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computer science
systems analysis design

Questions and Answers of Systems Analysis Design

In Section 6-1, Figure 6-2 (g) shows an air-tunable capacitor as one example of the capacitor types. This type of device can vary its capacitance similar to how a potentiometer can vary its
Find the equivalent capacitance of the capacitance bridge shown in Figure P6-5 6. CEO C C C C
In a particular radio frequency (RF) application, you determine there is a need for a small inductor of \(125 \mathrm{uH}\) and rather than trying to order one and wait for it to arrive, you decide
Circuits with memory storage are very useful in designing circuits that are frequency selective. Consider the circuit shown in Figure P6-5 . Build that circuit in Multisim. For the source, use the ac
Using Multisim, create the following waveforms and state if each waveform is causal or noncausal, periodic or nonperiodic:(a) A step voltage switching from 0 to \(5 \mathrm{~V}\) at \(t=100
Compressed High-Intensity Radiated Pulse (CHIRP) are signals that change frequency and possibly also amplitude. They have uses in radar detection when applied at GHz frequencies. Another common
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
Ventricular fibrillation is a life-threatening loss of synchronous activity in the heart. To restore normal activity, a defibrillator delivers a brief but intense pulse of electrical current through
Timing digital circuits is vital to the operation of any digital device. Using an ideal OP AMP (running open-loop, i.e., without feedback) and appropriate resistors, design a way to convert a
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 \(-4 \underline{6}\). When the sensor output reached \(1 \mathrm{~V}\), the
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
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)
A simulated ECG signal obtained from a patient is shown in Figure P5-4.9. Identify any abnormal pulses. For the normal pulses, estimate the PR interval, the QRS interval, and the ST segment. Does the
Cars are becoming increasingly autonomous. One necessary accessory is a collision avoidance radar. Such a radar emits a high-frequency modulated pulse traveling at the speed of light (3 \(\times
For \(t \geq 0\), the voltage across a \(1-\mu \mathrm{F}\) capacitor is \(v_{\mathrm{C}}(t)\) \(=10 u(t) \mathrm{V}\). Derive expressions for \(i_{\mathrm{C}}(t)\) and \(p_{\mathrm{C}}(t)\). Is the
The voltage across a 10000-pF capacitor is \(v_{\mathrm{C}}(t)=100\) \(\sin \left(2 \pi 10^{4} tight) \mathrm{V}\). Derive expressions for \(i_{\mathrm{C}}(t)\) and \(p_{\mathrm{C}}(t)\). Is the
The current through a \(0.2-\mu \mathrm{F}\) capacitor is a rectangular pulse with an amplitude of \(3 \mathrm{~mA}\) and a duration of 5 \(\mathrm{ms}\). Find the capacitor voltage at the end of the
The voltage across a 0.001- \(\mu \mathrm{F}\) capacitor is shown in Figure P6-1. Prepare sketches of \(i_{\mathrm{C}}(t), p_{\mathrm{C}}(t)\), and \(w_{\mathrm{C}}(t)\). Is the capacitor absorbing
The voltage across a \(0.01-\mu \mathrm{F}\) capacitor is shown in Figure P6-5 . Prepare sketches of \(i_{\mathrm{C}}(t), p_{\mathrm{C}}(t)\), and \(w_{\mathrm{C}}(t)\). Is the capacitor absorbing
For \(t \geq 0\), a current source delivers \(i_{\mathrm{S}}(t)=10\) \(\cos (4000 \pi t) \mathrm{mA}\) to two \(2.0-\mu \mathrm{F}\) capacitors connected in series. Using Multisim, plot
