MIT-circuits&electronics

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Massachusetts Institute of Technology󰀂

Department of Electrical Engineering and Computer Science󰀂

6.002 – Circuits & Electronics

Spring 2007

Quiz #1 13 March 2007

Name:

•󰀁There are 26 pages in this quiz, including this cover page. Please check that you have them all. •󰀁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: Theproblemsinthis quizvaryindiﬃculty;moreover, questionsofdiﬀerent levels of diﬃculty are distributed throughout the quiz. If you ﬁnd yourself spending a long time on a question, consider moving on to later problems in the quiz, and then working on the 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 of the 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.

•󰀁Thisis a closed-book quiz,butyou may usea calculator andyourdouble-sidedpage of notes. •󰀁You have 2 hours to complete this quiz. • Goodluck!

1. 6. 11. 16. 21.

2. 7. 12. 17. 22.

3. 8. 13. 18. 23.

4. 9. 14. 19. 24.

5. 10. 15. 20. 25. Final Score:󰀋

1󰀏

R2󰁿+V -+ v R1 -Graph the above network’s i−v relations as viewed from its port. Clearly label the intercepts

and the slope.

I Network (B)v

4󰀏

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].Problem 5: 4 points Write the node equations for the nodes el and e2 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].Problem 6: 4 points Thevenin Equivalent Circuit Thevenin Equivalent Circuit The current i is measured in two experiments which are performed on a Thevenin equivalent circuit as shown. What is the Thevenin equivalent resistance? 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].Problem 7: 4 points

A battery, which can be modelled by a Thevenin equivalent circuit, has an open circuit voltage of 2 volts. When a 500Ω resistor is connected to the battery, the terminal voltage drops to 1 volt. How muchpowerisdissipatedintheThevenin equivalent resistance of thebattery underthis condition?

Pdiss =

0.002W 0.005W 0.5W 2W 5W

1A 1Ω 1Ω 1V

1V VO

Vo =

−3/2V −1/2V 0V 1/2V 3/2V

9󰀏

2m󰀂Noise 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 take a signal, to which noise has been added so that it no longer meets the output speciﬁcations of the static discipline, and clean it up so that it once again meets the output speciﬁcations of the static discipline. These buﬀers, as well as the gates shown, obey the following static discipline:

VOL =1VVIL =2V

VOH =4V󰀂VIH =3V󰀂

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

01234

B A

Fill in the truth table for the above digital circuit.󰀏

A 0 0 1 1 B Z 0 1 0 1

11󰀏

A B

This gate is equivalent to:󰀏

A B

(b) Circuit B

A B

(d) Circuit D

(a) Circuit A

ABCD

none of the above

19kΩ 100Ω

10V

19kΩ

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

Pdiss =

0.25W 0.5W 0.75W 1W 2W

5V󰀂

RL 1kΩ

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

RL =

50Ω 150Ω 500Ω 1kΩ2kΩ

RTH IP

IS R1

VTH P VP

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

VTH = RTH =

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].Problem 15: 4 points 2 1 0 1 2 3 4 5 E v~(Volts) The device D embedded in the circuit shown above has the i--u relation illustrated in the plot located below the circuit schematic. Circle the value of the voltage source Vs required to bias the device at the operating point VD= 1V. 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].Problem 16: 4 points The device Q in the circuit shown above has the i--u relation Find the value of UQ in the circuit 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].vQ =0

(vS −1)2

vS ≥1 vS < 1󰀏

(2)󰀏

Let vS = VS + vs;then vQ = VQ + vq. Find vq/vs if VS =5V .

vq vs

6 12 20 24 48󰀋

18󰀏

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].Problem 18: 4 points For the above circuit, iL = 34. If Vs = 1V and us = 0.001 sin(wt), circle the correct expression for ii. A: 3 amps B: (3 x 21 = sin3(wt) amps sin(&) amps sin(&) amps sin2(wt) amps C: (1.11x D: (9.0 x E: (6.0 x 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].Problem 20: 4 points Following the node method, write a single node equation involving the node voltage el in terrns of I,Vl, V2, R1, R2 and R3. Node equation for el: 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].Problem 21: 4 points󰀂

2.5

VZ 0.7 0.5 0

3volts

0.5 0.7

2 2.5 3

VOL =0.5VVIL =0.7VVOH =2.5V󰀂VIH =2.0V󰀂

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 the AND gate satisﬁes the static discipline, and which boundary is broken if the static discipline is violated.

A: Yes, it satisﬁes the static discipline.

B:No,becausethe VIL threshold is not met for all valid inputs. C:No,becausethe VOL threshold is not met for all valid inputs. D:No,becausethe VOH threshold is not met for all valid inputs.

E: No, because the transition through the forbidden region is not instantaneous.

VS RL

A B

E VS RL

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

Z =󰀋

23󰀏

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].Problem 23: 4 points (a) Thevenin equivalent circuit A (b) Thevenin equivalent circuit B The i-u characteristics for each of two Thevenin equivalent circuits are plotted in the graphs corresponding to the labelled network. Using the graphs, estimate the current i~ when the circuits are connected as shown. Circle the answer corresponding to the value nearest your estimate. (Hint: This problem is most easily done graphically.) 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].Problem 24: 4 points

The NOR gate circuit shown operates in a digital system characterized by a static discipline with the voltage thresholds below.

10kΩ

For both of the MOSFETs, RON =2kΩ VT =2V

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

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

A: Yes, they can make this change.

B: No, because the MOSFETS will never turn on.

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

Calculate the equivalent resistance Req seen between the nodes A and B in the circuit shown above. Assumethatall oftheresistorshaveavalueof1Ω,andthat1amp ﬂowsintonode A and out of node B.(Note: this problem can be solved without writing any node equations.)

Req =

1/6Ω 1/3Ω 1/2Ω 5/6Ω 1Ω

26󰀏

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