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 Z₀, P₀, and P₁ are important parameteres of our transfer function.

Were we to graph it against frequency:

So, we determined the values of R₁, R₂, R₃, C₁, and C₂ so that Zo occurs at 0.1Hz (close to the estimated natural frequency of the levitated plate), Po=50Hz and P₁=200Hz Specifically, R₁=R₃13kΩ, R₂=1.5kΩ, C₁=2.2μF, and C₂=61nF. We did not have a 61nF capacitor, so instead we used a 47nF one (slightly changing our P₁ 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 R₁=13kΩ, R₂=4.3kΩ, R₃=R₄=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.