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computer science
systems analysis design
Questions and Answers of
Systems Analysis Design
Design a notch \(R L C\) filter to block the third harmonic of a triangular wave.(a) Use the results in Figure 13-4 in the text to find the Fourier coefficients of the input for \(V_{\mathrm{A}}=12
The current through a 1-H inductor is a triangular wave with \(I_{\mathrm{A}}=25 \mathrm{~mA}\) and \(f_{\mathrm{O}}=500 \mathrm{~Hz}\). Construct plots of the amplitude spectra of the inductor
A triangular wave with \(V_{\mathrm{A}}=10 \mathrm{~V}\) and \(T_{0}=20 \pi\) ms drives a circuit whose transfer function is\[T(s)=\frac{100 s}{(s+50)^{2}+400^{2}}\](a) Find the amplitude of the
The voltage across a \(1-\mathrm{k} \Omega\) resistor is\[v(t)=5+6.367 \sin (2000 \pi t)+2.122 \sin (6000 \pi t) \mathrm{V}\](a) Find the rms value of the voltage and the average power delivered to
The voltage across a 200- \(\Omega\) resistor is given by the \(a_{n}\) Fourier coefficients shown in volts in Figure P13=3o . All \(b n\) coefficients are zero, as is \(a_{0}\). The fundamental
Find the rms value of a square wave. Find the fraction of the total average power carried by the first three nonzero ac components in the Fourier series.
Find the rms value of a sawtooth wave. Find the fraction of the total average power carried by the first three nonzero ac components in the Fourier series. Compare with the results found in Problem
Find the rms value of a parabolic wave. Find the fraction of the total average power carried by the first three nonzero ac components in the Fourier series. Compare with the results found in Problem
Find the rms value of the periodic waveform in Figure \(\underline{\mathrm{P}} 3=34\) and the average power the waveform delivers to a resistor. Find the dc component of the waveform and the average
Repeat Problem 13-34 for the periodic waveform in Figure P13=35 .Data Form Problem 13-3413-34 Find the rms value of the periodic waveform in Figure \(\underline{\mathrm{P}} 3=34\) and the average
A first-order low-pass filter has a cutoff frequency of 5 \(\mathrm{krad} / \mathrm{s}\) and a passband gain of \(20 \mathrm{~dB}\). The input to the filter is \(v(t)=10+20 \cos 5000 t+12 \cos 15
There is a need for a simple first-order antialiasing filter prior to digitizing the EKG signal shown in Figure \(\underline{\text { P1 }} 3=37\).(a) Determine the fundamental frequency of the EKG
The input to the circuit in Figure P13=3 3 is:\[v_{\mathrm{S}}(t)=25 \cos 2000 t+5 \cos 10,000 t \mathrm{~V}\](a) Find the transfer function \(T(s)=V_{\mathrm{O}}(s) / V_{\mathrm{S}}(s)\).(b)
Find an expression for the average power delivered to a resistor \(R\) by a rectangular pulse voltage with amplitude \(V_{\mathrm{A}}\) , period \(T_{0}\), and pulse width \(T=T_{0} / 4\). How many
The only ac source available is a \(1-\mathrm{V}\) peak \(200-\mathrm{kHz}\) oscillator. You need a \(600-\mathrm{kHz}\) source. Your task is to convert your 200\(\mathrm{kHz}\) source so that it can
A periodic impulse train can be written as\[x(t)=T_{0} \sum_{n=-\infty}^{\infty} \delta\left(t-n T_{0}ight)\]Find the Fourier coefficients of \(x(t)\). Plot the amplitude spectrum and comment on the
The input to a power supply filter is a full-wave rectified sine wave with \(f_{0}=60 \mathrm{~Hz}\). The filter is a first-order low pass with unity dc gain. Select the cutoff frequency of the
A certain spectrum analyzer measures the average power delivered to a calibrated resistor by the individual harmonics of periodic waveforms. The calibration of the analyzer has been checked by
Electronic keyboards are designed using the following equation that assigns particular frequencies to each of the 88 keys in a standard piano keyboard:\[f(n)=440(\sqrt[12]{2})^{n-49}
Multisim has a useful Fourier analysis option. In this problem, you are to use this option to estimate the average power delivered to a 1 - \(\Omega\) resistor by the fundamental and the next two
Find the first four terms of the Fourier series of an offset square wave waveform shown in Figure 13-4 in the text if \(a_{\mathrm{o}}=\mathrm{A}\).
