Fundamentals of Electric Circuits
6th Edition
ISBN: 9780078028229
Author: Charles K Alexander, Matthew Sadiku
Publisher: McGraw-Hill Education
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Textbook Question
Chapter 14, Problem 61P
Find the transfer function for each of the active filters in Fig. 14.90.
Figure 14.90
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A plane wave propagating in the +z direction in medium 1 is normally incident to medium 2 located at
the z=0 plane as below. Both mediums are general, characterized by ( ε i, Mi, Ơi ).
tot
=
[ ει μη σ]
[ε, μη σε ]
Ex
Ex
tot
E₁₂ (z) = Ee
Ex
z=0
From conservation of energy: P₁AV'(z=0) + Piav'(z=0) = P2av²(z=0).
Using the above show for lossless media that: ( 1 - ||²) = (1/M2 )|T|² .
A plane wave propagating in the +z direction in medium 1 is normally incident to medium 2 located at
the z=0 plane as below. Both mediums are general, characterized by ( ε i, Hi, σ¡ ).
[ ει μη σ]
Ex
[ ει μη ση ]
Ex
tot
E₁₂ (z) = E'₁e¹²
-122
E(z) = Ee+ E₁₁₁²
E₁x
z=0
1. Specify the electric field reflection coefficient г and transmission coefficient T:
E
ΓΔ
E
E
TA
EL
2. Show that T=1+г. Can the transmitted electric field amplitude in region 2 be LARGER than the
incident electric field amplitude?
3. Determine expressions for P₁AV'(z), PIAV'(z) and P2AV'(z) (note the sign for the reflected power
direction should be (-z).
Chapter 14 Solutions
Fundamentals of Electric Circuits
Ch. 14.2 - Obtain the transfer function VoVs of the RL...Ch. 14.2 - Prob. 2PPCh. 14.4 - Draw the Bode plots for the transfer function...Ch. 14.4 - Sketch the Bode plots for H()=50j(j+4)(j+10)2Ch. 14.4 - Construct the Bode plots for H(s)=10s(s2+80s+400)Ch. 14.4 - Obtain the transfer function H() corresponding to...Ch. 14.5 - A series-connected circuit has R = 4 and L = 25...Ch. 14.6 - A parallel resonant circuit has R = 100 k, L = 50...Ch. 14.6 - Calculate the resonant frequency of the circuit in...Ch. 14.7 - For the circuit in Fig. 14.40, obtain the transfer...
Ch. 14.7 - Design a band-pass filter of the form in Fig....Ch. 14.8 - Design a high-pass filter with a high-frequency...Ch. 14.8 - Design a notch filter based on Fig. 14.47 for 0 =...Ch. 14.9 - Prob. 14PPCh. 14.10 - Obtain the frequency response of the circuit in...Ch. 14.10 - Consider the network in Fig. 14.57. Use PSpice to...Ch. 14.12 - For an FM radio receiver, the incoming wave is in...Ch. 14.12 - Repeat Example 14.18 for band-pass filter BP6....Ch. 14.12 - If each speaker in Fig. 14.66 has an 8- resistance...Ch. 14 - Prob. 1RQCh. 14 - On the Bode magnitude plot, the slope of 1/5+j2...Ch. 14 - On the Bode phase plot for 0.5 50, the slope of...Ch. 14 - How much inductance is needed to resonate at 5 kHz...Ch. 14 - The difference between the half-power frequencies...Ch. 14 - Prob. 6RQCh. 14 - Prob. 7RQCh. 14 - Prob. 8RQCh. 14 - What kind of filter can be used to select a signal...Ch. 14 - A voltage source supplies a signal of constant...Ch. 14 - Find the transfer function Io/Ii of the RL circuit...Ch. 14 - Using Fig. 14.69, design a problem to help other...Ch. 14 - For the circuit shown in Fig. 14.70, find H(s) =...Ch. 14 - Find the transfer function H(s) = Vo/Vi of the...Ch. 14 - For the circuit shown in Fig. 14.72, find H(s) =...Ch. 14 - For the circuit shown in Fig. 14.73, find H(s) =...Ch. 14 - Calculate |H()| if HdB equals (a) 0.1 dB (b) 5 dB...Ch. 14 - Design a problem to help other students calculate...Ch. 14 - A ladder network has a voltage gain of...Ch. 14 - Design a problem to help other students better...Ch. 14 - Sketch the Bode plots for H()=0.2(10+j)j(2+j)Ch. 14 - A transfer function is given by...Ch. 14 - Construct the Bode plots for...Ch. 14 - Draw the Bode plots for H()=250(j+1)j(2+10j+25)Ch. 14 - Prob. 15PCh. 14 - Sketch Bode magnitude and phase plots for...Ch. 14 - Sketch the Bode plots for G(s)=s(s+2)2(s+1), s = jCh. 14 - A linear network has this transfer function...Ch. 14 - Sketch the asymptotic Bode plots of the magnitude...Ch. 14 - Design a more complex problem than given in Prob....Ch. 14 - Sketch the magnitude Bode plot for...Ch. 14 - Find the transfer function H() with the Bode...Ch. 14 - The Bode magnitude plot of H() is shown in Fig....Ch. 14 - The magnitude plot in Fig. 14.76 represents the...Ch. 14 - A series RLC network has R = 2 k, L = 40 mH, and C...Ch. 14 - Design a problem to help other students better...Ch. 14 - Design a series RLC resonant circuit with 0 = 