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systems analysis and design

Questions and Answers of Systems Analysis And Design

6–35 The OP AMP differentiator in Figure P6–35 with R = 22 kΩ and C = 0:62 μF has the input vSðtÞ = 6ð1 −e−50tÞuðtÞ V. Find vOðtÞ for t > 0. vs(f) C R w FIGURE P6-35 + vo(t)
6–31 An OP AMP circuit from Figure 6–18 is in the box shown in Figure 6–31. The input and outputs are given. What is the function of the circuit in the box if:(a) vSðtÞ = cos 500t mV and
6–30 An OP AMP integrator with R = 1MΩ, C = 1μF, and vOð0Þ = 0 V has the input waveform shown in Figure P6–30. Sketch vOðtÞ for t > 0. Vs (f) (V) 3 t(s) 10 20 30 40 -1.5 FIGURE P6-30
6–29 Following the rationale used to derive the dynamic RC circuits in Figure 6–17, derive the input–output relationship for the circuit in Figure P6–29. What mathematical operation does the
6–27 The OP AMP integrator in Figure P6–27 has R = 33kΩ, C = 0:056μF, and vOð0Þ = 10 V. The input is vSðtÞ =5 e−500t u t ð Þ V. The OP AMP has a VCC = 15 V. Find vOðtÞ for t > 0. R
6–20 The inductor in Figure P6–20 carries an initial current of iLð0Þ = 0:2A:At t = 0, the switch opens, and thereafter the current into the rest of the circuit is iðtÞ = −0:2 e−2000t
6–19 A 33-μF capacitor and a 10-mH inductor are connected in parallel with a closed switch as shown in Figure P6–19. The inductor has – 5mA flowing through it at t = 0– . The switch opens at
6–18 The capacitor in Figure P6–18 carries an initial voltage vCð0Þ = – 25 V. At t = 0, the switch is closed, and thereafter the voltage across the capacitor is vCðtÞ = – 100 +75
6–11 The current through a 100-mH inductor is shown in Figure P6–11. Prepare sketches of vLðtÞ, pLðtÞ, and wLðtÞ.\ i(t) (mA) 20 20 10 t (us) 0 5 10 FIGURE P6-11
6–8 The current through a 1500-pF capacitor is shown in Figure P6–8. Given that vCð0Þ = −5 V, at what time will the voltage vCðtÞ first reach 50 V. i(t) (mA) 20 0 t(s) 0 5 10 FIGURE P6-8
6–7 The voltage across a 0:01-μF capacitor is shown in Figure P6–7. Prepare sketches of iCðtÞ, pCðtÞ, and wCðtÞ.Is the capacitor absorbing power, delivering power, or both? v(1)(V) 20 0
6–6 The voltage across a 0:01-μF capacitor is shown in Figure P6–6. Prepare sketches of iCðtÞ, pCðtÞ, and wCðtÞ. Is the capacitor absorbing power, delivering power, or both? v(t) (V) 50 0
Find the OP AMP output voltage in Figure 6–32. R R ww www vo(f) R R4 ww w 5 FIGURE 6-32
Determine the voltage across the capacitors and current through the inductors in Figure 6–31(a). HH 50 www 17 000 12 000 + 5V C (a) 50 2
Find the equivalent capacitance and the initial stored voltage for the circuit in Figure 6–30. 0.033 F HH +20 V- + + 10 V 0.1 F 0.15 F F 15 V + FIGURE 6-30 5V 0.022 uF
Find the equivalent capacitance and inductance of the circuits in Figure 6–28. 1 F 0.5 F 0.5 F 10 mH 80 mH 700 000 000 30 mH 000 0.1 F 300 KH 0.05 F 5 pF 0.1 F 000 1 mH FIGURE 6-28 (c)
Dynamic OP AMP circuits can function as integrators or differentiators.Given an equation or graph of an input waveform, we can predict output waveforms using the mathematical operations of
Design a circuit to solve the following differential equation: 10 dux (1) dt + -500x(t)=1V
Differential, integral, and integrodifferential equations can be solved using dynamic circuits. Suppose a second-order system can be described by the following differential equation:Develop a
Find the input–output relationship of the circuit in Figure 6–22. VSI(f) R w R R ww w + VS2(1) R w R + FIGURE 6-22 C vo(t) +
Use the functional blocks in Figure 6–18 to design an OP AMP circuit to implement the input–output relationship given below. Then simulate your circuit using Multisim to verify your results when
