chaotic oscillator design

Discussion in 'The Projects Forum' started by bearblock, Dec 20, 2010.

  1. bearblock

    Thread Starter Member

    Oct 24, 2008
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    hi everyone,

    i'm trying to implement a chaotic oscillator for an electronic music project. i've built a few different chaos circuits in the past, but this time i have a couple of requirements that are causing headaches:

    1) it needs to run on a single 9V battery. this isn't enough juice for an AD633 multiplier chip, which would seem to rule out the Lorenz and Duffing oscillators... (?)

    2) i need to be able to modify it for real-time frequency control - so the time constant can be changed by only changing resistors. Chua's circuit and a chaos-modified Wien bridge oscillator I found on the web both contain inductors which makes them unsuitable. the plan is to replace the resistors with OTAs or maybe just matched FETs (i only really need a single decade of adjustment)

    any advice, even just 'go read this book' or 'relax the specifications', would be much appreciated.
     
  2. thatoneguy

    AAC Fanatic!

    Feb 19, 2009
    6,357
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    Try to build a high gain audio amplifier. :D

    Old electronics joke.

    Are you looking for a fractal function, or purely random?
     
  3. #12

    Expert

    Nov 30, 2010
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    ROFL

    Love the joke. Thanks for the laugh. (Hope it doesn't put off the O.P.) After all, it WAS a good joke :)
     
  4. bertus

    Administrator

    Apr 5, 2008
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  5. bearblock

    Thread Starter Member

    Oct 24, 2008
    18
    1
    hi, i'm hoping to achieve fractal chaos with this project. it's true that running noise through a high-Q bandpass filter would be similar in a lot of ways, but then i'd miss out on the interesting transitions between periodicity and chaos, as seen in this vid:

    http://www.youtube.com/watch?v=tZt0YnIz5lY

    this particular attractor falls foul of the first requirement btw: the nonlinearity is in the form of a multiplication. seems to me that there's plenty of easier, cheaper nonlinear elements to choose from...

    currently reading 'nonlinear dynamics and chaos' by Strogatz which will hopefully make things a bit clearer.
     
  6. bearblock

    Thread Starter Member

    Oct 24, 2008
    18
    1
    hi bertus, the problem with those is the inductors, which make it hard to add a user-friendly 'rate' pot. i tried taking a Chua circuit and replacing the inductor with a virtual inductor (with opamp and RC network) but it didn't work properly... i guess the series resistance was too great?
     
  7. bertus

    Administrator

    Apr 5, 2008
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  8. bearblock

    Thread Starter Member

    Oct 24, 2008
    18
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    hi bertus, i did have a go at that approach - i've attached a screenshot of the simulation. when the inductor (A) is connected, i get the chaotic waveform shown in the plot, but when i disconnect it and connect the gyrator (B) instead, i just get an ordinary damped oscillation.
     
  9. bearblock

    Thread Starter Member

    Oct 24, 2008
    18
    1
    ok, so i've made some progress with this...

    http://w3.ele.tue.nl/fileadmin/ele/MBS/CS/Files/Courses/Dynamical_Systems/chuades.pdf

    about 2/3 of the way down page 2 of this document you can see the differential equations that describe Chua's oscillator. i designed an analogue computer circuit to solve these equations, and it works! i've attached a screenshot of the schematic. now i can go from a sine wave, through period doubling, to chaos, by changing a single resistor.

    the next task is frequency control. R9, R10 and R11 (in the red box) determine the time constants of the three integrators. i've tried using JFETs here to introduce voltage control, but haven't been able to get distortion down to acceptable levels (the distortion is asymmetric which obviously isn't good for a signal to be integrated). i can see a few possible paths to take...

    1) triple-gang potentiometer. this is pretty much the last-resort option due to cost & inconvenience

    2) OTA. the CA3080 looks like it will work with the low supply voltages i'm using, but i've heard it's discontinued. i'm wondering if the LM13700 will work here? the datasheet only specifies a maximum. also: anyone know how to add OTA models to the LTSpice component library?

    3) home made vactrol (optocoupler) - i.e. an LED & 3 light dependent resistors wrapped up in some heatshrink. the wide variation in light & dark resistance values between individual LDRs might be a problem here? would need to do some experiments to see if I can mitigate this with selected resistors in series & parallel.

    4) FETs. i've read up on this (i.e. googled 'fet variable resistor') but at this point i'm pretty much out of ideas to make it work. i noticed that there are some (discontinued) JFETs that are designed for this purpose - is it possible to use something more mainstream like a 2N5458 or BF245?

    any ideas? the chaos aspect is almost beside the point now - i just want voltage or current control of three resistances...

    thanks for reading!
     
  10. bertus

    Administrator

    Apr 5, 2008
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    Hello,

    You can "emulate" a variable resistor with an analog switch.
    You have a low value resistor with a high value resistor with the analog switch accross it, that is controlled with PWM.
    At a duty-cycle of 0 % the low resistor will be seen by the circuit.
    At a duty-cycle of 50 % the low resistor + 1/2 the value of the high resistor will be seen by the circuit.
    At a duty-cycle of 100 % the low + high resistor will be seen by the circuit.

    What voltages are you using, for selecting the analog switch?

    Bertus
     
  11. bearblock

    Thread Starter Member

    Oct 24, 2008
    18
    1
    Thanks Bertus, I didn't know about that technique. I wonder how fast the PWM needs to be in relation to the oscillator it's modulating? However, it still leaves the problem of how to implement the switch - using something like a DG412 or dealing with distortion from JFETs again...

    I think i'm going to go with OTAs after all. It turns out LM13700 can operate ok on +-4.5V and I figured out how to import the model into LTSpice.
     
  12. bertus

    Administrator

    Apr 5, 2008
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    Hello,

    The technique is used in capacitor switched filters.
    When the switching frequency is about 100 times higher as the maximum used frequency, you will hardly notice the switching.
    You can probably use the DG412 or even a simple 4066 for the job.

    Bertus
     
  13. bearblock

    Thread Starter Member

    Oct 24, 2008
    18
    1
    Of course! I forgot about the 4066. I think what I'll do is stripboard the circuit I posted on the other page, with the 3 resistors off-board, so I can compare different methods of controlling the time constant. Trying to keep unit cost & current draw to a minimum...
     
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