HomeworkAssignment#2EE477Spring2017ProfessorParker

Note:!" = $"%&'()*)

and!+ = $+%&'(,*,

Question1:Considerthefollowingcircuit.Attimet=0,nodesVx,VyandVoutarecompletelydischarged

(0Volts).Given:Vdd=1.8VandVtN=0.5Vwhenthereisnobodyeffect.

a) (3%)Showthesourceanddrainofeachtransistoronthediagram

b) (6%)Whatregioniseachtransistorinatt=0?

M1:-./ = -00 − -' = -00and-0/ = -00 − -' = -00 => -./ > -78and-0/ > -./ − -78 => 9:;<=:;>?@M2:-./ = -' − -A = 0=> -./ < -78 => D<;?EEM3:-./ = -00 − -&F7 = -00and-0/ = -A − -&F7 = 0=> -./ > -78and-0/ < -./ − -78 => G>@H:=

c) (6%)SolveforVx,VyandVoutatt=∞.Ignorebodyeffect.

-' = -00 − -78 = 1.3-.CannotgohigherbecauseM1cutsoff.

-A = -' − -78 = -00 − 2-78 = 0.8-.CannotgohigherbecauseM2cutsoff.

-&F7 = -A = 0.8-.CapacitoratVoutcannotchargebeyondthis.

d) (6%)Whatregioniseachtransistorinatt=∞?

M1: -./ = -00 − (-00 − -78) = -78=> P?HQ>@;?R<;?EEM2: -./ = -00 − -78 − (-00 − 2-78) = -78=> P?HQ>@;?R<;?EEM3: -./ = -00 − (-00 − 2-78) = 2-78and-0/ = -00 − 2-78 − (-00 − 2-78) = 0=> -./ > -78and-0/ < -./ − -78 => G>@H:=Note:AlthoughMOSisinlinearregion,currentis0becauseVds=0.

e) (3%)QualitativelydescribewhathappenstoVx,VyandVoutifyoutakebodyeffectintoaccount.Do

theyincreaseordecrease?

ForNMOS,thresholdvoltageincreasesifVsource-bodyincreases.AllNMOSbodiesareconnectedtogroundby

default,soVsb>0forall3transistors.So-78,TU7FTV > -78.Replacing-78,TU7FTV for-78intheexpressionsfor-',-Aand-&F7,wefindthatallofthemdecreaseifwetakebodyeffectintoaccount.

Question2:ThisNMOSisinlinearregion.Given:VtN=0.5V,$"%&' =60$A/V2,W=1$m,L=200nm

a) (2%)CalculateVgsandVdsandverifythattheNMOSisinlinearregion

-./ = 1.8 − 0.8 = 1-and-0/ = 1 − 0.8 = 0.2-=> -./ > -78and-0/ < -./ − -78 => G>@H:=

b) (4%)Findthecurrentflowingthroughit.TakecarewithSIunitsandpowersof10.

W0/ = $"%&'XY -./ − -78 -0/ −

-0/Z

2

=> W0/ = 60×10]^×1×10]^

200×10]_ 1 − 0.5 ×0.2 −0.2Z

2 = 24$b

c) (5%)IgnoringtheVds2term,drawtheequivalentcircuitofthetransistor.Whatistheresistancevalue?

Theequivalentcircuitissimplyaresistorbetweendrainandsource,controlledbyVgs.

Tofindresistance,ignorethe-0/Z termintheaboveequation.Thenweget:

W0/ ≅ $"%&'XY -./ − -78 -0/

=> dVe"fTg =-0/W0/

=1

$"%&'XY -./ − -78

= 6.66hΩ

Rlinear

d) (4%) Calculate the current through the device treating it as a simple resistance. What is the

percentageerrorfromtheactualcurrentvaluefrompartb)?

W0/ =-0/

dVe"fTg=

0.2-6.66hΩ = 30$b

=> jklmknopqkkllrl =24 − 3024 ×100 = 25%

e) (6%)Ifthesourcevoltageisnowincreasedfrom0.8V,atwhatvaluedoesthecurrentbecome0?

Whatistheregionofoperationwhenthishappens?

WhenVsource=1V,currentbecomes0.Thisisbecause:

-./ = 1.8 − 1 = 0.8-and-0/ = 1 − 1 = 0=> -./ > -78and-0/ < -./ − -78 => G>@H:=Inlinearregion,alltermsinthecurrentequationinvolveVds.SoifVds=0,currentis0.

Note:Thisshowsthatcurrentcanbe0evenwhentransistorisnotincutoff.ThisissimilartoM3inProb.1d).

Question3:Inthistransmissiongate,Voutisinitiallydischargedto0Volts.Given:VtN=0.5V,VtP=-0.6V.

a) (12%)WhataretheregionsofoperationoftheNMOSandPMOSasVoutchangesovertime?Show

yourcalculations.

