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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

The circuit in Figure P8–39 is operating in the sinusoidal steady state. Use superposition to find the phasor response IX. j2592 m 50 1x ww 145 A 25 23 =-150 1+ FIGURE P8-39 100-45 V
The circuit in Figure P8–40 is operating in the sinusoidal steady state. Use superposition to find the response vX(t).Note: The sources do not have the same frequency. |+ 5 cos 1500t V ww 500 + 10 cos 500t V = 2 F vx(t) FIGURE P8-40
An RC series circuit is excited by a sinusoidal source v(t)¼VA cos (vtþf) V. Determine the effects on the magnitudes of the current, voltages, and impedances caused by changes in the source parameters. Complete the following table.SOURCE jVRj jVCj jIj jZ Rj jZ Cj Increase/decrease VA
The circuit in Figure P8–42 is operating in the sinusoidal steady state. Use superposition to find the response vX(t). 10 cos 2000t V- 150 2 F + + 2002vx(t) -200 cos(2000t -30) mA FIGURE P8-42
The circuit in Figure P8–43 is operating in the sinusoidal steady state. Use superposition to find the response vX(t).Note: The sources do not have the same frequency. 100 cos 2000t V + 2 kn vx(t) 500 2 F -200 cos(1000t 30) mA FIGURE P8-43
The circuit in Figure P8–44 is operating in the sinusoidal steady state.(a) What impedance, if any, should be connected across VX to cancel the reactance in the circuit?(b) Is the bridge balanced, that is, VX¼0? 100 -30 V + 1 20 8 40 + Vx -j10 2 20 FIGURE P8-44
The circuit in Figure P8–45 is operating in the sinusoidal steady state. Use the unit output method to find the phasor responses VX and IX 1000 V + 10 w 100 ww -j20 k2= -j100 kn= Vx Ix FIGURE P8-45
Find the Thevenin equivalent of the source circuit to the left of the interface in Figure P8–46. Then use the equivalent circuit to find the steady-state voltage v(t) and current i(t)delivered to the load. Validate you answer using OrCAD. 1 mH m 1 ww 250 pF i(t) Load + v(t) ww 500 + I 30 cos
Find the phasor Thevenin equivalent of the source circuit to the left of the interface in Figure P8–47. Then use the equivalent circuit to find the phasor voltage Vand current I delivered to the load. 1 + 100 sin 25 kt V i(t) Load 50 100 w 1 F 5 cos 25 kt A FIGURE P8-47 + v(t) ee-w 100 10 mH
The circuit in Figure P8–48 is operating in the sinusoidal steady state.When ZL¼0, the phasor current at the interface is I¼4.8j3.6 mA.When ZL¼j20 kV, the phasor interface current is I¼10 þ j0 mA. Find the Thevenin equivalent of the source circuit. Source V ZL FIGURE P8-48
Design a linear circuit that will deliver an output phasor VO¼60ff45 V when an input phasor VS¼240 ff0 V is applied in Figure P8–49. Vs Linear Ckt Vo FIGURE P8-49
A load of ZL¼100þj100V is to be driven by a phasor source VS¼120 ff0 V. The voltage across the load needs to be VL¼100 ff0 V. Design an interface that will meet these conditions. Validate your answer using OrCAD.
Design an interface circuit so that an input voltage vS(t)¼100 cos(2104t) V delivers a steady-state output current of iO(t)¼10 cos (2104t30) mA to a 1-kV resistive load. Validate your answer using OrCAD.
Design an interface circuit so that an input voltage vS(t)¼15 cos (10 kt) V delivers a steady-state output voltage of vO(t)¼10 cos (10 kt45) V.
