MASSACHUSETTS INSTITUTE OF TECHNOLOGYweb.mit.edu/6.002/www/fall05/handouts/quiz/finsln.pdf · MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer

fa05_final v6.doc

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science

6.002 – Circuits and Electronics Fall 2005

Final Exam

December 20, 2005

YOUR NAME: ___________________________________________________________

Recitation Instructor / TA: __________________________________________________

General Instructions:

1. Please verify that there are 22 pages in your exam booklet.

2. Please do all of your work in the spaces provided in this examination booklet. In particular, try to do your work for each question within the boundaries of the question, or on the back side of the page preceding the question. Extra pages are also available at the end of the booklet. Place the answer to each question within the appropriate answer box.

3. You may use three double-sided pages of notes and a calculator while taking this exam.

For examiner’s use only:

Problem Points Score Grader

1 8

2 12

3 20

4 20

5 20

6 20

Total 100

6.002 Circuits and Electronics Fall 2005 Final Exam Name:______________________________________

Page 2 of 22

(8 points) This problem considers the following NMOS digital logic circuit. The circuit has four inputs A, B, C, and D and one output X.

If a high voltage represents a “1” and a low voltage represents a “0”, write the output X as a Boolean function of A, B, C, and D in the answer box at the bottom of this page. The truth table may be used as a guide to finding the function, but is not a requirement.

A B C D X0 0 0 00 0 0 10 0 1 00 0 1 10 1 0 00 1 0 10 1 1 00 1 1 11 0 0 01 0 0 11 0 1 01 0 1 11 1 0 01 1 0 11 1 1 01 1 1 1

X =


Page 3 of 22

(12 points) This problem concerns the following circuit:

(A) Assume that the network is operating in the sinusoidal steady state. Determine the response tvout to the input voltage tVtv SIin cos . Note that outv will take the form tVSO cos .

(answer box located on the following page)


Page 4 of 22

outv _______________________________________________

(B) If the input of this network is inv and the output of the network is outv , circle only one of the following terms that best describes the filtering function performed by the network.

Low Pass

High Pass

Band Pass

Band Stop

None of the Above


Page 5 of 22

(20 points) Consider the following circuit:

The excitation tvi is an impulse at 0t of area secondsvolt .

ttvi

(A) What are the values of ti , tvo , and tvc at 0t ?

0i ________________________________

0ov _______________________________

0cv _______________________________

(B) What are the values of ti , tvo , and tvc as t ?

ti _____________________________

tvo ____________________________

tvc ____________________________

There is no stored energy for 0t

HL 310

FC 710


Page 6 of 22

For the remaining parts of Problem 3, now assume that

CLZR

101

101

0

(C) Find the natural frequencies of this circuit (i.e. find the roots of the characteristic equation). Give numerical answers.

s1 = ____________________________________

s2 = ____________________________________


Page 7 of 22

(D) Sketch the approximate waveform for ti . Clearly label the important features of your sketch with numerical values. Assume that 100ZR .

ti

t


Page 8 of 22

(20 points) The following circuits are driven by a sinusoidal source tvi in the steady state. On the following pages, there are six sketches of magnitudes on log-log graphs (labeled A-F) and six sketches of phase on linear-log graphs (labeled G-L) for possible transfer functions io vvjH ˆˆ . For each circuit, circle the letters of the magnitude and phase plots which could represent the behavior of that circuit. Each circuit matches only one magnitude and one phase plot. Magnitude and phase plots may be reused.

Magnitude: A B C D E F

Phase: G H I J K L


Phase: G H I J K L


Phase: G H I J K L


Phase: G H I J K L


Page 9 of 22

(This page left blank for work – Problem 4 magnitude and phase plots on following page)


Page 10 of 22

Transfer function magnitude plots for Problem 4.

Note: The horizontal axes in these sketches indicate zero on the log scale. You are looking for the correct approximate shape of the plot; do not worry about the frequency scale along the horizontal axes. The vertical scales may differ among sketches.


Page 11 of 22

Transfer function phase plots for Problem 4.

Note: The horizontal axes in these sketches indicate zero phase angles. You are looking for the correct approximate shape of the plot; do not worry about the frequency scale along the horizontal axes. The vertical scale may differ among sketches. Recall that one may shift phase angles by multiples of 360 without changing the result.


