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Chapter 10 - Problems
Taeal 3V logic implies «
You? Mop * BEV. Vo. = 20 5
Mus Meda = Boe =bSV ,
Vins Moo = Vy Vey = Von/2=15¥
Ny = \ou-Vey = 30-15 = Ls¥
NMC 2 Mir Mo 2 es -0.08 ‘sv
The gain mm the transiTion vegion is:
Mow Mac)“ (Men -Vx) "
Mm (30-00) us=15)~ vo Wh
3 rvou
oa, L Abe Ve
SHAT Mew Mea Tauevti
oy. ~My Trait
ae sy ne Thavaaltas tie
fe}
Heavly ideal 3.39 Nogic .assumed ideal;
ew Now s BM. Ngee Meu (ya) ete
Now. at Vey Vor Ve ta tolveach Ups (aay
‘the Vequived iput & Laa/(-s0) = 264 WV)
244 V
—_
Thus . Yeu * 432- 2b Were
Likewise Vey = 32 + (21s Soe Lage
Best possible worse mavging Gre ©
Whig = Men-Viy = 2te- 1 reo Lave
Nc = MunVoy = 244-00 © Lay
Fay noise margins ely fio oF these. oud
Mow Mou stat ideal :
Vew = Ba -Oaliaue)s saa 2 Vang
Ney -= ceo 70.1 (294) = Oe06¥
‘re Invge-sigual Volts.
Cowespondingly ,
G 3 (0.906 -1443
se gainis
Here. You = *2V sand Vols Ov.
Mea. Vey=Men = tava 2 ON ---b)
Mow the Weise barging ee “atin 20" thane
eRe TMs Nitya (reo )NING ow
MP\= (i203) Min « Ths fa ¥emaiy bithin’
exthey Heyes Lath Cog Mews FON
fe ich cone. erthee MM 8 OF Th NM ae
Ny © oneg NIL
Foy the farmer cone Onbalvyy-Wey = Orc -Mboc}
ey oka (ia Mew} Vr =O whence
Mew ova = 0-789 Yew
News From (1), Vay oer rad.
Thus, Meue o9ay—o. aM, vay) eos O78,
wa Van = OMe = OY,
whence Ven #4 radars cov: fo)
Aitewa Tovey a NM sob HEL yon
(Van =Vew} soba (Mey =Vod) ow
Na Mews 9.084 Vy, 70 044 Vous [2s atdaVy
Wit GO) Mie 0.4 = 02-0264 Ure «ad
Waban + Ob uhewe Yin = otal’
fad Moy = 34 poss = ater
ai
Thus-coumvall , Voy) = LaV.Vou=a.eV,
Meu rays Bow enue fo 2.952 and
Mex veijes Grin GRU Vda ean, iy
heh case margins cam be as lous ae +
NAS Ve -Voe = enue. ana
NMas Mor - Vey t Lesatse = oie
2AM
aug as high 8s 2.452 md Oust,
— ES
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rue OS Toye
°) Senevally ote Cteyes Tyee Oy
bur due te curvent vatio , t,
Ths Mele sete) whence
Says 2HALS = Li bie aad Coy 28a
ese tee (ub oe Vy = haney
y ‘Senevally wtp # OWE 2 ke
Ovigisally oa kee eee ny
Thee. balua)s KOC +1) === (2)
Dividing (4) selene
They ate Say
507891 Ce hy age
(the combines ped, aad OvTpet epac tain)
6) WA the load iqusete vemaved ;
abide Cun cy Yen. e
Dividing OA) 5 ak = (ha Ca ies
“Ms. Sin 9 (13,6) © SPR Cay It 8 29 oF
Avevage state Cuyveat (at oS aety eye)
is (6442 -200n
When Switching @Y mothe cuir i soah
Wnomic cuvent de (eed) + te Acet
Aypdinie power ie B «CA wWXtayia) = uaQ aw,
Bat, Po FCVap cava Cw dane “Ccontend)
Thay Coy 2 C- O94RF
Mow.Py = ©OMp9 That fv Yop viele
$e BM ta BAY, pauel veces by a foto P26)
2wtb « For Raqutiecy Yeduceed ‘by o fees 24),
Additional power Saved ts (5-34) 45 }xi5 noygte
MUP RI
Shack: Fear vbeuctog ov Fo fo.yyg) <ieDhmtiont
The seid te Hoe EE by Wh 2a Lita
a) For curvent peepoetional te Yoo 5
Yedueton in carvet land Frequency ) is
(oebng 392)
b) For cument proportional to Vas" ,
Yeduction is to FAG) 's sb se44 Je oF
fo BAS = Sbb 1 662 ol iveue
Preasst (ow by $42)
fav cane a) delay Seoveaser by Vobb = hors
Mints asd pouty reduces (Grom Ey tay) tol
Oe CVS)" oan al premeus 6 Foe
met chewge te DP ty NrismQ ati.
