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systems analysis design

Questions and Answers of Systems Analysis Design

The linear transformer in Figure \(\mathrm{P} 15=31\) is in the sinusoidal steady state with reactances of \(X_{1}=32 \Omega, X_{2}=50 \Omega\), \(X_{\mathrm{M}}=40 \Omega\), and a load impedance of
An inductor \(L\) is connected across the secondary of an ideal transformer whose turns ratio is \(1: n\).(a) Derive an expression for the equivalent inductance \(L_{\mathrm{EQ}}\) seen looking into
A Transformer Thévenin Equivalent In the time domain, the \(i-v\) equations for a linear transformer are\[\begin{aligned}& v_{1}(t)=L_{1} \frac{d i_{1}(t)}{d t}+M \frac{d i_{2}(t)}{d t} \\&
Figure P15:34 is an equivalent circuit of a perfectly coupled transformer. This model is the basis for the transformer equivalent circuits used in the analysis of power systems. The inductance
A Equivalent T-Circuit Transformer Model The transformer model shown in Figure 15-17 can also be modeled using an Equivalent T-Circuit as shown in Figure P15= 35 . The three inductors are related to
Consider the circuit shown in Figure P15-3 2 . The \(5-\mathrm{V}\) dc source switches from \(5 \mathrm{~V}\) to \(\mathrm{O}\) at \(t=0\). Find the output \(v_{\mathrm{C}}(t)\) for six different
(a) Figure P15:37 shows a three-winding transformer that can be treated as ideal.Perfect coupling between all windings implies that \(v_{2}(t)=\frac{N_{2}}{N_{1}} v_{1}(t)\) and
The following sets of \(v(t)\) and \(i(t)\) apply to the load circuit in Figure P16-1. Find the average power, reactive power, and instantaneous power delivered to the load.(a) \(v(t)=220 \cos
The following sets of \(v(t)\) and \(i(t)\) apply to the load circuit in Figure P16-1. Calculate the average power, the reactive power, and instantaneous power delivered to the load.(a) \(v(t)=100
The following voltage and current phasors apply to the circuit in Figure P16-3. Calculate the average power and reactive power delivered to the impedance \(Z\). Find the power factor and state
The transfer function of a second-order low-pass filter has the form\[T(s)=\frac{K}{\left(\frac{s}{\omega_{0}}ight)^{2}+2 \zeta\left(\frac{s}{\omega_{0}}ight)+1}\]Show by replacing \(\mathrm{s} /
Interchanging the positions of the resistors and capacitors converts the low-pass filter in Figure 14=3 (a) into the high-pass filter in Figure 14-9. (a). This \(C R-R C\) interchange involves
Show that the circuit in Figure 14-17. has the bandstop transfer function in \(\underline{E q}_{-}(\underline{14}-20)\).
Find the transfer function of the active filter in Figure P14-4. Then using \(R_{1}=R_{2}=R_{3}=20 \mathrm{k} \Omega, C_{1}=0.3 \mu \mathrm{F}\), and \(C_{2}\) \(=0.0333 \mu \mathrm{F}\), find the
Find the transfer function of the active filter in Figure P14=5 . Then using \(R_{1}=10 \mathrm{k} \Omega, R_{2}=40 \mathrm{k} \Omega\), and \(C_{1}=C\) \({ }_{2}=0.05 \mu \mathrm{F}\), find the
For the filter in Figure P14-4, replace the three resistors with three capacitors, maintaining the same subscripts, and the two capacitors with two resistors, again maintaining the same subscripts.
The circuit in Figure 14–9(b) has a high-pass transfer function given in Eq. (14–11) and repeated below\[\begin{aligned}T(s) & =\frac{V_{2}(s)}{V_{1}(s)} \\& =\frac{\mu R_{1} R_{2} C_{1} C_{2}
Find the transfer function of the active filter in Figure P14-8 . Then using \(R_{1}=R_{2}=10 \mathrm{k} \Omega, R_{3}=20 \mathrm{k} \Omega\), and \(C_{1}=C_{2}\) \(=001 \mu \mathrm{F}\), find the
Aircraft use \(400 \mathrm{~Hz}\) power for electrical systems. However, sometimes the power radiates and affects some critical instruments. There is a need for a \(400-\mathrm{Hz}\) notch filter
For the circuit in Figure P14-10 find its transfer function. Then determine the circuit's gain and its pole-zero diagram. Is this a first- or second-order circuit? What would be the circuit's
Design a second-order low-pass filter with a cutoff frequency of \(2 \mathrm{krad} / \mathrm{s}, \mathrm{a} \zeta\) of 1 , and a gain of 20 . Use the unity-gain approach. Use Multisim to verify your
Design a second-order high-pass filter with a cutoff frequency of \(100 \mathrm{kHz}\), a \(\zeta\) of 0.02 , and a gain of \(40 \mathrm{~dB}\). Use the equal-element approach. Use Multisim to verify
The transfer functions of three different second-order low-pass filter design approaches shown in Figure P14-13 are as follows:\[\begin{aligned}& T_{\mathrm{a}}(s)=\frac{1}{R_{1} R_{2} C_{1} C_{2}
Construct second-order transfer functions that meet the following requirements. Use MATLAB to plot the transfer function's Bode diagram and validate the requirements. (rad/s) Low pass 200,000 * T(J
Construct second-order transfer functions that meet the following requirements. Use MATLAB to plot the transfer function's Bode diagram and validate the requirements. High pass WO (rad/s) 2513 M
Construct second-order transfer functions that meet the following requirements. Use MATLAB to plot the transfer function's Bode diagram and validate the requirements. Type @ (rad/s) Bandstop 200 3
Construct second-order transfer functions that meet the following requirements. Use MATLAB to plot the transfer function's Bode diagram and validate the requirements. Type @o (rad/s) Bandpass 1000
