Sam Palermo Analog & Mixed-Signal Center

Texas A&M University

ECEN620: Network Theory Broadband Circuit Design

Fall 2012

Lecture 22: Limiting Amplifiers (LAs)

Announcements

• Exam 3 is postponed to Dec. 11 during scheduled final time

• Project • Final report due Dec 4 • Project presentation will still need to be

prepared and turned in by 5PM on Dec 11, but will not be presented

• No office hours today

2

Limiting Amplifiers

• Limiting amplifier amplifies the TIA output to a reliable level to achieve a given BER with a certain decision element (comparator)

• Typically designed with a bandwidth of 1-1.2X data rate

• Want group delay variation

How to Achieve an Ampilfier GBW > fT?

4

( )( )

support.can logy our techno that 50.8GHzGBW stage-single a with and 31.6 ofgain our targetwith

316GHzGBW totala yield will thisn,compressiobandwidth stage-multiAfter

8.50or ,31 and 64.16.31 with stages, 7

is e,perspectivGBW maximum a from choice, optimalAn bandwidth.higher but gain,lower

withstages multiple intoamplifier break the slet' stage,-single a using of Instead

spec. 10GHzour below well,11.26.31

7.6630with

7.663

2003

GBW Stage-SingleMax

ofGBW amplifier stage-single a achieveonly

can wegenerally and 200GHz,only islogy our techno of peak theHowever,

316106.31

.10 and 30ith amplifer wan build toneed that wesystem 10Gb/s afor Assume

s

37

3

s

3

=

≈

=====

==⇒=

==≈

==

==

GHzGBWGHzfAn

GHzfdBA

GHzGHzf

f

GHzGHzGBW

GHzfdBA

sdBvs

dBv

T

T

tot

dBv

Multi-Stage Amplifier GBW

5 stage. single a torelative compress doesbandwidth but the tly,significan increased hasgain The

1

1

1

be illfunction wtransfer amplifier stage-multi totalThe

1

amplifier pole-single a is stageevery If

33

3

n

dBs

nvs

n

dBs

vs

in

out

dBs

vs

sAs

Avv

sA

+

=

+=

+

ωω

ω

Multi-Stage Amplifier Bandwidth Compression

6 approach.amplifier stage-multi a with achieved becan GBW in increaset significan a Thus,

gain.in increase than therateslower much aat although compress, doesbandwidth stage-multi totalThe

12

21

21

21

whereis , bandwidth, dB-3amplifier totalThe

1

33

2

3

3

2

3

3

3

3

3

−=

=

+

=

+

=+

=

ndBsdBtot

n

dBs

dBtot

nvs

n

dBs

dBtot

vs

n

n

dBs

dBtotin

out

dBtot

AA

AjA

vv

ωω

ωω

ωω

ωω

ω

Optimum Number of Gain Stages

7

12

stagesn with gain totala achieve will weand

1212

isbandwidth total that theRecall

bandwidth.gain potentail maximum afor stages ofnumber

optimuman bemust thereThus, stages. cascaded with compress willbandwidth theHowever, stages.

ofnumber theincrease andgain stage-per thereduce tohave webandwidth,high a achieve toneed weIf

rad/s)in isGBW here (Note,

supportcan y technolog that the stage-per maximum a is e that therAssuming

1

13

1

11

33

33

−=⇒=

−=−=

=⇒=

n

ntot

sdBtot

ntotvs

tot

n

vs

sndBsdBtot

vs

sdBsdBsvss

s

GGBWGA

G

AGBW

AGBWAGBW

GBW

ω

ωω

ωω

Optimum Number of Gain Stages

8

( ) ( ) ( ) 02lnlnln1ln21

2lnln1ln

optimum. same theyield should thisas

r,denominato theof log natural theminimize slet' easier, thismake toMoreover,

02ln

1

2ln1

stages ofnumber w.r.t thereciprocal its minimize slet' ,expression thismaximizing of instead Also,

2ln112

ionapproximat following

themake slet' this,do order toIn bandwidth. themaximize tolike would wegain, lgiven tota aFor

