Building the Circuit

A number of "electronic circuits for home hobbyists" have been described in various articles. This circuit has a number of advantages:

• It is self contained - you do not need an external oscillator, and you can carry the whole thing around in a "hobby box" (battery included) and give easy demonstrations.
• It operates at audio frequencies. This means you can listen to the signal! Also, higher frequency circuits are more sensitive to parasitic capacitance, and are difficult to model accurately by a simple circuit theory. I have found the circuit description used in the applet to be quite accurate.
• I am by no means an electronics whiz, but I built it and it works!

Nevertheless, the circuit is quite delicate (sensitive to component values) - as playing around with the parameters in the simulation will show - and a number of tips may lessen the frustration.

Tips

1. This is very much a "breadboard circuit". There is alot ot trial and error in getting the right components, which is much easier if you can just poke them into a breadboard rather than solder and desolder them. For example, successful results (i.e. oscillations, period doubling, chaos etc) depend on getting the "right" value for C₁ - I ended up using 3.2+1.1+0.2+0.1 nF capacitors in parallel to add to the 4.6nf I needed. (I measured these values with a meter since the component specs are not usually this accurate. Of course you do not need to know the actual value - you can keep adding those little capacitors until the signal looks good.) Once you have the right components, you can solder it up, but I just keep it on a breadboard in a small hobby box from Radio Shack, and it has worked for a couple of years.
2. I first used a smaller inductance (4mH) but had better luck with the larger one when I found it. Since this is the hardest component to find, get this first and design the rest of the circuit around it. You need to keep the ratios of the capacitances C₁ /C₂ and the ratio of the capacitance to the inductance e.g. C₁ / L about the same as in my circuit. The frequency of the oscillations will vary inversely as the square root of LC and so goes down as you make the inductance larger-an advantage if you are listening to the signal, since the high pitch is quite annoying!.
3. The op27 is roughly equivalent to the ubiquitous 741, but has better characteristics. Although I got a circuit working with the 741, the behavior is much nicer with the op27 (e.g. the symmetry between positive and negative voltage oscillations).
4. The resistance values R,R₁,R₂ are strongly constrained - for example to give the right sort of slopes in the effective nonlinear resistance. This is easy to arrange, either using high precision resistors or choosing from a bunch of low precision resistors with an ohm-meter . The other resistances are for bias, and the values are less crucial.
5. Try to find matching values for the various components that come in pairs. This is improves the symmetry of the behavior for the oscillations about the two different static load points, and the noisy switching between orbits around these points.
6. To tune the parameters to go from periodic to chaotic motion you need to delicately tune C₁ or R. (You can play around with the applet to find what range of variation is needed.) To give you some idea, I found that a variation of 50 pF (yes, that's picoFarads) took me from period 1 to period 8 motion in the subharmonic cascade. I was fortunate enough to have a beautiful precision variable 1000pF capacitor (in a box about 10 inches cube!) that let me smoothly change C₁. Usually it is easier to vary R. Since the behavior is very sensitive to the value of R, I found that having a 100K pot in parallel with a fixed 1.3K resistance gave me sufficient tuning range (after tweaking the fixed resistance or C₁ to get the right sort of behavior).
7. Since the circuit is sensitive to capacitances of 10-100pF we have to worry about the capacitance of leads connecting to oscilloscopes etc - standard oscilloscope leads are often 100pf, so keep them short! Also the resistance r (of about 90ohm) is the typical resistance of an inductor of this size, and is part of the inductor - do not add in a separate resistor here!