Loose Leaf for Engineering Circuit Analysis Format: Loose-leaf
9th Edition
ISBN: 9781259989452
Author: Hayt
Publisher: Mcgraw Hill Publishers
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Chapter 17, Problem 6E
(a)
To determine
Find the value of the Fourier series coefficients
(b)
To determine
Sketch the function
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QUESTION 3
a) Determine the Fourier series ao, an and bn of the periodic signal, x(t), illustrated
in Figure Q3(a). Then, calculate the first 3 non-zero harmonics of the series.
b)
where wo =
-T
x(t) =
ii.
x(t)
an
A
Knowing that the values of A = 1 and T = 4, put x(t) under the form:
n=3
+
Σ an cos(nwot) + bn sin(nwot)
n=1
T
4
T
2
-A
Figure Q3(a): Periodic signal
c)
The signal x(t) as described in b) is applied to a circuit whose transfer function
is given by:
Y(s)
0.25s
H(s) = =
x(s) 1 +0.25s
where X(s) and Y(s) are the Laplace transfer functions of the input x(t) and the
output y(t) of the circuit, respectively.
i.
Determine the gain and the phase of the circuit.
Find then the output of the circuit y(t). Explain and reflect on the results.
4. Consider the following periodic waveform (t). It is desired to find its Fourier series representations, where a = 10, b = 2.
x(t)
b
...
a
-a
0
a
a
За
2a
t
Σ
2
2
(a) Find the complex-exponential representation. Specifically, find the coefficient x and x ( 0).
[Hine: e=(-1) for any integer n]
20
24
2 -jn +jna) - 2π
1-e
2m
η π
1. Find the continuous time Fourier series coefficients of the following continuous time
periodic signal. Sketch the magnitude and phase spectrums separately.
-2
x(1) 4
1
0
1
2
Fig. 1: A continuous time domain periodic signal.
Chapter 17 Solutions
Loose Leaf for Engineering Circuit Analysis Format: Loose-leaf
Ch. 17.1 - Let a third-harmonic voltage be added to the...Ch. 17.1 - A periodic waveform f(t) is described as follows:...Ch. 17.2 - Prob. 3PCh. 17.2 - Prob. 4PCh. 17.3 - Prob. 5PCh. 17.3 - Prob. 6PCh. 17.4 - Prob. 7PCh. 17.5 - Prob. 8PCh. 17.5 - Prob. 9PCh. 17.6 - Prob. 10P
Ch. 17.6 - Prob. 11PCh. 17.7 - Prob. 12PCh. 17.7 - Prob. 13PCh. 17.8 - Find (a) F5sin23t); (b) FAsin20t); (c)...Ch. 17.9 - Prob. 15PCh. 17.10 - Prob. 16PCh. 17 - Determine the fundamental frequency, fundamental...Ch. 17 - Plot multiple periods of the first, third, and...Ch. 17 - Calculate a0 for the following: (a) 4 sin 4t; (b)...Ch. 17 - Prob. 4ECh. 17 - Prob. 5ECh. 17 - Prob. 6ECh. 17 - Prob. 7ECh. 17 - With respect to the periodic waveform sketched in...Ch. 17 - Prob. 9ECh. 17 - Prob. 10ECh. 17 - A half-sinusoidal waveform is shown in Fig. 17.31,...Ch. 17 - Plot the line spectrum (limited to the six largest...Ch. 17 - Prob. 13ECh. 17 - Prob. 14ECh. 17 - Prob. 15ECh. 17 - Prob. 16ECh. 17 - Prob. 17ECh. 17 - Prob. 18ECh. 17 - The nonperiodic waveform g(t) is defined in Fig....Ch. 17 - Prob. 20ECh. 17 - Prob. 21ECh. 17 - Prob. 22ECh. 17 - Prob. 23ECh. 17 - Prob. 24ECh. 17 - Prob. 25ECh. 17 - Prob. 26ECh. 17 - Prob. 27ECh. 17 - Prob. 28ECh. 17 - Prob. 29ECh. 17 - Prob. 30ECh. 17 - Prob. 31ECh. 17 - Prob. 32ECh. 17 - Prob. 33ECh. 17 - Prob. 34ECh. 17 - Prob. 35ECh. 17 - Prob. 36ECh. 17 - Use the Fourier transform to obtain and plot the...Ch. 17 - Prob. 38ECh. 17 - Prob. 39ECh. 17 - Prob. 40ECh. 17 - For g(t) = 3etu(t), calculate (a) G(j); (b) ().Ch. 17 - Prob. 42ECh. 17 - Prob. 43ECh. 17 - Prob. 44ECh. 17 - Prob. 45ECh. 17 - Prob. 46ECh. 17 - Find F(j) if f(t) is given by (a) 2 cos 10t; (b)...Ch. 17 - Prob. 48ECh. 17 - Prob. 49ECh. 17 - Prob. 50ECh. 17 - Prob. 51ECh. 17 - Prob. 52ECh. 17 - Prob. 53ECh. 17 - If a system is described by transfer function h(t)...Ch. 17 - Prob. 55ECh. 17 - (a) Design a noninverting amplifier having a gain...Ch. 17 - Prob. 57ECh. 17 - Prob. 58ECh. 17 - Prob. 59ECh. 17 - Prob. 60ECh. 17 - Prob. 61ECh. 17 - Prob. 62ECh. 17 - Design an audio amplifier with gain of 10, using...
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