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I was reading Ian Fritz overview on chaotic circuits.

As an example of non-linear circuit, he presents the following schematics Cubic non-linearity

This circuit is said to output a signal of the form x.(1-x^2) where x is the input signal.

As I understand the circuit, the face-to-face diodes are supposed to introduce a cubic non-linearity x^3.

Could someone explain how two face-to-face diodes can output a cubic non-linearity ?

Thank you.

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    Why not use a simulator and see what result you get. If it works, you'll see that the important thing is that they are zener diodes. – Andy aka May 24 '21 at 18:39

1 Answers1

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Note: it says "of the form", not "strictly", which means it's an antisymmetric waveform (odd function) due to the \$x^3\$ part. And if you look at the circuit closely, the two Zener diodes with the 2.2 kΩ form a so-called dead-zone, because the input voltage will need to be greater, or lesser than \$\approx\pm V_Z\pm 0.7\$. This makes the voltage at the noninverting input be (vortually) flat over a certain range, while at the other input the voltage is normal. Their difference will be S-shaped, or that of an odd function.

As suggested by Andy aka, grab your favourite SPICE simulator and convince yourself:

test

The purpose is to generate a voltage that has two slopes, positive and negative, with inflexion points, based on a linear input. This is one key step in creating chaotic circuits. See Chua's circuit, or Lorenz attractor (or other answers) for some more explanations. It's not mandatory to be Zener diodes as long as the circuit can behave like a dead-zone (but a Zener does simplify things).

a concerned citizen
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  • Ok thanks ! I actually tried to use a spice simulator (within Eagle), but I got a linear response .... I'm quite new to spice, so I guess I must have missed something. But the "dead zone" explanation is what I was looking for here, so thank you very much. – Peva Blanchard May 25 '21 at 17:34