2 (t) ST ST Problem 8.1 It is known that n(t) - a + bi sin wt + az cos 2ut + as cos dut + ...
2 (t) ST ST Problem 8.1 It is known that n(t) - a + bi sin wt + az cos 2ut + as cos dut + ...
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Part (b)

Transcribed Image Text:V1 (t)
v2 (t)
T
T
2
4
2
Problem 8.1
It is known that
v1 (t) =
do + bị sin wt + az cos 2wt + as cos dut +...
Vm
2Vm
Cos 2ut -
3
2Vm
sinwt -
cos 4ut -...
155
Verify this Fourier series expansion of a half-wave rectifier circuit by computing some of its Fourier
coefficients such as
1
1 "/2
Vm
%3D
(1)
di =
Jo
2
bị =
1 7/2
T. V sin wt dt
Vm
7 (t) sin st dt
T/2
2
en (t) cos 2wt dt
1
2V
=. Vm sinwt cos 2wt dt =
Jo
3x
2
ei (t) cos dut dt
T/2
Vm sinwt cos dut dt =
1
2Vm
15я
4
=
Jo
Problem 8.2
Translate e (t) by a quarter period and show that:
Vm
V
2Vm
Cos 2t-
3
2V
cos dut +...
15m
ty(t)
+
Cos wt +
2
- I-
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