Razavi_Lectures_Ch13_15

8/9/2019 Razavi_Lectures_Ch13_15

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Chapter 13 Output Stages and Power Amplifiers

13.1 General Considerations

13.2 Emitter Follower as Power Amplifier 13.3 Push-Pull Stage 13. !mpro"ed Push-Pull Stage 13.# $arge-Signal Considerations 13.% Short Cir&uit Prote&tion 13.' (eat )issipation 13.* Effi&ien&+ 13., Power Amplifier Classes

1


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h+ Power Amplifiers

)ri"e a load with high power.

Cell phone needs 1 of power at the antenna.

Audio s+stem needs tens to hundreds atts of power.

Ordinar+ /oltage0Current amplifiers are not euipped for

su&h appli&ations

2CH 13 Output Stages and Power Amplifiers


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Chapter Outline



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Power Amplifier Chara&teristi&s

Eperien&es small load resistan&e.

)eli"ers large &urrent le"els.

euires large "oltage swings.

)raws a large amount of power from suppl+.

)issipates a large amount of power4 therefore gets 5hot6.



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Power Amplifier Performan&e 7etri&s

$inearit+

Power Effi&ien&+

/oltage ating



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Emitter Follower $arge-Signal 8eha"ior !

As /in in&reases /outalso follows and 91 pro"ides more &urrent.



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Emitter Follower $arge-Signal 8eha"ior !!

(owe"er as /in de&reases4 /outalso de&reases4 shutting off 91and resulting in a &onstant /out.



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Eample: Emitter Follower

1

1ln

0.5 211

outin T out

L S

in out

VV V I V

R I

V V V mV

+ =

=

( )1 1 1

1 1

ln

0.01 390

Cin T C L

S

C in

IV V I I R

I

I I V mV

= +



9/161

$inearit+ of an Emitter Follower

As /in de&reases the output wa"eform will ;e &lipped4

introdu&ing nonlinearit+ in !0O &hara&teristi&s.

CH 13 Output Stages and Power Amplifiers


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Push-Pull Stage

As /inin&reases4 91is on and pushes a &urrent into $.

As /inde&reases4 92 is on and pulls a &urrent out of $.

1!CH 13 Output Stages and Power Amplifiers


11/161

!0O Chara&teristi&s for $arge /in

For positi"e /in4 91shifts the output down and for negati"e /in4

92shifts the output up.

Vout=Vin-VBE1 for large +Vin

Vout=Vin+|VBE2| for large -Vin



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O"erall !0O Chara&teristi&s of Push-Pull Stage

(owe"er4 for small /in4 there is a dead in the !0O &hara&teristi&4 resulting in gross nonlinearit+.



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Small-Signal Gain of Push-Pull Stage

?he push-pull stage ehi;its a gain that tends to unit+ when

either 91 or 92 is on.

hen /in is "er+ small4 the gain drops to


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!mpro"ed Push-Pull Stage

ith a ;atter+ of /8inserted ;etween the ;ases of 91and 924

the dead


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!mplementation of /8

Sin&e /8@/8E1B/8E2B4 a natural &hoi&e would ;e two diodes in

series.

!1 in figure =;> is used to ;ias the diodes and 91.16CH 13 Output Stages and Power Amplifiers


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Eample: Current Flow !

1 1 2in B BI I I I= +

Iin

If Vout=0 & 1=2>>1

=> IB1=IB2



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Eample: Current Flow !!

VD1VBE ! VoutVin

If I1=I2 & IB1IB2! Iin=0 "#en Vout=0



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Addition of CE Stage

A CE stage =9> is added to pro"ide "oltage gain from the input to

the ;ases of 91and 92.1CH 13 Output Stages and Power Amplifiers


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8ias Point Anal+sis

For ;ias point anal+sis4 the &ir&uit &an ;e simplified to the one

on the right4 whi&h resem;les a &urrent mirror.

?he relationship of !C1and !93is shown a;o"e.

