Analog and Mixed-Signal Design for SOCweng/courses/IC... · design architecture will be required to extend the trend for lower supply voltages for mixed-signal applications. An alternative

Dept. of Electrical Engineering

Analog and Mixed-Signal

Design for SOC

大同大學電機系

黃淑絹副教授

[email protected]

2

Outline

Analog and Mixed-Signal Design in the SOC EraCurrent Mirrors and Biasing CircuitsSingle-Stage AmplifiersOperational AmplifiersLayout of Analog and Mixed-Signal ICs

3

ITRS

International Technology Roadmap for Semiconductors (http://public.itrs.net)Minimum Gate Length for Digital Transistors

Gate Length Projections

0

10

20

30

40

50

60

70

80

90

100

2001 2003 2005 2007 2009 2011 2013 2015

Leng

th in

nm

http://public.itrs.net/

4

ITRS (cont.)

Supply Voltages for Digital and Analog ICsSupply Voltage Projections

0

0.5

1

1.5

2

2.5

3

3.5

2001 2003 2005 2007 2009 2011 2013 2015

Vol

tage

Analog Supply Range

Digital Supply Voltage

5

ITRS (cont.)

“The mixed-signal supply voltage continues to lag that of high-performance digital by two or more generations. A combination of multiple gate oxide thickness, multiple thresholds, and DC-DC conversion is needed to support the increased mixed-signal requirements. Solutions in active threshold regulation, substrate biasing, and novel design architecture will be required to extend the trend for lower supply voltages for mixed-signal applications. An alternative to full integration is the SIP that combines circuits made with different technologies and optimized for the desired functions. We expect that full-digital implementations in CMOS will replace most analog functions except for analog-to-digital conversion (ADC).”

6

Challenges for AMS designers

Major Issuesgm and go are both degrading. ⇒ difficult to build high gain amplifiers.Feedback is difficult to use.Signal swing is decreasing with VDD. ⇒ difficult to get acceptable SNRMany existing architectures will not functionGates are leaking. ⇒ Charge redistribution circuits may not workDevices becomes increasingly nonlinear. ⇒ Spectral performance of many circuits will degrade.Many existing architectures will not give acceptable performance.Matching is becoming worse. ⇒ difficult to obtain acceptable soft yieldsPerformance expectations are increasing.Increased mask and processing costsIncreased concerns about AMS test

7

AMS design in SOC

Increasing need for data converters Oversamped for low-frequency high resolutionNyquist rate structures for higher speeds

Feedback will be even more important in high spectral purity applications.Design for yield will become essential.New circuit architectures that operate at low voltages will become essential.

8

Outline


9

MOS Transistors

CMOS N-Well Process

Common Used Symbols NMOS

PMOS

G G

SiO2

p-subtrate

S DB D S B

PMOSNMOS

gateoxide

polyfieldoxide

p+ n+ n+

n-well

n+p+p+ SiO2SiO2

VSSVDD

G

D

S

B

GB

S

D

10

MOS Transistors (cont.)

Important Dimensions of a MOS Transistor

L: Channel lengthW: Channel widthtox: oxide thicknessCapacitance

W

tox

e)capacitanc (gate

area)unit per ecapacitanc (oxide

WLCCt

C

OXG

OX

OXOX

=

=ε

11

MOS Transistors (cont.)

Drain Current Equation in Saturation RegionIncluding channel-length modulation and body Effects

2

212

2

( ) (1 )

where (L )Ksi oqN A

DS eff B

WD n OX GS tn DSL

L V V

I C V V Vε

µ λ

λ λ− +Φ

= − +

= ↑ ⇒ ↓

)|2||2|(

)( and | where

)|2||2|(2

120

FFBStpotp

CqN

Vtntno

FFSBtnotn

VVV

VVV

VVV

OX

siSUB

SB

Φ−Φ+−=

==

Φ−Φ++=

=

γ

γ

γε

12

Small-Signal Model

Linear ComponentsLinear Resistor

Linear Capacitor

Dependent Circuits

RIV =

CVQ =

(CCVS) (CCCS) (VCVS) (VCCS)

12

12

12

12

rIVIIVV

gVI

====

βα

The slope corresponds to resistance, conductance, capacitance, transconductance, etc.

y

x

slope

13

Small-Signal Model (cont.)

