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EXAMPLE 25.1 Determine which components of the Fourier series
are present in the waveforms of Fig. 25.11.
FIG. 25.11
Example 25.1.
Solutions:
a. The waveform has a net area above the horizontal axis and therefore
will have a positive dc term A0. The waveform has axis symmetry, resulting in only cosine terms
in the expansion.
The waveform has half-cycle symmetry, resulting in only even
terms in the cosine series.
b. The waveform has the same area above and below the horizontal
axis within each period, resulting in A0 � 0.
The waveform has point symmetry, resulting in only sine terms
in the expansion.
EXAMPLE 25.2 Write the Fourier series expansion for the waveforms
of Fig. 25.12.
20 V
0
v
0
(a)
(a)
(b)
e
10 V
i
5 mA
T 2
–5 mA
T 2
T
T
t
FIG. 25.12
Example 25.2.
t
t
i
5 mA
20 V
0
(b)
0
(c)
v
FOURIER SERIES ⏐⏐⏐ 1129
Sinusoidal
waveform
t
t
V av = 8 V