Stochastic Resonance in a Hysteretic Circuit (Jr IS guest blog by Gabe Dale-Gau)

This project uses an electronic circuit to demonstrate something called stochastic resonance. Stochastic resonance (SR) is present many places in nature–from dictating the timing of ice ages to aiding in fish hearing. So, what is it? SR is simply when a random noise signal serves to boost the strength of another, cleaner signal. Audio is a good way to think about this. Imagine you are listening to a song, but the volume is so low that you cannot hear it. Then you add another speaker playing random noise. You start to turn up the noise, and at a certain point, you start to hear the song. This is pretty strange, and quite counterintuitive. Usually adding noise drowns out other sound, so how could random noise serve to boost a sound? This project seeks to examine that question by observing stochastic resonance in a circuit. Every signal running through the wires I used could easily be sent to a speaker and played aloud, as all of the frequencies involved are within the auditory range.

The circuit used here is called a Schmitt trigger. Its purpose here is to allow a signal to pass through if it is strong enough, but block weaker signals. The point at which the signal is strong enough to pass through the Schmitt trigger is called the threshold voltage. One other side effect of the Schmitt trigger is that the output signal will be a square wave rather than a sine wave. I ran a strong signal through at first to confirm that the circuit was operating as it should, then I ran a weak signal through and saw that the output disappeared. At this point, we have a weak signal entering the circuit, but no output, just like when you were playing a song, but it was too weak of a signal for your ear to register. So, I then added random noise to my signal. The random noise makes the input sign wave cover a larger range of voltages, puncturing the threshold voltage, and once again allowing the circuit to output a square wave. This is stochastic resonance in a hysteretic circuit.

Using this circuit I was able to determine the best possible noise volume to cause SR in the given parameters. The circuit itself could be used to make a hearing aid that listens for cleaner weak signals and filters out excess noise. This circuit is also interesting as a metaphor for other things in nature, as it behaves similarly to the human neuron.

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