LHS of preveous . @ Met checveate by IR
For sete b) delay fncveates by Voorn = 204
Fines, aud) Power Veedu ces To O46 (44) s
O.A00 aE previous for a weY Chaage ts
‘OP to aaveOuga = D435 Of pens (by 5432)
lst
9) Fav cuwent progavfisnal te Mbo-Ve)
i) For Veet: Change cunt te
Ga)Go-) = oss vow S252 2 preaaas
a decveae F423 B
Change delay Fe Yos = lay ov
an Incwease of WH Fa.
Change tn Frequency O15 or 51.5% L prion,
Chayge te Dynamic pouty due to change
Mr boty voltage, at Frequent ste
esis a (34 /5)h = 9+250 er 25] oF prince,
Change ia DP ty te 114 40.25 © C439 \ ey,
GSE af previa decvedia of $457
it) Fee Me eas:
Curege: Ga-0s)(s0-0.5}s04n baz
(nest)
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bo) Eq. 10-14, 10.15, 101:
Frou
Leming = 4D AGUA, (gli) ‘
een a eile (Mealeas ag - ANiaAl]
= Yak (WAS, [Map t—<)¥2 + Moy" (baled)
= Rb WA VS [eel sen) 7
Now, see the term 1 becames :
D-ae bath) cee A ete oe anos
ose
This Tris %n42 Vows? REM (ahaa)
2
oS * KW, Geban rine)
Chote Gores 02 fe aes pass Oa Meal elare hin
and he mullipite i The Mumtalar why = Ube ba”
[20
an 10
2
Foy Se ON tara. Ooh Modhatis = way
aud The muitighav becomes Wing Lat
Fow or 0.8, of ane 4 Se Gs MOS) sag woe
ava the multiplier become: Vos © hog
{0.24
Bynavsic Rootes Po fC We jStatic Rue 2 Pe.
Now, 20 =F + Rowe s*
i’ WFR eee
Subtvicting 42 = x y0°C (as)
Whence C4 4.25 «20 wip") « 26 oF
a
Ghd Pex Mo oni (es }avered F2-0-751) LOY
10
For 1D of the gates active. tatel ums &
Capacitance per qaets aneres Hones)
10.23
10.24
For Y= A+ BCCAB) the POM coy be
Avan directly ond thew Yhe PUN 93 clieet dual:
Ceol Dadi Aa
Bed
Ne
ony
BH, pa
(ie)
Y= foc . Abe y Age
Arte dvect \mpkuentatie, would need t
aver) © 1g Mot for the gate aselG gla
dea =h few the required imueutes , for
o Total oF 34 Avawsintos .
Fay the PUN diveetly « (avewting variables)
Ye
Fev He PON Y= Acs ABC + ABs.
