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systems analysis design
Questions and Answers of
Systems Analysis Design
The transfer function \(T_{\mathrm{V}}(s)=V_{2}(s) / V_{1}(s)\) for a particular circuit is\[T(s)=-\frac{100 s}{s+500}\](a) Identify the critical point of \(T_{\mathrm{V}}(s)\). What is the phase of
Find the transfer function \(T_{\mathrm{V}}(s)=V_{2}(s) / V_{1}(s\) ) for the circuit in Figure P12-45 .(a) Use MATLAB to generate a Bode plot of your transfer function. From the Bode plots, estimate
For the following transfer function\[T(s)=\frac{2(s+1)}{(s+100)}\](a) Use MATLAB to plot the Bode magnitude of the transfer function. Is this a low-pass, high-pass, bandpass, or bandstop function?
For the following transfer function,\[T(s)=\frac{-50(s+10)}{(s+1000)}\](a) Identify the critical points. What type of filter is this? Estimate the cutoff frequency and the passband gain. What is the
For the following transfer function\[T(s)=\frac{500 s}{s^{2}+1010 s+10,000}\](a) Use MATLAB to plot the Bode magnitude and phase of the transfer function. Measure the cutoff frequencies, the
For the following transfer function \(T_{\mathrm{V}}(s)=V_{2}(s\) )\(/ V_{1}(s)\)\[T_{\mathrm{V}}(s)=\frac{20(s+10)(s+100)}{(s+1)(s+1000)}\](a) What are the poles and zeros of the function? Is this a
For the following transfer function \(T_{\mathrm{V}}(s)=V_{2}(s) / V\) \(1(s)\)\[T(s)=\frac{10^{8}(s+100)^{2}}{(s+1000)^{4}}\](a) Use MATLAB to plot the Bode magnitude and phase of the transfer
For the following transfer function \(T_{\mathrm{V}}(s)=V\) \({ }_{2}(s) / V_{1}(s)\)\[T_{\mathrm{V}}(s)=K \frac{s}{s^{2}+B s+\omega_{0}^{2}}\](a) Select values of \(B\) and co \({ }_{0}\) so that
Consider the gain plot in Figure P12-52.(a) Find the transfer function corresponding to the straightline gain plot.(b) Use MATLAB to plot the Bode magnitude and phase of the transfer function.(c)
Consider the gain plot in Figure P12-53 .(a) Find a transfer function corresponding to the straight-line gain plot. Note that the magnitude of the actual frequency response must be exactly 5 at the
Consider the gain plot in Figure P12-54.(a) Find the transfer function corresponding to the straightline gain plot.(b) Use MATLAB to plot the Bode magnitude of the transfer function.(c) Design a
Consider the following transfer function:\[T_{\mathrm{V}}(s)=\frac{K}{s^{2}+B s+10^{10}}\](a) Select \(K\) so that the passband gain is \(+60 \mathrm{~dB}\).(b) Using MATLAB plot three different Bode
The step response of a linear circuit is\[g(t)=50 e^{-5000 t} u(t)\](a) Find the impulse response waveform, \(h(t)\).(b) Is the circuit a low-pass, high-pass, bandpass, or bandstop filter?(c) Use
A circuit has the following transfer function:\[T(s)=\frac{s^{2}}{s^{2}+1500 s+2 \times 10^{6}}\](a) Use MATLAB to find its Bode magnitude response.(b) Use MATLAB to find its step response.(c)
Select \(B\) in the following transfer function so that the step response is Case B (two equal roots).\[T_{\mathrm{V}}(s)=\frac{10^{7}}{s^{2}+B s+10^{8}}\]Verify your choice using MATLAB's step
The following two transfer functions look similar. The difference is that their numerators and denominators are reversed. One is a tuned (narrow bandpass filter), the other is a notch (narrow
There is a need for a passive notch filter at 10 \(\mathrm{krad} / \mathrm{s}\). The narrower the notch the better, but there should be minimal ringing of the signals passing through. The transforms
There is a need for a filter to reduce the interference from a powerline on radio equipment. The interference is not only at \(60 \mathrm{~Hz}\) but also at its second harmonic, \(120 \mathrm{~Hz}\).
