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systems analysis design
Questions and Answers of
Systems Analysis Design
Design an active high-pass filter to meet the specification in Problem 14-40. Use Multisim to verify that your design meets the specifications.Data From Problem 14-40Construct the lowest order,
Consider the specifications given in Problem 14-42.(a) Design an active Butterworth filter to meet the specification.(b) Design an active Chebyshev filter to meet the specification.(c) Use Multisim
A certain instrumentation system for a new hybrid car needs a bandpass filter to limit its output bandwidth prior to digitization. The filter must meet the following
You are working at an aircraft manufacturing plant on an altitude sensor that eventually will be used to retrofit dozens of similar sensors on an upgrade to a current airframe. You are required to
An amplified portion of the radio spectrum is shown in Figure P14-4 8 . You need to hear all of the signals from 1.0 to 2.0 MHz, but there is an interfering signal at 1.8 MHz. Design a notch filter
The portion of the radio spectrum known as the AM broadcast band ranges from \(540 \mathrm{kHz}\) to \(1700 \mathrm{kHz}\). You want to design a suitable filter and amplifier. The passband gain
Bessel filters are in the category of maximally flat filters similar to Butterworth but have a critically damped time-domain response similar to a First-Order Cascade filter. Bessel filters have a
You are the head engineer for a small start-up and a client asked for a filter with the following specifications: a third-order Butterworth low-pass filter with a cutoff frequency of \(2
One of your company's products includes the passive \(R L C\) filter and OP AMP buffer circuit in Figure P14=52. The supplier of the inductor is no longer in business and a suitable replacement is
Ten years after earning a BSEE, you return for a master's degree and sign on as the laboratory instructor for the basic circuit analysis course. One experiment asks the students to build the active
The three-terminal circuit in Figure P14=54. (a) has a bandpass transfer function of the formShow that the circuit in Figure P14=54 (b) has a bandstop transfer function of the
Show that the circuit in Figure P14=55 produces a third-order Butterworth low-pass filter with a cutoff frequency of \(\omega_{\mathrm{C}}=1\) / \(R C\) and a passband gain of \(K=4\). Then, design a
A biquad filter has the unique properties of having the ability to alter the filter's parameters, namely, gain \(K\), quality factor \(Q\), and resonant frequency \(\omega_{0}\). This is done in each
Although not an active filter, crystal (Quartz) filters are very high \(-Q\) filters. Some can have \(Q\) 's approaching 100,000. High \(Q\) means high selectivity; hence, crystal filters are used
A scientist has a need for a bandpass filter for an Amateur Satellite band in the HF frequency band. It must have a center frequency of \(89.4 \mathrm{Mrad} / \mathrm{s}\) and a \(32 \mathrm{Mrad} /
In Figure P15-1, \(L_{1}=10 \mathrm{mH}, L_{2}=50 \mathrm{mH}, k=0.4\) and \(v_{\mathrm{S}}(t)=200 \sin 100 t \mathrm{~V}\).(a) Write the \(i-v\) relationships for the coupled inductors using the
In Figure P15-1, \(L_{1}=10 \mathrm{mH}, L_{2}=5 \mathrm{mH}, M=7 \mathrm{mH}\), and \(v\) \(\mathrm{S}(t)=100 \sin 1000 t \mathrm{~V}\).(a) Write the \(i-v\) relationships for the coupled inductors
In Figure P1 5-1 \(, L_{1}=10 \mathrm{mH}, L_{2}=5 \mathrm{mH}, M=7 \mathrm{mH}\), and the outputs are \(v_{2}(t)=0\) and \(i_{2}(t)=35 \sin 1000 t \mathrm{~A}\).(a) Write the \(i-v\) relationships
In Figure P15-4, \(L_{1}=L_{2}=5 \mathrm{mH}, M=2 \mathrm{mH}, k=0.4\), and \(i_{\mathrm{S}}(t)=120 \sin 377 t \mathrm{~A}\).(a) Solve for \(v_{1}(t)\) and \(v_{2}(t)\) when the output terminals are
In Figure P15-4, \(L_{1}=L_{2}=4 \mathrm{mH}, M=3 \mathrm{mH}\), and \(i_{2}(\) \(t)=10 \sin 1000 t \mathrm{~mA}\) when the output terminals are short circuited. Solve for \(v_{1}(t)\) and
In Figure P15-6, \(L_{1}=2 \mathrm{H}, L_{2}=6 \mathrm{H}, M=3 \mathrm{H}\), and \(v_{\mathrm{X}}(\) \(t)=70 \cos (1000 t) \mathrm{V}\). Find the input current \(i_{1}(t)\) and the voltages