A 100- \(\mu \mathrm{F}\) capacitor has no voltage across it at \(t=0\). A current flowing through the capacitor is given as \(i_{\mathrm{C}}(t)=2 u(t\) )\(-3 u(t-3)+u(t-6) \mathrm{mA}\). Find the
For \(t \geq 0\), the current through a \(3300-\mu \mathrm{H}\) inductor is \(i_{\mathrm{L}}(t)\) \(=2 e^{-20,000 t} \mathrm{~A}\). Find \(v_{\mathrm{L}}(t), p_{\mathrm{L}}(t)\), and
For \(t \geq 0\), the voltage across a \(220-\mathrm{mH}\) inductor is \(v_{\mathrm{L}}(t)=25 e^{-200 t} \mathrm{~V}\). Plot \(i_{\mathrm{L}}(t)\) versus time when \(i_{\mathrm{L}}(\mathrm{o})=100\)
Repeat Problem 6-9 when the voltage across a 20-mH inductor is \(v_{\mathrm{L}}(t)=100 e^{-2500 t} \mathrm{~V}\). Plot \(i_{\mathrm{L}}(t)\) versus time when \(i_{\mathrm{L}}(\mathrm{o})=+1
A voltage \(v_{\mathrm{L}}(t)=5 \cos (1000 n t) \mathrm{V}\) appears across a \(50-\mathrm{mH}\) inductor, where \(n\) is a positive integer that controls the frequency of the input signal. The
A 1- \(\mu \mathrm{F}\) capacitor with \(\mathrm{o} \mathrm{V}\) initial value is connected i to an exponential source with the following properties: initial value: \(\mathrm{OV}\), final value: \(1
The capacitor in Figure P6-13 carries an initial voltage \(v_{\mathrm{C}}(0)=-25 \mathrm{~V}\). At \(t=0\), the switch is closed, and thereafter the voltage across the capacitor is
A1- \(\mu \mathrm{F}\) capacitor and a 100-mH inductor are connected in parallel with a closed switch as shown in Figure P6-14. The inductor has \(-10 \mathrm{~mA}\) flowing through it at \(t=0\).
The inductor in Figure P6-15 carries an initial current of \(i_{\mathrm{L}}(0)=20 \mathrm{~mA}\). At \(t=0\), the switch opens, and thereafter the voltage across the inductor is
A 4700-pF capacitor is connected in series with a \(100-\mathrm{k} \Omega\) resistor as shown in Figure P6-16. The voltage across the capacitor is \(v_{\mathrm{C}}(t)=10 \cos (1000 t) \mathrm{V}\).
For \(t>0\), the voltage across an energy storage element is \(v(t)=5 \times 10^{5}\left(1-e^{-100 t}ight) \mathrm{V}\) and the current through the element is \(i(t)=5 e^{-100 t} \mathrm{~mA}\). What
For \(t>0\), the voltage across a circuit element is \(v(t)=5\) \(t e^{-100 t} \cos (1000 t) \mathrm{V}\) and the current through the element is \(i(\) \(t)=2.5 t e^{-100 t} \cos (1000 t) \mu
The capacitor in Figure P6-19. has a 5 -V charge across it. The comparator is one-sided with \(v_{\text {HIGH }}=5 \mathrm{~V}\) and \(v\) LOW \(=0 \mathrm{~V}\). At \(t=0\), the switch closes. Using
The OP AMP integrator in Figure P6-20 has \(R=22\) \(\mathrm{k} \Omega, \mathrm{C}=0.068 \mu \mathrm{F}\), and \(v_{\mathrm{O}}(0)=10 \mathrm{~V}\). The input is \(v_{\mathrm{S}}(t)=6 e\) \(-250 t
Build the OP AMP circuit of Figure P6-20 in Multisim. Let \(R=33 \mathrm{k} \Omega, C=0.056 \mu \mathrm{F}\), and \(v_{\mathrm{O}}(0)=15 \mathrm{~V}\). The input is \(10\left(1-e^{-500 t}ight) u(t)
An OP AMP integrator with \(R=1 \mathrm{M} \Omega, C=1 \mu \mathrm{F}\), and \(v_{\mathrm{O}}\) (o) \(=0 \mathrm{~V}\) has the output waveform shown in Figure P6-22. Sketch \(v_{\mathrm{S}}(t)\) for
Design appropriate OP AMP circuits that will realize each of the functions in Problem 6-23. The OP AMPs available have a maximum \(K\) of 10,000 and a \(V_{\mathrm{CC}}= \pm 15 \mathrm{~V}\).Data
The OP AMP integrator in Figure P6-20 has \(R=22\) \(\mathrm{k} \Omega, C=0.001 \mu \mathrm{F}\), and \(v_{\mathrm{O}}(\mathrm{o})=\mathrm{o} \mathrm{V}\). The input is \(v_{\mathrm{S}}(t)=2 \sin\)
