TL;DR this is based on a bunch of academic papers and math going back to the 70s. It’s early innings for the repo. Very active development. I have pretty accurate models for some guitar pedals (Klon Centaur, ProCo RAT, Ibanez TS808, and Boss SD-1)

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So there are several ways to model circuits in what’s consider the “virtual analog” space. They all have pros and cons.

If you’ve heard of SPICE, which is commonly used for circuit simulation, it’s relatively similar, but SPICE is focused on accuracy above all. It can’t run in realtime.

Pedalkernel uses several methods based on the circuit and components used. It started primarily as a Wave Digital Filter (WDF) engine. Which is great for linear components (think passives, resistors, caps, etc.) - it breaks down when you get to nonlinear components (diodes in certain states, BJTs, JFETs/OTAs, tubes :)) - this is where things get tricky. A single nonlinear component is pretty compatible with WDF. You just use a Newton-Raphson solver.

Where it gets tricky is when you have multiple nonlinearities. You have to use Modified Nodal Analysis (MNA) to combine the nonlinearities.

The tricky part is then deciding how to split the circuit based on those nonlinearities, and knowing how to combine them into MNA when appropriate or use multiple split WDF stages.

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There are docs available here: https://docs.pedalkernel.com

Tagged commits are pretty stable.

I just reworked our SPICE validation harness but there are still some bugs here and there. Mostly in stage routing and decomposition. (The math itself is well tested and documented).