1

3

1

3

1

3

1

1

13

=

−+=

=

=

=

=

≈−=

stotn

totsdBtot

ntot

sdBtot

ntot

sdBtot

ntot

sn

ntot

sdBtot

GBWGn

ndndG

GBWn

dnd

dnd

GGBW

ndnd

dnd

GGBW

n

nGGBW

GGBW

ω

ω

ω

ω

Optimum Number of Gain Stages

9

( ) ( ) ( )

( )

( )

( )

( )

( ) ( ) ( )eA

GAG

GA

Gn

Gn

Gnn

GBWGn

ndndG

GBWn

dnd

dnd

optvs

totoptvstot

totG

optvs

totopt

tot

tot

stotn

totsdBtot

tot

=

=

=

=

=

=−

=

−+=

=

,

,

ln2,

2

1

3

lnlnln2

isgain stage optimum theand

ln2

is stages ofnumber optimum theThus,

21ln1

0ln121

02lnlnln1ln21

2lnln1ln

ω

Optimum Number of Gain Stages

10

( ) ( )

dBsdBs

vs

totopt

tot

e

A

Gn

G

39

1

33dBtot

9

283.012

tocompress willbandwidth amplifier total thebandwidth, stage-per the toRelative

65.1 toclose iswhich

67.1100

in results stages 9 Assuming

21.9100ln2ln2

have should 100with amplifier stage-multi a example,For

ωωω =−=

=

==

===

=

• Note, while this is the optimum number of stages from a maximum GBW perspective, the bandwidth doesn’t falloff too dramatically with lower n

• Thus, from a power and noise perspective, it may make sense to use a lower number of LA stages

• Typically high-gain LAs use between 3-7 stages

Bandwidth Extension Techniques

• In order to increase the bandwidth of our multi-stage amplifiers, we need to increase the bandwidth of the individual stages

• Passive bandwidth extension techniques • Shunt Peaking • Series Peaking • T-coil Peaking

• An excellent reference

11

Shunt Peaking

12

• Adding an inductor in series with the load resistor introduces a zero in the impedance transfer function

• This zero increases the impedance with frequency, compensating the decrease caused by the capacitor, and extending the bandwidth

Shunt Peaking

13

• While the inductor can increase the bandwidth significantly, frequency peaking can occur if the inductor is too big

• For a flat frequency response, ~70% bandwidth increase can be achieved

• A maximum 85% bandwidth increase is possible with 1.5dB of peaking

Bridged-Shunt Peaking

14

• Adding a bridge capacitor in parallel with the inductor allows for compensation of the frequency peaking with the possible maximum shunt peaking bandwidth increase

Series Peaking

• Introducing a series peaking inductor is useful to “split” the load capacitance between the amplifier drain capacitance and the next stage gate capacitance

• Without L, the transistor has to charge the total capacitance at the same time

• With L, initially only C1 is charged, reducing the risetime at the drain and increasing bandwidth

15

Series Peaking

• As the capacitance is more distributed with a higher kc value, a higher BWER is achieved

• Up to 1.5x bandwidth increase is achieved with no peaking

• Higher BWER is possible with some frequency peaking

16

Bridged-Shunt-Series Peaking

17

• Combining both shunt and series peaking can yield even higher bandwidth extension

Bridged-Shunt-Series Peaking

18

• Proper choice of component values can yield close to 4x increase in bandwidth with no peaking

• However, this requires tight control of these components, which can be difficult with PVT variations

T-Coil Peaking

19

• If the input transistor drain capacitance (C1) is relatively small, then the bandwidth extension through shunt-series peaking is limited

• T-coil peaking, which utilizes the magnetic coupling of a transformer, provides better bandwidth extension in this case • L2 performs capacitive splitting, such that the

initial current charges only C1 • As current begins to flow through L2,

magnetically coupled current also flows through L1, providing increased current to charge C2 which improves bandwidth and transition times

T-Coil Peaking

20

T-Coil Peaking

• A bandwidth extension of 4x is possible without any frequency peaking

• If peaking is acceptable, then a BWER near 5 can be achieved, depending on the size of C1

21

Active Bandwidth Extension Techniques

• While passive techniques offer excellent bandwidth extension at near zero power cost, there are some disadvantages • Generally large area • Process support/characterization of inductors/transformers

