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computer science
systems analysis design

Questions and Answers of Systems Analysis Design

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
Design a circuit to realize the transfer function below \(\pm 2 \%\) using only resistors and capacitors, but no OP AMPs, since no external power is available. You must use those \(100 \mathrm{pF}\)
Design a circuit to realize the transfer function below using only resistors, inductors, and no more than one OP AMP.Scale the circuit so that all inductors are exactly \(10 \mathrm{mH}\). Ty(s) =
Design a circuit to realize the transfer function below using only resistors, capacitors, and OP AMPs. All \(R\) s must be 1 \(\mathrm{k} \Omega\). or larger and the maximum OP AMP gain is \(\pm
The circuit shown in Figure P11-59. was designed to produce the following transfer function
Your employer needs a circuit that meets specific criteria. It must meet the following transfer characteristics:All capacitors must be exactly \(0.1 \mu \mathrm{F}\) and resistors greater than 1
Design a circuit to realize the transfer function below using only resistors, capacitors, and OP AMPs. Scale the circuit so that all resistors are greater than \(10 \mathrm{k} \Omega\) and all
Design a circuit to realize the following transfer function image in two ways:(a) As a passive circuit using only resistors, capacitors, and inductors with \(L \leq 50 \mathrm{mH}\).(b) Using only
A circuit is needed to realize the transfer function listed below.(a) Design the circuit using two OP AMPs.(b) Design the circuit using only one OP AMP.(c) Design the circuit using no OP AMPs. (s
It is claimed that both circuits in Figure P11-64. realize the transfer function(a) Verify that both circuits realize the specified \(T_{\mathrm{v}}(s)\).(b) Which circuit would you choose if the
It is claimed that both circuits in Figure P11-65 realize the transfer function(a) verify that both circuits realize the specified \(T_{\mathrm{V}}(s)\).(b) Which circuit would you choose if the
(a) Design a passive circuit that produces the following step response with all inductors having \(L=1 \mathrm{H}\).(b) validate your design using Multisim. g(t) = 2[e-50r e-100 ]u(t) -
A circuit is needed that will take an input of \(v_{1}(t)=\left[1-e^{-10,000} tight] u(t) \mathrm{V}\) and produce a constant \(-2 \mathrm{~V}\) output. Design such a circuit using practical parts
There is a need for a circuit with the following transfer function that must connect to a \(50-\Omega\) input and a \(1-\mathrm{k} \Omega\) load.In a parts catalog, your supervisor points out that
Figure P11-70 shows an interconnection of three basic OP AMP modules.(a) Does this interconnection involve loading?(b) Find the overall transfer function of the interconnection and locate its poles
Figure P11-71 shows an interconnection of three basic circuit modules. Does this interconnection involve loading? Find the overall transfer function of the interconnection and locate its poles and
A particular circuit needs to be designed that has the following transfer function requirements:Poles at \(s=-100\) and \(s=-10,000\); zeros at \(s=0\) and \(s=-1000\); and a gain of 50 as \(s
A circuit designer often is faced with deciding which analysis technique to use when attempting to solve a circuit problem. In this problem we will look at the circuit in Figure P11-7.3 and choose
There was a small black box that could not be opened to determine what was inside, but there were four terminals visible and accessible. A pair were marked input, the other pair were marked output.
Figure P11-7.5 shows the step response \(g(t)\) of a circuit.(a) From the graph, locate the step response poles on a pole-zero diagram.(b) From the graph, determine the circuit's rise time
How many \(500-\mathrm{MHz} 5 \mathrm{G}\) channels will be able to fit in the newly allocated C-band spectrum of \(3.7 \mathrm{GHz}\) to \(4.2 \mathrm{GHz}\) assuming no frequency space between
The US Navy talks to submerged submarines by using super low frequencies (SLF) that range from 30 to \(300 \mathrm{~Hz}\).Electromagnetic waves can penetrate a conducting medium, like seawater, up to
Blue light has a wavelength of \(400 \mathrm{~nm}\). What is its frequency and how much energy does it have?
Early telephone systems restricted voice signals to \(3 \mathrm{kHz}\) and added a \(1 \mathrm{kHz}\) guard band to keep signals separated. Those systems (and most land lines even today) use
Computer Axial Tomography (CAT) scans are invaluable medical diagnosis tools. They use X-rays with wavelengths between \(0.1 \mathrm{~nm}\) and \(10 \mathrm{~nm}\). What are the frequencies they
A transfer function has a passband gain of 500. At a particular frequency in its stopband, the gain of the transfer function is only 0.00025 . By how many decibels does the gain of the passband
A particular filter is said to be \(12 \mathrm{~dB}\) down at a desired stop frequency. How many times reduced is a signal at that frequency compared to a signal in the filter's passband?
A certain low-pass filter has the Bode diagram shown in Figure P12-8.(a) At what frequency is the filter \(10 \mathrm{~dB}\) down?(b) Estimate where the cutoff frequency occurs, then determine how
Find the transfer function \(T_{\mathrm{V}}(s)=V_{2}(s) / V_{1}(s)\) of the circuit in Figure P12-9.(a) Find the dc gain, infinite frequency gain, and cutoff frequency. Identify the type of gain
