Today, we analyzed the transfer function of our circuit:
Specifically, Vout/Vin= -((R_1 〖+R〗_2)R_3)/(R_1 R_2 ) {((s+Z_o)P_1)/((s+P_o)(s+P_1))} where Z_{0}, P_{0}, and P_{1 }are important parameteres of our transfer function.
Were we to graph it against frequency:
So, we determined the values of R_{1}, R_{2}, R_{3}, C_{1}, and C_{2 }so that Zo occurs at 0.1Hz (close to the estimated natural frequency of the levitated plate), Po=50Hz and P_{1}=200Hz Specifically, R_{1}=R_{3}13kΩ, R_{2}=1.5kΩ, C_{1}=2.2μF, and C_{2}=61nF. We did not have a 61nF capacitor, so instead we used a 47nF one (slightly changing our P_{1} point).
Our Hall-effect sensors give a constant 2.5V when no magnetic field is present. Therefore, we need to include an offset of 2.5V. We will achieve that with a voltage divider with R_{1}=13kΩ, R_{2}=4.3kΩ, R_{3}=R_{4}=2.2kΩ.
In the afternoon, I wired up 7 PCB boards for the Hall-effect sensors circuits. These include the -2.5 offset and the high-pass filter. We used the spectrum analyser to see whether the transfer function of our circuits are as predicted; the experimental and theoretical data agreed. |