• Active circuit techniques can also be employed to extend amplifier bandwidth

• Some active bandwidth extension techniques • Negative Miller Capacitance • Active Negative Feedback

• There are numerous other techniques, but that is all we have time for this semester

22

Negative Miller Capacitance

• In modern technologies, Cgd is a significant (50% to near 100%) fraction of Cgs

• Amplifier effective input capacitance can increase significantly due to the Miller multiplication of Cgd

• Without additional Cn:

23

( )

ecapacitancinput effective in the increaset significan

in result can thisamplifier, theofgain aldifferenti theisoften and negative, is As

111

gd

gdgdgsin

A

ACCC −+=

Negative Miller Capacitance

• In order to mitigate this Cgd multiplication, additional cross-coupled capacitors can be added from the amplifier inputs to the outputs

• Effectively, the charge on this additional capacitor charges a (large) portion of the Cgd capacitor

24

( ) ( )( )

achieved is ecapacitancinput effective in thereduction a 1, isgain amplifier theas long as Thus,

2

toequalset is If

11

11

1

11

>

+=

−−+−+=

gdgsin

gdn

gdngdgdgsin

CCC

CC

ACACCC

Active Negative Feedback

• Instead of using simple first-order amplifier cells, a second-order cell with active negative feedback can provide bandwidth enhancement

25

Active Negative Feedback • This second-order amplifier cell can be optimized for different

objectives, but Gmf can be set to yield a Butterworth response with a maximally-flat frequency response

26

Active Negative Feedback

• The second-order cell gain-bandwidth can potentially achieve a value greater than the technology fT

27

( )dB

TT

dB

TdBvo

Tmm

Tm

Tm

A

CG

CG

CG

CG

3

2

3

2

3

2

2

1

1 Assuming

y technolog the toalproportion is ratio The

−−− ==

≈≈

=

ωωωα

ωαωω

αω

αω

ω

Limiting Amplifier Example 1

28

[Galal JSSC 2003]

Resistive Load Only Active Negative Feedback Shunt Inductive Peaking Negative Miller Capacitance

Limiting Amplifier Example 2

• T-coils in LA stages allow for a combination of series and shunt peaking and close to 3x bandwidth extension

29

[Proesel ISSCC 2012]

Offset Compensation

• The receiver sensitivity is degraded if the limiting amplifier has an input-referred offset

• This is often quantified in terms of a Power Penalty, PP

30

• It is important to minimize the offset of these multi-stage limiting amplifiers!

Offset Compensation

• The DC offset, Vos, of the limiting amplifier is compensated by a low-frequency negative feedback loop

31

21

2

1

1

1

becomesoffset the, offset,an hasamplifier error theif However,

offset to thereduces thisIdeally,

+

A

VAAV

V

AAV

osos

os

os

Offset Compensation

• The low-pass filtering in the feedback loop causes a low-frequency cutoff

32

11

1 12/21

CRAAfLF

+=

π

• Thus, the feedback loop bandwidth should be made much lower than the lowest frequency content of the input data

• This may lead to large-area passive in the offset correction feedback • Some designs leverage Miller capacitive multiplication with the error

amplifier to reduce this filter area

ECEN620: Network Theory�Broadband Circuit Design�Fall 2012AnnouncementsLimiting AmplifiersHow to Achieve an Ampilfier GBW > fT?Multi-Stage Amplifier GBWMulti-Stage Amplifier Bandwidth CompressionOptimum Number of Gain StagesOptimum Number of Gain StagesOptimum Number of Gain StagesOptimum Number of Gain StagesBandwidth Extension TechniquesShunt PeakingShunt PeakingBridged-Shunt PeakingSeries PeakingSeries PeakingBridged-Shunt-Series PeakingBridged-Shunt-Series PeakingT-Coil PeakingT-Coil PeakingT-Coil PeakingActive Bandwidth Extension TechniquesNegative Miller CapacitanceNegative Miller CapacitanceActive Negative FeedbackActive Negative FeedbackActive Negative FeedbackLimiting Amplifier Example 1Limiting Amplifier Example 2Offset CompensationOffset CompensationOffset Compensation