### 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.

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:

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.

Series NavigationAnalog modeling of a diode clipper (2): Discretization >>

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