A sine wave has an amplitude of \(311.2 \mathrm{~V}\), a radian frequency of \(314 \mathrm{rad} / \mathrm{s}\), and a phase shift of \(90^{\circ}\). Find the Fourier series expression for this
Derive expressions for the Fourier coefficients of the periodic waveform in Figure P13=3 . v(t) (V) 20 0 1 2 3 -t (ms)
Derive expressions for the Fourier coefficients of the periodic waveform in Figure P13-4. v(t) VA To -VA t(s)
The equation for the first cycle \(\left(0 \leq t \leq T_{0}ight)\) of a periodic pulse train is\[v(t)=V_{\mathrm{A}}\left[-5 u(t)+5 u\left(t-T_{0} / 4ight)ight] \mathrm{V}\](a) Sketch the first two
Derive expressions for the Fourier coefficients of the periodic waveform in Figure P13-6. Use MATLAB to find the coefficients. Vs(t) (V) VA 0 To 2 To 3To 2 t(s)
Find the first five nonzero Fourier coefficients of the shifted and offset square wave in Figure P13=7. Use your results to write an expression for the corresponding Fourier series. v(1) (V) 10 0 2.5
Use the results in Figure 13-1 in the text to calculate the Fourier coefficients of the shifted triangular wave in Figure P13= 8. Write an expression for the first four nonzero terms in the Fourier
Derive expressions for the Fourier coefficients of the periodic waveform in Figure P13=9. .(a) Write an expression for the first four nonzero terms in the Fourier series.(b) Plot the line spectrum of
A particular periodic waveform with a period of \(10 \mathrm{~ms}\) has the following Fourier coefficients\[a_{0}=-5, \quad a_{n}=\frac{16}{n \pi} \sin \frac{n \pi}{4} \cos \frac{n \pi}{4}, \quad
A half-wave rectified sine wave has an amplitude of \(171 \mathrm{~V}\) and a fundamental frequency of \(60 \mathrm{~Hz}\). Use the results in Figure 13-4 to write an expression for the first four
The waveform \(f(t)\) is a 10-kHz triangular wave with a peak-to-peak amplitude of \(15 \mathrm{~V}\) and a \(+7 \cdot 5-\mathrm{V}\) dc offset. Use the results in Figure 13-1 in the text to write an
A sawtooth wave has peak-to-peak amplitude of \(5 \mathrm{~V}\) and a fundamental frequency of \(100 \mathrm{~Hz}\). Use the results in Figure 13-4 in the text to write an expression for the first
The equation for a periodic waveform is\[v(t)=V_{\mathrm{A}}\left[\sin \left(4 \pi t / T_{0}ight)+\left|\sin \left(4 \pi t / T_{0}ight)ight|ight]\](a) Sketch the first two cycles of the waveform and
The first four terms in the Fourier series of a periodic waveform are\[\begin{aligned}v(t)= & 5+2.064 \sin (2000 \pi t)+0.07645 \sin (6000 \pi t) \\& +0.01652 \sin (10,000 \pi t)\end{aligned}\](a)
The first five terms in the Fourier series of a periodic waveform are\[\begin{aligned}v(t)= & -12.5+25\left[\frac{\pi}{4} \cos (2 \pi \times 500 t)-\frac{1}{3} \cos (2 \pi \times 1000 t)ight. \\&
The equation for a full-wave rectified cosine is \(v(\) \(t)=V_{\mathrm{A}}\left|\cos \left(2 \pi t / T_{\mathrm{o}}ight)ight| \mathrm{V}\).(a) Hand Sketch \(v(t)\) for \(-T_{\mathrm{o}} \leq t \leq
An \(R C\) series circuit is driven by the following periodic source:\[v_{\mathrm{s}}(t)=10 \cos 10 \mathrm{k} t+5 \cos 30 \mathrm{k} t+3.33 \cos 50 \mathrm{k} t \mathrm{~V}\](a) Find the output
The periodic pulse train in Figure P13-19. is applied to the \(R L\) circuit shown in the figure.(a) Use the results in text Figure 13-4 to find the Fourier coefficients of the input for
The periodic sawtooth wave in Figure P13-20 drives the OP AMP circuit shown in the figure.(a) Use the results in Figure 13-4 in the text to find the Fourier coefficients of the input for
(a) Design a low-pass OP AMP circuit to pass only the fundamental and the next nonzero harmonic of a \(2 \pi \mathrm{ms}\) square wave. The gain of the OP AMP should be +10 .(b) Find the first four
