We introduce the technique of "Bit Bending," a particularly fertile technique for circuit bending which involves short circuits and manipulations upon digital serial information. We present a justification for computer modeling of circuit-bent instruments, with deference to the movement's aversion to "theory-true" design and associations with chance discovery [1]. To facilitate software modeling of Bit Bending, we also present a software library for modeling certain classes of digital integrated circuits. A synthesis architecture case study (frequency modulation via numerically controlled oscillators) demonstrates software modeling of Bit Bending in action.

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We present an analysis of the bass drum circuit from the classic Roland TR-808 Rhythm Composer, based on physical models of the device’s many sub-circuits. A digital model based on this analysis (implemented in Cycling 74’s Gen˜) retains the salient features of the original and allows accurate emulation of circuit-bent modifications—complicated behavior that is impossible to capture through black-box modeling or structured sampling. Additionally, this analysis will clear up common misconceptions about the circuit, support the design of further drum machine modifications, and form a foundation for circuit-based musicological inquiry into the history of analog drum machines.

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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.

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We present a computational model of the Hammond tonewheel organ vibrato/chorus, a musical audio effect comprising an LC ladder circuit and an electromechanical scanner. We model the LC ladder using the Wave Digital Filter (WDF) formalism, and introduce a new approach to resolving multiple nonadaptable linear elements at the root of a WDF tree. Additionally we formalize how to apply the well-known warped Bilinear Transform to WDF discretization of capacitors and inductors and review WDF polarity inverters. To model the scanner we propose a simplified and physically-informed approach. We discuss the time- and frequency-domain behavior of the model, emphasizing the spectral properties of interpolation between the taps of the LC ladder.

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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.

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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

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In this paper, we show how to expand the class of audio circuits that can be modeled using Wave Digital Filters (WDFs) to those involving operational transconductance amplifiers (OTAs). Two types of behavioral OTA models are presented and both are shown to be compatible with the WDF approach to circuit modeling. As a case study, an envelope filter guitar effect based around OTAs is modeled using WDFs. The modeling results are shown to be accurate when to compared to state of the art circuit simulation methods.

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The voltage-controlled low-pass filter of the Korg MS-50 synthesizer is built around a non-linear diode bridge as the cutoff frequency control element, which greatly contributes to the sound of this vintage synthesizer. In this paper, we introduce the overall filter circuitry and give an in-depth analysis of this diode bridge. It is further shown how to turn the small signal equivalence circuit of the bridge into the necessary two-resistor configuration to uncover the underlying Sallen-Key structure. In a second step, recent advances in the field of WDFs are used to turn a simplified version of the circuit into a virtual-analog model. This model is then examined both in the small-signal linear domain as well as in the non-linear region with inputs of different amplitudes and frequencies to characterize the behavior of such diode bridges as cutoff frequency control elements.

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Previous grouped-nonlinearity formulations for Wave Digital Filter (WDF) modeling of nonlinear audio circuits assumed that nonlinear (NL) devices with memoryless voltage–current characteristics were modeled as voltage-controlled current sources (VCCSs). These formulations cannot accommodate nonlinear devices whose equations cannot be written as NL VCCSs, and they cannot accommodate circuits with cutsets composed entirely of current sources (including NL VCCSs). In this paper we generalize independent and dependent variable choice at the root of WDF trees to accommodate both these cases, and review two graph theorems for avoiding forbidden cutsets and loops in general.

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In this paper a new technique is introduced that allows for the variable step-size simulation of wave digital filters. The technique is based on the preservation of the underlying network variables which prevents fluctuation in the stored energy in reactive network elements when the step-size is changed. This method allows for the step-size variation of wave digital filters discretized with any passive discretization technique and works with both linear and nonlinear reference circuits. The usefulness of the technique with regards to audio circuit simulation is demonstrated via the case study of a relaxation oscillator where it is shown how the variable step-size technique can be used to mitigate frequency error that would otherwise occur with a fixed step-size simulation. Additionally, an example of how aliasing suppression techniques can be combined with physical modeling is given with an example of the polyBLEP antialiasing technique being applied to the output voltage signal of the relaxation oscillator.

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