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Optimisation strategy used to extract the parameters of the Gummel-Poon model. The arrow indicates the flow of stages of extraction. The resultant parameters of each stage are passed on to the next.

Optimisation strategy used to extract the parameters of the Gummel-Poon model. The arrow indicates the flow of stages of extraction. The resultant parameters of each stage are passed on to the next.

Source publication
Conference Paper
Full-text available
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...

Context in source publication

Context 1
... optimisation procedure for the DC Gummel-Poon model is il- lustrated in Figure 5. After the direct extraction stage, three stages of optimisations are used. ...

Citations

... These transistors are less reliable than their silicon counterparts but are preferred by guitarists and pedal builders as they produce a smoother, warmer distortion. The Rangemaster (or similar) has been widely studied in existing VA literature [19], [34]- [37], but to the author's knowledge, never in the context of antialiasing. The transistor is a 2-port nonlinearity. ...
... The nonlinear behaviour of BJT transistors can be described via the Ebers-Moll model, which relates the base-emitter voltage, v be , and base-collector voltage v bc to the current at the base, i b , and the current at the collector, i c [34], [37]: ...
... where I s is the saturation current, β f is the forward current gain, β r is the reverse current gain and V t is the thermal voltage. The values used for these parameters are the same as those in [34], in which they were derived from direct measurements. ...
Thesis
Full-text available
Aliasing is an inherent problem in virtual analogue modelling when simulating nonlinear systems such as guitar amplifiers and distortion effects units. Such systems introduce harmonics into the signal, which in the discrete-time domain can exceed the Nyquist frequency, resulting in unpleasant aliasing distortion. Recent research has shown that aliasing can be significantly reduced by using the antiderivatives of the nonlinear function, and that this method can be applied to systems with state as well as memoryless nonlinearities. In this work, the application of antiderivative antialiasing in the state-space modelling of several nonlinear circuits will be outlined in detail. Existing literature has focused on one-port nonlinearities, so in this work a method for two-port nonlinearities is proposed and demonstrated by example. Furthermore, a second order antialiasing method for state-space models is presented. The antialiasing methods were found to significantly improve the signal to noise ratio and reduce aliasing at low oversampling rates. In the case of scalar nonlinearities, the methods introduced no notable extra computational cost, but for two-port nonlinearities the processing time increased with the order of antialiasing. Finally, the suitability of antiderivative antialiasing in a real-time context was demonstrated through the development of a virtual analogue guitar effects plug-in.
... Several Ph.D. theses have been written about this topic [102][103][104]. Further investigations, case studies and refinements of the method have been made by Holters et al. [42][43][44][45][46]55,65,69,71,76,85,105,106]. All of these works have in common that a state-space system is constructed from the circuit diagram using some form of circuit analysis. ...
... Additionally Holters proposed a method to automatically decompose the large statespace matrices into smaller ones to be able to solve the system quicker [105]. Several other publications address the computational load of the whitebox approaches and propose improvements to ensure real-time capability like [42,49,80,85,106,113,117]. A complete guitar amplifier circuit could be modeled with these approaches but without extensive optimization and simplification the digital model would not be real-time capable. ...
Thesis
Full-text available
Digital systems gain more and more popularity in todays music industry. Musicians and producers are using digital systems because of their advantages over analog electronics. They require less physical space, are cheaper to produce and are not prone to aging circuit components or temperature variations. Furthermore, they always produce the same output signal for a defined input sequence. However, musicians like vintage equipment. Old guitar amplifiers or legendary recording equipment are sold at very high prices. Therefore, it is desirable to create digital models of analog music electronics which can be used in modern digital environments. This work presents an approach for recreating nonlinear audio circuits using system identification techniques. Measurements of the input- and output-signals from the analog reference devices are used to adjust a digital model treating the reference device as a ‘black-box’. With this technique the schematic of the reference device does not need to be known and no circuit elements have to be measured to recreate the analog device. An appropriate block-based model is chosen, depending on the type of reference system. Then the parameters of the digital model are adjusted with an optimization method according to the measured input- and output-signals. The performance of the optimized digital model is evaluated with objective scores and listening tests. Two types of nonlinear reference systems are examined in this work. The first type of reference systems are dynamic range compressors like the ‘MXR Dynacomp’, the ‘Aguilar TLC’, or the ‘UREI 1176LN’. A block-based model describing a generic dynamic range compression system is chosen and an automated routine is developed to adjust it. The adapted digital models are evaluated with objective scores and a listening test is performed for the UREI 1176LN studio compressor. The second type of nonlinear systems are distortion systems like e.g. amplifiers for electric guitars. This work presents novel modeling approaches for different kinds of distortion systems from basic distortion circuits which can be found in distortion pedals for guitars to (vintage) guitar amplifiers like the ‘Marshall JCM900’, or the ‘Fender Bassman’. The linear blocks of the digital model are measured and used in the model while the nonlinear blocks are adapted with parameter optimization methods like the Levenberg–Marquardt method. The quality of the adjusted models is evaluated with objective scores and listening tests. The adjusted digital models give convincing results and can be implemented as real-time digital versions of their analog counterparts. This enables the musician to safe a snapshot of a certain sound and recall it anytime with a digital system like a VST plug-in or as a program on a dedicated hardware.
... The physical parameter values for the Mullard OC44 presented inTable 3.3 were extracted by Holmes at al. using measurements and optimization methods[29]. By using other parameter values in the Ebers-Moll equations, the Rangemaster can be simulated with a variety of different transistors, each of which provides a unique sonic character. ...
Thesis
Full-text available
This paper presents in detail the state-space approach to virtual analog modeling. A variety of different numerical methods are derived and implemented so that their performance may be compared. Four different guitar effects circuits are analyzed and simulated, and the detailed MATLAB code for each is provided.
Thesis
Full-text available
This work addresses the real-time simulation of nonlinear audio circuits. In this thesis, we use the port-Hamiltonian (pH) formalism to guarantee power balance and passivity. Moreover, we adopt a continuous-time functional framework to represent "virtual analog" signals and propose to approximate solutions by projection over time frames. As a main result, we establish a sufficient condition on projectors to obtain time-continuous power-balanced trajectories. Our goal is twofold: first, to manage frequency-bandwidth expansion due to nonlinearities, we consider numerical engines processing signals that are not bandlimited but, instead, have a "finite rate of innovation"; second, to get back to the bandlimited domain, we design "virtual analog-to-digital converters". Several numerical methods are built to be power-balanced, high-order accurate, with a controllable regularity order. Their properties are studied: existence and uniqueness, accuracy order and dispersion, but also, frequency resolution beyond the Nyquist frequency, aliasing rejection, reproducing and Peano kernels. This approach reveals bridges between numerical analysis, signal processing and generalised sampling theory, by relating accuracy, polynomial reproduction, bandwidth, Legendre filterbanks, etc. A systematic framework to transform schematics into equations and simulations is detailed. It is applied to representative audio circuits (for the UVI company), featuring both ordinary and differential-algebraic equations. Special work is devoted to pH modelling of operational amplifiers. Finally, we revisit pH modelling within the framework of Geometric Algebra, opening perspectives for structure encoding.