The input to the circuit in Figure 6–20(a) is υSðtÞ =VA cos 2000t V. The OP AMP saturates when υOðtÞ = 15 V.(a) Derive an expression for the output, assuming that the OP AMP is in the linear
The input to the circuit in Figure 6–20(a) is the trapezoidal waveform shown in Figure 6–20(b). Find the output waveform. The OP AMP saturates whenυOðtÞ = 15 V. vs(f) (V) 5 Vo(f) (V) 2 (b) 1
The input to the circuit in Figure 6–19(a) is υSðtÞ = 10uðtÞ V. Derive an expression for the output voltage. The OP AMP saturates when υOðtÞ = 15 V. + vs(t) 1 www 1 F HH -0V+ + Vo(t) (a)
A 50-mH inductor has an initial current of iLð0Þ = 0A. The following voltage is applied across the inductor starting at t =0:For t ≥ 0, use MATLAB to determine the inductor current, power, and
Using theMATLAB code fromExample 6–8, modify it to find the waveforms of the current, voltage, power, and energy of a 50-mH inductor with a current flowing through it given by 5 iL(t)
Figure 6–13 shows the current through and voltage across an unknown energy storage element.(a) What is the element and what is its numerical value?(b) If the energy stored in the element at t = 0
The current through a 2-mH inductor is iLðtÞ = 4 sin 1000t + 1 sin 3000t A as shown in Figure 6–12(a). Find the resulting inductor voltage. i(f) (A) 5T 0 2 4 -5- (a) f(ms)
Analog signals abound, but in today’s technological world, analog signals must be transformed into digital formats to ease electronic transmission and processing. At the end, these digital signals
The current through a capacitor is given byFind the capacitor’s energy and power. ic(t) = loe/Cu(t) A ic(t)=lo[e
Figure 6–6(a) shows the voltage across a 0:5-μF capacitor. Find the capacitor’s energy and power. vc(f) (V) 10 5 0 01 2 I 4 5 1 (ms) (a)
The iC(t) in Figure 6–5(a) is given byFind the voltage across the capacitor if υCð0Þ = 0 V. ic(t)=10(e/c)u(t) A
A 0:01-μF capacitor has the following voltage impressed across itFind the current iC(t) through the capacitor for t > 0. v(t)=100 [e-1000] u(t) V
The voltage in Figure 6–4(a) appears across a 1/2-μF capacitor. Find the current through the capacitor VC(D) (V) 10 5 0 01 23 (a) T (sw)1-T 45
A test is being run in a wind tunnel when a sensor on the trailing edge of a wing produces the response shown in Figure P5–62.When the sensor output reached 1 V, the test was terminated.You are
5–61 Partial Sinewave Descriptors Figure P5–61 shows a gated 60-Hz sine wave. For the portion shown, find Vp, Vpp, VMAX, VMIN, Vavg, and Vrms. Voltage (V) 150 125 100 75 50 0.005 s. 54.47 V 25 0-
5–59 Defibrillation Waveforms Ventricular fibrillation is a life-threatening loss of synchronous activity in the heart. To restore normal activity, a defibrillator delivers a brief but intense
5–57 Gated Function Some radars use a modulated pulse to determine range and target information. A gated modulated pulse is shown in Figure P5–57. Determine an expression for the waveform v(t),
5–51 Figure P5–51 displays the response of a circuit to a square wave signal. The response is a periodic sequence of exponential waveforms. Each exponential has a time constant of 1.6 ms.(a) Find
5–50 Figure P5–50 is the result of the sum of a fundamental and one of its harmonics (an integer multiple of the fundamental).Find VMAX, VMIN, Vp, Vpp, Vavg, Vrms, and T0 for the waveform. V(1),
5–49 Find VMAX, VMIN, Vp, Vpp, Vavg, Vrms, and T0 for the periodic waveform in Figure P5–49. v(t) (mV) 10 5 To 0 0 1 2 L. -1 (ms) 3 4 5 6 FIGURE P5-49
5–48 Find VMAX, VMIN, Vp, Vpp, Vavg, Vrms, and T0 for the periodic waveform in Figure P5–48 and determine if the waveform is causal or noncausal. v(t) (V) 3 2 To 1 0 t (ms) 0 15 30 45 60 FIGURE
5–44 A circuit response is shown in Figure P5–44 that occurs when one exponential stops and another begins where the prior one left off. Determine an approximate expression for the waveform.
