demonstration of chaos
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
Circuit Diagram
+
-
+
-
30.8
58 mH
330
330
2K 3.3K
20K
20K
5K
0.4 F 0.033 F
1 2 3
TL087TL087
Negative resistance - 1
Negative resistance - 2
LC tankcircuit
Critical controlFor CHAOS
Nonlinear negative resistance
+
-
330
330
2K
3
26
7
TL087mA
V
4
+
-
20K
20K
3.3K
3
26
7
TL087
4
Parallel Negative resistance
Damped and undamped oscillation
+
-
330
330
2K
3
26
7
TL087
4
5K
0.1 F
Find: L = ? RL = ?
RL
L
One negative resistance is connected to a LC tank circuit with some losses in the internal resistanceOf the inductor L. Connecting the negative resistance, forces the oscillation to continue
Oscillation will stop if this value is bigger than the negative resistance
V-I Characteristics of parallel NR
Negative resistance - 1
Negative resistance - 2
Parallel Negative resistance
Break points Critical adjustment of Resistance “R” stops Oscillation at these “Break points”. Then Oscillation can start from any point close toOrigin and go either negative or positiveDirection, which is chaotic.
The state equations
€
C1dvc1dt=G(vc2 − vc1) − g(vc1)
C2dvc2dt
=G(vc1 − vc2) + iL
LdiLdt= −vc2
G = 1/Rg is a piecewise linear function defined by:
€
g(vR) = m0vR +1
2m1 −m0( ) vR + Bp − vR − Bp[ ]
R
C2 C1 NR
Final circuit diagram with values
+
-
+
-
30.8
58 mH
330
330
2K 3.3K
20K
20K
5K
0.4 F 0.033 F
CH1 CH2
oscilloscope
TL087TL087
Oscilloscope traces
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
-4
-3
-2
-1
0
1
2
3
4
5
-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8
-4
-3
-2
-1
0
1
2
3
4
5
-0.03 -0.02 -0.01 0 0.01 0.02 0.03
Y-t X-Y