ECEN3713 Exam
#2 31 March 2005
1) [10] A black box takes an input x(t) and forms an output y(t) =
1/x(t). Is this box a Linear Time Invariant system?
Explain. [Answer:
No. If a sinusoid is input, the output is not a sinusoid.]
2) Mini Design Problem: You are a staff engineer in the Filter Division
at MegaMoron Communications, Inc., the world's premier communication
engineering firm. Your boss has just rushed in and stated he
needs an emergency design for a single pole active low pass filter,
with a 3db frequency of 10 radians/second, on his desk in 15
minutes. The D.C. voltage gain of the filter should be +1 or
-1. At high frequencies, the filter gain should be zero.
The design will be immediately EMailed to a technician in the Dry
Tortugas, and built on site. The remote site has a limited
selection of capacitors and resistors. The only capacitors
available are from 1 - 1,000 micro farads (integer values only).
Resistors available are from 1 - 10 ohms, 10 -100 ohms in 10 ohm
increments, 100 - 1,000 ohms in 100 ohm increments, 1K - 10K in 1K
increments, 10K - 100K in 10K increments, and 100K - 1M in 100K
increments. No inductors are available.
[15] Sketch a block diagram of a single pole, active, low pass
filter with a half power frequency of 10 rads/sec. Your design
should only use resistors and capacitors available at the remote
site. [This one has
several possible answers. One possible solution is to use the
circuit of Figure 15.1 in the text with R1 = 10K ohm, R2 = 1K ohm, and
C = 100 microfarads.]
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3) The switch has been open for a long time, and closes at t = 0
seconds.
[5] Compute the current through the inductor at t = 0- seconds. [1 amp]
[5] Compute the current through the inductor at t = ∞. [2 amps]
[15] Using Laplace transforms, find a time domain expression for the
current through the inductor. [i(t) = 2 - e-0.1t]
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4) Given the active filter shown...
[15] Find the transfer function H(s). [H(s) = -(2s+1)/s]
[5] If +4v D.C. is input, find the output D.C. voltage. [-20v DC out]
[5] If a 1 vpp, 3 radian/sec sinusoid is input, find the steady state
output peak-to-peak voltage. [2.028 vpp]
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4) Given the circuit shown...
[15] Find the half power frequency ω3dB. [ω3dB = 1/6 rad/sec]
[10] If a 1 ohm load resistor is attached to the output, what will be
the new half power frequency? [ω3dB = 1/12 rad/sec]
[10] If vin(t) = 8cos10t, find the steady state expression for
vout(t). [vout(t) = 0.066cos(10t - pi/2)]
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