40...Ch. 14 - Design a series RLC circuit with B = 20 rad/s and...Ch. 14 - Let vs = 20 cos(at) V in the circuit of Fig....Ch. 14 - A circuit consisting of a coil with inductance 10...Ch. 14 - Design a parallel resonant RLC circuit with 0 =...Ch. 14 - Design a problem to help other students better...Ch. 14 - A parallel resonant circuit with a bandwidth of 40...Ch. 14 - A parallel RLC circuit has R = 100 k, L = 100 mH,...Ch. 14 - A parallel RLC circuit has R = 10 k, L = 100 mH,...Ch. 14 - It is expected that a parallel RLC resonant...Ch. 14 - Rework Prob. 14.25 if the elements are connected...Ch. 14 - Find the resonant frequency of the circuit in Fig....Ch. 14 - For the tank circuit in Fig. 14.79, find the...Ch. 14 - Prob. 40PCh. 14 - Using Fig. 14.80, design a problem to help other...Ch. 14 - For the circuits in Fig. 14.81, find the resonant...Ch. 14 - Calculate the resonant frequency of each of the...Ch. 14 - For the circuit in Fig. 14.83, find: (a) the...Ch. 14 - For the circuit shown in Fig. 14.84. find 0, B,...Ch. 14 - For the network illustrated in Fig. 14.85, find...Ch. 14 - Prob. 47PCh. 14 - Find the transfer function Vo/Vs of the circuit in...Ch. 14 - Design a problem to help other students better...Ch. 14 - Determine what type of filter is in Fig. 14.87....Ch. 14 - Design an RL low-pass filter that uses a 40-mH...Ch. 14 - Design a problem to help other students better...Ch. 14 - Design a series RLC type band-pass filter with...Ch. 14 - Design a passive band-stop filter with 0 = 10...Ch. 14 - Determine the range of frequencies that will be...Ch. 14 - (a) Show that for a band-pass filter,...Ch. 14 - Determine the center frequency and bandwidth of...Ch. 14 - The circuit parameters for a series RLC band-stop...Ch. 14 - Find the bandwidth and center frequency of the...Ch. 14 - Obtain the transfer function of a high-pass filter...Ch. 14 - Find the transfer function for each of the active...Ch. 14 - The filter in Fig. 14.90(b) has a 3-dB cutoff...Ch. 14 - Design an active first-order high-pass filter with...Ch. 14 - Obtain the transfer function of the active filter...Ch. 14 - A high-pass filter is shown in Fig. 14.92. Show...Ch. 14 - A general first-order filter is shown in Fig....Ch. 14 - Design an active low-pass filter with dc gain of...Ch. 14 - Design a problem to help other students better...Ch. 14 - Design the filter in Fig. 14.94 to meet the...Ch. 14 - A second-order active filter known as a...Ch. 14 - Use magnitude and frequency scaling on the circuit...Ch. 14 - Design a problem to help other students better...Ch. 14 - Calculate the values of R, L, and C that will...Ch. 14 - Prob. 74PCh. 14 - In an RLC circuit, R = 20 , L = 4 H, and C = 1 F....Ch. 14 - Given a parallel RLC circuit with R = 5 k, L = 10...Ch. 14 - A series RLC circuit has R = 10 , 0 = 40 rad/s,...Ch. 14 - Redesign the circuit in Fig. 14.85 so that all...Ch. 14 - Refer to the network in Fig. 14.96. (a) Find...Ch. 14 - (a) For the circuit in Fig. 14.97, draw the new...Ch. 14 - The circuit shown in Fig. 14.98 has the impedance...Ch. 14 - Scale the low-pass active filter in Fig. 14.99 so...Ch. 14 - The op amp circuit in Fig. 14.100 is to be...Ch. 14 - Using PSpice or MultiSim, obtain the frequency...Ch. 14 - Use PSpice or MultiSim to obtain the magnitude and...Ch. 14 - Using Fig. 14.103, design a problem to help other...Ch. 14 - In the interval 0.1 f 100 Hz, plot the response...Ch. 14 - Use PSpice or MultiSim to generate the magnitude...Ch. 14 - Obtain the magnitude plot of the response Vo in...Ch. 14 - Obtain the frequency response of the circuit in...Ch. 14 - For the tank circuit of Fig. 14.79, obtain the...Ch. 14 - Using PSpice or MultiSim, plot the magnitude of...Ch. 14 - For the phase shifter circuit shown in Fig....Ch. 14 - For an emergency situation, an engineer needs to...Ch. 14 - A series-tuned antenna circuit consists of a...Ch. 14 - The crossover circuit in Fig. 14.108 is a low-pass...Ch. 14 - The crossover circuit in Fig. 14.109 is a...Ch. 14 - A certain electronic test circuit produced a...Ch. 14 - In an electronic device, a series circuit is...Ch. 14 - In a certain application, a simple RC low-pass...Ch. 14 - In an amplifier circuit, a simple RC high-pass...Ch. 14 - Practical RC filter design should allow for source...Ch. 14 - The RC circuit in Fig. 14.111 is used for a lead...Ch. 14 - A low-quality-factor, double-tuned band-pass...
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