Servegondingly | V Bac + Ade + Ree
= Rac AEC. ABE + (A+B 20. CR aco
e ABE HABE + RBC w AGT HAGE , oa veplaating ABE,
Y= pec MRE WANE + GC --—-@
fret
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lo
(zu) a
for the PON diveetly :
Fon Ou b = (We Bs EWAe SEMA E e)
From@, F< ABC SAR + RE vas
Whee pathy merging 1 inclu drat,
For the PDH fom the Pun GD
Sienply a replacing saves SOnMeCNons
Sith, pamela ComMectCns %
¥
oe 8S
a
= 7 > @
mw demi}
(neat)
By (veomyyest)
See thar Gaie wot the tame as Gi vt
Wiglly Wélatea 5 having Some Marable Gcehenge
te © randdle sad wane coluwny
Cleavly, Thee ove lots of waviations of the
completely ~ Cemmected array +
ee pe Mel
YeaRsAp + Y= Aaine + AB. RB
or ¥« (ResitnsB) = nas Re
Fut ¥e AB sAg: | POW dual QD:
we
za 34 —s"
_ a
a ac =
¥ a gs
(20) (15)
Far the Pun from the PONG)
See tar both pavalle| and Sevies coumectons
cay be Wdtutihed Fo Transformation,
bar haut the savies (Veetteal}ones (ar dimen)
Keates Vewnhes Gack TRG Comgttentatt,
ead awe There Gee aliags open
“Thet convertig pavalltl paths: be Stnel over
See thy iy the
same ashy)
"Hehe shautane tara a vearan a shaun,
Hen Vi Coltumy Geert links) conutited to vas,
Cgawaitet lias of oo PUM:
fie)
PDN Gr ¥eAB+AB: / Puthduat to @)
« @
OR edi ond
1
or a
a
The tea ctecaivts vequivea. = Beg
O.
TPE TRE -Dicactly, the PUN 9 4s Callow
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4 | tal i3r\ je
aay YeRGC + AEC. Directly the PUM os PON educa to lo Hancates
I ae below: ¥
® my
“| au] e+
tw ;
The Corresponding dual PDN 1 shawn above wigan EDM veducea te @ hewetovs : (x mak x4 jovrad)
[This creat vy
fot planay stat
ar one Cron =
aves "Gx) jit
har ho Convemeit
aol
* +
st
Even-pavity cteut : Yo Age, ABC + AGG ABE
POM .divectly cis ©
Tt ites ie, rel
‘twaseu ee PUN as the dual of Dy @
Cthik 26 He stwetoe iF
mf toe cheat of)
whew contnaerig thes A
eH &
il | a ag =
j = The Gamplete SHUT sg a
i, GG ers erste
ii | fis)
i i Fox outpar high With odd pastry
Yo MBE + Rods ABC + ABC = (NE BIC Aera)C
i Dray the PEN by: Crete Bat we Sum SABE. Ral +Ric 4 Bc
srvgctntere) Could c a a
ay = BAT 5 te
‘ee eliminatan by my Go® BRE SAGE Abe + Ane
Perak Wiig = Ay AC 4 BC ALBHC) 4 ae
Aod h epee
Sno mim nglanae
Creare the PBS chueeny ~shpthyig thet >
S$ i PIGAo above. as
‘agetogy |) S= Mees be) HAE +es)
x
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Mote that a design vith == sac fices
Vou for ingvoued geopagatisn - dtlay Symmetyy,
From Eq tong Vous Wowave) [tts vey"l
a(e-ealli- > AT uny
Hows, ba (Wide = 95 1e76-8) erp = 2(7575 I),
This Wp =Cavesle renltsorty elite.)
Hou Cggae walls) = bEtF Cys s rales) + Sate
Theos Sis RF A BER
Now ithe output capacitance jwcluaes CebawCga
at the load, plas Say oma tance Cqa of Haeswtin,
This, the total capacrawce ©F the o4tpur aud
the loading gute ine
Cog = Miler cls taleoralestbiay «ios ft
Now, form Eq1ony, Gye bISChe a),
add Tyg NTA APSA MOA) = 4.5 ps
Now fvomiqe 44 fue © lech esieelhe]
dd tp HPN OAL NSH (4 aoa <Oonba) Seba
Thus toe Ceci tone eCoareal/2 = Shape
Thus Caran) <bean)?
aad Maha ee gM) oe bear ay flees)
We TA 4h S & 4 nay nd eT ae eee te
Yea aend wy we tate wt
ty? - tet -2 eo
WO -e -ay — 45 eo
Test veVL ay 3%
Wee se dosed ye
vey Se ete bY =
ag eye 4b V.ay
veut Rated
Thas ve aa . aiken 5 .
