Wesley Thio Linear Circuits In linear circuits voltage is proportional to the current Linear circuit examples Tesla Coil RLC circuit Equipment Function Generator Oscilloscope Power supply ID: 673747
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Slide1
Chaos for the Home Electronics Lab
Wesley ThioSlide2
Linear CircuitsSlide3
In linear circuits, voltage is proportional to the current Slide4
Linear circuit examplesSlide5
Tesla CoilSlide6
RLC circuitSlide7
Equipment
Function Generator
Oscilloscope
Power supplySlide8
In nonlinear circuits, voltage is not proportional to currentSlide9Slide10
Van Der Pol Oscillator
Neon BulbSlide11
Neon Bulb nonlinearitySlide12
1927
1959
1983
Lorenz
Van Der Pol
ChuaSlide13
Step 1
: RLC circuit (parallel) Slide14
In a RLC circuit, there is
one stable equilibrium point at the originSlide15
Chua’s Nonlinear resistor
3 Equilibrium points (marked red) Slide16
Step 2: Nonlinear Resistor
Lorenz System
Rossler
System
Slide17
Step 3: Add a third capacitor or inductorSlide18
Chua’s CircuitSlide19
Phase Space: Take the voltage across the capacitors…
Voltage across capacitor
1
Voltage across capacitor 2
t
ime
t
imeSlide20
And plot them together!
Voltage across capacitor
1
Voltage across capacitor 2Slide21
3-D phase spaceSlide22
Period doubling bifurcation
Period-4
Period-1
Period-2
ChaosSlide23
Synchronization of Chua’s Circuit
Master
SlaveSlide24
Analog computation
Waterwheel behaving according to Lorenz equationsSlide25
Integrator
Adder
Op amp configurations
InverterSlide26
Analog computing example
Solve
Slide27
Lorenz circuit
Slide28
Bistability in a Hyperchaotic System with a Line Equilibrium (2014)
Coauthors: (C
. Li,
J.C Sprott, W
. Thio, )
Slide29
A New Piecewise Linear Hyperchaotic Circuit (2014)
Coauthors: (C
. Li,
J.C Sprott, W
. Thio, H. Zhu)
Slide30Slide31
What are the applications?Slide32
Secure communications
Master
SlaveSlide33
AMOS-WD06: Cockroach robot using chaos control Slide34
MemristorsSlide35
References
A Concise Guide to Chaotic Electronic Circuits (Buscarino, Fortuna, Frasca
,
Sciuto
2014)
A New Chaotic Jerk Circuit (Sprott 2011)A Practical Guide for Studying Chua’s Circuits (Kilic 2010)A simple circuit implementation of a Chaotic Lorenz System (Corron
2010) Chaos and Time Series Analysis (Sprott 2003) Chua’s Circuit Implementations: Yesterday, Today and tomorrow (Fortuna, Frasca, Xibilia 2009)
Development of Memristor Based Circuits (Lu, Fitch 2013)Elegant Chaos (Sprott 2010)Three Steps to Chaos - Part I: Evolution (Kennedy 1993)Three Steps to Chaos - Part II: A Chua’s Circuit Primer (Kennedy 1993
)