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systems analysis and design

Questions and Answers of Systems Analysis And Design

Construct a Butterworth low-pass transfer function that meets the following requirements:TMAX = 0 dB,TMIN = −40 dB, ωC = 250 rad=s, and ωMIN =1:5 krad=s.
The circuit design in Example 14–7 used the equal element method. Rework the problem using the unity gain technique. Use Multisim to validate your design. Comment on the two approaches.
(a) Construct a Butterworth low-pass transfer function that meets the following requirements:TMAX = 20 dB,ωC = 1 krad=s,TMIN = −20 dB, and ωMIN = 4 krad=s:(b) Design a cascade of active RC
Construct a first-order cascade transfer function that meets the following requirements:TMAX = 0 dB,TMIN = −30 dB,ωC = 200 rad=s, and ωMIN = 1 krad=s.
(a) Construct a first-order cascade transfer function that meets the following requirements:TMAX = 10 dB,ωC = 200 rad=s,TMIN = −10 dB, and ωMIN = 800 rad=s.Use MATLAB to visualize the gain
Design a notch filter using the realization in Figure 14–19 to achieve a notch at 200 krad=s, a B of 20 krad=s, and a passband gain of 10. C w R CR KR KRxl ww ww Rx (B www V(f) + Tuned filter Rxla
Use the active RC circuit in Figure 14–19 to design a bandstop filter with a notch frequency at 60 Hz and a notch bandwidth of 12 Hz. Find the circuit’s transfer function and use Multisim to plot
Construct a second-order bandstop transfer function with a notch frequency of 50 rad=s, a notch bandwidth of 10 rad=s, and passband gains of 5
Rework the circuit design in Example 14–4 starting with C1 =C2 =C =0:2 μF.
Use the active RC circuit in Figure 14–17 to design a bandstop filter with a notch frequency at 60 Hz and a notch bandwidth of 12 Hz. Find the circuit’s transfer function and use MATLAB to plot
Construct a second-order bandpass transfer function with a corner frequency of 50 rad=s, a bandwidth of 10 rad=s, and a center frequency gain of 4.
Rework the design in Example 14–3, starting with C = 2000 pF.
Use the active RC circuit in Figure 14–14 to design a bandpass filter with a center frequency at 10 kHz and a bandwidth of 4 kHz. Find the center frequency gain for the design. Use MATLAB to show
Construct a second-order high-pass transfer function with a corner frequency of 20 rad=s, an infinite-frequency gain of 4, and a gain of 2 at the corner frequency.
Develop a second-order high-pass transfer function with a corner frequency atω0 = 20 krad=s, an infinite-frequency gain of 0 dB, and a corner frequency gain of−3 dB. Use MATLAB to help visualize
Design circuits using both the equal element design and unity gain design techniques to realize the transfer function in Exercise 14–1. Use Multisim to simulate your designs and compare them to the
Develop a second-order low-pass transfer function with a corner frequency of 50 rad=s or 7:96 Hz, a dc gain of 2, and a gain of 4 at the corner frequency. Validate your result by using MATLAB to plot
Develop a second-order low-pass transfer function with a corner frequency atω0 = 1 krad=s and with corner frequency gain equal to the dc gain. Use MATLAB to help visualize the Bode plots of the
14-4 High-Pass, Bandpass, and Bandstop Filter Design(Sects. 14–6 and 14–7)Given a high-pass, bandpass, or bandstop filter specification:(a) Construct a transfer function that meets the
14-3 Low-Pass Filter Design (Sects. 14–4 and 14–5)Given a low-pass filter specification:(a) Construct a transfer function that meets the specification.(b) Design a cascade of first- and
14-2 Second-Order Filter Design (Sects. 14–2 and 14–3)(a) Construct a second-order transfer function with specified filter characteristics.(b) Design a second-order circuit with specified filter
14-1 Second-Order Filter Analysis (Sects. 14–1, 14–2 and 14–3)(a) Given a second-order filter circuit, find a specified transfer function.(b) Given the transfer function of a second-order
13–56 Virtual Keyboard Design Electronic keyboards are designed using the following equation that assigns particular frequencies to each of the 88 keys in a standard piano keyboard:where n is the
13–55 Spectrum Analyzer Calibration A certain spectrum analyzer measures the average power delivered to a calibrated resistor by the individual harmonics of periodic waveforms. The calibration of
13–53 Spectrum of a Periodic Impulse Train A periodic impulse train can be written asFind the Fourier coefficients of x(t). Plot the amplitude spectrum and comment on the frequencies contained in
13–52 Fourier Series from a Bode Plot The transfer function of a linear circuit has the straightline gain and phase Bode plots in Figure P13–52. The first four terms in the Fourier series of a
