Consider the following circuit for π
π
1 = π
π
2 = 2ππΞ© and πΆπΆ = 125ππππ:
a) (25pts) Derive the Fourier series represtation of the source π£π£π π (π‘π‘) by using complex exponentials
a. Plot π£π£π π (π‘π‘) in MATLAB by using 100 harmonics.
b. Plot the magnitude spectrum of π£π£π π (π‘π‘) from -10000ππ to 10000ππ
b) (25pts) Derive the Fourier series representation of the source π£π£ππππππ(π‘π‘) by using complex exponentials
a. Plot π£π£ππππππ (π‘π‘) in MATLAB by using 100 harmonics.
b. Plot the magnitude spectrum of π£π£ππππππ(π‘π‘) from -10000ππ to 10000ππ
c) (25pts) Determine the transfer function in the phasor domain π»π»(ππ) = ππππππππ
πππ π
where ππππππππ and πππ π are the
phasors for π£π£ππππππ (π‘π‘) and π£π£π π (π‘π‘) (Hint: page 213 in the book)
d) (25pts) By comparing the magnitude spectrum of π£π£π π (π‘π‘) and π£π£ππππππ (π‘π‘), interpret the behavour of this circuit.
Is it a high-pass filter (i.e., a filter that filters of sinusoids that has low frequencies). Why? Why not?