ans 15-7 In Figure P15-7 show that \(L_{\mathrm{EQ}}=L_{1}\left(1-k^{2}ight)\), where \(k\) is the coupling coefficient. LEQ M 100 L2
In Figure P15-8 show that the indicated open-circuit voltage is\[v_{\mathrm{OC}}=\left(k \sqrt{L_{2} / L_{1}}ight) v_{1}\]where \(k\) is the coupling coefficient. i(1) Mi(1) vs(t) + v(1) la L 42 +
Because of the numerous windings, transformers are likely to have a parasitic resistance associated with each coil.Figure P15-9. shows a pair of coupled coils with a series resistance associated with
A perfectly coupled (ideal) transformer is used to provide electricity to a \(1-\mathrm{k} \Omega, 12-\mathrm{V}\) doorbell from house voltage 169.7 sin \(377 t \mathrm{~V}\). Design the
In Figure \(\mathrm{P} 15-11 R_{\mathrm{S}}=50 \Omega, R_{\mathrm{L}}=1250 \Omega\), the turns ratio is \(n=5\), and the source voltage is \(v_{\mathrm{S}}(t)=240 \cos\) \(377 t \mathrm{~V}\). Find
The turns ratio of the ideal transformer in Figure P \(15-12\) is \(n=10\). The source and load impedances are \(Z_{\mathrm{S}}=50 \Omega\) and \(Z_{\mathrm{L}}=\) \(500-j 500 \Omega\). Find
Design the turns ratio of the ideal transformer in Figure P15-12 so that \(\mathbf{V}_{\mathrm{O}}=708
In Figure P15-14, the turns ratio is \(n=5, L=120 \mathrm{mH}\), and \(R_{\mathrm{L}}=1.5 \mathrm{k} \Omega\). Find \(i_{\mathrm{IN}}(t)\) and \(v_{2}(t)\) when \(v_{1}(t)=100\)\(\sin 377 t
(a) Design the turns ratio in Figure P15-14 if \(\mathbf{V}_{1}=100
The primary voltage of an ideal transformer used in a home furnace to connect to a thermostat is a \(120-\mathrm{V}, 60-\mathrm{Hz}\) sinusoid. The secondary voltage is a \(24-\mathrm{V},
In Figure P15-17 the impedances are \(Z_{1}=20-j 45\) \(\Omega, Z_{2}=45+j 30 \Omega\), and \(Z_{3}=300+j 250 \Omega\). Find \(\mathbf{I}_{1}, \mathbf{I}_{2}\), and \(\mathbf{I}\) 3. + Z 20020 V 1:2
The solenoid in Figure P15-18 needs \(24 \mathrm{~V}\) to operate properly. The source \(\mathbf{V}_{\mathrm{S}}=170 S +1 Zs ww 1:n 3118 Ideal Isol Rsol jXsol Solenoid Vo
The primary winding of an ideal transformer with \(N_{1}\) \(=100\) and \(N_{2}=250\) is connected to a \(480-\mathrm{V}\) source. A \(1-\mathrm{k} \Omega\) load is connected across the secondary
The input voltage to the transformer in Figure \(\mathrm{P} 15-20\) is a \(\operatorname{sinusoid} v_{\mathrm{S}}(t)=339 \sin (314 t) \mathrm{V}\). With the circuit operating in the sinusoidal steady
Repeat Problem 15-20 with \(v_{\mathrm{S}}(t)=10 \cos 2000 t \mathrm{~V}\).Data From Problem 15-2015-20 The input voltage to the transformer in Figure \(\mathrm{P} 15-20\) is a
A transformer has self-inductances \(L_{1}=200 \mathrm{mH}, L_{2}=\) \(200 \mathrm{mH}\), and a coupling coefficient of \(k=0.5\). The transformer is operating in the sinusoidal steady state with
Repeat Problem 15-22 when a 20-mH inductive load is connected across the secondary winding.Data From Problem 15-22A transformer has self-inductances \(L_{1}=200 \mathrm{mH}, L_{2}=\) \(200
The linear transformer in Figure P15-24 is operating in the sinusoidal steady state with \(\mathbf{V}_{\mathrm{S}}=500 \mathrm{~V}\) and \(Z_{\mathrm{L}}=10+j 10\) \(\Omega\). Use mesh-current
(a) Repeat Problem 15-24 with \(Z_{\mathrm{L}}=10-j 10 \Omega\).(b) What is the largest value of mutual inductance reactance \(X_{\mathrm{M}}\) possible for the transformer shown in Figure
Find the phasor current \(I\) and the input impedance seen by the source in Figure P15-26. 200
Find \(\mathbf{I}_{A}\) and \(\mathbf{I}_{\mathrm{B}}\) in Figure P15-27 and the input impedance seen by the voltage source. 24020 ZIN IA | el n=5 + ill
If \(f=50 \mathrm{~Hz}\), find \(\mathbf{V}_{1}\) and \(\mathbf{V}_{2}\) in Figure P15-27 using Multisim.
A transformer operating in the sinusoidal steady state has inductances \(L_{1}=800 \mathrm{mH}, L_{2}=320 \mathrm{mH}\), and \(M=500\) \(\mathrm{mH}\). A load \(Z_{\mathrm{L}}=6+j\) o \(\Omega\) is
A transformer operating in the sinusoidal steady state has inductances \(L_{1}=510 \mathrm{mH}, L_{2}=2 \mathrm{H}\), and \(M=1 \mathrm{H}\). The load connected across the secondary is
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
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