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systems analysis and design

The Analysis And Design Of Linear Circuits 8th Edition Roland E. Thomas, Albert J. Rosa, Gregory J. Toussaint - Solutions

+ 12–69 Consider theMATLABphase plot in Figure P12–69.Yourtask is to design a circuit that will realize that plot.Thepassband gain of the circuit needs to be 20 dB.(a) Find the transfer function corresponding to the phase plot.(b) Design a circuit that will realize the transfer function found
12–70 Consider the gain plot in Figure P12–70. The goal is to design a circuit that will result in the dashed curve shown on the plot.(a) Find the transfer function corresponding to the straightline gain plot.(b) Use MATLAB to plot the Bode magnitude of the transfer function.(c) Adjust the
12–71 For the following transfer function TVðsÞ =V2ðsÞ=V1ðsÞ(a) Construct the straight-line Bode plot of the phase.(b) Use the straight-line phase diagram to estimate the phase at ω = 10, 100, 1000, and 10,000 rad=s.(c) Use MATLAB to plot the Bode gain and phase and compare the phase plot
12–72 For the following transfer function TVðsÞ =V2ðsÞ=V1ðsÞ(a) Construct the straight-line Bode plot of the phase.(b) Use the straight-line phase diagram to estimate the phase at ω = 10, 100, 1000, and 10,000 rad=s.(c) Use MATLAB to plot the Bode gain and phase and compare the phase plot
12–73 The step response of a linear circuit is(a) Is the circuit a low-pass, high-pass, bandpass, or bandstop filter?(b) Construct the straight-line Bode gain plot and estimate the cutoff frequency and passband gain.(c) Use MATLAB to plot the Bode magnitude and step responses.(d) Design a circuit
12–74 The step response of a linear circuit is(a) Is the circuit a low-pass, high-pass, bandpass, or bandstop filter?(b) Construct the straight-line Bode gain plot and estimate the cutoff frequency and passband gain.(c) Use MATLAB to plot the Bode magnitude and step responses.(d) Design a circuit
12–75 The step response transform of a linear circuit is(a) Is the circuit a low-pass, high-pass, bandpass, or bandstop filter?(b) Construct the straight-line Bode gain plot and estimate the cutoff frequency and passband gain.(c) Use MATLAB to plot the Bode magnitude and step responses.(d) Design
12–78 There is a need for a passive notch filter at 10 krad=s. The narrower the notch the better, but there should be minimal ringing of the signals passing through.The transforms of three filters were submitted for consideration.Which would you recommend and why? s + 100s+108 T(s): = s +10%s+10%
12–79 There is a need for a passive tuned filter at 10 krad=s. The higher the Q the better, but there should be no ringing of the signals passing through. The transform of a prototype filter is shown. Design the filter by selecting the middle term of the denominator to maximize the Q while
12–80 Step Response of an RLC Bandpass Circuit The step response of a series RLC bandpass circuit is g(t)= = [e-200r sin (5001)]u(t)
(a) Find the passband center frequency and the two cutoff frequencies.(b) Design a circuit that would possess the above step response.(c) Validate your design using Multisim.12–81 A Tunable Tank Circuit The RLC circuit in Figure P12–81 (often called a tank circuit)has R=4:7 kΩ, C = 680 pF, and
12–82 Filter Design Specification Construct a transfer function whose gain response lies entirely within the nonshaded region in Figure P12–82. Validate your results using MATLAB. IT(jw)ldB 20 -20 -40 w (rad/s) 1 10 100 1000 10000 FIGURE P12-82
12–83 Chip RC Networks Integrated circuit (chip) RC networks are used at parallel data ports to suppress radio frequency noise. In a certain application, RF noise at 3:2 MHz is interfering with a 4-bit parallel data signal operating at 1:1 MHz. A chip RC network is to be used to reduce the RF
12–84 Design Evaluation Your company issued a request for proposals listing the following design requirements and evaluation criteria.Design Requirements: Design a low-pass filter with a passband gain of 9 ± 10% and a cutoff frequency of 90 ± 10%krad=s. A sensor drives the filter input with a
12–85 Design Evaluation In a research laboratory, you need a bandpass filter to meet the following requirements:Design Requirements: Passband gain: 10 ± 5%, B=10 krad=s ± 5%, ω0 = 5 krad=s ± 2%, ωCL = 2 krad=s ± 10%.Evaluation Criteria: Filter performance, parts count, use of standard
12–86 Design Evaluation In a cable service distribution station, you need a bandstop filter to meet the following requirements: Design Requirements: Passband gain: 10 ± 5%, B=3:3 kHz ± 5%, f0 =500Hz ± 2%, fCL =75Hz ± 10%. Filter must interface with a 50-Ω source and a 500-Ω load.Evaluation
12–77 The straight-line gain response of a linear circuit is shown in Figure P12–68. What are the initial and final values of the circuit step response? What is the approximate duration of the transient response?
