2008MT2 - EECS 413 Final 2008 Exam duration 1.5 hour 4...

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Unformatted text preview: EECS 413 Final 2008 Exam duration: 1.5 hour 4 questions Name: Honor Pledge I have not given or received aid on this exam Signed: Question 1 “0 VDD Assume )V=O and ignore all capacitance except C. Assume M1 is in saturation. What is the low-frequency small-signal gain? Ru: -3mk Write the pole(s)/zero(s). ’C =>LU :_.__’ F0 P Re What is the unity gain frequency? (b) A single pole amplifier has a low-frequency gain A0, an output resistant Rum, and a pole at (up. A0 is large. The amplifier is put in closed-loop feedback with a feedback factor of 1/3. What is the low-frequency closed-loop gain? f l ’ - - .__.—_- [3:3 _,(.L 301m" 3 3 What is the closed-loop 3dB bandwidth? . - Ho a)ch _._ (1+ Loopgam). CUPOL— (1+ 3 ) WP What is the output resistance of the closed loop system? R a} Boat = 0 0L ___ Roui CL 1+ bargain I+ 193—0 (c) A single—pole amplifier is in a closed-loop feedback system with a feedback factor of 1. The phase margin is 120 degrees. What is the low-frequency gain? [Hint A single pole amplifier does not always have a phase margin of 90 degrees] 0 pm; 110 _———> Phase: _6b° fa) I A: flow = (+55; [+34]? I Mam) = ._._§;—— é°° (3‘ I—a/Ta— 2.. fie = I __—p flor—Z 1+8 LIOSe Loop 3am = _‘g_ : £3 (d) Assume all transistors are in saturation. Also assume that r02, r03, and r04 are very large. What is the approximate low-frequency small-signal gain? Question 2 (a) What is the feedback factor, B? I/sc _ l l R. 05 (SC + l+—R Assuming that the amplifier gain is large, then write an expression for the frequency- dependent small-signal gain. gamer: $7 I+RCS What is the low frequency small signal gain? 8:0 NJ) galnzl (b) Given that the amplifier has a frequency gain given by AOS , then write an expression 1+— (0,, for the closed-loop frequency dependent gain. He 3 '+ 41;: F¢(I+SRC) .+ n Re m + Mira—Hairs“) 1+ 3m: I +£— A0 If the amplifier gain is — , and the phase margin is to be 45 degrees, then write an s expression for RC. Ho ' #- S I+SRC [5/4(S): we Know seconc‘ pole is 0:!- ctniti 8am quWcl J. Re no i “a [3 HF!- =| . l ‘7‘” . '1‘ ‘_+ ‘— / 12(1)] ——’ 3/“ Halt—:1 I/m; -——+ EC: E Ho :1?er wi’H‘ COnS‘ITA/n‘l' gab. BW=A4 Question 3 (a) Assume A=0, Ml=M2, and assume all devices are in saturation. Ignore all caps except CL and CC The first and second stage gains are fairly large. Write an expression for the low-frequency small-signal gain? A r. (a 1, .. . .. a A 2 ” fpgm'e‘ W’L Write expressions for the approximate pole and zero frequencies? C9 “7’1" ‘ W2: 9’” 9 a M ‘—~ 3 Ric CC In ‘ l S ch ( |+SS In; C 2 ( + in c) 3r- WP 2 = “(5%; / Write an expression for the frequency-dependent small-signal gain? (b) Assuming that the compensation establishes a dominant pole at the output of the first stage, then write an expression for the approximate unity-gain frequency of the entire amplifier? (for this ignore any zeros) 2 68w; 9mg? 6W5 \ = 8m 2 3m3RzCC. SLOC 10 (c) If the amplifier is operating in unity gain feedback, then again ignoring the effect of any zeros, derive an expression for the relationship between gm; and gmg, so that the phase margin is 60 degrees. [Hint for this assume the second pole does not significantly effect the unity gain frequency] l 0 l A .6124). = _80 'd, 4 = —3° 0 IJ'awpar. ’+ ngu3 M3 M 8m 2% 3m Y‘s-7 3m CUE 1 l (d) Sketch in a resistor in the schematic above that moves the zero frequency to infinite positive frequency. Write an approximate expression for the value of the resistance. No derivation necessary. 12 Question 4 (a) VDD The relative sizes of Ml-M4 are shown in the figure. Ignore channel length modulation. What is the maximum width/length ratio for M5 so that M] , M2 are in saturation? Assuming all devices are in saturation, then what is Iout? 4 loaf l3 (b) Rout All devices in saturation. Do not ignore channel length modulation Write an expression for the low-frequency small-signal output resistance Rout. Write an expression for the frequency-dependent small-signal output impedance, Rout. 14 , . (US—u“ 'um:?: )LZ‘ __ YO: 13; gm(n-.)m+ .————— 3 z- 413 i- 2 _.—_ .— r03 r03 2L; {3+ 53i+ mam-M232 r03 r03 __7 211an 11:1: T03 + z -I- 3m3( l+flm_,_r0-L )rog g 13 2014}: {03+ 2 +fim3amz rOlrogz : {03+ (g’ngflmlrolyo3 r0| I+SCr01 god : Yo3( 1+ Scrm) + cgmflm Folro3ro ] l+$Crol 206d, r03+ SCF03T03+ gmlflmgrofiolrog ~ W H» Scro‘ 1+ L 2002f: 3ml3m3roJ02Y03 ffmilm “’1 W ’+ Identify poles/zeros in this expression. 1 mac Sketch the frequency impedance versus frequency. Explain what happens at high frequency. gmzfing {0;YDZY‘03 I 6U; Rodi: 3—30: r03 j Ema-mst C. 15 ...
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This note was uploaded on 01/12/2012 for the course EECS 413 taught by Professor Staff during the Spring '08 term at University of Michigan.

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2008MT2 - EECS 413 Final 2008 Exam duration 1.5 hour 4...

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