Initialstate:-&F7 = 0

NMOS:-./ = 1.6 − -&F7 = 1.6-and-0/ = 1.8 − -&F7 = 1.8-=> -./ > -78and-0/ > -./ − -78 => 9:;<=:;>?@

PMOS: -./ = 0.3 − 1.8 = −1.5-and-0/ = -&F7 − 1.8 = −1.8-=> -./ < -7tand-0/ < -./ − -7t => 9:;<=:;>?@

Aftersometime:-&F7 = 0.9-

NMOS:-./ = 1.6 − -&F7 = 0.7-and-0/ = 1.8 − -&F7 = 0.9-=> -./ > -78and-0/ > -./ − -78 => 9:;<=:;>?@

PMOS: -./ = 0.3 − 1.8 = −1.5-and-0/ = -&F7 − 1.8 = −0.9-=> -./ < -7tand-0/ ≥ -./ − -7t => P?HQ>@;?x>@H:=

Aftersometime:-&F7 = 1.1-

NMOS:-./ = 1.6 − -&F7 = 0.5- => -./ ≤ -78 => P?HQ>@;?R<;?EE

PMOS: -./ = 0.3 − 1.8 = −1.5-and-0/ = -&F7 − 1.8 = −0.7-=> -./ < -7tand-0/ > -./ − -7t => G>@H:=

Fromthispoint,NMOSstaysincutoffandcurrentonlyflowsthroughPMOS,whichbehaveslikearesistor.

Finalstate:-&F7 = 1.8-

PMOS: -./ = 0.3 − 1.8 = −1.5-and-0/ = -&F7 − 1.8 = 0=> -./ < -7tand-0/ > -./ − -7t => G>@H:=

Note:Whentransferringlogic1throughatransmissiongate,NMOSeventuallyturnsoffandonlythePMOS

staysconducting.Theoppositewouldhavehappenediftheinputwaslogic0.

b) (5%)IsthereanyregionofoperationwhereitisimpossiblefortheNMOSorPMOStobein?Ifyes,

why?

NMOSfixedvoltages: -. = 1.6-, -0 = 1.8-, -78 = 0.5-=> -0/ > -./ − -78isalwaystrue.SofortheNMOS,linearregionisimpossible.

PMOSfixedvoltages: -. = 0.3-, -/ = 1.8-, -7t = −0.6-=> -./ < -7tisalwaystrue.SoforthePMOS,cutoffregionisimpossible.Thisensurespropertransferof

logic1.

Question4:Ids-VdscurvesforNMOStransistorsareshownbelow.

a) (3%)Whatistheredcurve?

Thehigher blue curves correspond to larger values of Vgs. The red curve showsz{Q = z|Q − z;}whichseparateslinearregion(left)fromsaturationregion(right).

b) (15%)DrawsimilarcurvesforPMOStransistors.

TheylookexactlythesameastheNMOScurvesifwereverseallpolaritiestomakeeverythingpositive:

• x-axis:-/0 • y-axis:W/0 • Redcurve:-/0 = -/. − (−-7t) => -/0 = -/. − |-7t|

Ifyouwanttokeepthesameaxesandworkwithnegativequantities,reflectabouttheorigin:

Question5:ConsidertheCMOSinvertershown.Given:VtN=-VtP=0.4VandKn=Kp

a) (15%)Makeaninitialguessregardingtheregionsofoperationofeachtransistorbasedontheanalysis

doneinlecture(refertotheVoutvsVincurveforinverter).Basedonyourguess,writethecurrentequationsof each transistor and solve forVout.Bighint:Don’t considerboth transistors tobe insaturationbecausethenyoucan’tsolveforVout.

From the voltage transfer curve for an

inverter, it seems that Vin = 1.1 V

correspondstoregionD.Theboundary

betweenDandEisVDD+VtP=1.4V,soit

cannot be E. It could have been C, but

thenyoucan’tsolveforVout.

Soourguess is regionD=>NMOSis in

linearandPMOSinsaturation.

EquatingcurrentsthroughNMOSandPMOSgives:

!8 -./8 − -78 -0/8 −-0/8Z

2 =!t2 -./t − -7t

Z

=> 1.1 − 0.4 -&F7 −-&F7Z

2 =1.1 − 1.8 + 0.4 Z

2

=> −0.5-&F7Z + 0.7-&F7 − 0.045 = 0

Solvingthisquadraticgives:-&F7 = 1.33-, 0.07-

b) (5%)IsthecalculatedVoutconsistentwithyourguess?Ifnot,makeadifferentguessandsolveagain.

IfwepickVout=1.33V,bothtransistorswillbeinsaturation.(Verifythis)!Thisgoesagainstourguess.

SopickVout=0.07V.Let’scheckthis:

NMOS:-./ = 1.1 − 0 = 1.1-and-0/ = -&F7 = 0.07-=> -./ > -78and-0/ < -./ − -78 => G>@H:=

PMOS: -./ = 1.1 − 1.8 = −0.7-and-0/ = -&F7 − 1.8 = −1.73-=> -./ < -7tand-0/ < -./ − -7t => 9:;<=:;>?@

ThisiscompletelyconsistentwithourguessJ