12–76 The straight-line gain response of a linear circuit is shown in Figure P12–65. What are the initial and final values of the circuit step response? What is the approximate duration of the transient response?
12–49 A series RLC bandstop circuit is to be used as a notch filter to eliminate a bothersome 120-Hz hum in an audio channel. The signal source has a Thévenin resistance of 75 Ω. Select values of L and C so that the upper cutoff frequency of the stopband is below 180 Hz. Use Multisim to verify
12–48 A series RLC bandpass filter is required to have resonance at f0 = 50 kHz. The circuit is driven by a sinusoidal source with a Thévenin resistance of 60 Ω. The following standard capacitors are available in the stock room:1 μF, 0:68 μF, 0:47 μF, 0:33 μF, 0:2 μF, and 0:12 μF. The
12–47 A parallel RLC circuit with R=1:5 kΩ has a center frequency of 50 krad=s and a bandwidth of 50 krad=s. Find the values of L and C. Find the Q of this circuit. Is it wide-band or narrow-band?
12–46 In a series RLC circuit, which element would you adjust(and by how much) to(a) Double the bandwidth without changing the center frequency?(b) Double the center frequency without changing the bandwidth?(c) Repeat parts (a) and (b) for a parallel RLC circuit.
12–44 A 20-mH inductor with an internal series resistance of 15 Ω is connected in series with a capacitor and a voltage source with a Thévenin resistance of 50 Ω.(a) What value of C is needed to produce ω0 = 10 krad=s?(b) Find the bandwidth and quality factor of the circuit.
12–43 A parallel RLC bandpass circuit with C =0:01 μF and Q= 10 has a center frequency of 500 krad=s. Find R, L, and the two cutoff frequencies. Could you design this circuit using a cascade connection of two first-order filters separated by a follower? Why or why not?
12–42 A series RLC bandpass circuit with R=20 Ω is designed to have a bandwidth of 2:5 Mrad=s and a center frequency of 50 Mrad=s. Find L, C, Q, and the two cutoff frequencies.Could you design this circuit using a cascade connection of two first-order filters separated by a follower? Why or why
12–41 Design an RLC bandpass filter with a center frequency of 1000 rad=s and a Q of 0:5. The passband gain is+ 20 dB. Use practical values for R, L, and C. Use no more than one OP AMP.
12–40 Design an RLC bandstop filter with a center frequency of 50 krad=s and a bandwidth of 5 krad=s. The passband gain is 0 dB. Use practical values for R, L, and C and do not use an OP AMP.
12–37 Design an audio amplifier that amplifies signals from 20 Hz to 20 kHz. Your approach should be to use a cascade connection of two first-order active OP AMP circuits.The source has a 1-kΩ series resistor, and the output of the filter feeds a 32-Ω audio transducer. Design a bandpass circuit
12–36 Design an audio amplifier that amplifies signals from 2 to 10 kHz. Your approach should be to use a cascade connection of two first-order passive circuits separated by a noninverting OP AMP. The source has a 50-Ω series resistor, and the output of the filter feeds a 10-kΩ audio
12–35 Design an audio amplifier that amplifies signals from 20 Hz to 20 kHz. Your approach should be to use a cascade connection of two first-order passive circuits separated by a noninverting OP AMP. The source has a 50-Ω series resistor and the output of the filter feeds a 10-kΩ audio
12–33 Suppose that the circuits in Figures P12–31 and P12–32 had to feed a 100-Ω instrument. Which circuit would you select and why?
12–30 Design a circuit with the transfer function in Problem 12–29. Validate your design using Multisim.
12–28 Design a circuit with the transfer function in Problem 12–27. Validate your design using Multisim.
12–26 Design a circuit with the transfer function in Problem 12–25. Validate your design using Multisim.
12–24 Astudent decided that she needed a low-pass filter that had a roll-off of –2 or – 40 dB=decade, with a cutoff frequency of 2000 rad=s. She correctly designed two identical passive RC filters, each with a cutoff of 2000 rad=s, and connected them in cascade. She cleverly separated them
12–21 A first-order low-pass circuit has a passband gain of 0 dB and a cutoff frequency of 5 krad=s. Find the gain (in dB) atω = 0, 500 rad=s, 50 krad=s, and 500 krad=s.
