[sdiy] Squaring volts

[Ian Fritz]

At 04:24 PM 11/21/05, M.A. Koot wrote:

>Hi everybody,
>
>I'm working on a project trying to make the van der Pol osscilator in analog
>electronics. To realize the circuit of the "negative resistor", I have
>developed a system wich involves squaring of the analog signal.
>It really seems this is needed. Now, the only way I know how to square an
>analog signal is using a ring modulator circuit with equal inputs. Though
>this really seems a clumsy way to achieve the squaring, and I'm also not
>sure if it would work.

According to the analysis in Strogatz, the vdP osc can be written in terms 
of a nonlinear function F(x) = (x^3)/3 - x.  If you can work in this 
transformed variable system, then you can use a simple nonlinear circuit 
that approximates F(x) using zener diodes, resistors and an opamp.  I 
happen to have such a circuit up on a temporary web page now.  It is the 
nonlinear limiting circuit for a quadrature limit-cycle oscillator, shown 
on the right-hand side of the schematic:

http://home.earthlink.net/~ijfritz/xfer.htm

As I have mentioned before, this is a very useful circuit for nonlinear 
applications including chaos generation and wave folding.

   Ian