Refer to the RLC series circuit shown in Figure P8–53.(a) What is the maximum output voltage and at what frequency does it occur? Consider using OrCAD and doing an ac sweep from 10 Hz to 1 MHz, and then narrow your sweep until you find the frequency atwhich the peak occurs and the output voltage
The circuit in Figure P8–54 is operating in the sinusoidal steady state with v¼5 krad/s. Use node-voltage analysis to find the steady-state response vX(t). 15 cos tot V 1 + 0.5 H 000 + 0.1 F 10 kvx(t) FIGURE P8-54 + I 30 cos(ot -45) V
Use node-voltage analysis to find the steady-state phasor response VO in Figure P8–55. j20 2 000 100 000 + 1200 V + 150 200 Vo FIGURE P8-55
The circuit in Figure P8–56 is operating in the sinusoidal steady state.(a) Find the node voltage phasors VA and VB.(b) If the circuit is operating with v¼10 krad/s, use OrCAD to verify your answer in (a). VA 400 w 20 A VB =-1200 2 100 1200 - - 150 FIGURE P8-56
Use mesh-current analysis to find the phasor branch currents I1, I2, and I3 in the circuit shown in Figure P8–57. 100 sin 104 V in(t) 1 w 10 mH eee 0.04 F HH Jiz(t) i2(t) iz(t) FIGURE P8-57 -100 cos 104 V
Use mesh-current analysis to find the phasor branch currents I1, I2, and I3 in the circuit shown in Figure P8–58. 2 ww iz(t) 1 0.04 F ww HP in(t) i2(t) 100 sin (104) V10 mH 00 FIGURE P8-58 1 + -100 cos (104 t) V
Use mesh-current analysis to find the phasor branch currents I1, I2, and I3 in the circuit shown in Figure P8–59. 100 sin (104) V ( + 1 w 41(t) 10 mH le FIGURE P8-59 212(1) i2(t) 0.04 F 2 kN 13(1)
Use mesh-current analysis to find the phasor currents IA and IB in Figure P8–60. 10 20 30 130 j100 j202 IA IB + 1200 V FIGURE P8-60
The OP AMP circuit in Figure P8–61 is operating in the sinusoidal steady state.(a) Show that(b) Find the value of the magnitude of Vo/Vs at v¼0 and v!1. Vo Vs (R + R (j + R 1 jw + (R+R2)C jw + RC
The circuit in Figure P8–62 is operating in the sinusoidal steady state.(a) If vS(t)¼2 cos 2128t V, find the output vO(t)(b) At what frequency is the magnitude of the output voltage equal to half of the magnitude of the input voltage in the circuit of Figure 8–62? Consider using OrCAD and
Use MATLAB to find the phasor current IO in Figure P8–63. 400 (D) -j300 S W IB A 200 w j200 2 m B 1+ IA Ic2/0 A -150 Io 200/0 V FIGURE P8-63
The circuit in Figure P8–64 is operating with v¼10 krad/s.(a) Find the phasor outputs VO and IO in Figure P8–64 when m¼50 and the phasor input is IS¼1þj1 mA.(b) Use OrCAD to verify your results above. 2 Is Aj20 k2 B + ee + -150 x lo + Vo FIGURE P8-64
Find the phasor responses IIN and VO in Figure P8–65 when VS ¼ 1 þ j0 V. Vs | + JIN 10 2 10 2 www 000 Vo 20 + -150 Vo 50 501IN FIGURE P8-65
For the circuit of Figure P8–66 find the Thevenin equivalent circuit seen at the output. 10 V +1 2 w + Vx j2 k el FIGURE P8-66 + 1 2Vx VTZT
The OP AMP circuit in Figure P8–67 is operating in the sinusoidal steady state with v ¼1 krad/s. Find the magnitude of the ratio of the output phasor VO to the input phasor VS.Repeat for v¼10 krad/s, v¼100 krad/s, v¼1 Mrad/s, and v¼10 Mrad/s. Use MATLAB to plot the log of jVO/VSj versus the
Find the phasor input VS in Figure P8–68 when the phasor output is VO¼300 þ j200 V. Vs 10 ww 20 m + | 100 2200 2 Vo FIGURE P8-68
The dependent source circuit in Figure P8–69 is operating in the sinusoidal steady state with v¼1 krad/s and m¼103.Find the phasor gain K¼VO/VS and the input impedance ZIN seen by VS. Validate your answer using OrCAD. Vs 1 + 10 ww -10 10 ww -j10 k + x ZIN FIGURE P8-69 + + x Vo
Find the phasor gain K¼VO/VS and input impedance ZIN of the circuit in Figure P8–70. ZIN 10 w -15 -25 + 1 Vs 33 FIGURE P8-70 Vo
Find the phasor gain K¼VO/VS, input impedance ZIN of the circuit, and the capacitor current IX in Figure P8–71. Vs 1 + 100 100 000 w -j100 100 Vo Ix ZIN FIGURE P8-71
Given the circuit in Figure P8–72:(a) Use node-voltage or mesh-current analysis to develop a set of matrix equations for the circuit.(b) Use MATLAB to solve the matrix equations and then find the phasor gain K¼VO/VS and input impedance ZIN of the circuit.(c) Without using the matrix equations,
A load consisting of a 2.2-kV resistor in series with a l -mF capacitor is connected across a voltage source vS(t)¼169.7 cos (377t) V. Find the phasor voltage, current, and average power delivered to the load.
