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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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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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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