13–49 The input to the circuit in Figure P13–49 is the voltage(a) Calculate the average power delivered to the 50-Ω load resistor.(b) Use Multisim to find the magnitude of the voltage across the
13–48 Estimate the rms value of the periodic voltage 1 v(t) =VA [2-cos(opt) + cos(3 opt) - cos(5 mot) 1 +cos(7 opt)
13–45 Repeat Problem 13–44 for the periodic waveform in Figure P13–45. Vs(f) (V) VA t(s) 0 2T FIGURE P13-45
13–44 Find the rms value of the periodic waveform in Figure P13–44 and the average power the waveform delivers to a resistor. Find the dc component of the waveform and the average power carried
13–38 The voltage across a 100-Ω resistor is given by the an Fourier coefficients shown in volts in Figure P13–38. All bn coefficients are zero, as is a0. The fundamental frequency is 250 Hz.(a)
13–37 The current through a 1-kΩ resistor isFind the rms value of the current and the average power delivered to the resistor. i(t)=50+36cos(120-30)-12 cos(360+45) mA
13–36 A triangular wave with VA = 10 V and T0 =20π ms drives a circuit whose transfer function is(a) Find the amplitude of the first four nonzero terms in the Fourier series of the steady-state
13–29 The periodic triangular wave in Figure P13–29 is applied to the RLC circuit shown in the figure.(a) Use the results in Figure 13–4 to find the Fourier coefficients of the input for VA = 5
13–26 The periodic sawtooth wave in Figure P13–26 drives the OP AMP circuit shown in the figure.(a) Use the results in Figure 13–4 to find the Fourier coefficients of the input for VA = 3 V and
13–25 The periodic triangular wave in Figure P13–25 is applied to the RC circuit shown in the figure. The Fourier coefficients of the input areIf VA = 10 V and T0 =2π ms, find the first four
13–24 The periodic pulse train in Figure P13–24 is applied to the RL circuit shown in the figure.(a) Use the results in Figure 13–4 to find the Fourier coefficients of the input for VA =12V, T0
13–22 Find the Fourier series for the waveform in Figure P13–22. v(t) (V) VA T/2 2T/3 ST/6 ST/6 To 0 To/6 To/3 -VA FIGURE P13-22
13–20 The first five terms in the Fourier series of a periodic waveform are(a) Find the period and fundamental frequency in rad/s and Hz. Identify the harmonics present in the first five terms.(b)
13–19 The first four terms in the Fourier series of a periodic waveform are(a) Find the period and fundamental frequency in rad/s and Hz. Identify the harmonics present in the first four terms.(b)
13–18 The equation for a periodic waveform is(a) Sketch the first two cycles of the waveform and identify a related signal in Figure 13–4.(b) Use the Fourier series of the related signal to find
13–17 The equation for the first cycle (0 ≤ t ≤ T0) of a periodic pulse train is(a) Sketch the first two cycles of the waveform and identify a related signal in Figure 13–4.(b) Use the
13–13 Use the results in Figure 13–4 to calculate the Fourier coefficients of the full-wave rectified sine wave in Figure P13–13.Use MATLAB to verify your results. Write an expression for the
13–12 A particular periodic waveform with a period of 10 ms has the following Fourier coefficients(a) Write an expression for the terms in the Fourier series up to n=8.(b) Convert your expression
13–11 Derive expressions for the Fourier coefficients of the periodic waveform in Figure P13–11.(a) Write an expression for the first four nonzero terms in the Fourier series.(b) Plot the
13–10 Use the results in Figure 13–4 to calculate the Fourier coefficients of the shifted triangular wave in Figure P13–10.Write an expression for the first four nonzero terms in the Fourier
13–9 Find the first five nonzero Fourier coefficients of the shifted and offset square wave in Figure P13–9. Use your results to write an expression in the corresponding Fourier series. v(t) (V)
13–8 Derive expressions for the Fourier coefficients of the periodic waveform in Figure P13–8. v(t) (V) VA 0 To 22 To -t(s) FIGURE P13-8
13–6 The equation for the first cycle (0 ≤ t ≤ T0) of a periodic pulse train is(a) Sketch the first two cycles of the waveform.(b) Derive expressions for the Fourier coefficients an and
13–5 Derive expressions for the Fourier coefficients of the periodic waveform in Figure P13–5. v(t) VA -To- -VA FIGURE P13-5 -t(s)
13–4 Derive expressions for the Fourier coefficients of the periodic waveform in Figure P13–4. v(f) (V) 10 t(ms) '0 0.5 1 1.5 FIGURE P13-4
13–3 Derive expressions for the Fourier coefficients of the periodic waveform in Figure P13–3. v(t) (V) 1 ms 10- I(s) FIGURE P13-3 200 s
In the rectangular-pulse waveform shown in Figure 13–4, the width of the pulse is one-third the period, T =T0=3. The waveform is to pass through a low-pass filter and then through a resistive load.
