EE 98: Fundamentals of Electrical Circuits - With Connect Access
6th Edition
ISBN: 9781259981807
Author: Alexander
Publisher: MCG
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Chapter 17, Problem 56P
The Fourier series trigonometric representation of a periodic function is
Find the exponential Fourier series representation of f(t).
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PSD
A certain signal f(t) has the following PSD (assume 12 load):
| Sƒ(w) = π[e¯\w\ + 8(w − 2) + +8(w + 2)]
(a) What is the mean power in the bandwidth w≤ 1 rad/sec?
(b) What is the mean power in the bandwidth 0.99 to 1.01 rad/sec?
(c) What is the mean power in the bandwidth 1.99 to 2.01 rad/sec?
(d) What is the total mean power in (t)?
Pav=
+
2T
SfLw) dw
- SALW)
An AM modulation waveform signal:-
p(t)=(8+4 cos 1000πt + 4 cos 2000πt) cos 10000nt
(a) Sketch the amplitude spectrum of p(t).
(b) Find total power, sideband power and power efficiency.
(c) Find the average power containing of each sideband.
Can you rewrite the solution because it is
unclear?
AM
(+) = 8(1+ 0.5 cos 1000kt +0.5 ros 2000ks)
=
cos 10000 πt.
8 cos wat + 4 cos wit + 4 cos Wat coswet.
-Jet
jooort
J11000 t
= 4 e
jqooort jgoort
+4e
+ e
+e
j 12000rt.
12000 kt
+
e
+e
jooxt
igoo t
te
(w) = 8ES(W- 100007) + 8IS (W-10000)
USB
Chapter 17 Solutions
EE 98: Fundamentals of Electrical Circuits - With Connect Access
Ch. 17.2 - Find the Fourier series of the square wave in Fig....Ch. 17.2 - Determine the Fourier series of the sawtooth...Ch. 17.3 - Prob. 3PPCh. 17.3 - Find the Fourier series expansion of the function...Ch. 17.3 - Prob. 5PPCh. 17.4 - Prob. 6PPCh. 17.4 - If the input voltage in the circuit of Fig. 17.24...Ch. 17.5 - The voltage and current at the terminals of a...Ch. 17.5 - Find the rms value of the periodic current i(t) =...Ch. 17.6 - Obtain the complex Fourier series of the function...
Ch. 17.6 - Obtain the complex Fourier series expansion of...Ch. 17.7 - Prob. 12PPCh. 17.8 - Rework Example 17.14 if the low-pass filter is...Ch. 17 - Which of the following cannot be a Fourier series?...Ch. 17 - If ft=t,0t,ft+n=ft, the value of 0 is (a) 1 (b) 2...Ch. 17 - Which of the following are even functions? (a) t +...Ch. 17 - Prob. 4RQCh. 17 - Prob. 5RQCh. 17 - If f(t) = 10 + 8 cos t + 4 cos 3t + 2 cos 5t + ,...Ch. 17 - Prob. 7RQCh. 17 - The plot of |cn| versus n0 is called: (a) complex...Ch. 17 - Prob. 9RQCh. 17 - Prob. 10RQCh. 17 - Evaluate each of the following functions and see...Ch. 17 - Using MATLAB, synthesize the periodic waveform for...Ch. 17 - Given that Fourier coefficients a0, an, and bn of...Ch. 17 - Find the Fourier series expansion of the backward...Ch. 17 - Prob. 5PCh. 17 - Find the trigonometric Fourier series for f t =...Ch. 17 - Determine the Fourier series of the periodic...Ch. 17 - Using Fig. 17.51, design a problem to help other...Ch. 17 - Determine the Fourier coefficients an and bn of...Ch. 17 - Find the exponential Fourier series for the...Ch. 17 - Obtain the exponential Fourier series for the...Ch. 17 - Prob. 12PCh. 17 - Prob. 13PCh. 17 - Find the quadrature (cosine and sine) form of the...Ch. 17 - Express the Fourier series...Ch. 17 - The waveform in Fig. 17.55(a) has the following...Ch. 17 - Prob. 17PCh. 17 - Prob. 18PCh. 17 - Obtain the Fourier series for the periodic...Ch. 17 - Prob. 20PCh. 17 - Prob. 21PCh. 17 - Calculate the Fourier coefficients for the...Ch. 17 - Using Fig. 17.61, design a problem to help other...Ch. 17 - Prob. 24PCh. 17 - Determine the Fourier series representation of the...Ch. 17 - Find the Fourier series representation of the...Ch. 17 - For the waveform shown in Fig. 17.65 below, (a)...Ch. 17 - Obtain the trigonometric Fourier series for the...Ch. 17 - Prob. 29PCh. 17 - Prob. 30PCh. 17 - Prob. 31PCh. 17 - Prob. 32PCh. 17 - Prob. 33PCh. 17 - Prob. 34PCh. 17 - Prob. 35PCh. 17 - Prob. 36PCh. 17 - If the periodic current waveform in Fig. 17.73(a)...Ch. 17 - Prob. 38PCh. 17 - Prob. 39PCh. 17 - The full-wave rectified sinusoidal voltage in Fig....Ch. 17 - Prob. 42PCh. 17 - The voltage across the terminals of a circuit is...Ch. 17 - Prob. 44PCh. 17 - A series RLC circuit has R = 10 , L = 2 mH, and C...Ch. 17 - Prob. 46PCh. 17 - Prob. 47PCh. 17 - Prob. 48PCh. 17 - Prob. 49PCh. 17 - Prob. 50PCh. 17 - Prob. 51PCh. 17 - Prob. 52PCh. 17 - Prob. 53PCh. 17 - Find the exponential Fourier series for the...Ch. 17 - Obtain the exponential Fourier series expansion of...Ch. 17 - The Fourier series trigonometric representation of...Ch. 17 - Prob. 57PCh. 17 - Find the exponential Fourier series of a function...Ch. 17 - Prob. 59PCh. 17 - Obtain the complex Fourier coefficients of the...Ch. 17 - The spectra of the Fourier series of a function...Ch. 17 - Prob. 62PCh. 17 - Plot the amplitude spectrum for the signal f2(t)...Ch. 17 - Prob. 64PCh. 17 - Prob. 65PCh. 17 - Prob. 66PCh. 17 - Prob. 67PCh. 17 - Prob. 68PCh. 17 - Prob. 69PCh. 17 - Design a problem to help other students better...Ch. 17 - Prob. 71PCh. 17 - Prob. 72PCh. 17 - Prob. 73PCh. 17 - Prob. 74PCh. 17 - Prob. 75PCh. 17 - Prob. 76PCh. 17 - Prob. 77CPCh. 17 - Prob. 78CPCh. 17 - Consider the full-wave rectified sinusoidal...Ch. 17 - Prob. 82CP
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- Can you rewrite the solution because it is unclear? AM (+) = 8(1+0.5 cos 1000kt +0.5 ros 2000 thts) = cos 10000 πt. 8 cos wat + 4 cos wit + 4 cos Wat coswet. J4000 t j11000rt $14+) = 45 jqooort +4e + e + e j 12000rt. 12000 kt + e +e +e Le jsoort -; goon t te +e Dcw> = 885(W- 100007) + 8 IS (W-10000) - USBarrow_forwardCan you rewrite the solution because it is unclear? Q2 AM ①(+) = 8 (1+0.5 cos 1000πt +0.5 ros 2000kt) $4+) = 45 = *cos 10000 πt. 8 cos wat + 4 cosat + 4 cos Wat coswet. j1000016 +4e -j10000πt j11000Rt j gooort -j 9000 πt + e +e j sooort te +e J11000 t + e te j 12000rt. -J12000 kt + с = 8th S(W- 100007) + 8 IS (W-10000) <&(w) = USB -5-5 -4-5-4 b) Pc 2² = 64 PSB = 42 + 4 2 Pt Pc+ PSB = y = Pe c) Puss = PLSB = = 32 4² = 8 w 32+ 8 = × 100% = 140 (1)³×2×2 31 = 20% x 2 = 3w 302 USB 4.5 5 5.6 6 ms Ac = 4 mi = 0.5 mz Ac = 4 ५ M2 = =0.5arrow_forwardA. Draw the waveform for the following binary sequence using Bipolar RZ, Bipolar NRZ, and Manchester code. Data sequence= (00110100) B. In a binary PCM system, the output signal-to-quantization ratio is to be hold to a minimum of 50 dB. If the message is a single tone with fm-5 kHz. Determine: 1) The number of required levels, and the corresponding output signal-to-quantizing noise ratio. 2) Minimum required system bandwidth.arrow_forward
- Find Io using Mesh analysisarrow_forwardFM station of 100 MHz carrier frequency modulated by a 20 kHz sinusoid with an amplitude of 10 volt, so that the peak frequency deviation is 25 kHz determine: 1) The BW of the FM signal. 2) The approximated BW if the modulating signal amplitude is increased to 50 volt. 3) The approximated BW if the modulating signal frequency is increased by 70%. 4) The amplitude of the modulating signal if the BW is 65 kHz.arrow_forwardAn FDM is used to multiplex two groups of signals using AM-SSB, the first group contains 25 speech signals, each has maximum frequency of 4 kHz, the second group contains 15 music signals, each has maximum frequency of 10 kHz. A guard bandwidth of 500 Hz is used bety each two signals and before the first one. 1. Find the BWmultiplexing 2. Find the BWtransmission if the multiplexing signal is modulated using AM-DSB-LC.arrow_forward
- An FM signal with 75 kHz deviation, has an input signal-to-noise ratio of 18 dB, with a modulating frequency of 15 kHz. 1) Find SNRO at demodulator o/p. 2) Find SNRO at demodulator o/p if AM is used with m=0.3. 3) Compare the performance in case 1) and 2).. Hint: for single tone AM-DSB-LC, SNR₁ = (2m²) (4)arrow_forwardFind Va and Vb using Nodal analysisarrow_forwardCalculate the nodal voltage in the circuitarrow_forward
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