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systems analysis and design

The Analysis And Design Of Linear Circuits 7th Edition Roland E Thomas, Albert J Rosa, Gregory J Toussaint - Solutions

Aparticular periodic waveform with a period of 10 ms has the following Fourier coefficients a0 ¼ 4; an ¼ 8 np sin np 2cos np 4; bn ¼8 np sin np 2sin np 4(a) Write an expression for the terms in the Fourier series a0 and n ¼ 1 through 8.(b) Convert your expression to amplitude and phase form
The equation for the first cycle (0 t T0) of a periodic waveform is vðtÞ ¼ VAet=2T0 V(a) Sketch the first two cycles of the waveform.(b) Derive expressions for the Fourier coefficients an and bn.
The equation for the first cycle (0 t T0) of a periodic pulse train is vðtÞ ¼ VA½2uðtÞ 2uðt T0=2ÞV(a) Sketch the first two cycles of the waveform.(b) Derive expressions for the Fourier coefficients an and bn.
Step Response of an RLC bandpass circuit The step response of a series RLC bandpass circuit is gðtÞ ¼ 4 5e200t sinð500tÞ uðtÞ(a) Find the passband center frequency and the two cutoff frequencies.(b) Design a circuit that would possess the above step response.
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 denominatortomaximizetheQwhileassuringthere
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?T1ðsÞ ¼ s2 þ 100s þ 108 s2 þ 104s
The straight-line gain response of a linear circuit is shown in Figure P12–54. What are the initial and final values of the circuit step response? What is the approximate duration of the transient response?
The straight-line gain response of a linear circuit is shown in Figure P12–52. What are the initial and final values of the circuit step response? What is the approximate duration of the transient response?
The impulse response transform of a linear circuit is HðsÞ ¼ 2500s2ðs þ 1000Þ2(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
The step response of a linear circuit is gðtÞ ¼ 2 2e20t þ 2e500t uðtÞ(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
The step response of a linear circuit is gðtÞ ¼ 6 4e100t 2e1000t uðtÞ(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
For the following transfer function TV(s) ¼ V2(s)/V1(s)TVðsÞ ¼ 10ðs þ 50Þðs þ 10Þðs þ 100Þ(a) Construct the straight-line Bode plot of the phase.(b) Use the straight-line phase diagram to estimate the phase at v ¼ 1, 10, 100, and 1000 rad/s.(c) Use MATLAB to plot the Bode gain and
For the following transfer function TV(s) ¼ V2(s)/V1(s)TVðsÞ ¼ 10ðs þ 100Þs þ 100(a) Construct the straight-line Bode plot of the phase.(b) Use the straight-line phase diagram to estimate the phase at v ¼ 1, 10, 100, and 1000 rad/s.(c) Use MATLAB to plot the Bode gain and phase and compare
For the following transfer function TV(s) ¼V2(s)/V1(s)TVðsÞ ¼ 4s 0:04s2 þ 0:2s þ 1(a) Construct the straight-line Bode plot of the gain. Is this a low-pass, high-pass, bandpass, or bandstop function?(b) Use the straight-line plot to estimate the maximum gain and the frequency at which it
For the following transfer function TV(s) ¼ V2(s)/V1(s)TðsÞ ¼ 108ðs þ 100Þ2ðs þ 1000Þ4(a) Construct the straight-line Bode plot of the gain. Is this a low-pass, high-pass, bandpass, or bandstop function? Estimate the cutoff frequency(ies) and passband gain.(b) Use MATLAB to plot the Bode
For the following transfer function TV(s) ¼ V2(s)/V1(s)TVðsÞ ¼ 10ðs þ 10Þðs þ 100Þðs þ 1Þðs þ 1000Þ(a) Construct the straight-line Bode plot of the gain. Is this a low-pass, high-pass, bandpass, or bandstop function?Estimate the cutoff frequency(ies) and passband gain.(b) Use MATLAB
For the following transfer function TðsÞ ¼ 100sðs þ 300Þðs þ 30Þðs þ 3000Þ(a) Construct the straight-line Bode plot of the gain. Is this a low-pass, high-pass, bandpass, or bandstop function?Estimate the cutoff frequency and passband gain.(b) Use MATLAB to plot the Bode magnitude of the
For the following transfer function TðsÞ ¼ 106s2ðs þ 1000Þ2(a) Construct the straight-line Bode plot of the gain. Is this a low-pass, high-pass, bandpass, or bandstop function?Estimate the cutoff frequency and passband gain.(b) Use MATLAB to plot the Bode magnitude of the transfer
For the following transfer function TðsÞ ¼ 100ðs þ 10Þsðs þ 100Þ(a) Construct the straight-line Bode plot of the gain. Is this a low-pass, high-pass, bandpass, or bandstop function?Estimate the cutoff frequency and passband gain.(b) Use MATLAB to plot the Bode magnitude of the transfer
A student was designing a passive tuned filter using a series RLC circuit with R ¼ 10V, L ¼ 10 mH, and C = 0.025mF. When he connected the output of the filter across the capacitor he was surprised by an output near the cutoff point that was greater than the input signal. Since the filter was
Aseries 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 Thevenin resistance of 300V. Select values of L and C so the upper cutoff frequency of the stopband is below 180 Hz. Use OrCAD to verify your design.