VA

=0 Vout

=0

I$1=%I'(1)I'D1*%I$3*



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Small-Signal Anal+sis

Assuming 2r)is small and =gm1gm2>$is mu&h greater than 14

the &ir&uit has a "oltage gain shown a;o"e.

,V=-g/r1||r 2/g1+g2



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Output esistan&e Anal+sis

3

1 2 1 2 1 2

||1/ / ||

O Oout

m m m m

r rRg g g g r r

++ +

!f is low4 the se&ond term of the output resistan&e will rise4

whi&h will ;e pro;lemati& when dri"ing a small resistan&e.22CH 13 Output Stages and Power Amplifiers


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Eample: 8iasing

CE AV=5Output Stage AV=0.8

RL=8

npn= 2pnp=100

IC1IC2

( )

1 2

1

1 2

1 2

1 2

3

1

2

4.5

|| 133

195

m m

m m

C C

C C

g g

g gI I mA

r r

I I A

+ =

=



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Pro;lem of 8ase Current

1,# DA of ;ase &urrent in 91&an onl+ support 1,.# mA of &olle&tor

&urrent4 insuffi&ient for high &urrent operation =hundreds of mA>.



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7odifi&ation of the PP Emitter Follower

!nstead of ha"ing a single PP as the emitter-follower4 it is now

&om;ined with an P =92>4 pro"iding a lower output resistan&e.

( )2 3

1

1out

mR g +



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Eample: !nput esistan&e

( )3

2 3

3 2 3

1

1

1

/ 1

Lin in in

Lm

in L

Ri v vr

Rg

r R r

= + + = + +



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Additional 8ias Current

!1is added to the ;ase of 92to pro"ide an additional ;ias &urrent

to 93 so the &apa&itan&e at the ;ase of 92&an ;e

&harged0dis&harged ui&l+.27CH 13 Output Stages and Power Amplifiers


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Eample: 7inimum /in

in Vin0

Vout|VEB2|

in VinVBE2Vout|VEB3|+VBE2



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(iFi )esign

sing negati"e feed;a&4 linearit+ is impro"ed4 pro"iding

higher fidelit+.



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Short-Cir&uit Prote&tion

9sand r are used to 5steal6 some ;ase &urrent awa+ from 91

when the output is a&&identall+ shorted to ground4 pre"enting

short-&ir&uit damage.



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Emitter Follower Power ating

12

Pav CC

VP I V

=

7aimum power dissipated a&ross 91o&&urs in the absenceof

a signal.

'a6 1av CC P TV=



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Eample: Power )issipation

( )1 10

1 1

17in

T

I p EE

I EE

P I V t V dt

TP I V

=

=

Avg Power Dissipated in I1



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Push-Pull Stage Power ating

CCP P

avL

VV VPR

=

2

'-a6 2CC

av

L

VPR

=

7aimum power o&&urs ;etween /p@H and /&&0I.



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Eample: Push-Pull Pa"

CCP P

avL

VV VPR

=

If V8= V$$) ! a:=0

I8o77i;le 7in


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(eat Sin

(eat sin4 pro"ides large surfa&e area to dissipate heat from the &hip.



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?hermal unawa+ 7itigation

1 21 2

' 1 ' 2 ' 1 ' 2

C CD D

S D S D S Q S Q

I II I

I I I I=

sing diode ;iasing pre"ents thermal runawa+ sin&e the

&urrents in 91and 92will tra& those of )1and )2as long as

theie !sJs tra& with temperature.36CH 13 Output Stages and Power Amplifiers


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Effi&ien&+

out

out !t

P

P P= +

Effi&ien&+ is defined as the a"erage power deli"ered to the loaddi"ided ;+ the power drawn from the suppl+

Emitter "o##ower Pus$%Pu## Stage

( )

2

21

2

2 2 2

P LE"

P L CC P

PE"

CC

V R

V R I V V

V

V

=+

= I1=V)

( )

2

21

2

2 2 )

P LPP

P L CC P

PP P CC

V R

V R I V V

V V

=+

= I1=V)



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Eample: Effi&ien&+

Emitter "o##ower

V=V$$)21

15=

Pus$%Pu##I1=/V))

1

P

CC P

V

V V

=

+ 38CH 13 Output Stages and Power Amplifiers


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Power Amplifier Classes

Class A: Hg! lnea"t#$ l%& e''(en(#

Class ): Hg! e''(en(#$ l%& lnea"t#

Class A): C%*p"%*se +et&een

Class A an, )



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Chapter 1 Analog Filters

1.1 General Considerations 1.2 First-Order Filters 1.3 Se&ond-Order Filters 1. A&ti"e Filters 1.# Approimation of Filter esponse

4!


