Midterm-2002-solutions

Midterm-2002-solutions - UNIVERSITY OF UTAH ELECTRICAL AND...

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Unformatted text preview: UNIVERSITY OF UTAH ELECTRICAL AND COMPUTER ENGINEERING DEPARTMENT EE/CS 5720/6720 Analog Integrated Circuit Design Midterm March 20, 2002 \ NAME: E { EEICS 5720 EHCS 6720 circle one (Please print) 0 Do not open the exam until instructed. a Draw a circle or box around your final answers. . All answers shOuld include units (e.g., V, mA, m) where appwpn‘ate. For frequencies, use Hz (or kHz, or MHz), not radiansfsecond. o If you want partial credit on incorrect answers, show your work on the pages you turn in! If you choose to turn in any sheets of scratch paper, write your name on those sheets! 0 Don‘t spend all of your time on one difficult problem. Don’t be afraid to skip ahead if you get stuck. You don’t have to work the problems in order. a Good luck! l. (15 points) Consider the op-amp shown below. You may assume that all the transistors are operating in active mode. Q10 Isms VDD=-V53= 3 V Isms: SOflA spec; = 40 pm? pflco, = 120 pm! V", = -le = 0.8 V VA = 40 V (for all devices) (W/Lh = (W/L); = (W/L); = (W/Lk = (W/L)m = 100 (W/L); = (W/Lh = 50 (W/L)g= (W/L); = 200 (Wag/no Cc = 5 pF 031 (a) What is the gain ofthis amplifier, in dB? \\ S X" x.- l ' _ .2- 47 J." 3%, _ a", (6.4%), ID. -— 2.4%N1.f00. 29—“ ’2 f’q/V 0‘01 61;)“ Kg“ 3m?” 2/016»: (EJ715157 ‘W .: /o?5;wq/V ’A‘Dc'vtfliw )3 VT! 3 -.: VA 9 ‘0 ”- WW 5-9-17, .— /.(M.(Z Av : Affirfis N5 is U‘ rat" :- (Tl/c E all} r: 5,00 kg : 3m, (fdsziit‘djq‘) -9m7(rdr(”ralg:h - 1 (b) What is the'dtihminam pole frequency, in Hz? : 3 ”7‘ 5’35"! = ”‘6’, 309 l “ (Hull-"c1393 Cccmm W 54?, :S‘mml/x «filler : “Jo _ __. | (“ed- 74" 27,- h 901 (ll/‘1'! (c) What is the slew rate, in Wps? \ Allfmxit “(mi-“m I' - t 9‘93 _ @1‘ “‘1‘ CW we“ - —-- / c 4" / . - -- fame flflMr. am *7 jun {’03- 3 9"" “BWFnJ-ae‘} 2. (20 points) Two-stage op-amps are commonly used because single—stage amplifiers typically yield insufficient gain. However, a high-gain single-stage amplifier can be built if cascode transistors are added to boost the drain resistance of other transistors. Consider the single-stage amplifier shown below. VDD Qw Isms Q3 Ignore the body effect in all calculations. (a) Write an approximate expression for the gain As of this amplifier. You answer should contain only gm’s and r435 of particular transistors. A“ 5 3%" (”53 3"6’m’f // ”’7 7'»; K357) \\ / (“4““le (’{FQC‘I- Ofi Ctr-dirt 06410“; (EffrJMQ Valgzd'rdsq (b) Assume all transistors have the same width-to-length ratio WIL. Derive an expression for the source voltage of Q] if the input common-mode voltage is zero. Assume V» > 0 and Vs; < 0, and all devices are in active mode. Your answer should contain some (but not necessarily all) of the following terms: 13;”, W11, MC“, V“, “DC“, Vrp. F ”f? fox W _. 2. (continued) (c) Derive an expression for the maximum allowable value of chp that keeps all transistors in active mode, assuming the input common-mode voltage is zero. Your answer should contain some (but not necessarily all) of the following terms: 13m. WIL, .“rICox; Vm, Macon Vrp- (d) Derive an expression for the minimum allowable value of chy that keeps all transistors in active mode, assuming the input common-mode voltage is zero. Your answer should contain some (but not necessarily all) of the following terms: Isms, WIL, MC“, Van lupcan Vip- \/ .