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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 =
6.002 Circuits and Electronics Fall 2005 Final Exam Name:______________________________________
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)
6.002 Circuits and Electronics Fall 2005 Final Exam Name:______________________________________
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
6.002 Circuits and Electronics Fall 2005 Final Exam Name:______________________________________
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
6.002 Circuits and Electronics Fall 2005 Final Exam Name:______________________________________
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 = ____________________________________
6.002 Circuits and Electronics Fall 2005 Final Exam Name:______________________________________
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
6.002 Circuits and Electronics Fall 2005 Final Exam Name:______________________________________
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
Magnitude: A B C D E F
Phase: G H I J K L
Magnitude: A B C D E F
Phase: G H I J K L
Magnitude: A B C D E F
Phase: G H I J K L
6.002 Circuits and Electronics Fall 2005 Final Exam Name:______________________________________
Page 9 of 22
(This page left blank for work – Problem 4 magnitude and phase plots on following page)
6.002 Circuits and Electronics Fall 2005 Final Exam Name:______________________________________
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.
6.002 Circuits and Electronics Fall 2005 Final Exam Name:______________________________________
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.
6.002 Circuits and Electronics Fall 2005 Final Exam Name:______________________________________
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
6.002 Circuits and Electronics Fall 2005 Final Exam Name:______________________________________
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)
6.002 Circuits and Electronics Fall 2005 Final Exam Name:______________________________________
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
6.002 Circuits and Electronics Fall 2005 Final Exam Name:______________________________________
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)).
6.002 Circuits and Electronics Fall 2005 Final Exam Name:______________________________________
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 = _______________________________________________________
6.002 Circuits and Electronics Fall 2005 Final Exam Name:______________________________________
Page 17 of 22
(This page left blank for work – exam continues on the following page)
6.002 Circuits and Electronics Fall 2005 Final Exam Name:______________________________________
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 = ______________________________________________________
6.002 Circuits and Electronics Fall 2005 Final Exam Name:______________________________________
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:_____________________________________________
6.002 Circuits and Electronics Fall 2005 Final Exam Name:______________________________________
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”
6.002 Circuits and Electronics Fall 2005 Final Exam Name:______________________________________
Page 21 of 22
(D) Find and plot the input vs. output transfer relation for the circuit. Clearly label your graph.
outv
inv
6.002 Circuits and Electronics Fall 2005 Final Exam Name:______________________________________
Page 22 of 22
(blank page for extra work)