5–43 A circuit response is shown in Figure P5–43. Determine an approximate expression for the waveform. Voltage (V) 654 3 2 0 -12 -13 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02
5–42 Write an expression for the damped sine waveform in Figure P5–42. Note: The exponential envelope was added to help in the determination of the damping exponential. 5 2 Voltage (V) 7 7 0
5–41 For the double exponential v t ð Þ=15 e−αt −e−500t u t ð Þ V shown in Figure P5–41, find α. Voltage (V) -10 -12 500 us,-1045 V 0 0.5 1 15 2 2.5 3 3.5 4 4.5 Time (s) FIGURE P5-41
5–39 Write an expression for the composite exponential waveform in Figure P5–39. Then use MATLAB to construct the same waveform and compare the results. Voltage (V) 25 20 20 15 10 in 5 5m 10m 15m
5–38 Write an expression for the composite exponential waveform in Figure P5–38. v(t) (V) 4 3 2.736 2 1.264 1 I 1 0 0 3 5 8 FIGURE P5-38 t (ms)
5–37 Write an expression for the composite exponential waveform in Figure P5–37. v(t) (V) 40 30 20 10 0 2 FIGURE P5-37 t (s)
5–35 Write an expression for the composite sinusoidal waveform in Figure P5–35 v(t) (V) 5 0 -1 -3 t (s) 1.6 -2 s- FIGURE P5-35
5–34 Write an expression for the composite sinusoidal waveform in Figure P5–34 v(f) (V) 15 ms -10 FIGURE P5-34 t (ms)
5–31 Consider the following composite waveforms.Sketch each by hand and then generate each using MATLAB and compare the results.5–32 Sketch the damped ramp v(t) = 2te−30tu(t) V.(a) Find the
5–30 Consider the following composite waveforms.Sketch each on paper and then generate each using MATLAB and compare the results. (a) vi(t)=-5 [1-e-100,000] u(t) V (b) v2(t)=15 [e-5-e-10]u(t) V
5–26 Write an expression for the sinusoid in Figure P5–26.What are the phase angle and time shift of the waveform? Voltage (V) 400 (6.25 ms, 339 V)_ (22.9 ms, 339 V) 300 200 100 0 -100 -200 -300
5–25 Write an expression for the sinusoid in Figure P5–25.What are the phase angle and time shift of the waveform? 3 v(t) (V) 3 s -3 t (s) 0 2.4 FIGURE P5-25
5–24 Write an expression for the sinusoid in Figure P5–24.What are the phase angle and time shift of the waveform? v(t) (V) 5 5 ms 0 FIGURE P5-24 1 (ms)
5–21 By direct substitution, show that the exponential function v (t)=VAe−αt satisfies the following first-order differential equation. dv(t) + av(t)=0 di
5–20 Construct an exponential waveform that fits entirely within the nonshaded region in Figure P5–20. v(t)(V) 20 18 282 12 t(ms) 01 5 10 12 20 FIGURE P5-20
5–19 Construct an exponential waveform that fits entirely within the nonshaded region in Figure P5–19. v(f) (V) 1.0 0.6 0.5 0 0 0.2 FIGURE P5-19 t(s)
5–17 Write an expression for the waveform in Figure P5–17. v(f) (V) 10 3.68 0 10 20 30 40 50 60 FIGURE P5-17 t (ms)
5–14 Write an expression for the waveform in Figure P5–14. 2.5 0.0 -2.5 -5.0 -75 -10.0 -12.5 Voltage (V) -15.0 -17.5 5 10 15 20 25 30 Time (s) FIGURE P5-14
5–13 Write an expression for the waveform in Figure P5–13 0 Voltage (V) 2 5 0 50 100 150 200 250 300 Time (s) FIGURE P5-13