Find the transfer function \(T_{\mathrm{V}}(s)=V_{2}(s) / V_{1}(s\) ) of the circuit in Figure P12-10.(a) Find the dc gain, infinite frequency gain, and cutoff frequency. Identify the type of gain
Find the transfer function \(T_{\mathrm{V}}(s)=V_{2}(s) / V_{1}(s\) ) of the circuit in Figure P12-11.(a) Find the dc gain, infinite frequency gain, and cutoff frequency. Identify the type of gain
Design a high-pass filter with a cutoff frequency of \(15.9 \mathrm{kHz}\) and a passband gain of 5 . Find the transfer function of your design and validate your design using MATLAB.
Design a low-pass filter with a cutoff frequency of \(50 \mathrm{krad} / \mathrm{s}\) and a passband gain of 200. Validate your design using Multisim. All \(R\) 's must be \(\geq 10 \mathrm{k}
Your task is to connect the modules in Figure P12-14. so that the gain of the transfer function is 5 and the cutoff frequency of the filter is \(500 \mathrm{rad} / \mathrm{s}\) when connected between
A young designer needed to design a low-pass filter with a cutoff of \(1 \mathrm{krad} / \mathrm{s}\) and a gain of -5 . The filter is to fit as an interface between the source and the load. The
Design an RCRC low-pass first-order filter with a cutoff frequency of 100krad/s100krad/s and a passband gain of +50 . What is the minimum GBGB that the OP AMP must have to not affect the filter's
Figure P12-17 shows the Bode characteristics of three one-pole circuits. Find the transfer functions for each circuit, then determine each circuit's gain and cutoff frequency. System T1 is in blue,
Find the transfer function \(T y(s)=V_{2}(s) / V_{1}(s)\) of the circuit in Figure P12-18.(a) Find the dc gain, infinite frequency gain, and cutoff frequency. Identify the type of gain response.(b)
(a) Find the transfer function TV(s)=V2(s)/V1(s)TV(s)=V2(s)/V1(s) of the circuit in Figure P12-19.(b) What type of gain response does the circuit have?(c) What is the passband gain?(d) Design a
A first-order high-pass circuit has a passband gain of \(20 \mathrm{~dB}\) and a cutoff frequency of \(1000 \mathrm{rad} / \mathrm{s}\).(a) Find the circuit's transfer function.(b) Find the gain (in
For a series \(R C\) circuit, find \(Z_{\mathrm{EQ}}(s)\) and then select \(R\) and \(C\) so that there is a pole at \(s=0\) and a zero at \(s=\) \(-10 \mathrm{krad} / \mathrm{s}\).
For the circuit of Figure P10-2 :(a) Find and express \(Z_{\mathrm{EQ}}(s)\) as a rational function and locate its poles and zeros.(b) Select values of \(R\) and \(C\) to locate a pole at \(s=-56\)
For the circuit of Figure P10-3 :(a) Find and express \(Z_{\mathrm{EQ}}(s)\) as a rational function and locate its poles and zeros.(b) Select values of \(R\) and \(C\) to locate a zero at \(s=-330\)
For the circuit in Figure P10-4:(a) Find and express \(Z_{\mathrm{EQ}}(s)\) as a rational function and locate its poles and zeros.(b) Select values of \(R\) and \(C\) to locate a zero at \(s=-3.0\)
Consider the circuits in Figure P10-6 and answer the following questions.(a) What is the maximum number of poles possible for each of the circuits?(b) Can any of the circuits shown have an unstable
For the circuit of Figure P10-7:(a) Find and express \(Z_{\mathrm{EQ}}(s)\) as a rational function and locate its poles and zeros.(b) Select values of \(R\) and \(L\) to locate a pole at \(-1.5
The shaded part of the circuit in Figure P10-8 is called a tank circuit. It is used in AM radios to tune to the intermediate frequency (IF) allowing the transmitted signal to be received. The IF is
For the circuit of Figure P10-9:(a) If \(R=560 \Omega, L=2 \mathrm{H}\), and \(C=0.5 \mu \mathrm{F}\) locate the poles and zeros of \(Z_{\mathrm{EQ}}(s)\) ?(b) If we were to increase the resistance
(a) Find \(Z_{\mathrm{EQ} 1}(s)\) and \(Z_{\mathrm{EQ} 2}(s)\) for the bridge-T circuit in Figure P10-10 . Express each impedance as a rationalfunction and locate its poles and zeros.(b) Suppose the
For the two-port circuit of Figure P10-11:(a) Find \(Z_{\mathrm{EQ} 1}(s)\) and \(Z_{\mathrm{EQ} 2}(s)\), and express each impedance as a rational function and locate its poles and zeros.(b) Select
Find the equivalent impedance between terminals 1 and 2 in Figure P10-12. Select values of \(R\) and \(L\) so that \(Z_{\mathrm{EQ}}(s)\) has a pole at \(s=-33 \mathrm{krad} / \mathrm{s}\). Locate
For the circuit of Figure P10-14:(a) Use voltage division to find \(V_{\mathrm{O}}(s)\).(b) Use the lookback method to find \(Z_{\mathrm{T}}(s)\).
Find the Norton equivalent for the circuit in Figure P10-16. Convert the Norton equivalent circuit to its Thévenin equivalent. Then select values for \(R\) and \(L\) so that the Thévenin voltage
The circuit in Figure P10-16 has \(R=10 \mathrm{k} \Omega\) and \(L\) \(=5 \mathrm{H}\). A load is connected across the output equal to \(Z_{\mathrm{L}}(s)=s\) \(+500 \Omega\). Identify the natural
If the input to the \(R L C\) circuit of Figure P10-18 is \(v_{\mathrm{S}}(t)\) \(=u(t)\) :(a) Find the output voltage transform across each element.(b) Compare the three outputs with regard to their
If the input to the \(R L C\) circuit of Figure \(\mathrm{P}_{10-18}\) is \(v_{\mathrm{S}}(i)=u(t)\) :(a) Find the output voltage transform \(V_{\mathrm{LC}}(s)\) across \(L\) and \(C\) taken

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