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Outline of the Chapter

41CH 14 Analog "ilters


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h+ e eed Filters

!n order to eliminate the unwanted interferen&e that

a&&ompanies a signal4 a filter is needed.



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Filter Chara&teristi&s

!deall+4 a filter needs to ha"e a flat pass ;and and a sharp roll-

off in its transition ;and.

ealisti&all+4 it has a rippling pass0stop ;and and a transition

;and.



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Eample: Filter !

-esgn g%al: Sgnal t% Inte"'e"en(e "at% %' 15 ,)

S%lut%n: A 'lte" &t! st%p +an, %' 0 ,)

/en: A,a(ent (!annel Inte"'e"en(e s 25 ,) a+%e t!e sgnal



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Eample: Filter !!

/en: A,a(ent (!annel Inte"'e"en(e s 0 ,) a+%e t!e sgnal

-esgn g%al: Sgnal t% Inte"'e"en(e "at% %' 20 ,)

S%lut%n: A 'lte" &t! st%p +an, %' 0 ,) at 0 H3



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Eample: Filter !!!

A ;andpass filter around 1.# G(< is needed to reKe&t the

adKa&ent Cellular and PCS signals.



47/161

Classifi&ation of Filters !



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Classifi&ation of Filters !!

C%ntnu%us4t*e -s("ete4t*e



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Classifi&ation of Filters !!!

asse A(te



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Summar+ of Filter Classifi&ations

5!CH 14 Analog "ilters


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Filter ?ransfer Fun&tion

Filter a> has a transfer fun&tion with -2Hd80de& roll-off

Filter ;> has a transfer fun&tion with -Hd80de& roll-off4 ;etter

sele&ti"it+.

, B



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General ?ransfer Fun&tion

n=n6t! p%le

7*=*6t! 3e"%( ) ( ) ( )( ) ( ) ( )

1 2

1 2

/ m

m

s & s & s &' ss P s P s P

=

L

L



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Pole-Lero )iagram


P iti f th P l


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Position of the Poles

ole7 on t#e ?n7ta;le

/no goo@

ole7 on t#e A a6i7C7


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!maginar+ Lero

!maginar+


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E l S iti it


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Eample: Sensiti"it+

( )

1

1

)1

0

1

1

1

0

0

1

2

11

0

110

=

=

=

=

RS

R

dRd

CRdR

d

CR


Fi t O d Filt


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First-Order Filters

1

1

/ s (

' ss p

+

=+

First-order filters are represented ;+ the transfer fun&tion

shown a;o"e.

$ow0high pass filters &an ;e reali


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Eample: First-Order Filter !

R2C2 R1C1 R2C29 R1C1


E ample First Order Filter !!


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Eample: First-Order Filter !!

R2C2 R1C1 R2C29 R1C1 6!CH 14 Analog "ilters

Se&ond Order Filters


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Se&ond-Order Filters

2

2 2/

nn

s s' ss s

Q

+ +=+ +

1'2 2

11

2

nnp )

Q Q

=

Se&ond-order filters are &hara&teri


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Se&ond-Order $ow-Pass Filter

( )

2

22

22 2

/

nn

' )

Q

=

+

==0


Eample: Se&ond Order $PF


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Eample: Se&ond-Order $PF

2

2

3

) 1 1)/ 3

1 1)/2 n n

Q

Q Q

Q

=


Se&ond Order (igh Pass Filter


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Se&ond-Order (igh-Pass Filter

2

2 2/ nn

s

' ss s

Q

= + + =;=0



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Eample: 3 d8 8andwidth


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Eample: -3-d8 8andwidth

1 12 2

1 1 1 1 1

R L s&

R L C s L s R=

+ +


$C eali


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$C eali102

.67CH 14 Analog "ilters

Eample: ?an


68/161

Eample: ?an

N@H4 the indu&tor a&ts as a short.

