Op. amps., quartz resonators, and noise: Find Circuit Characteristics from this Fit


		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

	PHYS 381La HOME
	Classes Page

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

Results

Now we analyze the tuning fork's characteristics

We had a voltage divider in the circuit. Multiplying by this constant changes the card's applied voltage to the voltage the circuit receives.

The maximum is determined by both the gain resistor and the power we apply to the circuit. We need to divide our maximum value by the input power.
This input power is determined by taking the expectation of y² (the power as a function of voltage is y²) across the uniform voltage range (V_min,V_max). A uniform distribution has a probability formula given by p(V)=1/V_max − V_min.

$(σ^2) _V = 20/2^16 (∫_Vmin^Vmaxy^2/(Vmax - Vmin) y)/.{Vmax→1, Vmin→ -1}//N$