Exploring audio circuits with ModelingToolkit.jl

The study of audio circuits is interdisciplinary. It combines DSP, analog circuits, differential equations, and semiconductor theory. Mathematical tools like Fourier Transforms and standard circuit analysis cannot explain the behavior of stateful nonlinearities. A complete description of a circuit can only be obtained through time-domain (or ‘transient’, in SPICE terms) simulation. ModelingToolkit.jl enables rapid design iteration and combines features that traditionally require multiple tools.

This talk is targeted at people who want to start using ModelingToolkit.jl for simulations in their domain. It shows a workflow that is possible today. Additionally, it hints that composability is the key to unlock future breakthroughs. As a bonus, we can implement recent audio processing papers in a few lines of code!

We begin with a survey of the numerical and symbolic software commonly employed in the field and explain our decision to use ModelingToolkit.jl. Typically, engineers working with audio systems face a 3-language problem: use SPICE-style software to analyze a circuit, then move on to Matlab/Scilab/Python to deliver a high-level prototype, and finally re-write that into a high-performance implementation in C/C++. Usually, the simplification of a circuit turns into a laborious, multi-week manual process. ModelingToolkit.jl covers these use cases and more.

Afterwards, we will explore increasingly complex audio circuits via simulation. Topics include:

• implementing Kirchhoff laws
• defining simple models (capacitor, diode)
• defining a circuit
• simulating the circuit and plotting the result
• defining hierarchical models (VCCS, vacuum tube)
• animated plotting
• defining controls (potentiometers)
• exploring variations on a venerable guitar pedal

Lastly, audio demos of the simulated circuits will be featured.

Assumed background: Attendees are expected to have some programming experience in e.g. Python. It is helpful, although not required, to have experience working with analog circuits and/or SPICE simulation software.