12–20 A first-order high-pass circuit has a passband gain of 20 dB and a cutoff frequency of 1000 rad=s.(a) Find the circuit’s transfer function.(b) Find the gain (in dB) at ω = 0, 500, 1000, and 5000 rad=s.(c) Verify your results using MATLAB.
12–17 An OP AMP has aGBW of 2 MHz. Can it be used in an RC high-pass first-order filter with a cutoff frequency of 2000 rad=s and a passband gain of – 104? Design the filter assuming you have a suitable OP AMP.
12–16 Design an RL high-pass first-order filter with a cutoff frequency of 250 Hz and a passband gain of – 25.
12–15 Design an RC low-pass first-order filter with a cutoff frequency of 100 krad=s and a passband gain of + 50.What is the minimum GBW that the OP AMP must have to not affect the filter’s cutoff?
12–14 Design a low-pass first-order filter with a cutoff frequency of 100 Hz and a passband gain of 1. What is its transfer function? Validate your design using MATLAB.
12–11 Design a passive high-pass filter with a cutoff frequency of 500 rad=s and a passband gain of 1. Validate your design using Multisim.
12–10 Design a low-pass filter with a cutoff frequency of 20 krad=s and a passband gain of 200. Validate your design using Multisim.
12–9 Design a high-pass filter with a cutoff frequency of 159 Hz and a passband gain of 5. Validate your design using Multisim.
12–8 Design a low-pass filter with a cutoff frequency of 2 krad=s and a passband gain of 1. Validate your design using Multisim.
12–2 A particular filter is said to be 80 dB down at a desired stop frequency. How many times reduced is a signal at that frequency compared to a signal in the filter’s passband?
12–1 A transfer function has a passband gain of 1000. At a particular frequency in its stopband, the gain of the transfer function is only 0:00025. By how many decibels does the gain of the passband exceed that of the frequency in the stopband?
The impulse response of a particular filter is h t ð Þ=104te−100tu t ð Þ.What type of filter is this? What is its passband bandwidth?
Use MATLAB to plot the actual Bode phase plot for the transfer function in Exercise 12–28.
Construct a Bode plot of the straight-line approximation to the phase response of the transfer function in Exercise 12–26. Use the plot to estimate the phase angles atω = 1, 15, 300, and 104 rad=s. Compare your results with those obtained using MATLAB.
Find the straight-line approximation to the phase response of the transfer function in Example 12–16. Verify your solution using MATLAB.
Use MATLAB to graph the Bode magnitude plot of the transfer function in Example 12–16.
Design a parallel RLC circuit with cutoff frequencies at 12 kHz and 16 kHz.
Use Multisim to verify that the circuit designed in Example 12–14 indeed meets the specifications.
Aparallel RLC circuit has a bandwidth of B= 12 krad=s, a quality factor ofQ= 3, and a 1-mH inductance. Find the values of R, C, ω0, ωC1, and ωC2.
Design a bandstop filter to eliminate a 13:5 kHz signal. The bandwidth of the notch should not exceed 10 kHz.
Avoltage source with a Thévenin resistance of 50 Ωhas a spurious (undesirable) conducted emission at 25 krad=s. Connecting an inductor and capacitor in series across the 50-Ω source produces a bandstop filter that can eliminate the troublesome signal.To avoid reducing nearby useful signals, the
Design a series RLC bandpass circuit that has a center frequency of ω0 = 10 krad=s, a maximum gain of 20 dB, and a bandwidth of 5 krad=s.
Design a bandpass circuit using a seriesRLCcircuit thatmeets the filter requirements in Example 12–9. Compare this RLC design with the circuit developed in Example 12–9
A series RLC circuit with the output taken across the resistor has a center frequency ofω0 = 500 krad=s, a resistance of 40 Ω, and a bandwidth B of 50 krad=s. Find Q, L, C, ωC1, and ωC2. Verify your results using Multisim
A series RLC circuit has a center frequency of ω0 = 20 krad=s, a quality factor of Q= 5, and a resistance R=50 Ω. Find the values of L, C, B, ωC1, and ωC2. Use Multisim and simulate the voltage gain across the resistor. Compare with the results calculated by hand
Select the element values in Figure 12–22(a) so that the passband gain is 6 dB and the cutoff frequencies are 1 and 50 krad=s. Validate your design using Multisim.