The OP AMP differentiator in Figure P6-26 with \(R=33\) \(\mathrm{k} \Omega\) and \(C=0.62 \mu \mathrm{F}\) has the input \(v_{\mathrm{S}}(t)=10\left(1-e^{-50 t}ight) u(t)\) \(\mathrm{V}\). Find
Redesign the circuit of Figure P6-26 using an \(R L\) circuit rather than the \(R C\) approach shown. vs(t) C R ww + vo(t)
Consider the circuit of Figure P6-28 \(\cdot R_{1}=R_{2}=1\) \(\mathrm{M} \Omega, C_{1}=C_{2}=1 \mu \mathrm{F}\), and the capacitors have zero initial conditions, the output should, in theory, be the
The input to the OP AMP differentiator in Figure \(\underline{\mathrm{P} 6-26}\) is \(v_{\mathrm{S}}(t)=5\left[\sin \left(2 \pi \times 10^{6} tight)ight] u(t) \mathrm{mV}\). Select \(R\) and \(C\) so
Find the input-output relationship of the RC OP AMP circuit in Figure P6-30 . vs(t)o CR R + Vo(1)
Show that the RC OP AMP circuit in Figure P6-31 is a noninverting integrator whose input-output relationship is\[v_{\mathrm{O}}(t)=\frac{1}{R \mathrm{C}} \int_{0}^{t} v_{\mathrm{S}}(x) d
Design an RC OP AMP circuit to implement the block diagram in Figure P6-32 . vs(t) d dt 200 1 -200-0 -Vo(1)
Repeat Problem 6-32 but use an RL OP AMP circuit.Data From Exercise 6-32Design an RC OP AMP circuit to implement the block diagram in Figure P6-32 . vs(t) d dt 1 200 200 S vo(1)
For the block diagram shown in Figure P6-34:(a) Find the differential equation it represents.(b) Design an RC OP AMP circuit to implement the block diagram using integrators.(c) Design an RC OP AMP
In this problem you will design an oscillator. The equation for your oscillator is\[\frac{d^{2} v_{\mathrm{O}}(t)}{d t^{2}}+v_{\mathrm{O}}(t)=0 \mathrm{~V}\](a) Draw a block diagram to solve your
For the differential equation:\[v_{\mathrm{O}}(t)=10 v_{\mathrm{S}}(t)+\frac{1}{10} \frac{d v_{\mathrm{S}}(t)}{d t}+\frac{1}{20} \frac{d^{2} v_{\mathrm{S}}(t)}{d t^{2}}\](a) Draw a block diagram
Find a single equivalent element for each circuit in Figure P6-37. 2.2 6.8 60 1000 100 100 Cl 000 rele 3.3 C2 3.3 2000 100 ell 100
Use the lookback method to find the equivalent capacitance of the circuit shown in Figure P6-3 (+1 v(t) C C C CEO
You need to have an equivalent inductance of \(235 \mathrm{mH}\) for a particular application. However, you only have \(100-\mathrm{mH}\) inductors available. How might you connect these to get
Find the equivalent capacitor in the circuit of Figure P6\(4 \underline{0}\). CAB 100 F A B 50 uF 100 F 80 F 40 F 20 uF 40 F 20 F 20 F
What is the equivalent capacitance and initial voltage of a series connection of a 33- \(\mu \mathrm{F}\) capacitor with \(100 \mathrm{~V}\) stored and a \(47-\mu \mathrm{F}\) capacitor with \(50
What is the equivalent inductance and initial current for the inductors shown in Figure P6-42? LEQ 50 . .. 25 15 1 30 . . | 50 150 S | 100 100
For the circuit in Figure P6-43, find an equivalent circuit consisting of one inductor and one capacitor. Select a value of an inductor and a capacitor from among the standard values in Appendix G to
Figure P6-44 is the equivalent circuit of a two-wire feedthrough capacitor.(a) What is the capacitance between terminal 1 and ground when terminal 2 is open?(b) What is the capacitance between
A switching power supply requires an inductor that can store at least \(1 \mathrm{~mJ}\) of energy. A list of available inductors is shown below. Select the inductor that best meets the requirement.
