# EE EXAM NO PAGE OF Name Problem Subtotal Bonus by lizbethbennett

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```									EE 3144-01

EXAM NO. 2

PAGE 0 OF 11

Name:

Problem 1a 1b 2a 2b 3a 3b 3c 3d Subtotal Bonus #1 Bonus #2 Total 20 10 20 10 15 10 5 10 100 10 10 100

Points

Score

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING Fall 02

EE 3144-01

EXAM NO. 2

PAGE 1 OF 11

Problem No. 1: The Op-Amp problem 1a) Find Vo/Vin for the circuit in Figure 1. Assume an ideal op-amp. 2kΩ

20kΩ

+ +

Vin

+ -

9.9 kΩ Vo

0.1 kΩ

-

Figure 1

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

Fall 02

EE 3144-01

EXAM NO. 2

PAGE 2 OF 11

1b) Replace the ideal op-amp in Figure 1 with the linear op-amp model. Draw the resulting circuit. Make and state realistic assumptions for the values of the linear op-amp model parameters. Write a set of linearly independent equations using mesh analysis and your assumed values. Do not solve for the unknowns, just provide N equations with N unknowns.

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

Fall 02

EE 3144-01

EXAM NO. 2

PAGE 3 OF 11

Problem 2: Superposition and Source Transformation 2a) Use superposition to ﬁnd Vo for the circuit in Figure 2a.

1 kΩ

1 kΩ

+
VS1=5V

+ -

1 kΩ

1 kΩ VS2=5V

Vo

-

+ -

1 kΩ

IS1= 5mA

Figure 2a

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

Fall 02

EE 3144-01

EXAM NO. 2

PAGE 4 OF 11

2b) Use source transformation (and only source transformation, resistor combination and source combination) to reduce the circuit in Figure 2b so that the resulting circuit contains no more than 3 components. Use the resulting circuit to ﬁnd Vo. Draw all intermediate circuit simpliﬁcations! 1 kΩ 1 kΩ

+
5V + 1 kΩ 10 mA Vo 0.5 kΩ

1 kΩ

1 kΩ 5V

Figure 2b

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

+ Fall 02

EE 3144-01

EXAM NO. 2

PAGE 5 OF 11

Problem No. 3: Thevenin, Norton and Maximum Power Transfer As we have seen throughout the semester, it is often advantageous in circuit analysis to break a circuit into several small parts and then analyze each part separately. The results of these individual analyses can then used to characterize the complete circuit. In the circuit of Figure 3, we have broken a complex circuit into 3 pieces: Sub-circuit I, Sub-circuit II and the load: RL. See the following pages for the questions...

4kΩ

A

4kΩ

4kΩ

4kΩ

+
20 V

+ -

Vx
2000

2kΩ

VX

RL

4kΩ

4kΩ

+ -

2000*IX

IX

Sub-circuit I

B

Sub-circuit II

Figure 3

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

Fall 02

EE 3144-01

EXAM NO. 2

PAGE 6 OF 11

3a) Find the Norton equivalent of Sub-circuit I of Figure 3. Draw the equivalency.

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

Fall 02

EE 3144-01

EXAM NO. 2

PAGE 7 OF 11

3b) Find the Thevenin equivalent of Sub-circuit II of Figure 3. Draw the equivalency.

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

Fall 02

EE 3144-01

EXAM NO. 2

PAGE 8 OF 11

3c) Simplify the circuit in Figure 3 using the two equivalents from 3a) and 3b). Draw the equivalent circuit and solve for Vo in terms of RL.

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

Fall 02

EE 3144-01

EXAM NO. 2

PAGE 9 OF 11

3d) Find the value of RL that maximizes the power delivered to RL by the rest of the circuit. What is the value of this maximum power?

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

Fall 02

EE 3144-01

EXAM NO. 2

PAGE 10 OF 11

Bonus #1: Use the Thevenin equivalence for the op-amp sub-circuit to solve for Vo in the circuit below. Use ideal op-amp assumptions. 20kΩ

2kΩ

+

2 kΩ

+

5V

+ -

9.9 kΩ 2 kΩ Vo 0.1 kΩ

-

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

Fall 02

EE 3144-01

EXAM NO. 2

PAGE 11 OF 11

Bonus #2: A rectangular piece of cake with icing is leftover from an ofﬁce party. Two engineering students (who are always in favor of free food) decide to split the cake equally amongst themselves. However, they are faced with an optimization problem. They desire to split the cake so that: a) Each of the two students gets an equal amount of the cake part. b) Each of the two students gets an equal amount of icing. c) They only have to make a single, straight-line cut with a knife. Assume the cake is as shown in the ﬁgure: it is iced on top; iced on sides A and B; not iced on sides C and D and not iced on the bottom. Draw the optimal, single straightline cut that satisﬁes all of the constraints. Explain your decision process. You may assume that the cake is equally dense throughout and that the icing is uniformly spread across all iced surfaces.

DE

C

S

SI

ID

E

D

TO P
3 inches
S ID E

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

4

in

es

c

h

in

ch

e

s

10

SI

DE

A

B

Fall 02

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