Step Response of an RLC Bandpass Circuit The step response of a series \(R L C\) bandpass circuit is\[g(t)=\left[\frac{4}{5} e^{-100 t} \sin (500 t)ight] u(t)\](a) Find the passband center frequency,
A Tunable Tank Circuit The RLC circuit in Figure P1263 (often called a tank circuit) has \(R=4.7 \mathrm{k} \Omega, C=68 \mathrm{opF}\), and an adjustable (tunable) \(L\) ranging from 64 to \(640 \mu
Filter Design Specification(a) Construct a transfer function whose gain response lies entirely within the nonshaded region in Figure P12-64. Validate your results using MATLAB.(b) If in addition to
Networks Integrated circuit (chip) \(R C\) networks are used at parallel data ports to suppress radio frequency noise. In a certain application, RF noise at \(3.2 \mathrm{MHz}\) is interfering with a
Design Evaluation Your company issued a request for proposals listing the following design requirements and evaluation criteria.Design Requirements : Design a low-pass filter with a passband gain of
Design EvaluationIn a research laboratory, you need a bandpass filter to meet the following requirements:Design Requirements: Passband gain: \(10 \pm 5 \%, B=10 \mathrm{krad} / \mathrm{s} \pm\) \(5
Design EvaluationIn a cable service distribution station, you need a bandstop filter to meet the following requirements:Design Requirements: Passband gain: \(10 \pm 5 \%, B=3.3 \mathrm{kHz} \pm\) \(5
The transfer function for a second-order LPF with \(T_{\max }=\mathrm{OdB}\) is\[T_{\mathrm{V}}(s)=\frac{\omega_{0}^{2}}{s^{2}+2 \zeta \omega_{0} s+\omega_{0}^{2}}\]Find the location of the poles
Determining the Cutoff Frequency of Two OnePole Filters in Cascade(a) Often one needs a simple cascaded low-pass \(R C\) filter that will achieve \(-40 \mathrm{~dB} / \mathrm{dec}\). Cascading two
Fiber-Optic Versus Cellular Communications Today, \(5 \mathrm{G}\) communications are necessary to deliver high band-widths and high-speed data to enable streaming of all types of information to
The OP AMP circuit in Figure P10-51 is in the zero state. Use node-voltage equations to find the circuit determinant. Select values of \(R, C_{1}\), and \(C_{2}\) so that the circuit has
Assume that the circuits in Figures P10-50 and P10-51 both have the same response characteristics. What are the advantages and disadvantages of each?
The switch in Figure P10-53 has been in position A for a long time and is moved to position B at \(t=0\).(a) Write an appropriate set of node-voltage or mesh current equations in the \(s\) domain.(b)
There is no energy stored in the circuit in Figure P10-54 at \(t=0\). Transform the circuit into the \(s\) domain. Then use the unit output method to find the ratio \(V_{\mathrm{O}}(s) /
The switch in Figure P10-55 has been open for a long time and is closed at \(t=0\). Transform the circuit into the \(\mathrm{s}\) domain and solve for \(V_{\mathrm{O}}(s)\) and \(v_{\mathrm{O}}(t)\).
Show that the circuit in Figure P10-5 \(\underline{6}\) has natural poles at \(s=-4 / R C\) and \(s=-2 / R C \pm j 2 / R C\) when \(L=R^{2} C / 4\).
Find the range of the gain \(\mu\) for which the circuit's output \(V_{\mathrm{O}}(s)\) in Figure P10-57. is stable (i.e., all poles are in the lefthand side of the \(s\) plane.)
