V1 (t)v2 (t)TT242Problem 8.1It is known thatv1 (t) =do + bị sin wt + az cos 2wt + as cos dut +...Vm2VmCos 2ut -32Vmsinwt -cos 4ut -...155Verify this Fourier series expansion of a half-wave rectifier circuit by computing some of its Fouriercoefficients such as11 "/2Vm%3D(1)di =Jo2bị =1 7/2T. V sin wt dtVm7 (t) sin st dtT/22en (t) cos 2wt dt12V=. Vm sinwt cos 2wt dt =Jo3x2ei (t) cos dut dtT/2Vm sinwt cos dut dt =12Vm15я4=JoProblem 8.2Translate e (t) by a quarter period and show that:VmV2VmCos 2t-32Vcos dut +...15mty(t)+Cos wt +2- I-

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Verify this Fourier series expansion of a half-wave rectifier cireuit by computing some of its Fourier coefficients such as

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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Concept explainers

Fourier Series

Most of the incidents studied in the field of Engineering and Science as a function of time. For example, current and voltage are in the alternating current circuit. These occasional activities can be analyzed in the activity components (fundamental frequency and harmonics) through a process called Fourier analysis.

Question

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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