A load consisting of a 50-V resistor in parallel with a 0.47-mF capacitor is connected across a current source delivering IS(t)¼12 cos (3000t) mA. Find the average power delivered to the load.
The circuit in Figure P8–75 is operating in the sinusoidal steady state at a frequency of 10 krad/s. Use OrCAD to find the average power delivered to the 100-V resistor. 1200 12 0 V +1 -120 6 90 V +1 PAVG j40 100 FIGURE P8-75
You have a task of designing a load that ensure maximum power is delivered to it. The load needs to be connected to a source circuit that is not readily observable, but that you can make measurements at its output terminals.You measure the open circuit voltage and read 120ff0 V. You then connect a
(a) Find the average power delivered to the load in Figure P8–77.(b) Find the maximum available average power at the interface shown in the Figure.(c) Specify the load required to extract the maximum average power. + 1 mH m 1k i(t) w + 500 pF v(t) W Load 500 30 cos 106t V FIGURE P8-77
(a) Find the maximum average power available at the interface in Figure P8–60.(b) Specify the values of R and C that will extract the maximum power from the source circuit. Load i(t) 500 mH 500 w 10 cos 10 kt V v(t) C R FIGURE P8-78
AC Voltage Measurement An ac voltmeter measurement indicates the amplitude of a sinusoid and not its phase angle. The magnitude and phase can be inferred by making several measurements and using KVL.For example, Figure P8–79 shows a relay coil of unknown resistance and inductance. The following
Home Power Distribution The circuit of Figure P8–80 emulates a typical 60-Hz residential power system. There are three wires entering the house, two are called ‘‘hot’’ and the remaining one is called the return or‘‘neutral.’’ Each hot line is protected by a circuit breaker–but
OP AMP Band Pass Filter Use the analysis methods discussed in Example 8–28 to find the input-output relationship Vo/Vs for the active band pass filter of Figure P8–81. Treat each stage separately and then multiply the input-output relationships from each stage to obtain the overall input-output
Power Transmission Efficiency A power transmission circuit with a source voltage of Vs¼440þj0 V can be modeled as shown in Figure P8–82. Find the average power produced by the source, lost in the wires, and delivered to the load. What is the transmission efficiency? Ps Vs + 1 Source PL 0.4 5
60 Hz Filter A 1-kV resistor models an important and sensitive laboratory instrument. The desired signal that the instrument measures, varies from 1 Hz to 500 Hz. However, interference from power lines in the laboratory causes the instrument to saturate. A vendor has designed a device that he
AC Circuit Design Select values of L and C in Figure P8–84 so that the input impedance seen by the voltage source is 50þj0V when the frequency is v¼106 rad/s. For these values of L and C, find the output Thevenin impedance seen by the 300-V load resistor. Vs +1 50 www jooL m 1 300 ZIN = 50+
AC Circuit Analysis Ten years after graduating with a BSEE, you decide to go to graduate schools for a masters degree. In desperate need of income, you agree to sign on as a grader in the basic circuit analysis course. One of the problems asks the students to find v(t) in Figure P8–85 when the
Find the Laplace transform of f(t) ¼ 500[l – e100t] u(t).Locate the poles and zeros of F(s).
Find the Laplace transform of f(t) ¼ 20 sin(377t) u(t).Locate the poles and zeros of F(s).
Find the Laplace transform of f(t) ¼ 10 d(t) þ 10 u(t).Locate the poles and zeros of F(s).
