A Nonlinear Analysis Framework for Electronic Synthesizer Circuits



John Sullivan

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François G. Germain

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M.A. Thesis, McGill University


This thesis presents a theoretical and experimental study of the nonlinear behaviour of analog synthesizers’ effects. The goal of this thesis is to evaluate and complete current research on nonlinear system modelling, both in and out of the field of music technology. The cases of single-input and multiple-input effects are considered.
We first present an electronic analysis of the circuits of common examples of analog effects such as Moog’s lowpass filter and Bode’s ring modulator, extracting the equations of each system. We then discuss the results of experiments made on these systems in order to extract qualitative information about the distortion found in the system input-output relationship.
Secondly, we look at the literature for methods used to model single-input nonlinear systems, and we investigate the opportunities to extend these techniques to multi-input systems. We focus on two different modelling approaches. The black-box approach seeks to model the input-output transfer function of the system as closely as possible without any particular assumption on the system. The circuit modelling approach uses the knowledge of electronic component behaviour to extract a transfer function from the known circuit of the system. The results of both approaches are compared to our experiments in order to evaluate their accuracy, identify flaws and, when possible, suggest potential improvements of the methods.

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Masters Thesis
Montreal, Canada

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