N@4 the &apa&itor a&ts as a short.


$C eali


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$C eali


70/161

$ow-pass Filter !mplementation with /oltage )i"ider


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$ow-pass Filter !mplementation with /oltage )i"ider

( ) 12

1 1 1 1 1

out

in

V Rs

V R C L s L s R=

+ +71CH 14 Analog "ilters

Eample: Freuen&+ Peaing


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Eample: Freuen&+ Peaing

( ) 12

1 1 1 1 1

out

in

V Rs

V R C L s L s R=

+ +

1

2

Q> eaing e6i7t7Voltage gain larger t#an unit


$ow Pass Cir&uit Comparison


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$ow Pass Cir&uit Comparison

?he &ir&uit on the left has a sharper roll-off at high freuen&+

than the &ir&uit on the right.

/%%, )a,


(igh-pass Filter !mplementation with /oltage )i"ider


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(igh pass Filter !mplementation with /oltage )i"ider

( )2

1 1 12

1 1 1 1 1

out

in

V L C R ssV R C L s L s R

= + +


8and-pass Filter !mplementation with /oltage )i"ider


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8and pass Filter !mplementation with /oltage )i"ider

( )2

12

1 1 1 1 1

out

in

V L ssV R C L s L s R

= + +


Sallen and e+ =S> Filter: $ow-Pass


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Sallen and e+ =S> Filter: $ow Pass

( )( )21 2 1 2 1 2 2

1

1

out

in

Vs

V R R C C s R R C s=

+ + +

11 2

1 2 2

1 C

Q R RR R C= + 1 2 1 2

1

n R R C C =

Sallen and e+ filters are eamples of a&ti"e filters. ?his

parti&ular filter implements a low-pass4 se&ond-order transfer

fun&tion.


Sallen and e+ =S> Filter: 8and-pass


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Sallen and e+ =S> Filter: 8and pass

( )

3

2 31 2 1 2 1 2 2 2 1 1

1

1

out

in

R

V Rs

V RR R C C s R C R C R C s

R

+=

+ + +


Eample: S Filter Poles


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Eample: S Filter Poles

R1=R2

C1=C2


Sensiti"it+ in 8and-Pass S Filter


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+

1 2 1 2

1

2n n n n

R R C CS S S S

= = = =

1 2

2 2

1 1

1

2

Q QR R

R CS S Q

R C= = +

1 2

2 2 1 2

1 1 2 1

1

2

Q QC C

R C R CS S Q

R C R C

= = + +

1 1

2 2

Q*

R CS Q*

R C= *+1,R-.R/


Eample: S Filter Sensiti"it+ !


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p +

1 2

1 2

1 1

2 3

1 2

2 3

3

Q QR R

Q QC C

Q*

S S*

S S*

*S

*

= = +

= = +

=

1 2

1 2

R R R

C C C

= =

= =

8!CH 14 Analog "ilters

Eample: S Filter Sensiti"it+ !!


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p +

2

2

Q

*

==

1

1

2 2

1 1

1 1

2 2

31

1 5

1.5

QR

QC

Q*

R CS

R C

R C SR C

S

= =

= =

=81CH 14 Analog "ilters

!ntegrator-8ased 8iuads


82/161

g

( )2

2 2

out

ninn

V ss

Vs s

Q

=+ +

( ) ( ) ( ) ( )2

2

1.n nout in out out V s V s V s V s

Q s s

=

!t is possi;le to use integrators to implement ;iuadrati&

transfer fun&tions.

?he ;lo&-diagram a;o"e illustrates how.


