Download A Measurement Technique for Highly Nonlinear Transfer Functions This paper presents a new method to estimate nonlinear transfer functions of tube amplifiers or distortion effect stages. A special test signal and a sorting algorithm allow the calculation of the nonlinear transfer functions. PSPICE simulations of a tube amplifier as well as real-time measurements of a tube amplifier with a high quality 24bit/96kHz sound card will be presented.
Download A Physically-motivated Triode Model for Circuit Simulations A new model for triodes of type 12AX7 is presented, featuring simple and continuously differentiable equations. The description is physically-motivated and enables a good replication of the grid current. Free parameters in the equations are fitted to reference data originated from measurements of practical triodes. It is shown, that the equations are able to characterize the properties of real tubes in good accordance. Results of the model itself and when embedded in an amplifier simulation are presented and align well.
Download Circuit Simulation with Inductors and Transformers Based on the Jiles-Atherton Model of Magnetization 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.
Download Black-box Modeling of Distortion Circuits with Block-Oriented Models 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.
Download Block-oriented Gray Box Modeling of Guitar Amplifiers In this work, analog guitar amplifiers are modeled with an automated procedure using iterative optimization techniques. The digital model is divided into functional blocks, consisting of lineartime-invariant (LTI) filters and nonlinear blocks with nonlinear mapping functions and memory. The model is adapted in several steps. First the filters are measured and afterwards the parameters of the digital model are adapted for different input signals to minimize the error between itself and the analog reference system. This is done for a small number of analog reference devices. Afterwards the adapted model is evaluated with objective scores and a listening test is performed to rate the quality of the adapted models.
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 Discretization of Parametric Analog Circuits for Real-Time Simulations The real-time simulation of analog circuits by digital systems becomes problematic when parametric components like potentiometers are involved. In this case the coefficients defining the digital system will change and have to be adapted. One common solution is to recalculate the coefficients in real-time, a possibly computationally expensive operation. With a view to the simulation using state-space representations, two parametric subcircuits found in typical guitar amplifiers are analyzed, namely the tone stack, a linear passive network used as simple equalizer and a distorting preamplifier, limiting the signal amplitude with LEDs. Solutions using trapezoidal rule discretization are presented and discussed. It is shown, that the computational costs in case of recalculation of the coefficients are reduced compared to the related DK-method, due to minimized matrix formulations. The simulation results are compared to reference data and show good match.
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.
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.