The single-line diagram of a three-phase power system is shown in Figure 9.17. Equipment ratings are given as follows:Synchronous generators:Transformers:Transmission lines:The inductor connected to
Faults at bus \(n\) in Problem 9.1 are of interest (the instructor selects \(n=1\), 2, or 3). Determine the Thévenin equivalent of each sequence network as viewed from the fault bus. Prefault
Determine the subtransient fault current in per-unit and in kA during a bolted three-phase fault at the fault bus selected in Problem 9.2.Problem 9.2Faults at bus \(n\) in Problem 9.1 are of interest
In Problem 9.1 and Figure 9.17, let \(765 \mathrm{kV}\) be replaced by \(500\mathrm{kV}\), keeping the rest of the data to be the same. Problem 9.1The single-line diagram of a three-phase power
Equipment ratings for the four-bus power system shown in Figure 7.14 are given as follows:Generator G1: \(\quad 500 \mathrm{MVA}, 13.8 \mathrm{kV}, \mathrm{X}_{d}^{\prime \prime}=\mathrm{X}_{2}=0.20,
Faults at bus \(n\) in Problem 9.5 are of interest (the instructor selects \(n=1\), 2,3 , or 4). Determine the Thévenin equivalent of each sequence network as viewed from the fault bus. Prefault
Determine the subtransient fault current in per-unit and in kA during a bolted three-phase fault at the fault bus selected in Problem 9.6.Problem 9.6Faults at bus \(n\) in Problem 9.5 are of interest
Equipment ratings for the five-bus power system shown in Figure 7.15 are given as follows:Generator G1: \(\quad 50 \mathrm{MVA}, 12 \mathrm{kV}, \mathrm{X}_{d}^{\prime \prime}=\mathrm{X}_{2}=0.20,
Faults at bus \(n\) in Problem 9.8 are of interest (the instructor selects \(n=\) 1, 2, 3, 4, or 5). Determine the Thévenin equivalent of each sequence network as viewed from the fault bus. Prefault
Determine the subtransient fault current in per-unit and in kA during a bolted three-phase fault at the fault bus selected in Problem 9.9.Problem 9.9Faults at bus \(n\) in Problem 9.8 are of interest
Consider the system shown in Figure 9.18.(a) As viewed from the fault at \(F\), determine the Thévenin equivalent of each sequence network. Neglect \(\Delta-Y\) phase shifts.(b) Compute the fault
Equipment ratings and per-unit reactances for the system shown in Figure 9.19 are given as follows:Synchronous generators:\(\begin{array}{lllll}\text { G1 } & 100 \text { MVA } & 25
Consider the oneline diagram of a simple power system shown in Figure 9.20. System data in per-unit on a 100-MVA base are given as follows:Synchronous generators:G1 & 100 MVA & \(20
Determine the subtransient fault current in per-unit and in kA, as well as the per-unit line-to-ground voltages at the fault bus for a bolted single line-to-ground fault at the fault bus selected in
Repeat Problem 9.14 for a single line-to-ground arcing fault with arc impedance \(Z_{\mathrm{F}}=15+j 0 \Omega\).Problem 9.14Determine the subtransient fault current in per-unit and in kA, as well as
Repeat Problem 9.14 for a bolted line-to-line fault.Problem 9.14Determine the subtransient fault current in per-unit and in kA, as well as the per-unit line-to-ground voltages at the fault bus for a
Repeat Problem 9.14 for a bolted double line-to-ground fault.Problem 9.14Determine the subtransient fault current in per-unit and in kA, as well as the per-unit line-to-ground voltages at the fault
Repeat Problems 9.1 and 9.14 including \(\Delta-Y\) transformer phase shifts. Assume American standard phase shift. Also calculate the sequence components and phase components of the contribution to
(a) Repeat Problem 9.14 for the case of Problem 9.4 (b).(b) Repeat Problem 9.19 (a) for a single line-to-ground arcing fault with arc impedance \(Z_{\mathrm{F}}=(15+j 0) \Omega\).(c) Repeat Problem
A 500-MVA, 13.8 -kV synchronous generator with \(\mathrm{X}_{d}^{\prime \prime}=\mathrm{X}_{2}=0.20\) and \(\mathrm{X}_{0}=0.05\) per unit is connected to a \(500-\mathrm{MVA}, 13.8 -\mathrm{kV}