5–12 Sketch the following exponential waveforms. Find the amplitude and time constant of each waveform. (a) vi(t)= [50e-100] u(t) V (b) v2(t)= [100e/50] u(1-2) V (c) v3(1)= [5e-1-5)] u(1-5) V (d)
5–10 Sketch the waveform described by the following: (a) v(t)=108(+10)-108(t) + 108(1-10) V (b) v(t)==18(1-k) V
5–9 Sketch the waveform described by the following: v(t)= + 1}}] |[u(t+e)u(t)] + [ ^_^t+}]}] [u(t)u(t [u(t)-u(t-e)] V
5–8 Express each of the waveforms in Figure P5–8 as a sum of singularity functions V(1) (V) V2(f) (V) 10 t(s) t(s) 3 0 10 20 1 (a) FIGURE P5-8 (b)
5–7 Express the waveform in Figure P5–7 as a sum of step functions -2 v(f) (V) 12 1(s) 012 3 4 34 5 -6 -12 FIGURE P5-7
5–6 Express each of the following signals as a sum of singularity functions. 2 (a) Vi(t)=(4 0 1
5–5 Sketch the following waveforms: (a) vi(t)=r(+2) - r(1-2) V v2(t)=4+r(1+1)-2r(1-1)+r(1-3) V (b) (c) v3(1)= d vi(t) dt d v(1) (d) va(t) di
5–4 Sketch the following waveforms: (a) vi(t)=5 u(t) V (b) i(t)=-2u(t+ 0.002) + 3u(t + 0.001) - u(t) mA (c) v3(1)=1 [u(1+1) - u(t-1)] V
5–3 Using appropriate step functions, write an expression for each waveform in Figure P5–3. -3 v(t)(V) (a) v(t)(V) 5 -2 (b) 1 2 t(s) t(s)
5–2 Using appropriate step functions, write an expression for each waveform in Figure P5–2. i(t)(mA) -2 120 v(f)(V) 30 2 t(s) t(s) 2 6 -6 -2 -120 (a) v(1)(V) -9-6 10 -30 (b) -t(s) -3 3 6 9 -10
5–1 Sketch the following waveforms: (a) vi(t)=5u(t) 5u(t - 1) V (b) v2(t)=3u(t+2)-2(1-2) V is(t)=-3u(1+3)+6u(t)-3u(1-3) mA (c) (d) is(t)=2u(-1) A
An electrocardiogram (ECG) is a valuable diagnostic tool used in cardiovascular medicine. The ECG is based on the fact that the heart emits measurable bioelectric signals that can be recorded to
The operation of a digital system is coordinated and controlled by a periodic waveform called a clock. The clock waveform provides a standard timing reference to maintain synchronization between
Classify each of the following signals as periodic or aperiodic and causal or noncausal. Then calculate the average and rms values of the periodic waveforms, and the peak and peak-to-peak values of
Find the peak, peak-to-peak, average, and rms values of the periodic waveform in Figure 5–43. v(f) 2VA VA To 370 To 5To -VA 4 FIGURE 5-43 4
Find the average and rms values of the sinusoid and sawtoothwaveforms in Figure 5–42. v(t) Areas are equal Vavs 0 + To + 2T + 1 v(t) Vavg -VA Areas are equal NAA To 2To 3To
For the pulse waveform in Figure 5–41 find VMAX, VMIN, Vp, Vpp, and Vavg. VA 0 -VA FIGURE 5-41 v(t) t
Find the peak, peak-to-peak, and average values of the periodic input and output waveforms in Figure 5–40 of a half-wave rectifier. VA 0 VA A To Input In Signal Out processor VA v(t) A To Output
Characterize the following waveform defined bywhere bn =4 VA=πn, VA =10V, f0 = 1000 Hz, and n=1,3,5,7, 9,11…by plotting thefirst sixn terms for a half period of the fundamental frequency fo.