Find the Laplace transform of f(t) ¼ 20[e200t 2e100t]u(t). Locate the poles and zeros of F(s).
Find the Laplace transform of f(t) ¼ A[(B þ at) eat] u(t).Locate the poles and zeros of F(s).
Find the Laplace transform of f(t) ¼ 0.005[10 10 cos(1000t)] u(t). Locate the poles and zeros of F(s).
Find the Laplace transform of f(t) ¼ 5[4 cos(50t) 5 sin(50t)] u(t). Locate the poles and zeros of F(s).
Find the Laplace transform of f(t) ¼ d(t) 200e20t cos(200t) u(t). Locate the poles and zeros of F(s).
Find the Laplace transform of f(t)¼10[35t2e15t] u(t).Locate the poles and zeros of F(s).
Find the Laplace transforms of the following waveforms and plot their pole-zero diagrams:(a) f 1ðtÞ ¼ 25e15t 20e10t uðtÞ(b) f 2ðtÞ ¼ 10½cos 10t þ cos 20tuðtÞ
Find the Laplace transforms of the following waveforms and plot their pole-zero diagrams.(a) f 1ðtÞ ¼ 2dðtÞ þ 200e200t þ 400e400t uðtÞ(b) f 2ðtÞ ¼ 15e200t þ 15 cos 500t uðtÞ
9–12 Find the Laplace transforms of the following waveforms.Locate the poles and zeros of F(s). Use MATLAB to verify your results.(a) f 1ðtÞ ¼ 5dðtÞ þ 625t e25t uðtÞ(b) f 2ðtÞ ¼ 10 þ 5e10tðcos 10t þ sin 10tÞ uðtÞ
9–13 Find the Laplace transforms of the following waveforms. Use MATLAB to verify your results.(a) f 1ðtÞ ¼ 5dðt 2Þ(b) f 2ðtÞ ¼ 10e50ðt1Þuðt 1Þ(c) f 3ðtÞ ¼ 20e50ðt10Þuðt 10Þ
9–14 Use MATLAB to find the Laplace transform of the following waveform f ðtÞ ¼ 10 þ 2e10t uðtÞ þ ½5 cos 100ðt 0:05Þuðt 0:05Þ
Find the Laplace transforms of the following waveforms.(a) f 1ðtÞ ¼ d dtð50e1000t cos 200ktÞuðtÞ(b) f 2ðtÞ ¼Rt 020e10xdx þ 10uðtÞ þ 20 de10t dt uðtÞ
Consider the waveform in Figure P9–16.(a) Write an expression for the waveform f(t) using step and ramp functions.(b) Use the time-domain translation property to find the Laplace transform of the waveform f(t) found in part (a).(c) Verify the Laplace transform found in (b) by applying the
Consider the waveform in Figure P9–17.(a) Write an expression for the waveform f(t) in Figure P9–17 using step functions.(b) Use the time-domain translation property to find the Laplace transform of the waveform f(t) found in part (a).(c) Verify the Laplace transform found in (b) by applying
For the following waveform: f ðtÞ ¼ 500 þ 100e500t tsin 1000tuðtÞ(a) Find the Laplace transform of the waveform. Locate the poles and zeros of F(s).(b) Validate your result using MATLAB.