Nive ot -(s.0-0,hf)~ {i Ye (i (2aed)
Sop-waLi-eaw oa = Lea
has, BU aw = Koh Eng 20 be [ae g
Maxi arts ett | es
Mee tr Fel eC) = lalebenll arm)
Fayave: bath sidens C= VV AY = tee tere
ee Thy = payee op
1O,42.
2
Frain Eq tout Ni iy = (Vege + = alae
Tas (i: 2ero wwhee 1- ue 2 oy
or fire Boy dred ver hr aD
Fov Vay Jy = 4a Ga b= tose
For bra yw suas ant)= S50
Foo vou Mey ae Malia = Luv
Fereg NM s Hal) aie = Zag
Sor rele Ny «ea (s alas Ea
But whet about MM, 2[Forvemoris os tav)
From Fy toni ami lon mise Margins ave equal
Se (Min oC Loeb Estat ™] ogg Et= Ata
we Maia Vg) = a= AAC" C= Hee A eben gy
whi
Here Vi/ (Wer Me) = a8 080.4) = azitoy
Ting Vena Vahas of ¥ re Sole Oe
ho}
Few Wars flee era 7e Me Ce a ye
=i o.8) er = Oak = G84
For ¥=35. Me) = 2-24 WY a ats (ayn fe
a2 -oGb-O-FL oan = oar
Tay ¥ 2 Kiel = ee asco) S life) eataal
= B= aha ~ 28 ~ 9110) 20,304
Wy we 2, fe) 2 = aA Caray ar 2 (Yfatial
22 - Oey ~ 0743 -2.4e = Guat
Conclude = Ran qforuhien the maqias ove}
MEN ati a Ube-Vel(1- 2/30"
Pl : Reeveilig ae au
\eH&
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Y= A+ BCD) , whee Pens B(C.d}
Thug the POH com be Favmed divectly a5 showy:
Vor
rl”
¢
ed
Now. tr “tonc © Che /belli-o.44)
= eli omi A) © BAL Bethe Zt
Howry teey 2 7 Coens YC asaie C1. Ive. w)5) Baton
get ty Ste /RAR Bebe
ana tye (hay ete A Bags
How dynamic powty Is appyorimaty Coop since
the outpur twurhy ta hot quite “oe.
For cayal ¢iahc and dynamic pomer
Frimio hash Weani?
Shere Fe Wea niontCag= io") © eae |
fow wel Thepenod hy 4 (tate a }= ae
Wo fe tyeusition tives th the tame Proportion
as peopagamon delays trey “bras Mynae he
Naw fie Gall oorpel twing Thine wast be te
for. 2 Gan Avansitiead sr each cycle t
Whos Tanne Beate © Maas and
Trey Mand tse) = Geta
Sie Thete’ values ave SF the some ovdev aa the
pevtaganin delings « Fall suty opeyation 1 hhaly
fot patter TEM.
ey
Fov an Exclusive OR YS AB+AB so
= Ap+ As ~\Asollas8)
ee
The POM ratty dwectly +
aay
aa Ad
E4Le
For 9 piewdo-NIMOS Nog gate siadepeada,
AF the sunbe of Input the Worst case ue
2F Vo securt Foo ane (npet high (and as
NMOS conducting q "
From Eq ioty ) Vou « Moo. e}Ey (wy)
Fovuhich Og = (S10 048P4— G.-Y 'A}
and (1 Wye ie OAL, 2 OSS
ew Olas
We = O99. . and be
Whos ketkp = soak = T5(LBAA(28 (HK Yp!
