Mixing Two Frequencies
A mixer is an analog multiplier; it approximately multiplies the signals that enter it. The mixer is what allows the sine wave applied by the synthesizer on the oscilloscope to be seen. In this case, two opposite signals are summed and then the result is multiplied by a third signal in the mixer. A sin^2 function is created, and this function produces a signal which one can amplify and show on the oscilloscope.
Two equal but opposite signals will be sent into the mixer so that the ideal output is zero. Then any output can be attributed to the movement of the mass due to ground vibrations. And the amplitude of the output waves will let one know how much the ground has moved up or down.
Where the mixer multiplies 2 such functions:
A1 is the known amplitude from the original sythesizer signal; A2 is the amplitude output from the accelerometer that we want to know; x is the output from the mixer; tc is the time constant of the filter.
Then the signal is sent through a low-pass filter. This filter averages the signal; thus, an integration is done:
The sine portion of this equation is oscillatory and high frequency, so it can be ignored.
Knowing A1 and x (the output from the mixer), one can determine the amplitude of A2, the amplitude of the signal coming from the capacitor.
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