How the circuit works

The circuit can be broken down into three parts:

  1. The inductor L (together with its associated resistance r), the resistor R, and the capacitors C1 and C2 make up a conventional linear oscillation circuit. With the rest of the circuit shorted out, this part would give damped oscillations.
  2. The op-amp and associate resistors have the effect of a negative resistance of size -R1. This is still a linear circuit element - it does not by itself give chaos, although it acts as the source of energy for the dynamics.
  3. The diode pair gives the nonlinearity in the circuit. The diodes simply serve to switch in the resistance R2 in parallel with the resistance -R1 when the voltage gets larger than the switch on voltage.

The combined effect of B and C is to give a nonlinear negative resistance of value -R1 for V<Vc and -R1R2/(R2-R1) for V>Vc so that the effective circuit is:

with the current-voltage characteristics of the effective nonlinear resistance given by

For DC signals the capacitors act as open circuits, and the inductor as a short circuit, so the operating point I0,V0 is given by one of the two intersections of the line of slope -1/R (the load line) with the nonlinear I-V characteristic. (This stationary operating point can be seen by running the applet with C2=75nF for example, when the oscillations gradually decay away.) For suitable values of C1,C2 and L these stationary solutions (fixed points) become unstable to oscillations, and then to chaotic dynamics, first circulating e.g. the I0,V0 fixed point, then switching back and forth between oscillating about the +I0,+V0 and then -I0,-V0 points.

Last modified Saturday, September 7, 1996
Michael Cross