This WY Lp 5 Usas\ ie ia\io * Oui
Thay far “
muha wt . Vetta da © fbi
ci) (io)
Faw a) .2te divsethy that a1 A «A
awd Ya AL
Fovb) . see Aweethy that Yr ALE
Fev eadh cieeuit - wrote “T hosenally Satis Res bath,
conditianr + Mowsues 6 wy eath A high ant
ome) Yay OT PACA Sowen Carmela teby Fo quound,
at veetainy ak Ve, due te Me (05 thverhol
Cihevit by dot at eve THI probleny tout mode x
fs Floating for AaB Wark bngh . Moweudy 26 iy
wat as autgar wade, The body effect makes this uae
Maree That b) Gy eanctly a Compl mtatawy C405
NER gate Gov which ¥R.E = BEB
Foe Veg Veplaced by Om Inverts dvivin by Cy
Ye Cena) = Bice = Bete
@ B-iapay Nom (fe oth #} any).
Practically speaking. Wdwevt-, theve t$ a probit
because jas uated above, the sewes PHos do
Rot epevete lietl tatty o four input, Ta Fier
Via puiled daw ouly fo owe Pivevhold
Awop bealow quand when Cis bigh,
ta]
Woth these weutraals the ou teat dy haigh
thst Bia law ov when Als toad.
These ASB, of AE a MANG Sancten
Circa being 6 Sully compltmettyy CMOS gates
r 3 a 1 4
Fametvons Ideally, Howeuey cieecir b) pyavides a
reiatwely loa Wgh Sutpat Soe A teu, Gt
Bhigh. Tu This case, THe outpal becomes
Mom Ven ute Mey ig waised Fram Vig by the
bey eb beer,
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Theve ae seuevel debetemcidy
Fist. theve 9€ tue. peastniities fe ther te
civevin When Boat C on low ond
and Dave eyes 514 whith Case
cuweat Slows ( For exnupte) Hrrough 4.0,
Qe. Gr THs problens occurs Re RmED
awd ATES
Lig]
Qecohd node Y is pulled dows to Vi (crtasay
by the body EFFect) Uhty Bow C ae
low With A oD highs Witpacterly . Ey
this Verpeey s this civeait (s hhe ther in
Ry Poiana.
With Verpeey to Y at a Function of Ato,
MEMWY Will Append om device Siaing ,
for Gaga qveletvely Weaker Hie, the
Dries. eR SEB AWames ene
% thay below |
Vow
+ =
Pow Q.96 velative
Wealas. Yu ap ste
ad Ys Alp. Ge
= AB(E+e)
Y = RSO+ACD
Wty ivpat E visi % tue. 40 Veplace boty
Noo cowveenion . ¥ = BES EB) is posite ,
bawring oW the ote probing this eweor
bing e-
SS eee
10
Foe Me suntel qate aud the input ode =
at 3.3V, the switch Burour is
Vou = 3.3- Ve chev Vie Veg Heliipe-tm)
Thus Vou = 3.3- 0.8 ~ 0.58 (Uoa vo
= 2H O50 Moy sony
oe by 54 = ou vou
9.50.4)"
Srisaring . oustong ~ Vou = t5.Miy aay
Mow ai Men + 31k wo een
Vows (-~ans a Samy Sone VA r
oe Mo a { ay.) NWA 1 gu (44d a agar)
Haw, Gor pet low aud switch, qete high .M, oy
Now The twuntee Curr; Fev Won = Wan, he
Pros
Mem Satavaton titty
yabay ot} YC asli') fb ocal™
wee Pat shah invertee cusietis leuuh
Fax tay: Hee Algaos Vt Daye, Vagelby a3)
Thar initially, ‘ohh AM /oayaa sea)’ Ldap
MM Moe 34a «© es *
Mer Say os (4s +0.0)" aster) = nia
Toe eGo UA) p
Th
ama loli)» PeOsiliervecKaa Lehi ins,
Thus Oo. Geb rs/y 2 vggun .
nd tory a(cumAlii, = dio) tfc Jamon
For tags HOE Mew and the bnitial cunvearis
felch = ‘alrs\iare.d 33 -0.8) > lead
AV hal? thom opbrahin Is te thede Mode au
“altel © slave ATC -ou)ner tay |at.4
Tha ThE quevage cuyeent is (are naw A = asyur
avd tea = inolis®) ies7a,
= Osan
ee
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