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Unformatted text preview: UNIVERSITY OF CALIFORNIA College of Engineering
Department of Electrical Engineering
and Computer Sciences Final Exam EECS 240
B. E. BOSER May 19, 2004 SPRING 2004 Show derivations and mark results with box around them. Erase or crossout erroneous
attempts. Simplify algebraic results as much as possible! Mark your name and SID at the
top of the exam and all extra sheets. 1. Derive an analytical expression for the variance of the thermal noise at the output V0
of the circuit below. State your result as a ﬁmction of RL, gml, yl, and kBT. For
simplicity, you may ignore the ﬁnite output resistance of the transistor and all
capacitors except CL. 2. Derive an expression for the low—ﬁequency diﬁerential—mode input referred thermal noise density “3’ of the circuit below. State your result in terms of the V* of individual transistors (devices with identical index, e. g. Mla and Mlb, have the same
V*), Ibias, and kBT. For simplicity you may assume that the output resistance of all
devices is inﬁnite. The “noise factor” for all devices is y=1. VDD
2Liiars1 l
V5554 M5a M50 M5b
M73 :“_Vbias5 l l: M=2 I VbIaSS V53 chfb V5b
Vbiasa M63 E M60 I MGb
M=2 l IbiasZ
l Zlbias1 bias1
C
V V V Rob cb
Voa H 28 xx 2b Fi— Vob
Cca Rea Via "l M13 M1b l—Vib
V .
M3a :I “332 M3b
FM—
V1a V1b
M4a V A M4
M28 :1 blas1 b M= M=2 OTA Core ‘2 e n:
h‘;
n
N
42
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I
l“
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4.
“I
\/ \/ ll
$2
fl ’\ +
)0
‘x
+ U) . Derive an expression for the standard deviation of the relative current mismatch AID/TD of the circuit below. State your result as a function of W, L, Vm, terminal voltages, _A
)/(W/L) — and and A1, A2 describing technology mismatches as aim 2 __A,
"My ‘ M1 M2 VBiasz
VBias1 . l
AL’D 0 A (IV/L) 2 A (61,; Lu 4. Calculate the “power—speeddynamic range ﬁgure~of—merit”, FOMPSD of the circuit
below. This metric is deﬁned as P B x DR ’ where P is the power dissipation of the circuit, B the unitygain bandwidth in [rad/sec],
and DR the dynamic range at the output Vo when the switch opens. Consider only
thermal noise from M1 and ignore ﬁnite output and switch on—resistance. Formulate
your result as a function of V*, IBias, CL, kBT, and the ratio r of the peakto—peak
output voltage range V0,“, to the supply voltage, VDD. 1’ MPSD = V U
U
s
\ ? 2 B a oFlr‘v‘x =2 QIﬂ'M If
Ca V" C;
v 1 r?
@(L : O‘PI’ K’1: ICE)” 2 L
g" 2 “(on/c. ’Vo‘ea fit:—
We 29.4 4’ hf“
I/ L
r V99
:5 ¢LLI ' (/vM  L " ’1 / 4
Va” ‘4’»
I/re m———.__ V; W “H_, / “‘ Vs
—.C. e_~’ " A
I Cy “‘2‘”
Mg: N E;— + g 21‘”
K / C9 3: has"
‘—v——"
r 1 ill \ és‘hw'fl 27’56/1:
Ad'ng “
\
i \\ E’: —(‘S 1, C2...
) \\ CV 277;? C9
 \\‘ —
£5; C,
CV 5. Sketch the magnitude response and derive expressions for the frequencies and
amplitude of all break points for the circuit shown below. Assume that all poles and zeros occur at frequencies that are much smaller than the sampling rate and that the
ampliﬁer is ideal. ...
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This note was uploaded on 08/01/2008 for the course EECS 240 taught by Professor Boser during the Spring '04 term at University of California, Berkeley.
 Spring '04
 Boser
 Integrated Circuit

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