For the following composite waveforms, determine the maximum amplitude, the approximate duration, and the type of waveform represented: (a) vi(t)=25 sin 1000t][u(t)-u(t-10)] V (b) 2(t)=[50 cos 1000]
Characterize the composite waveform defined by 10 v(t)=5-sin(2x500) - 10 10 sin(2x1000t)- sin(2x1500) V 2
A double exponential waveform is given as(a) What is the value of υ(t) at the maximum, and at what time does it occur?(b) What is the time constant of the dominant (longer-lasting) exponential?(c)
Underdamped second-order systems produce the damped sinusoidal waveform shown in Figure 5–32. When presented with such a display, it may be necessary to determine an expression for the resulting
The equation describing a damped ramp is as follows:(a) Find the time at which the function reaches its maximum value.(b) What is the value of v(t) at the maximum? VA [(++) e/Tc]u(t) V V(t) =VA Tc
Figure 5–30 contains a waveform that is called a double-sided exponential, which is defined as the sum of a normal exponential and a reversed exponential. This waveform is 1 at t = 0 and decays
Characterize the composite waveform generated by subtracting an exponential from a step function with the same amplitude 1++ (a) Sketch the waveform described by the following:(b) What is the value
Describe the following waveform v(t)= [VAu(t)-VAu(-1)][8(1+1)+8(t) +8(1-1)] V
Characterize the composite waveform generated by v(t)=VAu(t)-VAU(-1) V
You are in a Circuits laboratory and are required to characterize a voltage signal. You observe the signal on an oscilloscope as shown in Figure 5–26. You measure the voltage of two adjacent peaks
(a) Find the period and the cyclic and radian frequencies for each of the following sinusoids:(b) Find the waveform of υ3(t) = υ1(t) + υ2(t) V. v1(t) = 17 cos(2000t-30) V v2(t) = 12 cos(2000t+30) V
Sketch the waveform described by v(t) = 10 cos(2000-60) V
Derive an expression for the sinusoid displayed in Figure 5–24 when t = 0 is placed in the middle of the display 4 div 4 div 5.5 div - Amplitude (5 V/div) 4 div T (0.1 ms/div)
Figure 5–24 shows an oscilloscope display of a sinusoid. The vertical axis (amplitude)is calibrated at 5 V per division, and the horizontal axis (time) is calibrated at 0.1 ms per division. Derive
Find the amplitude and time constant for each of the following exponential signals: (a) vi(t)=-15e-1000r]u(t) V (b) (1)=[+12e10] u(t) mV (c) i3(1)= [15e-500 u(-1) mA (d) is(t)= [4e-200(1-100)]
Figure 5–21 shows three exponential waveforms. Match each curve with the appropriate expression. 1. vi(t)=100 e-(1/100) u(t-100) V 2. 12 (1) 100 e-(1/100)u(t) V 3. 3(1)=100 e-(-100)/100) (-100 )V
You are in a Circuits laboratory and are required to determine the time constant of a voltage signal. You observe the signal on an oscilloscope as shown in Figure 5–20. The scope tells you that
An oscilloscope is a laboratory instrument that displays the instantaneous value of a waveform versus time. Figure 5–19 shows an oscilloscope display of a portion of an exponential waveform. In the
Sketch the waveform described by v(t)=20e-10,000 u(t)V

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