The circuits in Figure P6-46 are driven by dc sources. Find the current through the source and the voltages across the capacitors. ide 100 V ide 12 V + + -I 1k L M00 m 1 C CI +Vdcl +Vdc2- C L3 L
The circuit in Figure P6-4.7 is driven by a 100-V dc source. Find the energy stored in the capacitor and each inductor under dc conditions. ide 100 V + WL2(1) mo 10 mH | 10 mH 0.02 F | wc(t) 1k WL
(a) The OP AMP circuits in Figure P6-48 have capacitors in their feedback loops. Determine the circuit gains at dc and as the frequency approaches \(\infty \mathrm{rad} / \mathrm{s}\).(b) Replace the
The OP AMP circuit shown in Figure P6-4.9 is a band (reject filter that will be studied later. Determine the circuit gain at dc and as the frequency approaches \(\infty \mathrm{rad} / \mathrm{s}\). V
Piezoelectric transducers (sensors) measure dynamic phenomenasuchaspressureand force. Thesephenomenacause stresses that "squeeze" a quantity of electric charge from piezoelectric material in the
At t=0t=0, the switch in Figure P6-51 is closed and thereafter the voltage across the capacitor isvC(t)=(10+10,000t)e−8000t VvC(t)=(10+10,000t)e−8000t VUse MATLAB to solve all of the following
The circuit in Figure P4-72 produces bipolar power supply voltages \(V_{\text {POS }}>0\) and \(V_{\text {NEG }}0\). Note that the OP AMP output is grounded and that its \(+V_{\mathrm{CC}}\) and
Electric Scooter Governor A town has a new light rail system. To encourage its use, the town council approved installing electric scooters at each station for riders to rent cheaply to take them to
A particular pressure sensor is designed to operate under constant pressure. The task is to detect a pressure increase and sound an alarm. The sensor produces \(1 \mathrm{mV}\) at \(100
A weathervane turns with the wind direction. The base of the weathervane is connected to a rotary potentiometer without stops, that is, the potentiometer turns from o \(\Omega\) to \(10 \mathrm{k}
The circuit in Figure P4=76 is a four-bit DAC. The DAC output is the voltage \(v_{\mathrm{O}}\) and the input is the binary code represented by bits \(b_{1}, b_{2}, b_{3}\), and \(b_{4}\). The input
(a) A Find the input-output relationship of the circuit in Figure \(\mathrm{P}_{4}=77\).(b) Design a circuit that realizes the relationship found in part (a) using only \(15-\mathrm{k} \Omega\)
Strain gauges measuring the deflection of a sintered metal column are connected to a Wheatstone bridge. The output of the bridge is balanced when there is no strain producing o \(\mathrm{V}\) output.
A strain gauge with an unstressed resistance of \(120 \Omega\) is used in a bridge as shown in Figure P4=79. The reference voltage is +25 \(\mathrm{V}\). When fully stressed the resistance of the
Figure P4-80 shows two circuits using the same transistor connected in different ways. The transistor has a \(\beta\) of 90 and a \(V\) \(\gamma\) of \(0.7 \mathrm{~V}\). Find the current gain of
As a young designer at a firm that builds lithium batteries, you are tasked with designing a sensor system that displays the temperature inside the battery pack. The range of temperatures that need
Sketch the following waveforms:(a) \(v_{1}(t)=u(t)-u(t-3) \mathrm{V}\)(b) \(v_{2}(t)=5 u(t+1)-5 u(t-2) \mathrm{V}\)(c) \(i_{3}(t)=-2 u(t)-u(t-1)+3 u(t-2) \mu \mathrm{A}\)(d) \(i_{4}(t)=10 u(-t)
Using appropriate step functions, write an expression for each waveform in Figure P \(5=\). i(t)(mA) 10 -10 1 (a) 3 t(s) -300 Y(7)(V) 30 L 30 3 6 v(r)(V) -100 (b) 5 100 -(us) - 1(s)
Sketch the following waveforms:(a) \(v_{1}(t)=12-2 u(t) \mathrm{V}\)(b) \(i_{2}(t)=-2 u(t+0.003)+2 u(t-0.003) \mu \mathrm{A}\)(c) \(v_{3}(t)=t[u(t-1)-u(t-2)] \mathrm{mV}\)(d) \(i_{4}(t)=5 u(-t)
