Bio: M. Karjalainen is an academic researcher from Helsinki University of Technology. The author has contributed to research in topics: Vacuum tube & Signal processing. The author has an hindex of 2, co-authored 2 publications receiving 60 citations.
TL;DR: A physical model of a tube stage circuit using wave digital filters that enables the simulation of interstage coupling and blocking distortion and is an extension of the wave digital tube presented in Wave digital simulation of a vacuum-tube amplifier.
Abstract: Electric circuits containing vacuum tubes form an integral part of various audio equipment, such as guitar amplifiers, certain equalizers, microphone preamplifiers, and dynamic range compressors. Although most audio signal processing operations are straightforward to implement with modern computers, real-time digital simulation of vacuum tubes poses a significant challenge due to the dynamic nonlinearities of the tube circuits. Most of the current vacuum-tube emulators model the unidirectional signal path of the circuit using linear filters and nonlinear waveshapers, possibly with signal-dependent parameters. This paper introduces a physical model of a tube stage circuit using wave digital filters. In contrast to previous unidirectional signal models, the wave digital model implements bidirectional signal propagation. This allows realistic simulation of interesting dynamical nonlinearities, such as the bias variation under reactive load. The new model is an extension of the wave digital tube presented in ?Wave digital simulation of a vacuum-tube amplifier? (M. Karjalainen and J. Pakarinen Proc. Int. Conf. Acoustics, Speech, Signal Processing, 2006, vol. V, pp. 153-156). In particular, the enhanced model for the tube grid-to-cathode connection enables the simulation of interstage coupling and blocking distortion.
TL;DR: Methods to realize consolidated impedance or admittance wave ports that are compatible to WDFs and digital waveguides are explored and attention is paid to simplicity of parametric control.
Abstract: Wave digital filters (WDFs) were originally developed for robust discrete-time simulation of analog filters, but recently they have been applied successfully to modeling of physical systems such as musical instruments and to model-based sound synthesis. While basic WDF elements are sufficient to implement arbitrary passive lumped-element models, the computational efficiency of such models is not optimal. In this paper, we explore methods to realize consolidated impedance or admittance wave ports that are compatible to WDFs and digital waveguides. In addition to efficiency, attention is paid to simplicity of parametric control. A modeling and sound synthesis case study of the bell is presented to demonstrate the performance obtained by the consolidated approach.
TL;DR: The next step in the evolution of tube-amplifier emulation has been to simulate the amplifiers using computers and digital signal processors (DSP).
Abstract: Although semiconductor technologies have displaced vacuum-tube devices in nearly all fields of electronics, vacuum tubes are still widely used in professional guitar amplifiers. A major reason for this is that electric-guitar amplifiers are typically overdriven, that is, operated in such a way that the output saturates. Vacuum tubes distort the signal in a different manner compared to solid-state electronics, and human listeners tend to prefer this. This might be because the distinctive tone of tube amplifiers was popularized in the 1950s and 1960s by early rock and roll bands, so musicians and listeners have become accustomed to tube distortion. Some studies on the perceptual aspects of vacuum-tube and solid-state distortion have been published (e.g., Hamm 1973; Bussey and Haigler 1981; Santo 1994). Despite their acclaimed tone, vacuum-tube amplifiers have certain shortcomings: large size and weight, poor durability, high power consumption, high price, and often poor availability of spare parts. Thus, it is not surprising that many attempts have been made to emulate guitar tube amplifiers using smaller and cheaper solid-state analog circuits (e.g., Todokoro 1976; Sondermeyer 1984). The next step in the evolution of tube-amplifier emulation has been to simulate the amplifiers using computers and digital signal processors (DSP). A primary advantage of digital emulation is that the same hardware can be used for modeling many different tube amplifiers and effects. When a new model is to be added, new parameter values or program code are simply uploaded to the device. Furthermore, amplifier models can be implemented
TL;DR: A new model for an ideal operational amplifier that does not include implicit equations and is thus suitable for implementation using wave digital filters (WDFs) is introduced and a novel WDF model for a diode is proposed using the Lambert W function.
Abstract: This brief presents a generic model to emulate distortion circuits using operational amplifiers and diodes. Distortion circuits are widely used for enhancing the sound of guitars and other musical instruments. This brief introduces a new model for an ideal operational amplifier that does not include implicit equations and is thus suitable for implementation using wave digital filters (WDFs). Furthermore, a novel WDF model for a diode is proposed using the Lambert W function. A comparison of output signals of the proposed models to those obtained from a reference simulation using SPICE shows that the distortion characteristics are accurately reproduced over a wide frequency range. Additionally, the proposed model enables real-time emulation of distortion circuits using ten multiplications, 22 additions, and two interpolations from a lookup table per output sample.
30 Nov 2015
TL;DR: A novel framework for developing Wave Digital Filter models from reference circuits with multiple/multiport nonlinearities that significantly expands the class of appropriate WDF reference circuits and suggests a derivative of the K-method.
Abstract: We present a novel framework for developing Wave Digital Filter (WDF) models from reference circuits with multiple/multiport nonlinearities. Collecting all nonlinearities into a vector at the root of a WDF tree bypasses the traditional WDF limitation to a single nonlinearity. The resulting system has a complicated scattering relationship between the nonlinearity ports and the ports of the rest of the (linear) circuit, which can be solved by a Modified-NodalAnalysis-derived method. For computability reasons, the scattering and vector nonlinearity must be solved jointly; we suggest a derivative of the K-method. This novel framework significantly expands the class of appropriate WDF reference circuits. A case study on a clipping stage from the Big Muff Pi distortion pedal involves both a transistor and a diode pair. Since it is intractable with standard WDF methods, its successful simulation demonstrates the usefulness of the novel framework.
TL;DR: A procedure to search for explicit wave mappings, for both one-port and multi-port NLEs containing diodes, and an extended version of the BJT Ebers-Moll model, suitable for implementing feedback between terminals, is described.
Abstract: A large class of transcendental equations involving exponentials can be made explicit using the Lambert W function. In the last fifteen years, this powerful mathematical tool has been extensively used to find closed-form expressions for currents or voltages in circuits containing diodes. Until now almost all the studies about the W function in circuit analysis concern the Kirchhoff (K) domain, while only few works in the literature describe explicit models for diode circuits in the Wave Digital (WD) domain. However explicit models of NonLinear Elements (NLEs) in the WD domain are particularly desirable, especially in order to avoid the use of iterative algorithms. This paper explores the range of action of the W function in the WD domain; it describes a procedure to search for explicit wave mappings, for both one-port and multi-port NLEs containing diodes. WD models, describing an arbitrary number of different parallel and anti-parallel diodes, a transformerless ring modulator and some BJT amplifier configurations, are derived. In particular, an extended version of the BJT Ebers-Moll model, suitable for implementing feedback between terminals, is introduced.
TL;DR: The results suggest the use of function approximation to represent the solved system nonlinearity of the K-method and invite future work along these lines.
Abstract: This is the second part of a two-part paper that presents a procedural approach to derive nonlinear filters from schematics of audio circuits for the purpose of digitally emulating musical effects circuits in real-time. This work presents the results of applying this physics-based technique to two audio preamplifier circuits. The approach extends a thread of research that uses variable transformation and offline solution of the global nonlinear system. The solution is approximated with multidimensional linear interpolation during runtime to avoid uncertainties in convergence. The methods are evaluated here experimentally against a reference SPICE circuit simulation. The circuits studied here are the bipolar junction transistor (BJT) common emitter amplifier, and the triode preamplifier. The results suggest the use of function approximation to represent the solved system nonlinearity of the K-method and invite future work along these lines.