- (ArcN V5: ‘l' Vfigq L V657 3. (10 points) Circuit design often involves trade-offs between small-signal ac performance (e.g., gain), and large-signal dc performance (e.g., voltage swing limitations). Consider the following common-source amplifier: The transistor has an Early voltage VA. Let Vourmn be the minimum output voltage that keeps the transistor in active (saturation) region. Express the gain of this circuit (A) in terms of VA and VOUTmin only. To Evade Q)“ in Sak'i'kr‘a'i‘mij V0r1> Vc‘mj‘l I 10; _ 21 , 21“ ya) ‘- V_.._2—~ 2 PH QQI udThrn 4. (20 points) We are testing a nMOS transistor fabricated in a new CMOS process. The device has a width of 211m and a length of 2pm. We set the substrate and source voltage to zero volts. We make the drain voltage equal 5V. With the gate voltage at 1.0V, we measure 8.0uA of drain current. With the gate voltage at 2.0V, we measure 98.0uA of drain current. (a) What is the nMOS threshold voltage of this process? (You may neglect channel- length modulation effects.) Circle your answer! *0 “1 £7..an '2!- [Val—£49): 9,141 = siwsczxfl-Vgfi } ? 73M 3 ELL/u .(Lx {ZFHQL (b) Given that the gate oxide' 15 made of SiO; and has a thickness of 150 A (15 nm), What is the electron mobility in this process? Express your answer in units of cm [(Vs). Circle your answer! /”‘u (a: :-_./UO/Mfl/fi/1 {la/9"? qfiw’f) l4”? 0.€V fan ‘“ ”(OO/V/q/VZ -12 (ex _ Zox - 6a _ 3.7 e 3.3579“? F" : 2,3010% 7F/ch - NM 1’ {4350: J /?E afloat/6'71”“ Suppose we now test a pMOS transistor in this process. The device has a width of 2pm and a length of 2pm. We set the well and source voltage to 5.0V. We make the drain voltage equal zero volts. With the gate voltage at 3.5V, we measure 9.8% of drain current. With the gate voltage at 2.5V, we measure 57.811A of drain current. (0) What is the pMOS threshold voltage of this process? (You may neglect channel— length modulation effects.) Circle your answer! ((1) Given that the gate oxide is made of SK): and has a thickness of 150 A (15 nm), What is the hole mobility in this process? Express your answer in units of cmle' 5). Circle your answer! 5. (20 points) Consider the common-source amplifier shown below. Assume the current source is ideal (i.e., it has an infinite output impedance). Assume that Early voltage is preportional to transistor length. (a) If we decrease the transistor length L by a factor of two, what happens to the gain and bandwidth of this simple amplifier? The gain increases; a factor of M 2* circle a : The bandwifif: lincreases )decreases) by a factor of 2' ‘ ' 019 one (b) If we decrease the bias current I by a factor of two, what happens to the gain and bandwidth of this simple amplifier? The gai ‘- decreases by a factor of ‘l a ‘ e one The bandwidth a factor of 2 circle a - 6. (15 points) Consider the amplifier shown below. Ignore the body effect in all calculations. (a) Derive an approximate expression for the gain Av of this amplifier. You answer should contain only gm’s and rds’s of particular transistors. Hint: You may find it useful to draw a small-signal model, substituting the T model for Q; and Q;. You may neglect r035 and r431. A” / __ ..— fwd: fa( //% 7M ‘1 M34 3:: Jrgfif gw + 4”? “i 1&0“ 7a,» A __ (Ar? flfi’fi; (I * ?M%m7-)] f V 6;: * ”M“ 5w * 77M (b) If all transistors in this amplifier have the same width-to-length ratio WIL, derive an expression for the minimum allowable common-mode input voltage to keep all transistors in active mode. Your answer should contain some (but not necessarily all) of the following terms: 13m. WKL, AC“, Vm, “9C“, KP. V‘“Cmm:n: V3“; 4' V65; +. 5x! ZIBJAI + Z IE IA We: Cox“ .. [4"4- 6 :1 ...
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