pedal, also called stompbox, for electrical guitars is analyzed and simulated. The nodal DK method is used to create a non-linear state-space system with Matlab as a physical model for the MXR Phase 90 guitar effect pedal. A crucial component of the effect are Junction Field Effect Transistors (JFETs) which are used as variable resistors to dynamically vary the phase-shift characteristic of an allpass-filter cascade. So far, virtual analog modeling in the context of audio has mainly been applied to diode-clippers and vacuum tube circuits. This work shows an efficient way of describing the nonlinear behavior of JFETs, which are wide-spread in audio devices. To demonstrate the applicability of the proposed physical model, a real-time VST audio plug-in was implemented.
Download Comparison of Germanium Bipolar Junction Transistor Models for Real-time Circuit Simulation The Ebers-Moll model has been widely used to represent Bipolar Junction Transistors (BJTs) in Virtual Analogue (VA) circuits. An investigation into the validity of this model is presented in which the Ebers-Moll model is compared to BJT models of higher complexity, introducing the Gummel-Poon model to the VA field. A comparison is performed using two complementary approaches: on fit to measurements taken directly from BJTs, and on application to physical circuit models. Targeted parameter extraction strategies are proposed for each model. There are two case studies, both famous vintage guitar effects featuring germanium BJTs. Results demonstrate the effects of incorporating additional complexity into the component model, weighing the trade-off between differences in the output and computational cost.
Download Physical Modelling of a Wah-wah Effect Pedal as a Case Study for Application of the Nodal DK Method to Circuits with Variable Parts The nodal DK method is a systematic way to derive a non-linear state-space system as a physical model for an electrical circuit. Unfortunately, calculating the system coefficients requires inversion of a relatively large matrix. This becomes a problem when the system changes over time, requiring continuous recomputation of the coefficients. In this paper, we present an extension of the DK method to more efficiently handle variable circuit elements. The method is exemplified with the Dunlop Crybaby wah-wah effect pedal, as the continuous change of the potentiometer position is an extremely important aspect of the wah-wah effect.
Download Revisiting the Second-Order Accurate Non-Iterative Discretization Scheme In the field of virtual analog modeling, a variety of methods have been proposed to systematically derive simulation models from circuit schematics. However, they typically rely on implicit numerical methods to transform the differential equations governing the circuit to difference equations suitable for simulation. For circuits with non-linear elements, this usually means that a non-linear equation has to be solved at run-time at high computational cost. As an alternative to fully-implicit numerical methods, a family of non-iterative discretization schemes has recently been proposed, allowing a significant reduction of the computational load. However, in the original presentation, several assumptions are made regarding the structure of the ODE, limiting the generality of these schemes. Here, we show that for the second-order accurate variant in particular, the method is applicable to general ODEs. Furthermore, we point out an interesting connection to the implicit midpoint method.
Download Antiderivative Antialiasing for Stateful Systems Nonlinear systems, like e.g. guitar distortion effects, play an important role in musical signal processing. One major problem encountered in digital nonlinear systems is aliasing distortion. Consequently, various aliasing reduction methods have been proposed in the literature. One of these is based on using the antiderivative of the nonlinearity and has proven effective, but is limited to memoryless systems. In this work, it is extended to a class of stateful systems which includes but is not limited to systems with a single one-port nonlinearity. Two examples from the realm of virtual analog modeling show its applicability to and effectiveness for commonly encountered guitar distortion effect circuits.
Download Simulation of Fender Type Guitar Preamp using Approximation and State-Space Model This paper deals with usage of approximations for simulation of more complex audio circuits. A Fender type guitar preamp was chosen as a case study. This circuit contains two tubes and thus four nonlinear functions as well as it is a parametric circuit because of an integrated tone stack. A state-space approach was used for simulation and further, precomputed solution is approximated using nonuniform cubic splines.
Download Antialiased State Trajectory Neural Networks for Virtual Analog Modeling In recent years, virtual analog modeling with neural networks experienced an increase in interest and popularity. Many different modeling approaches have been developed and successfully applied. In this paper we do not propose a novel model architecture, but rather address the problem of aliasing distortion introduced from nonlinearities of the modeled analog circuit. In particular, we propose to apply the general idea of antiderivative antialiasing to a state-trajectory network (STN). Applying antiderivative antialiasing to a stateful system in general leads to an integral of a multivariate function that can only be solved numerically, which is too costly for real-time application. However, an adapted STN can be trained to approximate the solution while being computationally efficient. It is shown that this approach can decrease aliasing distortion in the audioband significantly while only moderately oversampling the network in training and inference.
Download Taming the Red Llama—Modeling a CMOS-Based Overdrive Circuit The Red Llama guitar overdrive effect pedal differs from most
other overdrive effects because it utilizes CMOS inverters, formed
by two metal-oxide-semiconductor field-effect transistors (MOSFETs), instead of a combination of operational amplifiers and
diodes to obtain nonlinear distortion. This makes it an interesting
subject for virtual analog modeling, obviously requiring a suitable
model for the CMOS inverters. Therefore, in this paper, we extend
a well-known model for MOSFETs by a straight-forward heuristic
approach to achieve a good match between the model and measurement data obtained for the individual MOSFETs. This allows a
faithful digital simulation of the Red Llama.
Download Automatic Decomposition of Non-linear Equation Systems in Audio Effect Circuit Simulation In the digital simulation of non-linear audio effect circuits, the arising non-linear equation system generally poses the main challenge for a computationally cheap implementation. As the computational complexity grows super-linearly with the number of equations, it is beneficial to decompose the equation system into several smaller systems, if possible. In this paper we therefore develop an approach to determine such a decomposition automatically. We limit ourselves to cases where an exact decomposition is possible, however, and do not consider approximate decompositions.
Download The Influence of Small Variations in a Simplified Guitar Amplifier Model A strongly simplified guitar amplifier model, consisting of four stages, is presented. The exponential sweep technique is used to measure the frequency dependent harmonic spectra. The influence of small variations of the system parameters on the harmonic components is analyzed. The differences of the spectra are explained and visualized.