A series RLC bandpass filter is required to have resonance at f0 ¼ 50 kHz. The circuit is driven by a sinusoidal source with a Thevenin resistance of 60V. The following standard capacitors are available in the stock room: 1mF, 0.68mF, 0.47mF, 0.33mF, 0.2 mF, and 0.12mF. The inductor will be
A parallel RLC circuit with R ¼ 1 kV has a center frequency of 50 kHz and a bandwidth of 50 kHz. Find the values of L and C. Could you design this circuit using a cascade connection of two first-order filters separated by a follower? Why or why not?
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.
A 20-mH inductor with an internal series resistance of 25V is connected in series with a capacitor and a voltage source with a Thevenin resistance of 50V.(a) What value of C is needed to produce v0 ¼ 5 krad/s?(b) Find the bandwidth and quality factor of the circuit.
A parallel RLC bandpass circuit with C ¼ 0.01mF and Q ¼ 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?
A series RLC bandpass circuit with R ¼ 30V is designed to have a bandwidth of 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 not?
Design an RLC bandpass filter with a center frequency of 1000 rad/s and a Q of 20. The passband gain is+20 dB. Use practical values for R, L, and C.
Design an RLC bandstop filter with a center frequency of 33 krad/s and a bandwidth of 3.3 krad/s. The passband gain is 0 dB. Use practical values for R, L, and C.
Impulse Generator Theoretically, an impulse has an amplitude spectrum that is constant at all frequencies. In practice, a constant spectrum across an infinite bandwidth cannot be achieved, nor is it really necessary. What is required is an amplitude spectrum that is ‘‘essentially’ ’
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 50-V series resistor and the output of the filter feeds a 10-kV audio transducer. Design a bandpass circuit with the
Design an audio amplifier that amplifies signals from 2 kHz to 10 kHz. Your approach should be to use a cascade connection of two first-order passive circuits separated by a non-inverting OP AMP. The source has a 50-V series resistor and the output of the filter feeds a 10-kV audio transducer.
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 non-inverting OPAMP. The source has a 50-V series resistor and the output of the filter feeds a 10-kV audio transducer.Design
Suppose the circuits you designed in problems 12–21 and 12–22 had to feed a 500V instrument. Which circuit would you select and why?
A student decided that she needed a low-pass filter that had a roll-off of 2 or 40dB/decade, with a cutoff frequency of 1000 rad/s. She correctly designed two identical passive RC filters, each with a cutoff of 1000 rad/s, and connected themin cascade or one after the other. She cleverly
The transfer function of a first-order circuit is TðsÞ ¼ 5s s þ 15000(a) Identify the type of gain response. Find the cutoff frequency and the passband gain.(b) Use MATLAB to plot the magnitude of the Bode gain response.(c) Design a circuit to realize the transfer function.(d) Use OrCADto
The transfer function of a first-order circuit is TðsÞ ¼ 10; 000 s þ 2000(a) Identify the type of gain response. Find the cutoff frequency and the passband gain.(b) Use MATLAB to plot the magnitude of the Bode gain response.(c) Design a circuit to realize the transfer function.(d) Use OrCAD to
A first-order low-pass circuit has a passband gain of 0 dB and a cutoff frequency of 2 krad/s. Find the gain (in dB) at v ¼ 0, 200 rad/s, 20 krad/s, and 200 krad/s.