Consider what a pole-zero diagram can tell about the behavior of signals represented by their poles.(a) For example, consider a single pole, say \(V(s)=V_{\mathrm{A}} /(s\) \(+\alpha\) ). Let
The circuit in Figure P10-59. 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
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 voltage between
In order to match the Thévenin impedance of a source, the load impedance in Figure P10-61 must be a equation(a) What impedance \(Z_{2}(s)\) is required if \(R=10 \Omega\) ?(b) How would you realize
The \(R C\) circuits in Figure P10-62 represent the situation at the input to an oscilloscope. The parallel combination of \(R_{1}\) and \(C_{1}\) represents the probe used to connect the
The OP AMP circuit in Figure P10-63 is in the zero state.(a) Transform the circuit into the \(s\) domain and use the \(\mathrm{OP}\) AMP circuit analysis techniques developed in Section 4-4 to find
The purpose of the test setup in Figure P10-64 is to deliver damped sine pulses to the test load. The excitation comes from a 1 -Hz square wave generator. The pulse conversion circuit must deliver
In transistor amplifier design, a by-pass capacitor is connected across the emitter resistor \(R_{\mathrm{E}}\) to effectively short out the emitter resistor at signal frequencies. This design
The Acme Pole Eliminator company states in their online catalog that the circuit shown in Figure P10-66 can eliminate any realizable pole. Their catalog states "Suppose you have a need to eliminate
The OP AMP circuit in Figure P10-67 is an audio band-pass filter-amplifier.(a) Your task is to design such a filter so that the lowfrequency cutoff is \(80 \mathrm{~Hz}\) and the high-frequency
(a) Find the driving point impedance seen by the voltage source in Figure P11-1 and the voltage transfer function \(T_{\mathbf{V}}(s)=V_{\mathbf{2}}(s) / V_{1}(s)\).(b) Select values of \(R\) and
(a) Find the driving point impedance seen by the voltage source in Figure P11-2 and the voltage transfer function \(T_{\mathrm{V}}(s)=V_{2}(s) / V_{1}(s)\).(b) Select values of \(R\) and \(L\) so
(a) Find the driving point impedance seen by the voltage source in Figure P11-3 and the voltage transfer function \(T_{\mathbf{V}}(s)=V_{\mathbf{2}}(s) / V_{1}(s)\).(b) Select values of \(R, L\), and
The transfer impedance function \(T_{\mathrm{Z}}(s)\) for the parallel circuit in Figure P11-4 isShow that the poles of the driving point impedance Z(s) are the poles of the transfer impedance
(a) Find the driving point impedance seen by the voltage source in Figure P11-5 and the voltage transfer function \(T_{\mathrm{V}}(s)=V_{\mathbf{2}}(s) / V_{1}(s)\).(b) Select values for \(R_{1},
(a) Find the driving point impedance seen by the voltage source in Figure P11-6 and the voltage transfer function \(T_{\mathrm{V}}(s)=V_{\mathbf{2}}(s) / V_{\mathbf{1}}(s)\).(b) Select values for
(a) Find the voltage transfer function \(T_{\mathrm{V}}(s)=V_{2}(s\))/ \(V_{1}(s)\) in Figure P11-7.(b) With \(L=1 \mathrm{H}\), select values of \(C\) and \(R\) so that poles are located at \(-2000
(a) Find the driving point impedance seen by the voltage source in Figure P11-8 and the voltage transfer function \(T_{\mathrm{V}}\) \((s)=V_{2}(s) / V_{1}(s)\).(b) Insert a follower at A and repeat.
(a) Find the driving point impedance seen by \(V_{1}(s)\) in Figure P11-9.(b) Find the voltage transfer function \(T_{\mathrm{V}}(s)=V_{2}(s) / V_{1}\) ( \(s\) ).(c) Select values of \(R_{1}, R_{2},
(a) Do a source transformation for \(I_{1}(s)\) and \(R\).(b) Use the new Thévenin source to find the transfer function \(T_{\mathrm{Z}}(s)=V_{2}(s) / I_{1}(s)\).(c) Select values of \(R\) and \(L\)
Find the voltage transfer function \(T_{\mathrm{V}}(s)=V_{2}(\) \(s) / V_{1}(s)\) of the cascade connection in Figure P11-11. Locate the poles and zeros of the transfer function.
The circuit of Figure P11-12 consists of two stages - a voltage divider stage and an OP AMP stage.(a) Compute the transfer function \(T_{\mathrm{V}_{1}}(s)=V_{\mathrm{X}}(s) / V_{1}(\) \(s)\).(b)
For the circuit in Figure P11-13 :(a) Find the impulse response \(h_{2}(t)\).(b) Find the step response \(g_{2}(t)\).
Find \(v_{2}(t)\) in Figure P11-14 when \(v_{1}(t)=\delta(t)\). Repeat for \(v_{1}(t)=u(t)\).
(a) Find \(h(t)\) and \(g(t)\) for the circuit in Figure P11-15 .(b) Swap the inductor and capacitor in the shaded portion of the circuit and repeat (a).