Figure 13–8 shows a series RL circuit driven by a sawtooth voltage source. Estimate the average power delivered to the resistor for VA =25V, R= 50, Ω, L=40 μH, T0 =5 μs, and ω0 =2π=T0 =1:26
The full–wave rectified sine wave shown in Figure 13–4 has an rms value of A=ffiffiffi p2. What fraction of the average power that the waveform delivers to a resistor is carried by the first two
Figure 13–11 shows a block diagram of a dc power supply. The ac input is a sinusoid that is converted in to a full-wave sine by the rectifier. The filter passes the dc component in the rectified
(a) Identify the symmetries in the waveform f t ð Þ whose Fourier series is(b) Write the corresponding terms of the function gðtÞ = f ðt−T0=4Þ. f(t)= 23A 11 1 cos (wot)-cos (5 wot) + cos (7
Given that f ðtÞ is a square wave of amplitude A and period T0, use the Fourier coefficients in Figure 13–4 to find the Fourier coefficients of gðtÞ = f ðt + T0=4Þ. Waveform Constant (dc) A
Derive expressions for the amplitude An and phase angle ϕn for the triangular wave in Figure 13–4 and write an expression for the first three nonzero terms in the Fourier series with A= π2=8 and
Derive expressions for the amplitude An and phase angle ϕn of the Fourier series of the sawtooth wave in Figure 13–4. Sketch the amplitude and phase spectra of a sawtooth wave with A= 5 and T0 = 4
The triangular wave in Figure 13–4 has a peak amplitude of A= 10 and T0 = 2 ms. Calculate the Fourier coefficients of the first nine harmonics. Waveform Constant (dc) A Cosine wave fit) Fourier
Verify the Fourier coefficients given for the square wave in Figure 13–4 and write the first three nonzero terms in its Fourier series. Waveform Constant (dc) A Cosine wave fit) Fourier
Given a rectangular pulse waveform as shown in Figure 13–1, letA= 10,T0 = 5 ms,and T = 2 ms. (a) UseMATLABto calculate the Fourier coefficients for the first 10 harmonics. (b) Use the 10 harmonics
Find the Fourier coefficients for the rectangular pulse wave in Figure 13–1. f(t) To- A f(t) To- Square wave A f(t) To Triangular wave f(t) ninaiva Rectangular pulse wave FIGURE 13-1 Examples of
Find the Fourier coefficients for the sawtooth wave in Figure 13–1. Square wave A A f(t) f(t) To- To Triangular wave A f(t) f(t) To- ninaia Rectangular pulse wave FIGURE 13-1 Examples of periodic
10–83 Pole Eliminator Circuit The Acme Pole Eliminator Company states in their online catalog that the circuit shown in Figure P10–83 can eliminate any realizable pole. Their catalog states
10–82 By-Pass Capacitor Design In transistor amplifier design, a by-pass capacitor is connected across the emitter resistorRE to effectively short out the emitter resistor at signal frequencies.
10–81 Pulse Conversion Circuit The purpose of the test setup in Figure P10–81 is to deliver damped sine pulses to the test load. The excitation comes from a 1-Hz square wave generator. The pulse
10–80 s-domain OP AMP Circuit Analysis The OP AMP circuit in Figure P10–80 is in the zero state.Transform the circuit into the s domain and use the OP AMP circuit analysis techniques developed in
10–79 RC Circuit Analysis and Design The RC circuits in Figure P10–79 represent the situation at the input to an oscilloscope. The parallel combination of R1 and C1 represents the probe used to
10–78 Design a Load Impedance In order to match the Thévenin impedance of a source, the load impedance in Figure P10–78 must(a) What impedance Z2ðsÞ is required if R = 20 Ω?(b) How would you
10–77 Thévenin’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
10–76 The circuit in Figure P10–76 is shown in the t domain with initial values for the energy storage devices.(a) Transform the circuit into the s domain and write a set of node-voltage
10–74 Find the range of the gain μ for which the circuit’s output VOðsÞ in Figure P10–74 is stable (i.e., all poles are in the lefthand side of the s plane.) Vs(s) +1 R R www w 1/Cs Vx(s)
10–73 Show that the circuit in Figure P10–73 has natural poles at s = −4=RC and s = −2=RC ± j2=RC when L = R2C=4: vs(t) R L FIGURE P10-73 L 000 + R vo(t)
10–72 With the circuit in the zero state, the input to the integrator shown in Figure P10–72 is v1ðtÞ = cos 2000 t V. The desired output is v2ðtÞ = −sin 2000 t V. Use Laplace to select
10–71 There is no initial energy stored in the circuit in Figure P10–71.(a) Transform the circuit into the s domain.(b) Then use the unit output method to find the ratio VOðsÞ=VSðsÞ.(c) If
