ECE 3100
Final Exam
Sum 2014
Name:__________________________________
Date:___________________________________
Instructions:
The test is 1hr 40mins in length starting at 8:00am and ending 9:40am. At the end of the
allotted time promptly turn in your test. You will be given a 10min warning at 9:30am. This is
time to finalize your work.
You are allowed to use your text book or relevant print outs from the text and your calculator.
Other materials such as notes or note cards are not permitted. You may use scrap paper, but
make sure you include your name on any additional work.
Make sure your work is neat and readable. Box your final answer. Partial credit for your work
will be considered, so attempt all problems. Partial credit is given for work which is clearly an
attempt at a specific question or sub question. Since this is an open book exam copying book
equations will not be given points.
ECE 3100
Final Exam
Summer 2014
1. (30pt) The Magnitude of a Bode plot is shown in the figure. Using opamps, choose the
resistor and capacitor values needed to build a filter capable of meeting the
specifications shown below.
f1 = 100 Hz
f2 = 3.18 kHz
Gain = 24 dB
a. (15pt) Solve for the highpass component values.
b. (15pt) Solve for the lowpass component values.
dB
-40 dB/dec
f
f1
f2
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ECE 3100
Final Exam
Summer 2014
2. (30pt) Convolution
The input to a circuit is given by 𝑥(𝑡) and the transfer function of the circuit is ℎ(𝑡).
Using convolution determine the output of the circuit 𝑦(𝑡).
𝑥(𝑡) = 2[𝑢(𝑡) − 𝑢(𝑡 − 4)]
ℎ(𝑡) = 𝑡𝑒 −𝑡 ∙ 𝑢(𝑡)
a. (10pt) Sketch the initial setup for the convolution.
b. (10pt) Determine 𝑦(𝑡).
c. (10pt) Determine the regions of 𝑦(𝑡).
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ECE 3100
Final Exam
Summer 2014
3. (30pt) Fourier Series Expansion
For the waveform shown solve for the Fourier Series representation.
5
-2
-1
1
2
3

a. (5pt) Solve for the period and natural frequency of the waveform.
b. (10pt) Solve for the DC component of the waveform.
c. (15pt) Solve for the AC component of the waveform.
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ECE 3100
Final Exam
Summer 2014
4. (30pt) CTFT Proof
The input, x(t), into a circuit is a delayed pulse shown in the figure.
a. (15pt) Solve for the Fourier Transform of the signal, X().
b. (5pt) What is the DC value of X()?
c. (10pt) Solve for the Energy Spectral Density, |X()|2.
d. (Bonus 10pt) Use Parseval’s Theorem to solve for the energy in the signal.
2
t
1
5
5
ECE 3100
Final Exam
Summer 2014
5. (30pt) 2-Port Network Impedance
Solve for the Impedance Parameters of the two port network shown below.
V1 = X-Y
V2 = A-B
R1 = 1 k
R2 = 1 k
R3 = 1 k
R4 = 1.5 k
a. (12pt) Solve for z11 and z21.
b. (12pt) Solve for z21 and z22.
c. (6pt) Draw the general equivalent circuit.
I1
I2
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ECE 3100
Final Exam
6. (30pt) The circuit below has the values shown in the table.
R1 = 1 k
C1 = 1.59 F
R2 = 5 k
Summer 2014
C2 = 3.18 nF
a. (10pt) Solve for the transfer function of the circuit, H(S). What are the poles and
zeros of circuit? Is the circuit stable?
b. (10pt) The input, Vin(t) is a unit step. What are the partial fraction coefficients?
c. (10pt) Solve for vo(t).
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