(a) Find \(H(s)\) for the circuit in Figure P11-16 in terms of \(R_{\mathrm{F}}\).(b) Select a value of \(R_{\mathrm{F}}\) so that there is pole in \(H\) ( \(s\) )at \(s=\) \(-5000 \mathrm{rad} /
If \(R_{\mathrm{F}}\) in Figure \(\mathrm{P}_{11-16}\) is \(25 \mathrm{k} \Omega\), find \(G(s)\) and \(g\) \((t)\). What are the initial value and final value of the step response?
Find \(v_{2}(t)\) in Figure P11-18 when \(v_{1}(t)=\delta(t)\). Repeat for \(v_{1}(t)=u(t)\).
The impulse response of a linear circuit is \(h(t)\) \(=\delta(t)-500 e^{-100 t} u(t)\). Find the circuit's step response \(g(t)\), impulse response transform \(H(s)\), step response transform \(G(\)
The step response transform of a linear circuit is \(G(s)=200 / s(s+100)\).(a) Find the circuit's transfer function, \(T(s)\).(b) Design a circuit to produce that transfer function. ( Hint : See
The pole-zero diagram of a circuit's step response is shown in Figure P11-21. The \(K\) of the circuit is 500.(a) Find \(G(s), g(t), H(s), T(s)\), and \(h(t)\).(b) Design an \(R C\) circuit that can
Find \(h(t)=\) image when \(g(t)=\left(3-e^{-10 t}ight) u(t)\). Verify your answer by first transforming \(g(t)\) into \(G(s)\) and finding \(H(s)=s G(s)\) and then taking the inverse transform of
The impulse response of a linear circuit is \(h(t)\) \(=45,000\left[e^{-5000 t}ight] u(t)\). Find the output waveform when the input is \(x(t)=9 t u(t) \mathrm{V}\).
The step response of a linear circuit is \(g(t)=0.5\) [1\(\left.e^{-250 t}ight] u(t)\). Find the output waveform when the input is \(v_{1}(\) \(t)=\left[20 e^{-200 t}ight] u(t)\). Use MATLAB to find
(a) Design a circuit that has the following step response:(b) Validate your design using Multisim(c) Plot its pole-zero diagram What is its scaling factor \(K\) ? or) u(t) 8(1) = 5(1-e-20000r)
The step response of a linear circuit is \(g(t)=100\left[\mathrm{e}^{-100}ight.\) \(\left.{ }^{t} \cos 2000 tight] u(t)\). Find the circuit's impulse response \(h(t)\), impulse response transform
The transfer function of a linear circuit is \(T\) ( \(s)=(s+2000) /(s+1000)\). Find the output waveform when the input is \(x(t)=5 e^{-1000 t} u(t)\). Use MATLAB to find the Laplace transform of
The circuit in Figure P11-28 is in the steady state with \(v_{1}\) \((t)=10 \cos 1414.21 t \mathrm{~V}\). Find \(v_{2 S S}(t)\). Repeat for \(v_{1}(t)=10\) \(\cos 10 \mathrm{k} t \mathrm{~V}\). And
The circuit in Figure P11-29. is in the steady state with \(v_{1}(t)=1.0 \cos 2020 t \mathrm{~V}\). Find \(v_{2 S S}(t)\). Repeat for \(v\) \({ }_{1}(t)=1.0 \cos 20.2 \mathrm{k} t \mathrm{~V}\), and
The output in Figure P11-30 is \(v_{2 S S}(t)=25.5 \cos\) \(\left(10,000 t+11.8^{\circ}ight) \mathrm{V}\). Find the input \(v_{1}(t)\) that produced that output.
The circuit in Figure P11-31 is in the steady state with \(i_{1}(t)=100 \cos (25 \mathrm{k} t) \mathrm{mA}, R_{1}=4 \mathrm{k} \Omega, R_{2}=6 \mathrm{k} \Omega\), and \(L\) \(=500 \mathrm{mH}\).(a)
The circuit in Figure P11-32 is in the steady state.(a) If \(i_{1}(t)=10 \cos 500 t \mathrm{~mA}\), find \(v_{2 S S}(t)\)(b) If \(i_{1}(t)=10 \cos 5000 t \mathrm{~mA}\), find \(v_{2 S S}(t)\).(c) If
The impulse response transform of a circuit is(a) Find \(v_{1 \mathrm{SS}}(t)\) if \(i_{1}(t)=10 \cos 5000 t \mathrm{~mA}\).(b) Design a circuit to achieve \(H_{Z}(s)\). The circuit in Figure P11-32
The transfer function of a linear circuit is \(T(s)=(s\) \(+100) /(s+200\). Find the sinusoidal steady-state output for an input \(x(t)=15 \cos 200 t\).
