Calculation 1: Comparing dBm to mW
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,
Calculation 2: Using Data to Find Power VariationThe 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
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:
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:
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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