Consider the waveform in Figure P9–19.(a) Write an expression for the waveform f(t) in Figure P9–19 using a delayed exponential.(b) Use the time-domain translation property to find the Laplace transform of the waveform f(t) found in part (a).(c) Verify the Laplace transform found in (b) by
Find the inverse Laplace transforms of the following functions:(a) F1ðsÞ ¼ 50 sðs þ 50Þ(b) F2ðsÞ ¼ s þ 1ðs þ 2Þðs þ 3Þ
Find the inverse Laplace transforms of the following functions:(a) F1ðsÞ ¼ s þ 30 sðs þ 40Þ(b) F2ðsÞ ¼ðs þ 10Þðs þ 20Þsðs þ 50Þðs þ 100Þ
Find the inverse Laplace transforms of the following functions:(a) F1ðsÞ ¼ 5000ðs þ 1000Þðs þ 500Þðs þ 5000Þ(b) F2ðsÞ ¼ 5s2ðs þ 100Þðs þ 500Þ
Find the inverse Laplace transforms of the following functions:(a) F1ðsÞ ¼ 900ðs þ 10Þ2 þ 302(b) F2ðsÞ ¼ 3ðs þ 10Þðs þ 10Þ2 þ 302
Find the inverse Laplace transfonns of the following functions and sketch their waveforms for b > 0:(a) F1ðsÞ ¼ bðs þ bÞsðs2 þ b2Þ(b) F2ðsÞ ¼ sðs þ bÞs2 þ b2
Find the inverse Laplace transforms of the following functions:(a) F1ðsÞ ¼ a2 s2ðs þ aÞ(b) F2ðsÞ ¼ a2 sðs þ aÞ2
Find the inverse Laplace transforms of the following fiinctions:(a) F1ðsÞ ¼ 600ðs þ 10Þðs þ 20Þðs þ 30Þ(b) F2ðsÞ ¼ 2ðs þ 10Þðs þ 15Þðs þ 20Þ
Find the inverse Laplace transforms of the following functions then validate your answers using MATLAB:(a) F1ðsÞ ¼ 16sðs þ 3Þðs2 þ 11s þ 10Þ(b) F2ðsÞ ¼ 5ðs2 þ 9Þsðs2 þ 25Þ
Find the inverse transforms of the following functions:(a) F1ðsÞ ¼ðs þ 10000Þðs þ 100000Þsðs þ 1000Þðs þ 50000Þ(b) F2ðsÞ ¼ 3ðs4 þ 10s2 þ 4Þsðs2 þ 1Þðs2 þ 4Þ
Find the inverse transforms of the following functions:(a) F1ðsÞ ¼ 300ðs þ 50Þsðs2 þ 40s þ 300Þ(b) F2ðsÞ ¼ 1000sðs þ 5Þðs2 þ 4s þ 8Þ
Find the inverse transforms of the following functions:(a) F1ðsÞ ¼ 16ðs2 þ 256Þsðs2 þ 8s þ 32Þ(b) F2ðsÞ ¼ 3ðs2 þ 20s þ 400Þsðs2 þ 50s þ 400Þ
9–31 Find the inverse Laplace transforms of the following functions then validate your answers using MATLAB:(a) F1ðsÞ ¼ðs þ 100Þ2ðs þ 50Þ2ðs þ 200Þ(b) F2ðsÞ ¼ðs þ 50Þ2ðs þ 100Þ2ðs þ 200Þ
A certain transform has a simple pole at s¼20, a simple zero at s¼g, and a scale factor of K ¼ 1. Select values for g so the inverse transform is(a) f ðtÞ ¼ dðtÞ 5e20t (b) f ðtÞ ¼ dðtÞ (c) f ðtÞ ¼ dðtÞ þ 5e20t
Find the inverse transforms of the following functions:(a) F1ðsÞ ¼ sðs þ 10Þðs þ 20Þðs þ 5Þðs þ 30Þðs þ 50Þ(b) F2ðsÞ ¼ðs þ 1000Þðs þ 5000Þðs þ 2000Þ
Find the inverse transforms of the following functions:(a) F1ðsÞ ¼ s2ðs þ 5Þ(b) F2ðsÞ ¼ðs þ 1000Þ2ðs þ 2000Þ2
Find the inverse transforms of the following functions:(a) F1ðsÞ ¼ e5sðs þ 20Þðs þ 10Þðs þ 30Þ(b) F2ðsÞ ¼ se5s þ 20ðs þ 10Þðs þ 30Þ(c) F3ðsÞ ¼ s þ 20e5sðs þ 10Þðs þ 30Þ
Use MATLAB to find the inverse transform and plot the poles and zeros of the following function:FðsÞ ¼ 300sðs2 þ 30s þ 400Þðs þ 20Þðs3 þ 6s2 þ 16s þ 16Þ
Use MATLAB to find the inverse transform and plot the poles and zeros of the following function:FðsÞ ¼ 500ðs3 þ 2s2 þ s þ 2Þsðs3 þ 4s2 þ 4s þ 16Þ
Find the transform F(s) from the pole-zero diagram of Figure P9–38. K is 5. jo s-plane 10 at oo j5 -10 -j5 FIGURE P9-38
