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Massachusetts InstituteofTechnologyDepartmentofElectricalEngineeringandComputerScience

6.002Circuits&ElectronicsSpring2007Quiz#1

13March2007

Name:

There are 26 pages in this quiz, including this cover page. Please check that you have themall. Please write your name in the space provided above, and circle the name of your recitation

instructor along with the time of your recitation.

IMPORTANT: The problems in this quiz vary in difficulty; moreover, questions of differentlevels of difficulty are distributed throughout the quiz. If you find yourself spending a longtime on a question, consider moving on to later problems in the quiz, and then working onthe challenging problems after you have finished all of the easier ones.

Do your work for each question within the boundaries of that question, or on the back ofthe preceding page. When finished, enter your answer to each question in the corresponding

answer box that follows the question.

Remember to include the sign and units for all numerical answers. This is a closed-book quiz, but you may use a calculator and your double-sided page of notes. You have 2 hours to complete this quiz.

Good luck!

1. 2.

6. 7.11. 12.

16. 17.

21. 22.

3.

8.13.

18.

23.

4.

9.14.

19.

24.

5.

10.15.

20.

25.

Final Score:

1

Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007.MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]

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Problem 1: 4 pointsVO

18

12

12

12VS

VOVS = 1/4 1/3 1/2 2/3 3/4

2

Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007.MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].

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Problem 2: 4 points

3

3

3

3

IS

IO

IOIS = 1/4 1/3 1/2 2/3 3/4

3


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Network B)

Problem 3: 4 points

iR2

R1 V -+

I

+

-

v

Graph the above networks iv relations as viewed from its port. Clearly label the interceptsand the slope.

i

v

4


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Problem 4: 4 pointsR R R R R

(resistor patternR R R RReq R

continues)

Req = R/2 R 1+23 R 1 +3 R 1+25 2R

5


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Problem : points

Write the node equations for the nodes l and e in the box below

Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007.MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY

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Problem : points

Thevenin TheveninEquivalent Equivalentircuit ircuit

The current is measured in two experiments which are performed on a Thevenin equivalentcircuit as shown What is th e Thevenin equivalent resistance?


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Problem 7: 4 pointsA battery, which can be modelled by a Thevenin equivalent circuit, has an open circuit voltage

of 2 volts. When a 500 resistor is connected to the battery, the terminal voltage drops to 1volt. How much power is dissipated in the Thevenin equivalent resistance of the battery under thiscondition?

Pdiss = 0.002W 0.005W 0.5W 2W 5W

8


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Problem 8: 4 points

11

1 V1 V

1 A

VO

Vo = 3/2V 1/2V 0V 1/2V 3/2V

9


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Problem 9: 4 points

2 mNoise in the 2 meter digital channel shown above is added in at the rate of 0.6 V per meter.

To correct for that noise, we introduce buffers into the channel. The purpose of a buffer is to takea signal, to which noise has been added so that it no longer meets the output specifications of thestatic discipline, and clean it up so that it once again meets the output specifications of the staticdiscipline. These buffers, as well as the gates shown, obey the following static discipline:

VOL = 1 V VOH = 4 VVIL = 2 V VIH = 3 V

What is the minimum number of buffers required to connect between the digital links in orderto insure correct operation?

0 1 2 3 4

10


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Problem 10: 4 pointsBA Z

Fill in the truth table for the above digital circuit.

A B Z0 00 11 01 1

11


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Problem 11: 4 pointsA

CB

This gate is equivalent to:

CA A C

CB B

A B A B(a)CircuitA (b)CircuitB (c)CircuitC (d)CircuitD

none ofA B C D

the above

12

C


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Problem 12: 4 points

19 k

19 k

100

VO10 V

Find the power dissipated in RON, if the MOSFETs are accurately represented by the switch-resistor model, where the threshold voltage VT = 2 V and the on-resistance RON = 100.

Pdiss = 0.25W 0.5W 0.75W 1W 2W

13


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Problem 13: 4 points5 V

1 kRLVO

VI

Given that VI = 5 V and VO = 5 V, and that the MOSFETs are accurately represented by theswitch-resistor model, where the threshold voltage VT = 2 V and the on-resistance RON = 100,find the minimum value of RL which will allow this buffer to operate correctly.

RL = 50 150 500 1 k 2 k

14


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P RTHIPIP

VP

P VPR1 VTHVS IS

The device P in the circuits above is a nonlinear device. The circuit in the left-hand figureabove that includes this device can be represented by the equivalent circuit which is illustrated inthe right-hand figure. Find expressions for VTH and RTH.

VT H = RT H =

15


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Problem 5: points

5

Volts)

The device D embedded in the circuit shown above has the i u relation illustrated in the plotlocated below the circuit schematic

Circle th e value of the voltage source Vs required to bias the device at the operating pointV D = 1 V .


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Problem 6: points

The device in the circuit shown above has the i u relation

ind th e value of U in the circuit


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Problem 17: 4 points1

1 QvQvS

iQ

The result of analyzing the above circuit yields the following relationship for the 2-terminalnonlinear device Q:

3vQ = 2(vS 1)2 vS 1 (2)vQ = 0 vS

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Problem 8: points

For the above circuit, iL 3 4 . If s 1 and us 0.001 sin(wt), circle the correct expressionfor ii

A: 3 ampsB: (3 sin3(wt)amps

2 C: (1.11 sin( ) ampsD: (9.0 sin( ) ampsE: (6.0 sin2(wt)amps


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A B C F(A,B,C)0 0 0 10 0 1 00 1 0 00 1 1 0

1 0 0 11 0 1 11 1 0 01 1 1 1

Write a logic expression corresponding to the function F(A ,B,C ) in the above truth table. Youneed not simplify your expression.

F(A,B,C) =

20


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Problem 2 : points

Following th e node method write a single node equation involving the node voltage el in terrnsof Vl V2 R1 R2 and R3.

Node equation for el:


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Problem 21: 4 points3

2.5

2

3 voltsVZ

VA

0.7

0.5

0

VA

VOL= 0.5 V VOH = 2.5 VVIL= 0.7 V VIH = 2.0 V

The voltage at the output Z of the 2-input AND gate is a function of the voltage at input A,as graphed above. Circle the correct entry in the following list which indicates whether or not theAND gate satisfies the static discipline, and which boundary is broken if the static discipline isviolated.

0 0.5 0.7 2 2.5 3

VZ

A: Yes, it satisfies the static discipline.B: No, because the VIL threshold is not met for all valid inputs.C: No, because the VOL threshold is not met for all valid inputs.D: No, because the VOH threshold is not met for all valid inputs.E: No, because the transition through the forbidden region is not instantaneous.

22


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Problem 22: 4 pointsVS

RL VS

Z RLA

B

D EC

Write a boolean expression for Z in terms of A, B, C, D, and E. You need not simplify yourexpression.

Z =

23


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Problem 24: 4 pointsThe NOR gate circuit shown operates in a digital system characterized by a static discipline

with the voltage thresholds below.

5 V

10 kFor both of the MOSFETs,

C RON = 2 kVT = 2 V

A B

VOL = 1 V VOH = 4.5 VVIL = 1.9 V VIH = 3 V

The supply voltage is currently 5 V. In order to save power, the designers are thinking ofreducing the supply voltage to 4 V. Can the designers make this change and still satisfy the staticdiscipline?

A: Yes, they can make this change.B: No, because the MOSFETS will never turn on.

C: No, because the gate will not meet the VOH part of the static discipline.D: No, because the gate will not meet the VIH part of the static discipline.E: No, because the gate will not meet the VIL part of the static discipline.

25


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