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| === Noise Spectrum == | === Noise Spectrum === |
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| == Displacement sensitivity == | === Displacement sensitivity === If we assume that the transfer function between the voltage output of the Hall-sensor and the magnetic field strength is frequency independent, we can easily obtain the corresponding noise spectrum for the field strength, which in turn gives the displacement sensitivity of the hall sensor. |
We measured the voltage fluctuation of the Hall-effect sensor, from which we infer the displacement sensitivity given the suspended magnet we used. The circuit for this experiment is shown in the following figure, which is a simple high-pass filtering of the sensor output.
attachment:hall_sensor_mea_config.JPG
The corresponding transfer function of the filter is shown below. It has a corner frequency around 0.1 Hz.
attachment:high_pass_TF.JPG
Noise Spectrum
The raw data from the spectrum analyzer by measuring different frequency bands are shown in the figure below.
attachment:Vout_rawdata.JPG
By normalizing with respect to the high-pass transfer function and piecing different frequency bands together, we obtain the entire spectrum from 0.005 Hz to 1600 Hz of the voltage fluctuation in the Hall-effect sensor. As we can see that the noise spectrum is almost flat from low frequencies to high frequencies.
attachment:Vout_normalized_spectrum.JPG
Displacement sensitivity
If we assume that the transfer function between the voltage output of the Hall-sensor and the magnetic field strength is frequency independent, we can easily obtain the corresponding noise spectrum for the field strength, which in turn gives the displacement sensitivity of the hall sensor.