Calculation 1: Comparing dBm to mW


Formula 1:

where P1 = 1mW and P2 = PmW

Substituting these values and taking the derivative with respect to PmW:

Formula for taking the derivative of a log:

In this case,


Formula 2:




Calculation 2: Using Data to Find Power Variation

The amplitude setting of the synthesizer was put at:.

Using Formula 1, one finds that

Formula 3: Plugging the above value for into Formula 2 (the slope formula), one finds that

(this value was known because and total volts = )

Plugging the value for into Formula 3, one finds that

This is the power variation of the synthesizer.




Calculation 3: Amplitude Fluctuation of Synthesizer Signal


Formula 4:

In this case:


Plugging these values into Formula 4, one finds that V = .750732 Volts

To find the fluctuation in amplitude of the signal, one takes the derivative of Formula 4 with respect to Volts:


Formula 5:

Plugging the known quantities for V, R, and (recall that ) into Formula 5, one finds:

The amplitude variation of the synthesizer (its noise) is equivalent to the percent change in voltage. This is given by:

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This value is used in a later calculation to find the acceptable offset distance of the plate gaps such that nanometer motion can still be read with this synthesizer noise.





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