0195136047.pdf

PROBLEMS 181

3.1.19Determine the Fourier series for the periodic wave-

forms given in Figure P3.1.19.

3.1.20Find the exponential form of the Fourier series of

the periodic signal given in Figure P3.1.20. Also

determine the resulting series ifT= 2 τ.

*3.1.21The first four harmonics in the Fourier series of a
current waveform given by
i(t)=
2 Im
π

sin

2 πt

T

−

Im

π

sin

4 πt

T

+

2 Im

3 π

sin

6 πt

T

−

Im

2 π

sin

8 πt

T

whereIm = 15 mA andT = 1 ms. If such

a current is applied to a parallel combination of

R = 5kandC = 0. 1 μF, determine the

output waveform of the voltagevO(t) across the

load terminals.

3.1.22The full-wave rectified waveform, approximated

by the first three terms of its Fourier series, is given

byv(ωt)=Vmsin(ωt/ 2 ), for 0≤ωt≤ 2 π, and

v(t)=

2 Vm

π

−

4 Vm

3 π

cosωt+

4 Vm

15 π

cos 2ωt

whereVm=100 V andω= 2 π×120 rad/s. Ifv(t)

is applied to the circuit shown in Figure P3.1.22,

find the output voltagevO(t).

3.2.1Determinei(t) in the circuit of Figure P3.2.1 and

sketch it.

*3.2.2Obtaini(t) in the circuit of Figure P3.2.2 and

sketch it.

−T −ττ 0 T

0

v(t)

A

(a)

−T −τ

τ T

t

t

i(t)

A

−A

(b)

Figure P3.1.19

t

i(t)

A

−T −τ τ T

Half-cycle of cosine

0

Figure P3.1.20