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Scholars Day 2006, Wednesday, April 12

Chaos in a Resistor-Inductor-Diode Circuit

The behavior of a sinusoidally driven Resistor-Inductor-Capacitor circuit is a well-known and an often referred-to example of: resonance, Lissajous figures and phase difference between the voltage across the various components of the circuit. The behavior of a sinusoidally driven series R-L-Diode Circuit is not as predictable as the classical RLC Circuit. The circuit is constructed using a rectifier diode, a variable inductor and resistor in series with a sinusoidal driver. National Instruments’ LabVIEW is used to collect data from the circuit in two ways, first at a rate of 250,000 samples/sec simultaneously in two channels. One channel measured the current, i, by measuring the voltage across the resistor and the other measured the derivative of the current, di/dt, by measuring the voltage across the inductor. In the second way, the data was taken once every cycle of the driver. Then the di/dt vs. i plot results in a Poincaré section. This circuit is driven at approximately 25 kHz which is over 400 times greater than the normal operating frequency (60Hz) of a rectifier diode. In this range, the circuit can exhibit chaotic behavior. The parameters that can be varied are frequency, DC offset and amplitude of the driver, the resistance and the inductance of the circuit and the temperature of the diode. To keep things simple, only the DC offset was varied. This circuit exhibits many characteristic behaviors such as period doubling, period 3 orbits and chaotic behavior. For chaotic behavior, the Poincaré section is a strange attractor. Preliminary determination of the correlation dimension of the strange attractor is 1.2. More measurements need to be taken to increase confidence in the value determined for the correlation dimension and several avenues of further research exist, such as varying the temperature of the diode to observe the sequence of behavior as the diode returns to room temperature after being cooled. The ultimate goal of this experiment is to determine the dynamic behavior of the diode.

Presenter: Joseph Murphy (Undergraduate Student)
Topic: Physics
Location: 101 Edwards
Time: 10 am (Session I)