CHAOS IN A DIODE: PERIOD DOUBLING AND CHAOTIC BEHAVIOR IN A DIODE DRIVEN CIRCUIT

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CHAOS IN A DIODE PERIOD DOUBLING AND CHAOTIC
BEHAVIOR IN A DIODE DRIVEN CIRCUIT Maxwell
Mikel-Stites University of Rochester, Rochester,
NY, 14627
Abstract
The purpose of this experiment was to examine
period doubling and chaotic behaviour in a
diode-driven circuit. This allows us to learn
more about the physics behind the diode and its
interaction with the circuit, as well as the
manifestation of chaos in a system as a result of
increasing bifurcation in the diode voltages. It
was possible to observe this type of behaviour
clearly, even with varying data quality even in
the worst case, the bifurcations leading into
chaos were clearly defined and were relatively
easy to examine.
Physical Characteristics

• The Diode Itself
• Constructed out of a combination of a p and n
  type semiconductors
• Diode not perfect causes finite time for current
  reversal.
• Causes forward and reverse bias to alternate
• Forward diode acts as a resistor
• Reverse causes diode to act as a capacitor
• The interactions between these parameters with
  increasing voltage causes the signal to bifurcate
  as it is read from the diode.

The below photos detail the setup for the entire
lab and the provided equipment. For the
experiment, the inductor was set to approximately
10mH, since it was the lowest inductance value
possible with the given inductor.
To the left is the Lissajous graph of the third
bifurcation, since the diode voltage graph is
nearly indistinguishable from the second
bifurcation in many cases.
1) Diode 2)2400 ohms 3)185 ohms 4)590 ohms
Conclusion
Overall, the data gathered accurately
demonstrates only the progress of increasing
bifurcations leading to chaos, and also showed
that the inductance of the system also greatly
affects the voltages at which the bifurcations
are observed. In this way, by increasing the
inductance value, one could cause the bifurcation
pattern to emerge earlier and earlier. Similarly,
one could decrease the inductance to cause
bifurcations to appear at later intervals. In
order to improve the lab, it would be beneficial
to obtain better equipment, such as more reliable
inductors and a digital oscilloscope.

• Measurable Quantities
• Feigenbaums ConstantThe ratio of the difference
  between the bifurcations as the number of
  bifurcations goes to infinity, it approaches
  4.6669.
• Driving voltage
• Peak to peak diode voltage
• Frequency
• Inductance

Special Thanks To
Chris Osborn, for the code involved in producing
the chaos model and Dan Richman and Chris Osborn
for their assistance in gathering data.