A first-order high-pass circuit has a passband gain of 20 dB and a cutoff frequency of 1000 rad/s. Find the gain (in dB) at v ¼ 0, 500, 1000, and 5000 rad/s.
Design an RC high-pass first-order filter with a cutoff frequency of 2000 rad/s and a passband gain of 100.
Design an RL high-pass first-order filter with a cutoff frequency of 120 Hz and a passband gain of 15.
Design an RC low-pass first-order filter with a cutoff frequency of 10,000 rad/s and a passband gain of þ10.
Design a low-pass first-order filter with a cutoff frequency of 2000 rad/s and a passband gain of 1.
A particular filter is said to be 56 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 pass-band?
Designing to Specifications A particular circuit needs to be designed that has the following transfer function requirements: Poles at s ¼ 100 and s¼10,000; zeros at s¼0 and s¼1000; and a gain of 10 as s ! 1. Find the circuit’s transfer function and use MATLAB to plot its step response.
A circuit is needed that will take an input of v1(t) ¼[1 e10,000t] u(t) V and produce a constant 5 V output.Design such a circuit using practical parts values. Validate your design using OrCAD.
A circuit is needed that will take an input of v1(t) ¼25 e10tu(t) mVand produce an output of v2(t) ¼ 500 e200t u(t) mV. Design such a circuit using practical parts values.Validate your design by using OrCAD.
Design a circuit that produces the following step response.gðtÞ ¼ 24½1 e50t 50te50t uðtÞ
A circuit is needed to realize the impulse response transform listed below. Scale the circuit so that all parts use practical values.HðsÞ ¼ 200s þ 106 s2 þ 200s þ 106
Design a circuit to realize the transfer function below using only resistors, capacitors, and OP AMPs. Use only values from the inside rear cover. Your design must be within 10% of the desired response.TVðsÞ ¼ 500ðs þ 100Þsðs þ 10000Þ
A circuit is needed to realize the transfer function listed below.TVðsÞ ¼ðs þ 125Þðs þ 500Þðs þ 250Þðs þ 1000Þ(a) Design the circuit using two OP AMPs.(b) Design the circuit using only one OP AMP.(c) Design the circuit using no OP AMPs.In all cases, scale the circuit so that all
Design a passive circuit to realize the transfer function below using only resistors, capacitors, and inductors.Scale the circuit so that all inductors are 50 mH or less.TVðsÞ ¼ s2ðs þ 2000Þ2
Design a circuit to realize the transfer function below using only resistors, capacitors and not more than one OP AMP. Scale the circuit so that the final design uses only 20-kV resistors.TVðsÞ ¼ 20;000sðs þ 1000Þðs þ 5000Þ
Design a circuit to realize the transfer function below using only resistors, capacitors and not more than one OP AMP. Scale the circuit so that all capacitors are exactly 0.01 mF.TVðsÞ ¼ 100ðs þ 1000Þðs þ 100Þðs þ 10;000Þ
Design a circuit to realize the transfer function below using only resistors, capacitors, and OP AMPs. Scale the circuit so that all resistors are greater than 10 kV and all capacitors are less the 1 mF.TVðsÞ ¼ 5 108ðs þ 100Þðs þ 10;000Þ
Design a circuit to realize the transfer function below using only resistors, capacitors, and OP AMPs.TVðsÞ ¼ 50000sðs þ 50Þðs þ 1000ÞScale the circuit so that all capacitors are exactly 0.1 mF.
Design a circuit to realize the transfer function below using only resistors, capacitors, and OP AMPs.TVðsÞ ¼50000sðs þ 2500ÞScale the circuit so that all capacitors are exactly 0.1 mF.
Design a circuit to realize the transfer function below using only resistors, inductors, and OP AMPs.TVðsÞ ¼ s þ 5000 sScale the circuit so that all inductors are exactly 100 mH.
Design a circuit to realize the transfer function below using only resistors, capacitors, and OP AMPs.TVðsÞ ¼ 20000 s þ 1000 Scale the circuit so that all resistors are exactly 1 kV.
