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Demonstration of Chaos

Demonstration of Chaos. Circuits. Sajjad. Circuit Diagram. 3. 2. 1. 330 . 5K . 20K . 30.8 . +. +. TL087. TL087. -. -. 0.4  F. 0.033  F. 58 mH. 330 . 20K . 2K . 3.3K . LC tank circuit. Critical control For CHAOS. Negative resistance - 2.

kermit-cameron
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Demonstration of Chaos

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  1. Demonstration of Chaos Circuits Sajjad

  2. Circuit Diagram 3 2 1 330  5K  20K  30.8  + + TL087 TL087 - - 0.4 F 0.033 F 58 mH 330  20K  2K  3.3K  LC tank circuit Critical control For CHAOS Negative resistance - 2 Negative resistance - 1

  3. Negative Resistance 330  Negative resistance I 7 + 3 mA TL087 6 2 - I 4 V 330  V 2K 

  4. Nonlinear negative resistance Parallel Negative resistance 330  20K  7 7 + + mA 3 3 TL087 TL087 6 6 2 - 2 - 4 4 330  20K  V 2K  3.3K 

  5. Damped and undamped oscillation One negative resistance is connected to a LC tank circuit with some losses in the internal resistance Of the inductor L. Connecting the negative resistance, forces the oscillation to continue Oscillation will stop if this value is bigger than the negative resistance 330  5K  7 + RL 3 TL087 6 2 - 4 L 0.1 F 330  2K  Find: L = ? RL = ?

  6. V-I Characteristics of parallel NR Negative resistance - 2 Negative resistance - 1 Break points Critical adjustment of Resistance “R” stops Oscillation at these “Break points”. Then Oscillation can start from any point close to Origin and go either negative or positive Direction, which is chaotic. Parallel Negative resistance

  7. The state equations R C2 NR C1 G = 1/R g is a piecewise linear function defined by:

  8. Final circuit diagram with values oscilloscope CH2 CH1 330  5K  20K  30.8  + + TL087 TL087 - - 0.4 F 0.033 F 58 mH 330  20K  2K  3.3K 

  9. Oscilloscope traces X-Y Y-t

  10. Photograph of the fabricated circuit

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