EC312 Twelve Week Exam Spring 2015
March 30, 2015
United States Naval Academy
Electrical and Computer Engineering Department
EC312 - 12 Week Midterm (Version A) – Spring 2015
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Do a page check: you should have 6 pages including this cover sheet.
You have 50 minutes to complete this exam.
An FE-approved calculator may be used for this exam.
This exam is closed book and closed notes. You may use two single-sided hand-written pages of notes.
Turn in your two single-sided hand-written pages of notes with your exam.
This exam may be given as a makeup exam to several midshipmen at a later time. No communication is
permitted concerning this exam with anyone who has not yet taken the exam.
Name:
____________________
Instructor:
____________________
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EC312 Twelve Week Exam Spring 2015
March 30, 2015
Question 1. Consider the signal below on the left.
Time-Domain
__________ (____)
Frequency-Domain
15
Voltage (V)
10
5
0
-5
-10
-15
0
0.1
0.2
0.3
0.4
0.5
0.6
Time (µs)
0.7
0.8
0.9
1
__________ (____)
1) (5 pts) Write out the time-domain equation for the signal: 𝑉𝑉(𝑡𝑡) = ______________________________
2) (5 pts) On the axes to the right, plot the frequency domain representation of the signal. (Make sure to
label axes and relevant values.)
Question 2. (5 pts) Circle all of the following which are advantages of using modulation. (Could be more than
one answer.)
(i) Systems can have smaller antennas due to higher carrier frequencies
(ii) Modulated signals have smaller bandwidth than baseband signals
(iii) Signals can be deconflicted by modulating at different carrier frequencies (i.e. Frequency Division
Multiplexing)
(iv) Modulation enables a more extensive use of the EM spectrum since higher frequencies are available
(v) Modulation makes it possible to transmit digital signals via free space, which would otherwise be
impossible since antennas can’t send DC signals
Question 3. (6 pts) What is the length of the driven element in a 300 MHz Yagi antenna?
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EC312 Twelve Week Exam Spring 2015
March 30, 2015
Question 4. (12 pts) Given the frequency domain representation of an AM signal shown below, write out the
equation for the carrier signal 𝑣𝑣𝑐𝑐 (𝑡𝑡) and the equation for the baseband signal 𝑣𝑣𝑚𝑚 (𝑡𝑡), including units.
𝑣𝑣𝑐𝑐 (𝑡𝑡) = ____________________________________________________________________
𝑣𝑣𝑚𝑚 (𝑡𝑡) = ____________________________________________________________________
Amplitude (V)
10
5
1
~
145
147.5 150.0 152.5
155
Frequency(kHz)
Question 5. (8 pts) Suppose that the AM signal from the previous question was provided as the input signal
𝑉𝑉𝑆𝑆 (𝑡𝑡) for the low-pass filter shown below. If R = 1kΩ and C = 1.07nF, draw the frequency domain
representation for the output 𝑉𝑉𝑜𝑜𝑜𝑜𝑜𝑜 in the box below, labelling all relevant values and axes. (Note: assume that
all frequencies in the passband of the filter are passed without attenuation.)
Draw your answer in this box, with
appropriate labels
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EC312 Twelve Week Exam Spring 2015
March 30, 2015
Question 6. (8 pts) You are designing an amplifier for a sensor system, which must take 5 mW as input power
and amplify it to produce an output of 14 dBm (+/- .5dBm). You check with the lab techs, and they have the
three amplifiers 𝐴𝐴1 , 𝐴𝐴2 , 𝐴𝐴3 (shown here to the right) available. Select which amplifiers you would use (in which
arrangement) and draw them into the box below. Show all work for full credit.
Question 7. (4 pts) If an RLC bandpass filter has the correct resonant frequency but is not selective enough (i.e.
it passes frequencies that should be attenuated), explain how could you make the filter more selective without
changing the resonant frequency.
Question 8. (3 pts) Circle all of the following which are true about the frequency domain representation of the
square wave shown to the right:
(i) The frequency domain representation has a fundamental
frequency at 𝑓𝑓0 = 1/𝑇𝑇
(ii) The frequency domain representation will also look like a
square wave
(iii) The frequency domain representation will have equally
spaced integer multiples of the fundamental frequency
Question 9. Consider the antenna radiation pattern shown to the
right.
1) (3 pts) What is the half-power beamwidth for the main lobe?
2) (3 pts) What is the Side-Lobe-Level (SLL) for the rear lobe?
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EC312 Twelve Week Exam Spring 2015
March 30, 2015
Question 10. The radio tower for WNAV AM 1430 in Annapolis is approx. 386 feet tall.
1) (2 pts) What is the nominal radio horizon line-of-sight distance for this radio tower (in miles)?
2) (2 pts) A friend in Gaithersburg (approx. 40 miles from Annapolis) claims that she regularly hears
WNAV broadcasts at all hours of the day. Which radio propagation phenomenon would be the MOST
likely reason for this?
3) (2 pts) Another friend who lives in New York City (approx. 200 miles from Annapolis) claims that one
night he heard a radio broadcast from WNAV, but your friend in Philadelphia (approx. 100 miles from
Annapolis) didn’t hear it. Which radio propagation phenomenon would be the MOST likely reason for
this?
Question 11. (10 pts) You and your lab partner stand 100m apart from each other, each holding a standard
dipole antenna. Your lab partner transmits a signal with a transmit power of 10W, and you receive .153mW.
Assuming an ideal propagation environment, at what frequency is your lab partner transmitting?
Question 12. (6 pts) A communication system uses the QPSK digital modulation scheme illustrated by the
constellation diagram to the right. A signal is received (below left) with the indicated phase changes. Write out
the bitstream that has been received.
01
90°
00
180°
0°
10
11
270°
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EC312 Twelve Week Exam Spring 2015
March 30, 2015
Question 13. The figure below is a graph of the signal
𝑉𝑉𝑠𝑠 (𝑡𝑡) = sin( 2𝜋𝜋(22)𝑡𝑡) + 2 sin( 2𝜋𝜋(15)𝑡𝑡) + 5 sin(2𝜋𝜋(2)𝑡𝑡)
8
6
Voltage (V)
4
2
0
-2
-4
-6
-8
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Time (s)
Suppose the signal is sampled at a 20Hz sampling rate and quantized with a 3-bit quantizer with a range of -8V
to +8V.
1) (4 pts) Circle the 5th sample point.
2) (4 pts) Next to the 5th sample point, write the binary number that will be assigned to that sample.
3) (4 pts) Will the conversion from digital back to analog suffer from aliasing? Briefly explain why or why
not.
Question 14. (4 pts) Two Systems Engineering majors both want to use the “free space” communication
channel at the same time for their Capstone projects. List two different ways they can simultaneously use this
communication channel without interfering with each other.
Turn in your equation sheets with your exam!
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