Design a circuit to realize the transfer function below using only resistors, capacitors, and OP AMPs.TVðsÞ ¼ 20000 s þ 100000 Scale the circuit so that all capacitors are exactly 1000 pF.
The impulse responses of two linear circuits are h1(t) ¼2e2tu(t) and h2(t) ¼ 5e5tu(t). What is the impulse response of a cascade connection of these two circuits?
The impulse response of a linear circuit is h(t) ¼ 50 e5t u(t) and x(t) ¼ tu(t). Use s-domain convolution to find the zero-state response y(t).
The impulse response of a linear circuit is h(t) ¼ 2u(t).Use MATLAB to compute theconvolution integral and find the response due to an input x(t) ¼ t[u(t) u(t 1)].
If the input to a linear circuit is x(t) ¼ tu(t), then the output y(t) is called the ramp response.Use the convolution integral to show that dyðtÞdt¼Zt 0hðtÞdt ¼ gðtÞThat is, show that the derivative of the ramp response is the step response.
Use the convolution integral to show that if the input to a linear circuit is x(t) ¼ u(t) then yðtÞ ¼ gðtÞ ¼Zt 0hðtÞdt That is, show that the step response is the integral of the impulse response.
Show that if h(t) ¼ u(t), then output y(t) for any input x(t) is y(t) ¼Rt 0xðtÞdt.That is, a circuit whose impulse response is a step function operates as an integrator.
Show that f(t)d(t) ¼ f(t). That is, show that convolving any waveform f(t) with an impulse leaves the waveform unchanged.
The impulse response of a linear circuit is h(t) ¼ etu(t).Use the convolution integral to find the response due to an input x(t) ¼ tu(t).
The impulse response of a linear circuit is h(t) ¼10 [u(t) u(t 1)]. Use the convolution integral to find the response due to an input x(t) ¼ etu(t).
The impulse response of a linear circuit is h(t) ¼ etu(t).Use the convolution integral to find the response due to an input x(t) ¼ u(t).
The impulse response of a linear circuit is h(t) ¼ [u(t) u(t 3)]. Use the convolution integral to find the response due to an input x(t) ¼ u(t 3).
The impulse response of a linear circuit is h(t) ¼ u(t). Use the convolution integral to find the response due to an input x(t) ¼ u(t).
The step response of a linear circuit is g(t) ¼ [1 20te10t]u(t). Find the sinusoidal steady-state response for an input x(t) ¼ 50 cos 10t.
The step response of a linear circuit is g(t) ¼ [ e60t sin 80t]u(t). Find the sinusoidal steady-state response for an input x(t) ¼ 20 cos 100t.
The impulse response of a linear circuit is h(t) ¼ 800[e100t e400t]u(t). Use MATLAB to find the sinusoidal steady-state output for an input x(t) ¼ 8 cos 200t. Use MATLAB to plot y(t).
The impulse response of a linear circuit is h(t) ¼[500e5000t]u(t) d(t). Find the sinusoidal steady-state output for an input x(t) ¼ 10 cos 10 kt.
The step response of a linear circuit is g(t) ¼ [2eþ100t]u(t).Find the sinusoidal steady-state output for an input x(t) ¼5 cos 500t.
The step response of a linear circuit is g(t) ¼ [15e500t]u(t). Find the sinusoidal steady-state output for an input x(t)¼ 5 cos 1000t.
The transfer function of a linear circuit is T(s) ¼ (s+ 100)/(s þ 10). Find the sinusoidal steady-state output for an input x(t) ¼ 5 cos 100t.
The impulse response transform of a circuit is HRðsÞ ¼ V2ðsÞ=I1ðsÞ ¼ 5000s=s þ 2500. Find v2SS(t) if it(t) ¼10 cos 5000t mA. Compare your answer to that found in Problem 11–39.
The impulse response of a linear circuit is h(t) ¼ 20u(t) þd(t). Find the output waveform y(t) when the input is x(t) ¼2[e20t]u(t).
The impulse response transform of a linear circuit is H(s)¼ (s þ 2000)/(s þ 1000). Find the output waveform when the input is x(t)¼5e1000tu(t). UseMATLAB to find the Laplace transform of x(t). Then find Y(s). Finally, use the inverse Laplace function to find the waveform y(f) and plot the
The step response of a linear circuit is g(t) ¼ 10[e50t cos 200t]u(t). Find the circuit’s impulse response h(t), impulse response transform H(s), step response transform G(s), and the circuit’s transfer function T(s).
The step response of a linear circuit is g(t) ¼ 0.25[l e150t]u(t). Find the output waveform when the input is v1(t)¼ [20e200t]u(t). Use MATLAB to find the Laplace transforms of g(t) and v1(t). Then find V2(s). Finally, use the inverse Laplace function to find the waveform v2(t) and plot the
The impulse response of a linear circuit is h(t) ¼ 1000[e1000t]u(t). Find the output waveform when the input is x(t)¼ 5tu(t).
Find h(t) ¼ dgðtÞdt when g(t) ¼ (3 e10t) u(t). Verify your answer by first transforming g(t) intoG(s) and findingH(s) ¼sG(s) and then taking the inverse transform of H(s). Did you get the same answer?
The step response of a linear circuit is g(t) ¼ 15(e20kt e30kt)u(t). Find the circuit’s impulse response h(t), impulse response transform H(s), step response transform G(s), and the circuit’s transfer function T(s).
The step response transform of a linear circuit is G(s) ¼1000/s(s þ 1000). Find the circuit’s impulse response h(t), step response g(t), impulse response transform H(s), and the circuit’s transfer function T(s).
The impulse response of a linear circuit is h(t) ¼ d(t) 2000e200t u(t). Find the circuit’s step response g(t), impulse response transform H(s), step response transform G(s), and the circuit’s transfer function T(s).
The impulse response of a linear circuit is h(t) ¼(100e200t 100e1000t)m(t). Find the circuit’s step response g(t), impulse response transform H(s), step response transform G(s), and the circuit’s transfer function T(s).
Select an appropriate RF for the circuit of Figure P11–21 so that the step response of the circuit is g(t) ¼(10e1000t 10) u(t)V.
Find the input impedance Z(s) in Figure P11–15.
Thevenin’s Theorem from Time-domain Data A black box containing a linear circuit has an on-off switch and a pair of external terminals. When the switch is turned on, the open-circuit voltage between the external terminals is observed to be vOCðtÞ ¼ 10e10t 10e50t uðtÞV The short circuit
Compare the results of your designs of the circuits in Figures P10–52 and P10–53. Since both circuits purport to have the same response characteristics, what are the advantages and disadvantages of each?
Find the transform of the Thevenin equivalent circuit looking into the V2(t) terminals for the circuit of P10–45.
There is no initial energy stored in the bridged-T circuit in Figure P10–45.(a) Transform the circuit into the s domain and formulate node-voltage equations.(b) Use the node-voltage equations to find the s-domain relationship between the input V1(s) and the output V2(s).
There is no initial energy stored in the circuit in Figure P10–43. The Thevenin equivalent circuit to the left of point A when a unit step is applied is VTðsÞ ¼ 1 s þ 103 V-s; and ZTðsÞ ¼ 106 s þ 103 V Select values for R2 and C2 such that the output transform is V2ðsÞ ¼ s s2 þ 3000s
There is no initial energy stored in the circuit in Figure P10–41.(a) Transform the circuit into the s domain and formulate node-voltage equations.(b) Show that the solution of these equations for V2(s) in symbolic form is V2ðsÞ ¼ R1V1ðsÞðR1 þ R2ÞLCs2 þ ðR1R2C þ LÞs þ R1(c) Identify
The equivalent impedance between a pair of terminals is ZEQðsÞ ¼ 2000 s þ 3000 s þ 2000 V A voltage v(t) ¼ 10u(t) is applied across the terminals.Find the resulting current response i(t).
For the circuit of Figure 10–34:(a) Find the Thevenin equivalent circuit that the 5R load resistor sees in when vC(0) ¼ VO V.(b) Then find the voltage delivered to the load vO(t) if vC(0)¼10 V, iS(t) ¼ 10 u(t) mA, R ¼ 1 kV, and C ¼ 2 mF.(c) Identify the forced, natural, zero state, and zero

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