Page 12 of 22

(20 points) The circuit symbol for the exponentially acting transistor, or EXPAT for short, is drawn to the right. The voltage KTv between the Knob, K, and the Thingamijig, T, is the input voltage and it controls the current Wi between the Whatchamacallit, W, and the Thingamajig, T. The equations relating the input current, Ki , and the output current, Wi , to the input and output voltages, KTv and

WTv , respectively are the following:

0for1 KTVv

MK veIi MKT , and 0,0for10,0for0

WTKTVv

KTM

WTKTW vvevG

vvi

MWT

These relationships are drawn below for 0KTv , and VvWT 3 for an EXPAT for which mAI M 1.0 , VVM 5.0 , and mSGM 4 . The asymptotic values of the curves at large

voltages are indicated, and a one volt increment has been used when plotting the family of Wi curves.

vKT = 1V

vKT = 2V

vKT = 3V


Page 13 of 22

(A) In general the small signal linear equivalent circuit for a three-terminal transistor like the EXPAT has four elements and can be represented by the following circuit.

Find expressions for the four small-signal elements ig , rg , mg , and og for a bias point KTV , WTV , where 0KTV and 0WTV . ig , rg , mg , and og all have units of conductance. Be sure to indicate the differential relationship you are using to determine each element, as well as the element’s value expressed in terms of the device and bias point parameters.

(answer box located on the following page)


Page 14 of 22

gi = _____________________________________for VKT > 0 V and VWT > 0 V

gr = _____________________________________for VKT > 0 V and VWT > 0 V

gm = _____________________________________for VKT > 0 V and VWT > 0 V

go = _____________________________________for VKT > 0 V and VWT > 0 V


Page 15 of 22

For the remaining parts of Problem 5, consider the common-Thingamajig amplifier shown below.

(B) In the space below, sketch the small signal linear equivalent circuit for this amplifier for a bias point KTV , WTV , where 0KTV and 0WTV . For this part, assume that the model of part (A) has known parameters, in which ig , mg , and ogare finite and non-zero, and 0rg . (Note: This is not necessarily correct for your answers in part (A)).


Page 16 of 22

(C) Find an expression for the small signal voltage gain, inoutv vvA , of this amplifier for a bias point KTV , WTV , where 0KTV and 0WTV . Express your answer in terms of IR , ig , rg , mg , og , and WR .

Av = _______________________________________________________


Page 17 of 22

(This page left blank for work – exam continues on the following page)


Page 18 of 22

(20 points) Consider the following circuit for parts (A) and (B). You may treat the op-amps in the circuit as ideal ( 0i , 0i , and op-amp gain is infinite).

(A) Find an expression for Xv in terms of INv .

Xv = ______________________________________________________


Page 19 of 22

(B) Find the input impedance at the port indicated by INZ . Also, provide a brief description of what the circuit does.

ZIN = ______________________________________________________

Circuit Function:_____________________________________________


Page 20 of 22

For the remainder of Problem 6, consider the circuit below. For simplicity, we will consider a simplified model of the diodes shown to the right in which the diode is either “off” ( FD Vv , 0Di ),or “on” ( FD Vv , 0Di ), where VVF 6.0 . You may treat the op-amp as ideal ( 0i , 0i , and op-amp gain is infinite).

(C) In the answer box below, circle the appropriate diode states for the two cases: 0inv and 0inv .

for vIN < 0 D1 OFF D1 ON D1 OFF D1 ON (circle one combination) D2 OFF D2 OFF D2 ON D2 ON

for vIN > 0 D1 OFF D1 ON D1 OFF D1 ON (circle one combination) D2 OFF D2 OFF D2 ON D2 ON

Di

DvFV

Diode“on”

Diode “off”


Page 21 of 22

(D) Find and plot the input vs. output transfer relation for the circuit. Clearly label your graph.

outv

inv


Page 22 of 22

(blank page for extra work)

Documents

MASSACHUSETTS INSTITUTE OF TECHNOLOGYweb.mit.edu/6.002/www/fall05/handouts/quiz/finsln.pdf · MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer