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Mitch Richling: Coupled RC Chaos

Author: Mitch Richling
Updated: 2023-01-09

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Table of Contents

1. Introduction

Masuda et al. (MSUN2009) describe a simple chaotic circuit composed of two coupled RC circuits with comparators. This page documents my experiments with this circuit.

2. The Circuit

The diagram below differs from Masuda in two ways 1) I provide circuitry for the driving square wave oscillator and 2) I'm using component values from page 220 of Sprott et al. (SCT2022).

schematic.png

Notes:

  • Chaotic behavior is possible with a wide range of values for R4 & R5.
  • The 555 is the Texas Instruments NE555P – this version of the 555 can run with supply voltages up to \(15\mathrm{V}\).
  • D1 can be any small signal type
  • The op-amp is not critical, and can be most anything

Files:

3. Simulation Results

plot.png

4. Physical Prototype

4.1. Solderless Breadboard Prototype

bboard_40.jpg

Notes:

  • R4 & R5 have been replaced with \(10\mathrm{K}\Omega\) pots.
  • D1 is a 1N914B
  • The Amps are 741's.

4.2. Final Version

pcb_40.jpg

Notes:

  • R4 & R5 have been replaced with \(10\mathrm{K}\Omega\) pots.
  • D1 is a 1N914B
  • The Amps are 741's.

5. Behavior & Measurements

Notes:

  • R4 is \(7\mathrm{K}\Omega\)
  • R5 is \(8\mathrm{K}\Omega\)

5.1. Analog Scope

Scope
Tektronix AN/USM488 (military version of the 2235). Equipped with the clear plexiglass CRT filter minus the wire mesh.
Capture Device
Samsung Note 9

The full sized movie is here.

5.2. Digital Scope

Scope
Siglent SDS2354X Plus

6. References

  • Doike, Yoshinori, Yoko Uwate, Yoshifumi Nishio, and Jingmin Xin. "Investigation of Chaos-Generating Circuit Composed of RL Circuits." 2013 Shikoku-Section Joint Convention Record of the Institutes of Electrical and Related Engineers, 2013, 14.
  • Masuda, Shuhei, Yumiko Uchitani, and Yoshifumi Nishio. "Simple Chaotic Oscillator Using Two RC Circuits." Proceedings of RISP International Workshop on Nonlinear Circuits and Signal Processing (NCSP'09), 2009, 89–92.
  • Sprott, Julien Clinton, and Wesley Joo-Chen Thio. "Elegant Circuits: Simple Chaotic Oscillators." New Jersey: World Scientific, 2022.
  • Check out the chaos in electronics section of my reading list.
  • For more about chaos in general, take a look at the fractals section of my reading list.