( 8iuads


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( ) ( ) ( ) ( )2

2

1.n nout in out out V s V s V s V s

Q s s

=

5 4

5 3

1R R

R R R

= + +

5 1 1

1.n

R

Q R R R C

=

+

2 4

3 1 2 1 2

1.n

R

R R R C C =



84/161

Sensiti"it+ in ( 8iuads


85/161

+

1 2 1 2 5 3 4' ' ' ' ' ' ' 0.5n

R R C C R R R RS

=1 2 1 2' ' '

0.5QR R C C

S =

3 4

3 4 2 2'

5 3 4 1 1

21

QR R

R R R CQS

R R R R C

R

=

+ 55

' 5

1Q

R R

RS

R R=


89/161

1 35

2 in

& && &

& &

=

!t is possi;le to simulate the ;eha"ior of an indu&tor ;+ usinga&ti"e &ir&uits in feed;a& with properl+ &hosen passi"eelements.


Eample: Simulated !ndu&tor !


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8+ proper &hoi&es of L1-L4 Linhas ;e&ome an impedan&e that

in&reases with freuen&+4 simulating indu&ti"e effe&t.

2

in 0 1 & R R Cs=

!CH 14 Analog "ilters

Eample: Simulated !ndu&tor !!


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1 2 3

2

1

in 0

& & & R

&Cs

& R R Cs

= = ==

=1CH 14 Analog "ilters

(igh-Pass Filter with S!


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ith the indu&tor simulated at the output4 the transfer fun&tion

resem;les a se&ond-order high-pass filter.

( )2

12

1 1 1 1 1

out

in

V L ss

V R C L s L s R=

+ +


Eample: (igh-Pass Filter with S!


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1

out0

RV V

R

= +

Fo@e i7 al7o an out8ut no@e


$ow-Pass Filter with Super Capa&itor


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( )

1

1in

0

&Cs R Cs

=+

2 21 1 1

1

1

out in

in in 0

V &

V & R R R C s R Cs= =

+ + +

o"-a77


Eample: Poor $ow Pass Filter


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( ) 2out 0

V V R Cs

= + ode is no longer a s&aled "ersion of the /out. ?herefore the

output &an onl+ ;e sensed at node 14 suffering from a high

impedan&e.



96/161

8utterworth esponse


97/161

2

0

1/

1

n' )

=

+

4


98/161

Eample: 8utterworth Order


99/161

?he 8utterworth order of three is needed to satisf+ the filter

response on the left.

n= or the 5trip point6 of the in"erter iswhen /outeuals /in.

!f /in?@/dd024 then 201@Dn0Dp131CH 15 #igital C$OS Cir%uits


132/161

Eample: /?C


133/161

As the P7OS de"i&e is made stronger4 the /?C is shifted to the

right.

M2

133CH 15 #igital C$OS Cir%uits

oise 7argins


134/161

63L +VIL

63' +Vdd%VI'

( )

( )

1 2 1 22

11 3

dd T' T' dd T' T' IL

a V V V V aV V

V aa a

= +

( )( )

1 2 1 2211 1 3

dd T' T' dd T' T' I'

a V V V V aV V Vaa a

= +

1

2

n

p

5L

a5

L

=

VILs t!e l%&4leel nput %ltage

at &!(! JKV%utF KVn=41

VIHs t!e !g!4leel nput %ltage

at &!(! JKV%utF KVn=41


/!$ of a S+mmetri& /?C


135/161

( ) ( )( )

1 12 2 3 1

1 3

DD T' DD T'

IL

a V V a V a V V

a a

+ + = +

S#**et"( V?C: a=1

1

3 1

E IL DD T'V V V= +


oise 7argins of an !deal S+mmetri& /?C


136/161

' ' 2

DD' idea# L idea#

V

63 63= =


Floating Output


137/161

1

2

) 2

) 2

T' DD

T' DD

V V

V V

>

>

hen /in@/))024 72and 71will ;oth ;e off and the output floats.


Charging )+nami&s of C7OS !n"erter


138/161

As /outis initiall+ &harged high4 the &harging is linear sin&e 72is in

saturation. (owe"er4 as 72enters triode region the &harge rate

;e&omes su;linear.