Design a bandpass circuit with a passband gain of 10 and cutoff frequencies at 20 Hz and 20 kHz. Verify the design using Multisim
Suppose that the evaluation task of Example included the requirement that the filter feed a 500-Ω recorder. Would the choice be different?
Design an RL high-pass filter with a cutoff of 10 krad=s and a passband gain of 1.
There are hundreds of different operational amplifiers that are designed to meet many varying needs. Gain-bandwidth is only one parameter. For example, an LF347D is a general-purpose OP AMP with a 3 MHzGBW, a LH4161 is a high-speed OP AMP with a GBW of 50 MHz, while an NJM2043D is a low-noise OP
Design a low-pass filter with a gain of – 1000 and a cutoff frequency of 20 kHz. Compare the frequency response of the same design between an ideal OP AMP and a UA741 general-purpose OP AMP using Multisim. If there is a problem with the UA741 design, suggest how to fix it
Design a low-pass active filter that has a gain of −10 and a cutoff frequency of 10 krad/s.
The circuit of Figure 12–8(a) has the following sinusoids applied to its input. Using only the plot in Figure 12–8(b), find the approximate amplitude of the sinusoid exiting the circuit.(a) v1ðtÞ = 100 cos 2π t mV(b) v1ðtÞ = 100 cos 200π t mV(c) v1ðtÞ = 100 cos 2000π t mV
(a) Show that the transfer function TðsÞ =V2ðsÞ=V1ðsÞ in Figure 12–7 has a low-pass gain characteristic.(b) Select element values so the passband gain is −4 and the cutoff frequency is 100 rad/s.(c) Use Multisim to simulate the frequency response of the results in part (b).
Design an RC low-pass filter with a cutoff of 100 rad=s and a passband gain of + 4.
Design an RC low-pass filter with a cutoff frequency of 1 krad/s and a passband gain of 1.
A student designed a low-pass filter with a required cutoff frequency of 1000 Hz using the circuit of Figure 12–4. When he measured the output at the −3 dB frequency, he was surprised that the output had decreased by 16:1 dB. He checked his values of R and L and their ratio R=L = 1000, just as
Select values of R and L for the circuit of Figure 12–4 so that the cutoff frequency occurs at 10 kHz
Consider the circuit in Figure 12–4. Find the transfer function TðsÞ =V2ðsÞ=V1ðsÞ, α, and ωC, and construct the straight-line approximations to the gain and phase responses.
A particular filter is said to be 83 dB down at a desired stop frequency. How many times reduced is a signal at that frequency compared to a signal in the filter’s passband?
A transfer function has a passband gain of 25. At a particular frequency in its stopband, the gain of the transfer function is only 0.0006. By how many decibels does the gain of the passband exceed that of that frequency in the stopband?
A sinusoidal signal with a peak voltage of 3:7 V is input into a frequency-dependent circuit.What is its peak voltage at its −3 dB frequency?
12-5 Frequency Response and Step Response (Sect.12–8)Given a circuit or a transfer function:(a) Find the gain response corresponding to a given step response or vice versa.(b) Use the relationship between frequency and step responses to choose the best solution for a design specification
12-4 Bode Plots (Sects. 12–6 and 12–7)Given a linear circuit or transfer function:(a) Plot the gain and phase responses using straight-line approximations and computer tools.(b) Develop a transfer function from a straight-line Bode gain plot.(c) Design a circuit that produces a given
12-3 The Frequency Response of RLC Circuits (Sect.12–5)Given an RLC circuit connected asab and passor ab and stop filter:(a) Find the frequency-response descriptors such as Q and B.(b) Design circuits to produce a specified frequency response.(c) Compare the bandpass and bandstop responses
12-2 Bandpass and Band stop Responses (Sect. 12–4)Given a cascade or parallel connection of two first-order circuits:(a) Find and classify the frequency response.(b) Plot the gain and phase responses using straight-line approximations and computer tools.(c) Design circuits to produce a specified
12-1 First-Order Circuit Frequency Response (Sects.12–1–12–3)Given a first-order circuit or transfer function:(a) Understand and use frequency response descriptors.(b) Find and classify the frequency response.(c) Plot the gain and phase responses using straight-line approximations and
5–64 MATLAB Signal Analyzer Create a MATLAB function to analyze signals represented numerically. The function should have the following two inputs:(1) a vector containing equally spaced samples of the signal of interest and (2) the time step used to sample the signal contained in the vector. The
5–63 Voltmeter Calibration Most dc voltmeters measure the average value of the applied signal. A dc meter that measures the average value can be adapted to indicate the rms value of an ac signal. The input is passed through a rectifier circuit. The rectifier output is the absolute value of the
5–60 Digital Clock Generator Timing digital circuits is vital to the operationofany digital device.Using an ideal OP AMP (running open-loop, i.e., without feedback)and appropriate resistors,designaway toconvert a sinusoid into a square wave that varies from −15 to 15 V with a period of 1 ms.
