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. This in turn gives the displacement sensitivity of the hall sensor using the calibration results we obtained before.

The suspended magnet we will use in the prototype is half inch in diameter and 1/8 inch in thickness. We performed a single measurement of its magnetic field strength along the axial axis with a similar setup of the calibration measurement.