Sketch the following waveforms:(a) \(v_{1}(t)=r(t+2)-r(t-2) \mathrm{V}\)(b) \(v_{2}(t)=4+r(t+1)-2 r(t-1)+r(t-3) \mathrm{V}\)(c) \(v_{3}(t)=\frac{d v_{1}(t)}{d t}\)(d) \(v_{4}(t)=\frac{d^{2}
Express each of the following signals as a sum of singularity functions. (a) (b) (c) in(t)=4 0 (1)= 0 1
Express the waveform in Figure P5 5 as a sum of singularity functions. -2 -1 i(t) (mA) 40 30 20 101 0 I 1 2 3 4 t (s)
Express each of the waveforms in Figure P \(5=7\) as a sum of singularity functions. V (1) (V) -1 (a) 3 1 (s) V/(1) (V) 10 0 (b) 10 20 t (s)
Using its pulse voltage source, generate on Multisim a waveform \(v(t)\) that starts at \(t=1 \mathrm{~ms}\) and consists of a pulse train of \(5-\mathrm{V}\) pulses with a \(2-\mathrm{ms}\) pulse
Sketch the following exponential waveforms. Find the amplitude and time constant of each waveform.(a) \(v_{1}(t)=5 e^{-2 t} u(t) \mathrm{V}\)(b) \(v_{2}(t)=5 e^{-2 t} u(t-1) \mathrm{V}\)(c)
In the lab, you see the waveform on the oscilloscope shown in Figure P5-10. Write an expression for the waveform. Note that \(t=0\) is on the far-left side of the display. 0 Amplitude (10 V/div) (0.2
Half-life, \(t_{1 / 2}\), is the time required for a quantity to shrink to half its initial value. Radioactive elements are often defined by their half-life radioactive decay given by \(N(t)=N_{0}
Write an expression for the waveform in Figure P5-12 . v(1) (V) 20 7.36 0 10 20 30 40 50 60 1 (ms)
Design an exponential waveform that fits entirely within the nonshaded region in Figure P \(5=13\). v(t) (V) 10 6 0 0 2 t(s)
Design an exponential waveform that fits entirely within the nonshaded region in Figure P5-14. y(t)(V) 20 18 12 4 0 01 5 10 12 20 -I (ms)
Find the period, frequency, amplitude, time shift, and phase angle of the following sinusoids.(a) \(v_{1}(t)=240 \cos (120 \pi t)-240 \sin (120 \pi t) \mathrm{V}\)(b) \(v_{2}(t)=-30 \cos (50
(a) Plot the waveform of each sinusoid in Problem 5-15 by hand.Data From Problem 5-15Find the period, frequency, amplitude, time shift, and phase angle of the following sinusoids.(b) Use Multisim to
Write an expression for the sinusoid in Figure P \(5=17\). What are the phase angle and time shift of the waveform? v(1) (V) 0 12 us. 9.6 t (s)
Write an expression for the sinusoid in Figure P \(5=-18\). What are the phase angle and time shift of the waveform? Voltage (V) 400 300 200 100 0 -100 -200 -300 -400 0 (0 s.-237 V)- (6.25 ms, 339 V)
Find the Fourier coefficients, cyclic frequency, and radian frequency of the following sinusoids:(a) \(v(t)=50 \cos \left(100 \pi t+36.9^{\circ}ight) \mathrm{V}\)(b) \(i(t)=240 \cos \left(1200 \pi
For the following sinusoid: \(v(t)=10 \cos (2 \pi 200 t+\) \(\left.60^{\circ}ight) \mathrm{V}\)(a) Find the Fourier coefficients, cyclic frequency, and radian frequency.(b) Plot the waveform by
Consider the following composite waveforms.(a) \(v_{1}(t)=15\left[1-e^{-25,000 t}ight] u(t) \mathrm{V}\)(a) \(v_{2}(t)=-2\left[e^{-t}-e^{-5 t}ight] u(t) \mathrm{V}\)Sketch each on paper and then
Consider the following composite waveforms.(a) \(i_{1}(t)=10+5 \sin (500 \pi t) u(t) \mathrm{mA}\)(b) \(i_{2}(t)=50\left[e^{-1000 t}+\cos (2000 \pi t)ight] u(t) \mathrm{mA}\)Sketch each by hand and
The two signals shown in Figure \(\mathrm{P}_{5}-23\) are multiplied together. Write an expression for their output. -500(-)u(-1) -2.5 Vj(t) 0 V(t) -0.5 0 1.5 -500 u(t) 3.5 - 1 (ms) 1 (ms)
Write an expression for the composite sinusoidal waveform in Figure P \(5=24\). v(1) (V) 40 0 -100 10 s +
Write an expression for the composite sinusoidal waveform in Figure P \(5=25\). v(1) (V) FAL 1.6 -2 s- 0 t (s)
Write an expression for the composite exponential waveform in Figure P5-26. v(t) (V) 80 60 40 20 0. 0 4 -1 (1)

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