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Unformatted text preview: Carnegie Mellon University
Department of Electrical and Computer Engineering 18100: Introduction to Electrical and Computer Engineering Fall 2009
Exam 2: October 29, 2009 Closed Book Write your answers in the space provided. Do your work as neatly as possible. Cross out any
work that is not pertinent to your final solution. The grader reserves the right to mark solutions
as incorrect if she cannot follow your train of thought in the problem, or read your handwriting.
BE CLEAR AND CONCISE IN YOUR ANSWERS. Show all work! Answers that have incorrect
units (or no units at all) will have points taken off. We recommend that you do the problems that
you are comfortable with ﬁrst and then attack the ones that may take you more time last. Problem 1 (30 points)
Problem 2 (25 points)
Problem 3 (25 points) Problem 4 (20 points) Total = ("r H”/ Name QLLU \ 3,0[08 Section (A: Monday eve., B: Tuesday eve“I C: Wednesday eve., D: Thursday eve., E: Friday aft.) Problem 1: (30 points total) Miscellaneous For each of the circuits below, calculate the value requested. For all parts, assume
VD,0N = 0.6 V, VBE,0N = 0.6V, VCE,SAT = 0.2V, and [3 = 99. a) (10 points) Let VLEDDN = 1.4 V.
Vcc=l 0V ' Vin Let Vin = 10V. What is ILED? (Hint: doing a Thevenin equivalent can make this part easier.) 1119mm C Wu M W” ‘ Len.
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b) (10 points) Let R1, R2, and R3 all = lkﬂ, and C = lpF for this circuit. Vo(t) If Vi(t) = 100030 000t) V, what is Vo(t)? (Note: functions of time don’t have j’s in them! Hint: break
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,— ﬁ 050 ‘ Li) H V0(t) = ‘" lAJ 4 c) (10 points) For the Circuit shown below, assume we have a sinusoidal input voltage of V50) = 205in(211:*1000*t) and that the zener voltage for the diodes is Vz = 5v. On the axes below, sketch Vo(t)
for two periods of the input sinusoid, beginning at t = US. Label your axes and your sketch well. SKQ 6'). Problem 2: (25 points total) Olaamps For the op amp circuit below, you can assume the op amps are ideal and that the rules for circuits with
negative feedback hold. The op amps are operating in their linear range. All voltages reference ground. a) (7 points) Find an expression for Vx as a function of.Vs.
b) (8 points) Find an expression for Vx as a function of 15.
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Problem 3 (25 points total) Transistor circuit problem. For the transistor, assume that VBE,ON = 0.6v, Vce,sar = 0.2v, [3 = .99. All capacitors are “very large”, so
they’re open circuits at DC and short circuits at AC. Let Vs(t) = 3.6v + Vs,ac Vs(t) (a) (10 points) Draw the large signal (DC) model for the circuit. What is the value of Rb that we would need if we desire the DC operating current, [[30, to be = 20uA? What is the value of V0,dc under
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{wotecvoéﬂ‘ﬁ 1* (LU. 9 (b) (15 points) Draw the smallsignal (AC) model for the circuit. Calculate r“ for this part of the circuit.
Find the AC gain, Av = Vo,ach,ac for this circuit. (Suggestion: Solve for the gain symbolically as a
function of the components and parameters in the small signal circuit ﬁrst, then plug in values at the end.) (Ms mt: W" chiCrJlr mitt SIMS? CI/Lmﬂ
Fm {pg 5‘”.ka S’LMJPK meta \ ’10 ‘11 Problem 4 (20 points total) Signal Processing. Assume we have a signal m(t) containing some voice or music. The spectrum (frequency content) of
m(t), the ﬁmction M(f), looks like a triangle with maximum value A at DC and maximum frequency fm
as we represented it in class: a) (5 points). Recall the modulation system below that we discussed for AM transmission: m(t) x(t) (modulatcdi’transmitted signal) c(t) = cos(e)ct) lfthe frequency of c(t) is (so = 27t* l 00 kHz, sketch X(f) for the MG) we have above if the frequency fm
= lOkHz. Use the axes below (you must label them to get full credit). XU) Al. ' /\ i / "WWI JIM“ +614“ '. Himus f
ﬂaw“; ID‘v't'shc b) (5 points). Suppose we use the modulation system below that we discussed for commercial AM
transmission: m(t) Mg—p x(t) (modulatedftransmitted signal) 1 c(t) = cos(mct) For the same m(t) and c(t) from part a), sketch X(f). Use the axes below (you must label them to get full
credit). (The triangle is the ﬂow diagram symbol for a simple amplifying/attenuating function.) X09 12 c) (5 points) Sketch the diagram for a demodulating system for a receiver that would work for both
schemes a) and b) above such that we could hear the original m(t) content. To WWW3U )er mm owme
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