Find the transform F(s) from the pole-zero diagram of Figure P9–39. K is 5106. jo 10at 10 at oo j500 j250 s-plane (2) -100 -50 -1250 -j500 FIGURE P9-39
Find the transform F(s) from the pole-zero diagram of Figure P9–40. K is 50. jo *j50 s-plane * 0 -100 -50 50 *-j50 FIGURE P9-40
Use the Laplace transformation to find the v(t) that satisfies the following first-order differential equations:(a) 250 dvðtÞdtþ 2500vðtÞ ¼ 0; vð0Þ ¼ 50 V(b)dvðtÞdtþ 300vðtÞ ¼ 600uðtÞ; vð0Þ ¼ 150 V
Use the Laplace transformation to find the i(t) that satisfies the following first-order differential equation:diðtÞdtþ 500 iðtÞ ¼ 0:100e100t uðtÞ; ið0Þ ¼ 0A
The switch in Figure P9–43 has been open for a long time and is closed at t ¼ 0. The circuit parameters are R ¼ 1 kV, L ¼ 100 mH, and VA ¼ 15 V.(a) Find the differential equation for the inductor current iL(t) and initial condition iL(0).(b) Solve for iL(t) using the Laplace transformation.
The switch in Figure. P9–43 has been closed for a long time and is opened at t ¼ 0. The circuit parameters are R ¼50 V, L ¼ 200 mH, and VA ¼ 50 V.(a) Find the differential equation for the inductor current iL(t) and initial condition iL(0).(b) Solve for iL(t) using the Laplace transformation.
The switch in Figure P9–45 has been open for a long time.At t= 0 the switch is closed.(a) Find the differential equation for the capacitor voltage and initial condition vC(0).(b) Find vO(t) using the Laplace transformation for vS(t) ¼25 u(t) V. vs(t) t=0 + I 100 www 50 ww 1000 pF 150 kvo pF150
Repeat Problem 9–45 for the input waveform vS(t) ¼169 [cos 377t] u(t) V.
Repeat Problem 9–45 for the input waveform vS(t) ¼24 e1000tu(t) V.
Use the Laplace transformation to find the v(t) that satisfies the following second-order differential equation:d2vðtÞdt2þ 20 dvðtÞd tþ 1000vðtÞ ¼ 0; vð0Þ ¼ 20 V and dvð0Þdt¼ 0:
Use the Laplace transformation to find the v(t) that satisfies the following second-order differential equation:d2vðtÞdt2þ 50 dvðtÞd tþ 400 vðtÞ ¼ 0; vð0Þ ¼ 0 and dvð0Þdt¼ 1000 V/s
The switch in Figure P9–50 has been open for a long time and is closed at t ¼ 0. The circuit parameters are R ¼ 500 V, L ¼ 2.5 H, C ¼ 2.5 mF, and VA ¼ 1000 V.(a) Find the circuit differential equation in iL(t) and the initial conditions iL(0) and vC(0).(b) Use Laplace transforms to solve for
The switch in Figure P9–50 has been open for a long time and is closed at t ¼ 0. The circuit parameters are R ¼ 500 V, L ¼ 2.5 H, C ¼ 2.5 mF, and VA ¼ 50 V.(a) Find the circuit differential equation in vC(t) and the initial conditions iL(0) and vC(0).(b) Use Laplace transforms to solve for
The switch in Figure P9–52 has been closed for a long time and is opened at t ¼ 0.(a) Find the circuit differential equation in vC(t) and the initial conditions iL(0) and vC(0).(b) The circuit parameters are L ¼ 50 H, C ¼ 0.25 mF, R1 ¼10 kV, R2 ¼ 20 kV, and vS ¼ 10u(t) V. Use Laplace
9–53 The switch in Figure P9–52 has been open for a long time and is closed at t ¼ 0.(a) Find the circuit differential equation in iL(t) and the initial conditions iL(0) and vC(0).(b) The circuit parameters are L ¼ 50 H, C ¼ 0.25 mF, R1 ¼10 kV, R2 ¼ 10 kV, and vS ¼ 10u(t) V. Use Laplace

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