The step response of a linear circuit is \(g(t)\) \(=\left[5 e^{-1000 t}ight] u(t)\). Find the sinusoidal steady-state output for an input \(x(t)=10 \cos 1000 t\).
A student looks back at some notes she took in class. She sees Figure P11-3 6 and an equation \(v_{2}(t)=(1-\) \(\left.e^{-2 \text { equation }}ight) u(t)\) after it. How are the figure and the
The impulse response of a linear circuit is \(h(t)=800\left[e^{-100 t}-\mathrm{e}^{-400 t}ight] u(t)\). Use MATLAB to find the sinusoidal steady-state output for an input \(x(t)=\) \(8 \cos 200 t\).
The step response of a linear circuit is \(g(t)=\left[2 e^{-}ight.\) \(\left.{ }^{50 t} \sin 200 tight] u(t)\). Find the sinusoidal steady-state response for an input \(x(t)=50 \cos 200 t\).
The step response of a linear circuit is \(g(t)\) \(=\left[1-10ight.\) te \(\left.e^{-10 t}ight] u(t)\). The sinusoidal steady-state response is noted to be \(y_{\mathrm{SS}}(t)=18.03 \cos \left(20
The impulse response of a linear circuit is \(h(t)=u\) \((t)\). Use the convolution integral to find the response due to an input \(x(t)=\delta(t)\).
The impulse response of a linear circuit is \(h\) ( \(t)=[3 u(t)-u(t-1)-2 u(t-2)]\). Use the convolution integral to find the response due to an input \(x(t)=\delta(t)\).
The impulse response of a linear circuit is \(h(t)=u(\) \(t)-u(t-2)\). Use the convolution integral to find the response due to an input \(x(t)=u(t)-u(t-1)\).
The impulse response of a linear circuit is \(h\) \((t)=t[u(t)-u(t-1)]\). Use the convolution integral to find the response due to an input \(x(t)=u(t-2)\).
(a) The impulse response of a linear circuit is \(h\) ( \(t\) )\(=e^{-2 t} u(t)\). Use the convolution integral to find the response due to an input \(x(t)=\delta(t)\). Repeat for \(x(t)\)
(a) The impulse response of a linear circuit is \(h(t)=e\) \({ }^{-2 t} u(t)\). Use the convolution integral to find the response due to an input \(x(t)=t u(t)\).(b) Convert the impulse response into
Show that \(f(t) * \delta(t)=f(t)\). That is, show that convolving any waveform \(f(t)\) with an impulse leaves the waveform unchanged.
Use the convolution integral to show that if the input to a linear circuit is \(x(t)=u(t)\), thenThat is, show that the step response is the integral of the impulse response. y(t) = g(t) = S 0 h(t)dt
If the input to a linear circuit is \(x(t)=t u(t)\), then the output \(y(t)\) is called the ramp response. Use the convolution integral to show thatThat is, show that the derivative of the ramp
The impulse response of a linear circuit is \(h(t)=t u(t)\). Use MATLAB to compute the convolution integral and find the response due to an input \(x(t)=t[u(\) \(t)-u(t-2)]\).
The step response of a linear circuit is \(g(t)=2(1-\) \(\left.e^{-50 t}ight) u(t)\) and \(x(t)=' t u(t)\) Use \(s\)-domain convolution to find the zero-state response \(y(t)\)
The impulse responses of two linear circuits are \(h_{1}(t)=5 e^{-5 t} u(t)\) and \(h_{2}(t)=15 e^{-3 t} u(t)\) What is the impulse response of a cascade connection of these two circuits?
The impulse response of a linear circuit is shown in Figure P11-52. Graphically find the convolution of the impulse response shown and a unit step function, \(x(t)=u\) \((t)\).
Solve Problem 11–40 graphically.
Design an \(R C\) circuit using practical values to realize the following transfer function: Ty(s) = 500 s + 500
Design an \(R L\) circuit using practical values to realize the following transfer function: Ty(s) = 5 x 105 s+1x 106
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