ECE137B Final Exam. There are 5 problems on this exam and you have 3 hours There are pages 1-19 in the exam: please make sure all are there.

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1 ECE37B Final Exam There are 5 problems on this exam and you have 3 hours There are pages -9 in the exam: please make sure all are there. Do not open this exam until told to do so Show all work: Credit will not be given for correct answers if supporting work is not shown. Class Crib sheets and 4 pages of your own notes permitted. Don t panic. Time function LaPlace Transform δ (t) U(t) /s α e t U (t) / α or s +α + s / α αt e cos( ω dt) U ( t) s + α s + α + ω αt e sin dt ( ω ) U ( t) ( ) ω d d ( s + α ) + ω d Name: Problem points possible Problem points possible a 3a b 3b c 4 d 5a a 5b b a

2 Problem, 5 points method of first-order and second-order time constants Rd dd Q3 Q, Q, and Q3 have v c W = 0 ms, =0.5 volts, and λ =0 -. t sat dd and ss are +/- 3.3 olts. Rgen=50 kohm and Iss= ma. ox g gen Rgen in Q Q Iss ss Rd3 out Q has C = 0 =5.9 ff. gs C gd Q has C = 0 =5.9 ff. gs C gd Q3 has C = 0, =3.8 ff. gs C gd Part, 4 points Q and Q are to be biased at ma drain current,q3 is to be biased at ma drain current and out is to be at zero volts DC. Find Rd and Rd3 Rd= Rd3= a

3 Part b, 5 points Find the mid-band value of out/gen. out/gen= 3 a

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5 Part c, 4 points Find the f τ of transistors Q and Q3. Q: f = Q3: f = τ τ 5 a

6 Part d, points Using MOTC, you will find the frequency, in Hz (not rad/sec), of the two major poles in the transfer function. The degeneration approximation may help. capacitor : Cgs of transistor (possibly the degernerated Cgs) capacitor : Cgd of transistor capacitor 3: Cgd of transistor R = R = R = R 33 = f p = f p = 0 R 33 = R33 = 6 a

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8 Problem : 0 points method of time constants analysis C in R R3 out R C C3 R4 R= KOhm R= KOhm R3=3 KOhm R4=4 KOhm C= nf C=nF C3=3 nf Part a, 5 points Using MOTC, find the transfer function out(s)/gen(s). Give the answer in standard form out gen ( s) = ( s) out gen DC + b s + b s + a s + a s +... HINT: b = R and 0 b = b = L C = R = R = R 33 = R = R33 = R 33 = a = out a = = gen DC 8 a

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10 Part b, 5 points Draw a Bode Plot (Straight-line asymptotes) of the circuit transfer function out/gen, labeling all pole and zero frequencies and labeling the slopes of all asymptotes. Bode Magnitude plot-please label axes db Frequency 0 a

11 Problem 3 0 points Nodal analysis and transistor circuit models in=gen out Rb RL Above is the AC small signal representation of transistor circuit. Rb= 000 Ohms. RL= 0,000 Ohms. The transistor is biased at ma DC emitter current, so that re=3ohms. τ = 0 ps, C = 0 ff, C =0 ff. β =infinity, A =infinity volts. f be, depl cb Part a, 7 points Draw an accurate small-signal equivalent circuit model of the circuit above, with the transistor represented by the common-base T model a

12 Part b, 3 points Using NODAL ANALYSIS, find the transfer function out(s)/gen(s). The answer must be in standard form out gen ( s) = ( s) out gen DC + b s + b s + a s + a s HINT: Think carefully; how many nodal equations are really needed here out gen DC =, a =, a = b =, b = (note that a3, a4,..., b3,b4,... are all zero) a

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15 Problem 4, 0 points negative feedback in out 7 The amplifier has a differential gain of 0. R= kohm, R=9 kohm. The op-amp has infinite differential input impedance and zero differential output impedance. R R The differential amplifier has poles in its openloop transfer function at khz, and one pole at 0 MHz. It has a single zero in its transfer function at 0 MHz. Using the Bode plot on the next page, plot the open-loop gain ( A or A ), the inverse of the feedback factor ( / β ), closed loop gain ( ), and determine the following: Loop bandwidth= phase margin= out/gen at DC= A CL d ol 5 a

16 Draw open loop gain and /beta on this plot Frequency, Hz draw closed loop gain on this bode plot Frequency, Hz 6 a

17 Problem 5: 5 points transfer functions Part a, 5 points A transistor circuit has a step response (input is a - step function) as shown.. output voltage with in(t) = step function 0.8 out(t) time, seconds What is the circuits' 3-dB bandwidth? = f 3dB 7 a

18 Part b, 0 points Another transistor circuit has a step response (input is a - step function) as shown. output voltage with in(t) = step function.5 out(t) time, seconds This is clearly a second-order response. Approximately what is the damped resonant frequency? f n = Estimate the damping factor? ζ = (35% accuracy is fine here) 8 a

19 Sketch the transfer function below, labeling both axes, key slopes, and key frequencies. Bode Magnitude plot-please label axes db Frequency 9 a