PHYS 381/504: Op. amps., quartz resonators, and noise

Analyzing the Undriven Circuit

We determine that there is some external noise source that keeps the background noise level at −125 dB.  We add this in quadrature to the Johnson Noise coming from our tuning fork, and define this result as our noiseFunction.
The Johnson Noise of the tuning fork is given by LC(f) where LC( f ) is the fitted Lorentz Curve that matches the resonance peak of this particular tuning fork with its specified RLC values, k is Boltzmann's constant, T is the temperature of the experiment and R the tuning fork's equivalent resistor.

Read in the undriven data and zoom in on the peak.

First we show that there is a whole lot of noise across the whole frequency band

We prune out all the data outside a small window around our regular resonance peak

Now we show how successfully the noise prediction matches the data:

Determine the maximum predicted value of our noise output

We then find the height of our data at this maximum, and observe that the actual measured noise value is less than the predicted.

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