Modelling of the Fender Bassman 5F6-A Tone Stack

TL;DR

This paper presents a method for accurately modeling the complex tone shaping filter of the Fender Bassman 5F6-A amplifier using mathematical analysis and MATLAB, addressing challenges posed by non-orthogonal controls.

Contribution

It introduces a novel analytical approach and MATLAB model for the Fender Bassman 5F6-A tone stack, facilitating better understanding and emulation of its complex filter behavior.

Findings

Derived general expressions for filter coefficients.

Developed a MATLAB model matching the circuit's frequency response.

Provided a practical method for analyzing similar complex analogue filters.

Abstract

This paper outlines the procedure for the effective modelling of a complex analogue filter circuit. The Fender Bassman 5F6-A is a circuit commonly employed in guitar amplifiers to shape the tonal characteristics of the amplifier output. On first inspection this circuit may look rather simple, however the controls are not orthogonal, resulting in complicated filter coefficients as the controls are varied. This in turn can make the circuit difficult to analyse without the use of mathematical emulation tools such as PSPICE or MATLAB. First the circuit is described, a method of analysis is proposed and general expressions for continuous-time coefficients are given. A MATLAB model is then produced and the frequency responses of which are shown.