Charging Current /ariation with ?ime


139/161

?he &urrent of 72 is initiall+ &onstant as 72is in saturation. (owe"er as 72enters triode4 its &urrent de&reases.


Si


140/161

As the P7OS si


141/161

Similar to the &harging d+nami&s4 the dis&harge is linear when 71

is in saturation and ;e&omes su;linear as 71enters triode region.


ise0Fall ?ime )ela+


142/161

2 2

22

2

2ln 3

T'L T'PL'

DD T' DDp o4 DD T'

VC VT

5 V V VC V V

L

= +

Rse ?*e -ela#

1 1

11

1

2ln 3

T'L T'P'L

DD T' DDn o4 DD T'

VC VT

5 V V VC V V

L

= +

@all ?*e -ela#


Eample: A"eraged ise ?ime )ela+


143/161

( )2

22

1

AV7 p o4 DD T'

5I C V V

L

=

( )

( )22

22

2

) 2.

DD DD T' LPL'

DD T'p o4 DD T'

V V VCT

5 V VC V V

L

=

2 2

3PL' on LT R C



144/161

Eample: !n&reased Fall ?ime )ue to 7anufa&turingError


145/161

( )

N1 1 1N

11 1

1|| 2on on O6

n o4 DD T'

R R R

5 5C V VL L

= =

+

Sin&e pull-down resistan&e is dou;led4 the fall time is also dou;led.


Power )issipation of the C7OS !n"erter


146/161

2K 1

2Dissipation P3OS L DD inP C V 2=

2K

1

2Dissipation 63OS L DD inP C V 2=

2supp#8 L DD inP C V 2=



147/161

Power )ela+ Produ&t


148/161

2 2 1 1

11

1

2 ln 3 T'in L DD T'

DD T' DDn o4 DD T'

V2 C V VPDP5 V V V

C V VL

= +

R%n1=R%n2


Eample: P)P


149/161

2 2

1

3

J.25

on

n o4 DD

o4 in DD

n

R5

C VL

5L C 2 V PDP

=


Crow;ar Current


150/161

hen /inis ;etween /?(1and /))-B/?(2B4 ;oth 71and 72are on

and there will ;e a &urrent flowing from suppl+ to ground.

15!CH 15 #igital C$OS Cir%uits

7OS Se&tion of O


151/161

hen either A or 8 is high or if ;oth A and 8 are high4 the

output will ;e low. ?ransistors operate as pull-down de"i&es.


Eample: Poor O


152/161

?he a;o"e &ir&uit fails to a&t as a O ;e&ause when A is high

and 8 is low4 ;oth 7and 71are on and produ&es an ill-defined

low.


P7OS Se&tion of O


153/161

hen ;oth A and 8 are low4 the output is high. ?ransistors

operate as pull-up de"i&es.


C7OS O


154/161

Com;ing the 7OS and P7OS O se&tions4 we ha"e the

C7OS O.



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)raw;a& of C7OS O


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)ue to low P7OS mo;ilit+4 series &om;ination of 73and 7

suffers from a high resistan&e4 produ&ing a long dela+. ?he widths of the P7OS transistors &an ;e in&reased to &ounter

the high resistan&e4 howe"er this would load the pre&eding

stage and the o"erall dela+ of the s+stem ma+ not impro"e.


7OS A) Se&tion


157/161

hen ;oth A and 8 are high4 the output is low.


P7OS O Se&tion


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hen either A or 8 is low or if ;oth A and 8 are low4 the output

is high.



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Eample: ?hree-!nput A)


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( )N

outV ABC =

Eual Rse M @all JGn2Gp

1=2=


161/161

! th C7OS hil h th P7OS ti ; ;t i d f

C s n Npa"allel &t! t!e

Nse"es (%*+nat%n %' A an, )

C s n Nse"es &t! t!eNpa"allel (%*+nat%n %' A an, )

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Razavi_Lectures_Ch13_15