Determine the subtransient fault current in per-unit and in kA, as well as contributions to the fault current from each line and transformer connected to the fault bus for a bolted single
Repeat Problem 9.21 for a bolted line-to-line fault.Problem 9.21Determine the subtransient fault current in per-unit and in kA, as well as contributions to the fault current from each line and
Repeat Problem 9.21 for a bolted double line-to-ground fault.Problem 9.21Determine the subtransient fault current in per-unit and in kA, as well as contributions to the fault current from each line
Determine the subtransient fault current in per-unit and in \(\mathrm{kA}\), as well as contributions to the fault current from each line, transformer, and generator connected to the fault bus for a
Repeat Problem 9.24 for a single line-to-ground arcing fault with arc impedance \(Z_{\mathrm{F}}=0+j 0.1 \) per unit.Problem 9.24Determine the subtransient fault current in per-unit and in
Repeat Problem 9.24 for a bolted line-to-line fault.Problem 9.24Determine the subtransient fault current in per-unit and in \(\mathrm{kA}\), as well as contributions to the fault current from each
Repeat Problem 9.24 for a bolted double line-to-ground fault.Problem 9.24Determine the subtransient fault current in per-unit and in \(\mathrm{kA}\), as well as contributions to the fault current
As shown in Figure 9.21 (a), two three-phase buses \(a b c\) and \(a^{\prime} b^{\prime} c^{\prime}\) are interconnected by short circuits between phases \(b\) and \(b^{\prime}\) and between \(c\)
Repeat Problem 9.28 for the two-conductors-open fault shown in Figure 9.21 (b). The fault conditions in the phase domain are \[ I_{b}=I_{b^{\prime}}=I_{c}=I_{c^{\prime}}=0 \text { and } V_{a
For the system of Problem 9.11, compute the fault current and voltages at the fault for the following faults at point \(\mathrm{F}\) :(a) a bolted single line-to-ground fault;(b) a line-to-line fault
For the system of Problem 9.12, compute the fault current and voltages at the fault for the following faults at bus 3:(a) a bolted single line-toground fault,(b) a bolted line-to-line fault,(c) a
For the system of Problem 9.13, compute the fault current for the following faults at bus 3:(a) a single line-to-ground fault through a fault impedance \(Z_{\mathrm{F}}=j 0.1 \) per unit,(b) a
For the three-phase power system with single-line diagram shown in Figure 9.22, equipment ratings and per-unit reactances are given as follows:Machines 1 and 2: \(\quad 100\) MVA \(20 \mathrm{kV}
At the general three-phase bus shown in Figure 9.7 (a) of the text, consider a simultaneous single line-to-ground fault on phase \(a\) and lineto-line fault between phases \(b\) and \(c\), with no
Thévenin equivalent sequence networks looking into the faulted bus of a power system are given with \(Z_{1}=j 0.15, Z_{2}=j 0.15, Z_{0}=j 0.2\), and \(E_{1}=1 \angle 0^{\circ}\) per unit. Compute
The single-line diagram of a simple power system is shown in Figure 9.23 with per unit values. Determine the fault current at bus 2 for a three-phase fault. Ignore the effect of phase shift.Figure
Consider a simple circuit configuration shown in Figure 9.24 to calculate the fault currents \(I_{1}, I_{2}\), and \(I\) with the switch closed.(a) Compute \(E_{1}\) and \(E_{2}\) prior to the fault
The zero-, positive-, and negative-sequence bus impedance matrices for a three-bus three-phase power system areDetermine the per-unit fault current and per-unit voltage at bus 2 for a bolted
Repeat Problem 9.38 for a bolted single line-to-ground fault at bus 1.Problem 9.38The zero-, positive-, and negative-sequence bus impedance matrices for a three-bus three-phase power system
Repeat Problem 9.38 for a bolted line-to-line fault at bus 1.Problem 9.38The zero-, positive-, and negative-sequence bus impedance matrices for a three-bus three-phase power system areDetermine the