10–70 The switch in Figure P10–70 has been open for a long time and is closed at t = 0. Transform the circuit into the s domain and solve for IOðsÞ and iOðtÞ. 1=0 50 V 500 0.1 0.1 H www 750
10–69 There is no energy stored in the circuit in Figure P10–69 at t = 0: Transform the circuit into the s domain. Then use the unit output method to find the ratio VOðsÞ=VSðsÞ. Subsequently,
10–68 The switch in Figure P10–68 has been in positionAfor a long time and is moved to position B at t = 0:(a) Write an appropriate set of node-voltage or meshcurrent equations in the s
10–67 Three mesh currents are shown in Figure P10–67.(a) Explain why only two of these mesh currents are independent.(b) Write s-domain mesh-current equations in the two independent mesh
10–66 Three node voltages are shown in Figure P10–66.(a) Explain why only one of the node voltages is independent.(b) Write a node voltage equation in the independent node voltage.(c) If VCðsÞ
10–64 The OP AMPcircuit in Figure P10–64 is in the zero state. Use node-voltage equations to find the circuit determinant.Select values of R, C1, and C2 so that the circuit hasω0 = 20 krad=s and
10–63 The circuit in Figure P10–63 is in the zero state.Use mesh-current equations to find the circuit determinant.Select values of R, L, and C so that the circuit hasω0 = 20 krad=s and ζ =
10–62 The circuit in Figure P10–62 is in the zero state.Use node-voltage equations to find the circuit determinant.Select values of R, C, and μ so that the circuit hasω0 = 10 krad=s and ζ =
10–61 The two-OP AMP circuit in Figure P10–61 is a bandpass filter.(a) Your task is to design such a filter so that the lowfrequency cutoff is 2000 rad=s and the high-frequency cutoff is 200,000
10–59 There is no external input in the circuit in Figure P10–59.(a) Find the zero-input node voltages vAðtÞ and vBðtÞ, and the voltage across the capacitor vCðtÞ when vCð0Þ = −5 V and
10–58 There is no initial energy stored in the circuit in Figure P10–58.(a) Find the zero-state mesh currents iAðtÞ and iBðtÞwhen v1ðtÞ = 10 e−2000tuðtÞ V.(b) Validate your answers
10–55 There is no initial energy stored in the bridged-T circuit in Figure P10–55.(a) Transform the circuit into the s domain and formulate mesh-current equations.(b) Use the mesh-current
10–54 There is no initial energy stored in the circuit in Figure P10–53. The Thévenin equivalent circuit to the left of point A when a unit step is applied isSelect values for R2 and C2 such
10–53 There is no initial energy stored in the circuit in Figure P10–53.(a) Transform the circuit into the s domain and formulate node-voltage equations.(b) Solve these equations for V2ðsÞ in
10–52 There is no initial energy stored in the circuit in Figure P10–51.(a) Transform the circuit into the s domain and formulate node-voltage equations.(b) Show that the solution of these
10–51 There is no initial energy stored in the circuit in Figure P10–51.(a) Transform the circuit into the s domain and formulate mesh-current equations.(b) Show that the solution of these
10–50 Find VOðsÞ in terms of the input and the elements for the zero state, dependent source circuit of Figure P10–50. Locate the natural poles and zeroes of the circuit. R www RF + + Vs(s)
10–49 There is no initial energy stored in the circuit in Figure P10–49. Use circuit reduction to find the output network function V2ðsÞ=V1ðsÞ. Then select values of R and C so that the poles
10–48 The equivalent impedance between a pair of terminals isA voltage vðtÞ = 10 e−10tuðtÞ is applied across the terminals.Find the resulting current response iðtÞ. ZEO(S)=2000 [S+3000] s+
10–47 There is no initial energy stored in the circuit in Figure P10–47. Transform the circuit into the s domain and use superposition to findV s ð Þ. Identify the forced and natural poles in V
10–46 The Thévenin equivalent shown in Figure P10–46 needs to deliverto a 2-kΩ load. Design an interface to allow that to occur. 10 Vo(s)= s+2000) (s+10) V-s
10–45 Find the required impedance ZXðsÞ that needs to be inserted in series as shown in Figure P10–45 to make the output voltage equal to ||V2(8)= s(s+1000) $+2000s+1061(s)
10–43 The circuit in Figure P10–43 is in the zero state. Find the Thévenin equivalent to the left of the interface. 20 0.1 ww HH + 100u(t) 20 k Interface FIGURE P10-43

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