Tag Archives: Numerical methods

Analog modeling: Comparing preamps

In a previous post, I explained how I modeled the triode inverter circuit. I’ve decided to put it inside two different plugins, so I’d like to present in 4 pictures their differences.

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Analog modeling: Triode circuit

When I started reviewing the diode clippers, the goal was to end up modeling a triode simple preamp. Thanks to Ivan Cohen from musical entropy, I’ve finally managed to drive the proper equation system to model this specific type of preamp.

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Analog modeling: SD1 vs TS9

There are so many different distortion/overdrive/fuzz guitar pedals, and some have a better reputation than other. Two of them have a reputation of being closed (one copied on the other), and I already explained how one of these could be modeled (and I have a plugin with it!). So let’s work on comparing the SD1 and the TS9.

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On modeling posts

I’m currently considering whether I should do more posts on preamps modeling or just keep implementing filters/plugins. Of course, it’s not one or the other, there are different options in this poll:

Modeling preamps: more or less?

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So the idea is to ask my readers what they actually want. I can explain how the new triodes filters are implemented, how they behave, but I can also add new filters in Audio Toolkit (based on different preamp and amp stages, dedicated to guitars, bass, other instruments), try to optimize them, and finally I can include them in new plugins that could be used by users. Or I can do something completely different.

So if you have any ideas, feel free to say so!

Analog modeling of a diode clipper (4): DK-method

DK method is explained at large by David Ye in his thesis. It’s based around nodal analysis and was also extensively used by cytomic in his papers.

When analyzing a circuit form scratch, we need to replace all capacitors by an equivalent circuit and solve the equation with this modified circuit. Then, the equivalent currents need to be updated with the proper formula.
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Analog modeling of a diode clipper (3a): Simulation

Now that we have a few methods, let’s try to simulate them. For both circuits, I’ll use the forward Euler, then backward Euler and trapezoidal approximations, then I will show the results of changing the start estimate and then finish by the Newton Raphson optimization. I haven’t checked (yet?) algorithms that don’t use the derivative like the bisection or Brent algorithm.

All graphs are done with a x4 oversampling (although I also tried x8, x16 and x32).

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Analog modeling of a diode clipper (2): Discretization

Let’s start with the two equations we got from the last post and see what we can do with usual/academic tools to solve them (I will tackle nodal and ZDF tools later in this series).

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Analog modeling of a diode clipper (1): Circuits

I’ve published a few years ago an emulation of the SD1 pedal, but haven’t touched analog modeling since. There are lots of different methods to model a circuit, and they all have different advantages and drawbacks. So I’ve decided to start from scratch again, using two different diode clippers, from the continuous equations to different numerical solutions in a series of blog posts here.

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