Repeat Problem 9.38 for a bolted double line-to-ground fault at bus 1.Problem 9.38The zero-, positive-, and negative-sequence bus impedance matrices for a three-bus three-phase power system
(a) Compute the \(3 \times 3\) per-unit zero-, positive-, and negative-sequence bus impedance matrices for the power system given in Problem 9.1. Use a base of \(1000 \mathrm{MVA}\) and \(765
The zero-, positive-, and negative-sequence bus impedance matrices for a two-bus three-phase power system areDetermine the per-unit fault current and per-unit voltage at bus 2 for a bolted
Repeat Problem 9.43 for a bolted single line-to-ground fault at bus 1.Problem 9.43The zero-, positive-, and negative-sequence bus impedance matrices for a two-bus three-phase power system
Repeat Problem 9.43 for a bolted line-to-line fault at bus 1.Problem 9.43The zero-, positive-, and negative-sequence bus impedance matrices for a two-bus three-phase power system areDetermine the
Repeat Problem 9.43 for a bolted double line-to-ground fault at bus 1.Problem 9.43The zero-, positive-, and negative-sequence bus impedance matrices for a two-bus three-phase power system
Compute the \(3 \times 3\) per-unit zero-, positive-, and negative-sequence bus impedance matrices for the power system given in Problem 4(a). Use a base of \(1000 \mathrm{MVA}\) and \(500
Using the bus impedance matrices determined in Problem 9.47.Problem 9.47Compute the \(3 \times 3\) per-unit zero-, positive-, and negative-sequence bus impedance matrices for the power system given
Compute the \(4 \times 4\) per-unit zero-, positive-, and negative-sequence bus impedance matrices for the power system given in Problem 9.5. Use a base of \(1000 \mathrm{MVA}\) and \(20
Using the bus impedance matrices determined in Problem 9.42.Problem 9.42(a) Compute the \(3 \times 3\) per-unit zero-, positive-, and negative-sequence bus impedance matrices for the power system
Compute the \(5 \times 5\) per-unit zero-, positive-, and negative-sequence bus impedance matrices for the power system given in Problem 9.8. Use a base of 100 MVA and \(15 \mathrm{kV}\) in the zone
Using the bus impedance matrices determined in Problem 9.51.Problem 9.51Compute the \(5 \times 5\) per-unit zero-, positive-, and negative-sequence bus impedance matrices for the power system given
The positive-sequence impedance diagram of a five-bus network with all values in per-unit on a 100-MVA base is shown in Figure 9.25. The generators at buses 1 and 3 are rated 270 and 225 MVA,
For the five-bus network shown in Figure 9.25, a bolted single-line-toground fault occurs at the bus 2 end of the transmission line between buses 1 and 2. The fault causes the circuit breaker at the
A single-line diagram of a four-bus system is shown in Figure 9.27 . Equipment ratings and per-unit reactances are given as follows.On a base of \(100 \mathrm{MVA}\) and \(345 \mathrm{kV}\) in the
The system shown in Figure 9.28 except that the transformers are now \(\mathrm{Y}-\mathrm{Y}\) connected and solidly grounded on both sides. (a) Determine the bus impedance matrix for each of the
The results in Table 9.5 show that during a phase \(a\) single line-to-ground fault the phase angle on phase \(a\) voltages is always zero. Explain why we would expect this result.Table 9.5
The results in Table 9.5 show that during the single line-to-ground fault at bus 2 the \(b\) and \(c\) phase voltage magnitudes at bus 2 actually rise above the prefault voltage of 1.05 per unit. Use
Plot the variation in the bus 2 phase \ (a, b, c\) voltage magnitudes during a single line-to-ground fault at bus 2 as the fault reactance is varied from 0 to 0.30 per unit in 0.05 per-unit steps the
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