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Fall 2009
Exam 2
WRITE YOUR NAME HERE § AlAsiv-v
All questions must be answered on test paper!
Open Book, Open Notes
1, The delays for a two input NAND gate were calculated in the notes as follows.
A BI|Y ‘ tgp/At
Rout R
Waa
1 Wa
2 4 Ct DF ng + Wit Wop)
SA BT pA” pb}
Won
+ Koa Wool + 2KW in
Wap
1i+ C+ N44 24 3+ Wat Wop)
4 K\W na ~ ¥ nal + KW 4 Walt 3K Win
W, ,
min,“ min
Wis Woe
a
Wa
Waa
Loi t | GG st 2¥ iat Wat Won)
4 Koa ~F nal + KP ya — Wal + 3KW sig
a pa py min
min
ECEN 6263 Fall 2009 Exam 2 November 13, 2009
page 1 of 6
typ/At
RoudR
!
2
C+ K)\F,3 + ¥4+ Wop)
ee pg Spd pp)
+
+
+
Waa
|W 4~ Won] + 2KW pig
ps pe ain
Was
(+KQ\V 3+ 4+ Wp)
Wig
K|W4—W, a + 2KW in
Wap
W W
in i
min, “' min
Wa Wap
+Wayt Wp)
+H) A ng t Moat W,
+
Ws
K|Wy4—Wop| + 2K W in
LBA pay min
Wop
2 Poin
ECEN 6263 Fall 2009 Exam 2
November 13, 2009
page 2 af 6
2. Two NOR gates are connected as shown.
A2 Al
B2 1 Y
Bl
B2 —4 Bld
aa df Bed ell, op Sons
Assume that the delays for each gate are as follows (each gate has equal size nFETs and
pFETS and 1/ parasitic delay terms are neglected).
A BY Cif tap/At Roy fR
to 7 501+ K)2+32) (+2)
+ o/t W 31+ 4 +42) ss Dain min
o tlt) F | ja+merg wan
o vit re 2a + K(4422) 4042) Faia
a. Find the falling output path delay, tapate from A2 to Y in tems of K, Z;, 2, W1,
\~ We and Cioag-
bag pam = Edgy * SOD = A ar ye, + tara
= &(8) (2432 ate aay YW eR C ipa
FB (iaeylyia) + 10 1 Dt
: ton
Re
ECEN 6263 Fall 2009 Exam 2 ‘November 13, 2009 page 5 of 6
e
b. Find the rising output path delay, tap ATH: from A2 to Y in terms of K, 2, Z>, W,, Wy
iv and Cigad-
Lis pm = far) x bur
= &l (ree) Gane at p (AS) 2) Ter ® amd
(homens pm) a
4 c. If the transistors in gate 2 are all minimum size (Wy. = Wr = Wonin), What are Zy and
Wy?
Bre Whi, 2 WR ge S|
we Wray = We mis a AS = 2 Man
1 d. With the above choices for Z) and W, find Z; so that the parasitic rise/fall path delays
are equal (‘app aT = tapPaTH)- 4
corks Cl pg path= BU) (2432) at + z HEYMAN) at
fem bs be pat 2 ZH (ne)lards)at 4 y (ad) (23a) ae
%, l
wrthy 252)
Wet (2tge,) $2040 (449) > Z(rBlareas + LoOi2)
32h.+ | 4b = ers + Elz, 7
32+ 132,-[b =0 Bc BEV BAA BNE ={
SSS oo
e. With the above choices for Z;, Z> and W., find W, that minimizes the effort fall path
ae delay, tgrpaty- Hint: find 8, = : WilW.
a = al 4lMZt oy.
bt 4 i tder 24 ee > 8S,
. . We
Wray bay my atte Lela, Re foe bop ry < Clee,
Algo bgorx hee = (ue yd = “Hy _
ui
7 Bh “yd Sg 2 UNS
x 1b os BS sor roe
bbe st it
Adppe T Adee, = 1 Vm - | ozw Ca
3S = a, i rE 3T,
ECEN 6263 Fall 2009 Exam 2 November 13, 2009 ‘ oe at
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