ECE 202 – Fall 2013
Exam #3
November 13, 2013
Circle your division:
Division 0101: Furgason (8:30 am)
Division 0201: Bermel (9:30 am)
Name (Last, First)______________________________
Purdue ID #_____________________________
There are 10 multiple choice problems (7 points each),
and 2 workout problems (15 points each).
Instructions
1.
2.
3.
4.
5.
6.
7.
8.
DO NOT START UNTIL TOLD TO DO SO.
Write your name, division, professor, and student ID# on your scantron sheet and this packet.
This is a CLOSED BOOKS and CLOSED NOTES exam.
Calculators are not allowed.
If extra paper is needed, use back of test pages.
Cheating will not be tolerated. Cheating in this exam will result in an F in the course.
If you cannot solve a question, be sure to look at the other ones and come back to it if time permits.
As described in the course syllabus, we must certify that every student who receives a passing grade in this
course has satisfied each of the course outcomes. On this exam, you have the opportunity to satisfy outcomes i,
ii, and iii. (See the course syllabus for a complete description of each outcome.) On the chart below, we list the
criteria we use for determining whether you have satisfied these course outcomes.
Course
Outcome
Exam
Questions
Total Questions
iii
iv
vi
6-7,10
1
2-5,8,9,11,12
3
1
8
Minimum #
correct responses
required to satisfy
course outcome
2
1
4
If you fail to satisfy any of the course outcomes, don’t panic. There will be more opportunities for you to do so.
9. You will find Laplace transforms on the final pages of this exam. You can tear them out if needed.
Multiple Choice Problems (7 points each)
1. Given the mutually inductive system depicted in the circuit below, with 4 cos V, what is the output
voltage (in V)? Hint: the additional voltage in the left-hand inductor from mutual inductance, as well as the
self-inductance of the inductor on the right-hand side, can be safely ignored.
(1) 4 cos
(2) 4 sin
(3) 2 cos
(4) 2 sin
(5) cos
(6) sin
(7) 0
(8) None of these
2. Given the circuit below, what capacitance (in F) is required to realize a third-order
Butterworth filter with a filter function (1) 0.1
(2) 0.25
(3) 0.5
(4) 1.0
(5) 2.0
(6) 3.0
(7) 4.0
(8) None of these
?
3. Consider the 3 dB normalized low pass filter in the circuit depicted below, with 10 rad/s and 40 dB.
What capacitance would be needed to transform this circuit into one offering 100 rad/s?
(1) 0.25 mF
(2) 2.5 mF
(3) 25 mF
(4) 50 mF
(5) 125 mF
(6) 250 mF
(7) 1 F
(8) None of these
4. Given the circuit depicted below, with ! 6 cos, what is the maximum average power (in W) that can be
delivered to the variable impedance load #$ ?
(1) 0.5
(2) 1.0
(3) 1.5
(4) 2.0
(5) 2.5
(6) 3.0
(7) 3.5
(8) None of these
5. Given the 3 dB normalized low pass filter depicted below, what capacitance should be chosen to achieve a 3 dB
normalized high pass filter instead?
(1) 25 µF
(2) 25√2 µF
(3) 50 µF
(4) 50√2 µF
(5) 25√2 mF
(6) 50 F
(7) 20 kF
(8) None of these
The following two questions (6 and 7) concern the circuit shown below.
+
5Ω
Iin(s)
Vout(s)
5Ω
–
6. For the circuit shown above, the maximum absolute value of the equivalent impedance
# &'() *+, is given by:
(1) 0.5Ω
(2) 1 Ω
(3) 5 Ω
(4) 10 Ω
(5) 20 Ω
(6) 50 Ω
(7) 100 Ω
(8) None of these
7. The quality factor Qp of the circuit shown above is:
(1) 1
(2) 2
(3) 6
(4) 8
(5) 10
(6) 20
(7) 40
(8) None of these
8. The circuit shown below consists of a 10 Ω resistor in parallel with a real 10 µF capacitor having a
quality factor Q =10 @ 1000 rad/sec. The input admittance -./ of this combination (in Ω-1) is:
(1) 0.010 + 10-5·s
(2) 0.011 + 10-5·s
(3) 0.101 + 10-5·s
(4) 0.110 + 10-5·s
(5) 0.2 + 10-5·s
(6) 1.1 + 10-5·s
(7) 10 + 10-5·s
(8) None of these
9. Given the circuit below, find the load impedance #$ that will maximize the power transfer to the load (in Ω).
(1) 1
(2) 1+2j
(3) 1.2+1.6j
(6) 3+4j
(7) 5
(8) None of these
(4) 2
(5) 1.6+1.2j
10. If a low-pass filter (not a Butterworth) having a transfer function of H ( s ) =
2s + 6
is excited by a
s + 2s + 3
2
sinusoidal voltage of vS ( t ) = 3cos ( 3 t − 450 ) V , the output signal will have the form
(
)
vout ( t ) = A cos 3 t + θ0 V .
The magnitude, A, in volts will be:
(1) 1
(5)
5
137
(2)
3
2
(3)
3
2
(4) 3
(6)
5
11
(7)
13
40
(8) None of these
Workout Problems (15 points each)
11. In the following problem, we wish to transform a Butterworth low pass filter into a high-pass filter with the
following final specifications: 20 rad/s, = 6.3 rad/s, 23 = 3dB, = 20 dB.
a. What is the filter order n? Use 5
≥
=>>.=?@AB C=
9:;< =>>.=?@DE C= F
8
8. Note that 10M.N ≈ 2 and log 3 ≈ 0.5.
9:;GHI /HK L
7
5 =_____________________________________________
b. What is the corresponding normalized low pass Butterworth transfer function?
S$T =__________________________________________
c. Transform the NLP filter from part (b) into a normalized high-pass filter, and write down the corresponding
transfer function.
SUT =__________________________________________
d. Use the target to effect a final frequency transformation, and write down the final filter transfer function.
UT =__________________________________________
e. Draw a passive implementation of the final filter function from (d), given V = 125mF. Be sure to label the
values of each circuit element.
12. Consider a low-pass filter depicted below, made from a ‘practical’ inductor and capacitor, with
effective internal resistances depicted in parallel for each element:
a. Find the resonant frequency of this circuit, and the resulting quality factor associated with both the
practical inductor and capacitor (hint: use approximate formulas from the right-hand column of the chart):
= _____________________ W$ = _____________________ WX = WY = _____________________
b. Transform the circuit into an equivalent RLC series circuit, and write down the values of each element:
Z = ______________________ [ = ______________________ V = _______________________
c. Determine the transfer function, , and the quality factor W\] of the circuit.
= _______________________________________________________________
W^_` = _____________________________________________________________________
Butterworth Transfer Functions
First order
1/ + 1
Second order
1/ 7 + √2 + 1
Third order
1/b + 1 7 + + 1c