When finding a relationship between v_{ag} and v_{hall1}, remember that the relationship depends on the value of V_{DC} as given in the MATLAB model. Your answer must account for this. In other words for the relationship v_{ag}=f(V_{DC},v_{hall1}), find the function f.
Post-lab
The Fourier series of a 2π-periodic function f(x) that is integrable on [-π,π], is given by
where
and
To relate v_{s} to V_{dc}, you need to find the fundamental component of the Fourier series of the functions v_{as}, v_{bs} and v_{cs}. The fundamental component is the component with the lowest frequency, specifically
To solve for the coefficients a_{0}, a_{1} and b_{1} from the equations above, the integral must be broken down into a sum of integrals over continuous regions.
φ_{v} is the angle between V_{as} and e_{as}. To find this angle, compare zero-crossings near the middle of both curves. If you triggered the oscilloscope on channel 1, then V_{as} should be crossing zero with a rising edge in the exact middle of the plotted time. e_{as} will cross zero with a rising edge some small time after this point. Measure this difference in time and convert it from seconds to degrees or radians by dividing by the time in one period and multiplying by 360 (for degrees) or 2π (for radians).