Yale University

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

Introduction
Johnson Noise
Macroscopic Derivation
Microscopic Derivation
Install and Test the Optical Amplifier
Install the Tuning Fork
Welcome to LabView
Tune out the Package Capacitance
Gather Data
Load the Driven Circuit Data
Fit the Driven Circuit Data
Find Circuit Characteristics from this Fit
Analyze the Undriven Circuit from Characteristics
Final Results
References
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Yale University

Andrew Pariser, December 2005
modified S.M., January 2006

© 2006 Yale University, New Haven, Connecticut 06520

Tuning Fork Setup

We are ultimately going to measure the Johnson Noise that comes from the internal resistance of a quartz tuning fork. These devices run at 215 (32768) Hertz. Many of your watches contain these circuit elements, which function to count time.

Take the standard amplifier circuit and replace R1 with the tuning fork and R2 with a very large resistor (around 5 MΩ). Observe changes in the amplitude of the output signal with changes in this signal's frequency. This effect is due to the fact that the tuning fork is a resonance device.

The tuning fork can be modeled as an RLC circuit with an impedance that varies with frequency. Additionally, the tuning fork has a package capacitance (due to being encased inside a metal cylinder) which we will investigate later. An appropriate tuning fork model could be:

circuit schema

Now turn the function generator's output voltage as low as possible. Find the resonance frequency of the tuning fork (at 215 Hertz) by sweeping frequencies on the input signal. Try and approximate the gain of the circuit both on and off resonance. Good measurements here will aid in later calculations.

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