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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 lowfrequency smallsignal 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 lowfrequency gain A0, an output resistant Rum, and a pole at
(up. A0 is large. The ampliﬁer is put in closedloop feedback with a feedback factor of 1/3. What is the lowfrequency closedloop gain? f
l ’   .__.—_
[3:3 _,(.L 301m" 3 3 What is the closedloop 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 closedloop feedback system with a feedback factor of 1.
The phase margin is 120 degrees. What is the lowfrequency 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 lowfrequency smallsignal 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 smallsignal 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 closedloop 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 lowfrequency smallsignal 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 frequencydependent smallsignal gain? (b) Assuming that the compensation establishes a dominant pole at the output of the ﬁrst
stage, then write an expression for the approximate unitygain 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‘s7 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 MlM4 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 lowfrequency smallsignal output resistance Rout. Write an expression for the frequencydependent smallsignal output impedance, Rout. 14 , . (US—u“ 'um:?: )LZ‘ __ YO:
13; gm(n.)m+ .————— 3 z 413 i 2 _.—_
.— r03 r03 2L; {3+ 53i+ mamM232
r03 r03
__7 211an 11:1: T03 + z I 3m3( l+ﬂm_,_r0L )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 Emamst
C. 15 ...
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