1. Consider the following signal: V(t) T The signal is a square wave of period T with a duty cycle of 2a (The square wave is at a high voltage for a fraction 2a of its period). 2πη =a₂ + Σ(ancos(² -t) + bn sin(: T a. Find the coefficients a, a, and b in the fourier expansion: 2πη T V(t) = n+1 aT T Vm Vm b. What are av, an and bn if we shift V(t) down by a voltage 2 ? V(t) -t)) T t c. Find the coefficients av, An and On in the expansion: Σπη V(t) = ) = av + Σ Ancos (² n=1 (Use the down-shifted version of V(t).) -t - On) Vm/2 t -Vm/2
1. Consider the following signal: V(t) T The signal is a square wave of period T with a duty cycle of 2a (The square wave is at a high voltage for a fraction 2a of its period). 2πη =a₂ + Σ(ancos(² -t) + bn sin(: T a. Find the coefficients a, a, and b in the fourier expansion: 2πη T V(t) = n+1 aT T Vm Vm b. What are av, an and bn if we shift V(t) down by a voltage 2 ? V(t) -t)) T t c. Find the coefficients av, An and On in the expansion: Σπη V(t) = ) = av + Σ Ancos (² n=1 (Use the down-shifted version of V(t).) -t - On) Vm/2 t -Vm/2
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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Transcribed Image Text:1. Consider the following signal:
V(t)
at
T
The signal is a square wave of period T with a duty cycle of 2a (The square wave is at
a high voltage for a fraction 2a of its period).
2πη
=a₂ + Σ(ancos(² -t) + bn sin(:
T
a. Find the coefficients a, a, and b in the fourier expansion:
2πη
T
V(t) =
n+1
V(t) =
aT
Vm
b. What are av, an and bn if we shift V(t) down by a voltage 2 ?
V(t)
T
Vm
-t))
c. Find the coefficients av, An and On in the expansion:
Σπη
) = av + Σ Ancos (² -t - On)
T
n=1
(Use the down-shifted version of V(t).)
d. Find the coefficients Cn in the expansion:
V(t) =
₂³(²)
t
7= ∞
(Use the down-shifted version of V(t).)
Vm/2
t
-Vm/2
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