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.

First clipper

Let’s start with the first circuit, which I implemented originally in Audio Toolkit.

Diode clipper 1
Diode clipper 1

It consists of a resistor, a capacitor and antiparallel diodes. What is interesting with this circuit is that in constant mode, the output is actually null.

V_i - 2 R_1 I_s sinh(\frac{V_o}{nV_t}) - \int \frac{2 I_s}{C_1} sinh(\frac{V_o}{nV_t}) - V_o = 0

Second clipper

The second circuit is a variation of the first one:

Diode Clipper 2
Diode Clipper 2

More or less, it’s a first order low-pass filter that is clipped with antiparallel diodes. The first result is that in constant mode, there is a non-null output.

\frac{dV_o}{dt} = \frac{V_i - V_o}{R_1 C_1} - \frac{2 I_s}{C_1} sinh(\frac{V_o}{nV_t})

The two equations are quite different. If the first one has an integral, the second one uses a derivative. This should be interesting to discretize and compare.

Conclusion

The equations are simple enough so that we can try different numerical methods on them. They are still too complex to get an analytical solution (no closed-form solution), so we have to use more or less complex numerical algorithms to get an approximation of the result.

And we will start working on this in a future post.

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