ChaoticCircuits

Project Chaotic circuits
Status	Completed
Contact	gori
Last Update	2011-12-23

see also IgorsProjectIdeas

Build a simple electronic chaos demo for my course. Chaos can be observed using an oscilloscope. A portable one can be built with an arduino

Background reading

• One of the simplest possible chaotic circuits : http://www-physics.ucsd.edu/~des/DSmithChaosExperiment.pdf
• This one seems particularly interesting - possibility o encrypt analog sygnal : http://www.fortunecity.com/emachines/e11/86/circsync.html
• http://www.cornellcollege.edu/physics/courses/phy312/Student-Projects/Chaotic-circuits/Chaos.html
• Original paper: [httphttp://link.aps.org/doi/10.1103/PhysRevLett.47.1349 Period Doubling and Chaotic Behavior in a Driven Anharmonic Oscillator]

Version 2.0

Create the circuit that works at a lower frequency. Smith also describes a circuit that operates at 75 KHz instead of 2 MHz. Main bottle neck is the required large inductance

Goal is to :

• Be able to hear the chaos
• Have the whole thing portable, without the need for an external oscilloscope and signal generator
• Have it nice and presentable so it can be used as a demo

Todo:

• Calculate the inductance and capacitance required to achieve a resonant frequency in the audible range, preferably around 440 Hz. Conservative human hearing range is from 20 Hz to 15 kHz.
• Identify the operational limits of the [httphttp://code.google.com/p/arduinoscope/ arduinoscope] - max seems to be around 200 kHz, well above audible range
• Make sure that an arduino based scope can observe the signal.
• salvage/build/buy an appropriate spool
• create a suitable analogue signal generator that can drive the whole thing. Arduino can no do this, as it has no analogue circuitry for the job. PWM will (propbably) not do.
• Add speakers in order to hear the chaotic harmonics under/overtones
• package it is something transparent so that it makes a nice demo

Version 1.0

• Following : http://www-physics.ucsd.edu/~des/DSmithChaosExperiment.pdf
• Working oscilloscope and signal generator present, capable of 2Mhz
• Components according to the manual :
  • 200 ohm resistor
  • inductor, 100 microHenry needed, available a PE-53653 , with 16.1�H
  • diode - either works: 1N4001, 1N4004, 1N4005, 1N4007
• As built, the circuit does not display any chaotic behavior as we change the amplitude, The inductor is almost 5 times to weak.
• I have several spools, adding an extra spool in series, bringing the inductance up to 32 �H does not help.
• When adding random spools, it is good to measure its inductance. Here is a way to do it : http://www.daycounter.com/Articles/How-To-Measure-Inductance.phtml

BOM

• 1N4007 diode
• 220 ohm resistor
• (2 x 16) 32 �H + a random spool (code 471K 98139)
• Signal:
  • 1.5 MHz
  • Amplitude op 0 dB
  • sinus signaal
• Improvements needed :
  • Calculate / measure the currently installed inductance, and bring it up to spec, so that we get a nicer signal split than now
• With smedings help, we determined that the inductance of the three coils is 1351 uH or approx 1.4 mH

Results