Building the Circuit
A number of "electronic circuits for home hobbyists" have been
described in various articles. This circuit has a number of
- 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
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
- 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.
- 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!.
- 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).
- The resistance values R,R1,R2 are
strongly constrained - for example to give the right sort of
slopes in the effective nonlinear
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
- 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.
- 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
- 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!
Last modified Thursday, September 26, 1996