5–58 Exponential Signal Descriptors Several of the time descriptors used in digital data communication systems are based on exponential signals. In this problem, we explore three of these descriptors.(a) The time constant of fall is defined as the time required for a pulse to fall from 70.7% to
5–56 UsingMultisim, create the following waveforms and state if eachwaveformiscausalornon-causal,periodicornon-periodic:(a) A step voltage switching from 0 to 5 V at t = 100 ms.(b) A triangular wave that has amplitude of 75 V and a period of 10 ms.(c) A cosine with amplitude of 100 V, radian
5–55 A periodic waveform can be expressed as vðtÞ = 20 + 16 cos 500πt − 8 sin 1000πt + 4 cos 2000πt V(a) What is the period of the waveform? What is the average value of the waveform? What is the amplitude of the fundamental(lowest frequency) component? What is the highest frequency in the
5–54 The first cycle ðt > 0Þ of a periodic waveform with T0 = 500 ms can be expressed as vðtÞ = 2uðtÞ−3uðt−0:2Þ + 2uðt−0:4Þ V Sketch the waveform and find VMAX, VMIN, Vp, Vpp, and Vavg.
5–53 Find VMAX, VMIN, Vavg, and Vrms of the full-wave rectified sine wave vðtÞ =VA sinð2πt=T0Þ V in terms of VA. Is the waveform causal or non-causal?
5–52 Find VMAX, VMIN, Vavg, and Vrms of the offset sine wave vðtÞ =V0 + VA cosð2πt=T0Þ V in terms of V0 and VA.
5–47 An exponential waveform given by vðtÞ = 25 e−5000t uðtÞ V repeats every five time constants.(a) Find Vp, Vpp, VMAX, and VMIN.(b) Find Vavg and Vrms.(c) Find the period T0 of the waveform.
5–46 Find VMAX, VMIN, Vp, Vpp, Vavg, and Vrms for each of the following sinusoids.(a) v1ðtÞ = 84:84 cosð377tÞ + 84:84 sinð377tÞ V(b) v2ðtÞ = −30 cosð1000πtÞ − 40 sinð1000πtÞ V(c) v3ðtÞ = 10 + 10 cosð5000πt + 45Þ V
5–45 Sketch or use MATLAB or Excel to graph three or four cycles of a damped sinusoid with a damping coefficient of 1ms, a vð0Þ amplitude of 15 V, a frequency of 1 kHz, and a phase shift of 0.
5–40 For the double exponential v t ð Þ=10 e−200t −e−2000t u t ð Þ V(a) Find the maximum value of the waveform and the time at which it occurs.(b) Determine the dominant exponential.(c) Generate the waveform in MATLAB and validate the result.
5–36 A waveform of the form vðtÞ = 5 − 10 cosðβt − 45Þ periodically reaches a minimum every 10 ms.(a) Find themaximumandminimumvalues of vðtÞ, the value of β, and then sketch the waveform.(b) Generate the waveform in Multisim.(c) Generate the waveform in MATLAB.
5–33 The value of the waveformvðtÞ = VA − VBe−αt ð Þu t ð Þ is 5 V at t =0, 8V at t = 5 ms, and approaches 12 V as t ! ∞.(a) Find VA, VB, and α, and then sketch the waveform.(b) Validate your answers by plotting your result in MATLAB.
5–29 For the following sinusoid: v(t) = 10 cosð2π200t + 60Þ V(a) Find the Fourier coefficients, cyclic frequency, and radian frequency.(b) Plot the waveform by hand.(c) Use MATLAB to produce the waveform.(d) Use Multisim to produce the waveform
5–28 Use MATLAB or Excel to display two cycles of the following waveform:v(t) = 19:1 sin 1000πt + 6:37 sin 3000πt + 3:82 sin 5000πt + 2:73 sin 7000πt +2:1 sin 9000πt V What are the period and amplitude of the resulting waveform?What common waveform is this waveform approximating?

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