A switched power supply produces a periodic voltage of period that is for the first…

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Fourier analysis and integral transforms · Fourier analysis and integral transforms

Mathematical Methods for Physics, Ch Fourier series and periodic decomposition

Problem

A switched power supply produces a periodic voltage

g(x)

of period

L

that is

V_0 = 8.00\,\mathrm{V}

for the first half of each period and zero for the second half:

g(x) = \begin{cases} 8.00\,\mathrm{V}, & 0 < x < L/2 \\ 0, & -L/2 < x < 0 \end{cases}, \qquad g(x+L) = g(x).

The square wave of amplitude

A

(equal to

A

(0,L/2)

and

-A

(-L/2,0)

) has known coefficients

b_n = 4A/(n\pi)

for odd

n

, zero otherwise, and

a_n=0

for all

n

. ((a)) Find

a_0

. ((b)) Find

b_1

. ((c)) Find

b_3

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