Design second-order active filters that meet the following requirements. Simulate your designs in Multisim to validate the requirements Low pass 100 k @o (rad/s) M Constraints 0.5 Use 10-k resistors
Design second-order active filters that meet the following requirements. Simulate your designs in Multisim to validate the requirements Low pass 50 k Wo 0 (rad/s) 3 1 Constraints de gain of 60 dB
Design second-order active filters that meet the following requirements. Simulate your designs in Multisim to validate the requirements High pass wo (rad/s) 10 k 3 Constraints Use 0.2-F capacitors
Design second-order active filters that meet the following requirements. Simulate your designs in Multisim to validate the requirements wo High pass (rad/s) 250 M Constraints 0.25 High-frequency
Design second-order active filters that meet the following requirements. Simulate your designs in Multisim to validate the requirements Bandpass (rad/s) 20 k 3 * Constraints B = 2000 rad/s
Design second-order active filters that meet the following requirements. Simulate your designs in Multisim to validate the requirements Wo (rad/s) Bandstop 1000 3 * Constraints Q = 20
Design second-order active filters that meet the following requirements. Simulate your designs in Multisim to validate the requirements wo Tuned (rad/s) 3.45 M 3 Constraints 0.001 Use 200-pF
Design second-order active filters that meet the following requirements. Simulate your designs in Multisim to validate the requirements Type Notch wo (rad/s) 314 3 0.01 Constraints Use 0.01-F
Construct the lowest-order transfer functions that meet the following low-pass filter specifications. Calculate the gain (in \(\mathrm{dB}\) ) of the transfer function at
Construct the lowest-order transfer functions that meet the following low-pass filter specifications. Calculate the gain (in \(\mathrm{dB}\) ) of the transfer function at
Construct the lowest-order transfer functions that meet the following low-pass filter specifications. Calculate the gain (in \(\mathrm{dB}\) ) of the transfer function at
Construct the lowest-order transfer functions that meet the following low-pass filter specifications. Calculate the gain (in \(\mathrm{dB}\) ) of the transfer function at
Design an active low-pass filter to meet the specification in Problem 14-26. Use Multisim to verify that your design meets the specifications.Data From Problem 14-26Construct the lowest-order
Design an active low-pass filter to meet the specification in Problem 14-27. Use Multisim to verify that your design meets the specifications.Data From Problem 14-27Construct the lowest-order
(a) Design an active low-pass filter to meet the specification in Problem 14-29. Use Multisim to verify that your design meets the specifications.(b) Now design a Chebyshev filter to meet the same
A low-pass filter is needed to suppress the harmonics in a periodic waveform with \(f_{0}=1 \mathrm{kHz}\). The filter must have unity passband gain, less than \(-60 \mathrm{~dB}\) gain at the third
Design a low-pass filter with \(6 \mathrm{~dB}\) passband gain, a cutoff frequency of \(2 \mathrm{krad} / \mathrm{s}\), and a stopband gain of less than\(14 \mathrm{~dB}\) at \(6 \mathrm{krad} /
Design a low-pass filter with \(10 \mathrm{~dB}\) passband gain, a cutoff frequency of \(10 \mathrm{kHz}\), and a stopband gain of less than \(-20 \mathrm{~dB}\) at \(20 \mathrm{kHz}\). Overshoot is
A pesky signal at \(45 \mathrm{kHz}\) is interfering with a desired signal at \(20 \mathrm{kHz}\). A careful analysis suggests that reducing the interfering signal by \(75 \mathrm{~dB}\) will
A \(50 \mathrm{kHz}\) square wave must be bandwidthlimited by attenuating all harmonics after the third. Design a low-pass filter that attenuates the fifth harmonic and greater by at least \(20
There is a need for a fifth-order low-passButterworth filter with a cutoff frequency of \(100 \mathrm{rad} / \mathrm{s}\) to use in a medical instrumentation system with frequencies below 100
Construct the lowest order, high-pass transfer functions that meet the following filter specifications. Calculate the gain (in \(\mathrm{dB}\) ) of the transfer function at
Construct the lowest order, high-pass transfer functions that meet the following filter specifications. Calculate the gain (in \(\mathrm{dB}\) ) of the transfer function at
Construct the lowest order, high-pass transfer functions that meet the following filter specifications. Calculate the gain (in \(\mathrm{dB}\) ) of the transfer function at
Construct the lowest order, high-pass transfer functions that meet the following filter specifications. Calculate the gain (in \(\mathrm{dB}\) ) of the transfer function at
The periodic triangular wave in Figure P13-22 is applied to the \(R L C\) 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
The Fourier coefficients of a periodic input signal are:\[a_{0}=0 \quad a_{n}=0 \quad b_{n}=\frac{8 V_{\mathrm{A}}}{(n \pi)^{2}} \sin \left(\frac{n \pi}{2}ight)\]The signal has \(V_{\mathrm{A}}=10
Design a tuned \(R L C\) filter to pass 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}}=15
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

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