Linear Approximation for Nonlinear Components

xdx

xdyxyxyy

xxx

xxdx

xydxxdx

xdyxyxy

∆≈−=∆

−=∆

+−+−+=

)()()(

, smallFor

)()()()()()(

00

0

202

02

00

0 L

y 1. Find the operation point.2. Determine the slope,

which determine the value for the linear component.

3. Remove the DC bias, and replace the device with the linear components.

dxxdy )( 0∆y

∆xy0

xx0

14

MOS Small-Signal Model

gmvgs

+vgs

-

G

S

Drdsgmbvbs

+vbs

-B

tnGS

DDOXntnGSOXnQ

GS

Dm VV

IIL

WCVVL

WCvig

−==−=

∂∂

=22)( µµ

|2|1

2

)|2||2|(

||22

FSBBS

tn

FFSBtnotn

mFSB

m

BS

tn

tn

DQ

BS

Dmb

VvV

VVV

gV

gvV

Vi

vig

Φ+−=

∂∂

Φ−Φ++=

=+

=∂∂

∂∂

=∂∂

=

γγ

ηφ

γD

DS

Ddsds I

vigr λα =

∂∂

=== −1

15

MOS Device Capacitances

Variation of CGS and CGD versus VGS

Saturation region

channel theoadjacent t side theexcluding perimetersdrain and source :,

areasdrain and source :,

)(

cap.) (overlap 32

ds

ds

swjdjdddb

swjsjsssb

OVOXgd

OVOXOXgs

PPAA

CPCAC

CPCWLAC

WLCC

WLCWLCC

−

−

+=

++=

=

+=

fixed

16

MOS Device Capacitances (cont.)

Triode region

Cut-off regionswjdjdddb

swjsjsssb

OVOXOXgd

OVOXOXgs

tnGSOXnDS

Ddsds

CPCWLAC

CPCWLAC

WLCWLCC

WLCWLCC

VVL

WCVIgr

−

−

−

++=

++=

+=

+=

−≅∂∂

==

)(

)(

)(

21

21

21

21

1 µ

deplOX

deplOXgb

swjdjdddb

swjsjsssb

OVOXgd

OVOXgs

CWLCCWLC

C

CPCAC

CPCAC

WLCC

WLCC

+=

+=

+=

=

=

−

−

17

Basic Current Mirrors

MOSFETs as Current SourceBiasing in saturation with a fixed gate voltage

Using resistive divider to provide the gate voltage

)1()(21 2

21

2

efftnbOXnout

DDb

VVVL

WCI

VRR

RV

λµ +−=

+= Sensitivity to

supply, process and temperature

18

Basic Current Mirrors (cont.)

Current Copiers

Diode-Connected device providing inverse functionAssume λ=0.

)(

)(1

REFGS

GSD

IfV

VfI−=

=

Current Mirror

REFout

tnGSOXnout

tnGSOXnREF

ILWLWI

VVL

WCI

VVL

WCI

1

2

22

21

)/()/(

)()(21

)()(21

=

−=

−=

µ

µ

19

Errors in Current Mirrors

Simple Current Mirror

Output resistance

Iout

+

-

Vout

Iin

M1 M2+-VGS

ineff

effout

efftnGS

IVV

LWLWI

VVV

×+

+=

=−≥

1

2

1

2

out

11

)/()/(

V:region saturationin M2

λλ

2dsout rR =

Μ1 Μ2

20

Cascode Current Mirror

Suppressing Channel-Length Modulation Effect⇒cascode structure

Output Resistance

0

1

mg

1

1

mg2dsr

3dsr233 )( dsdsmout rrgR ≈

21

Cascode Current Mirror (cont.)

Head-room consumed by a cascode mirror

1103

11

00

10 )/(2

)/(2

tneffefftnNout

tnOXn

REFtn

OXn

REFGSGSN

VVVVVV

VLWC

IVLWC

IVVV

++=−≥

+++=+=µµ

1

500M 1.50 2.50 3.50 4.50Vout (V)

120U

80.0U

40.0U

0

-40.0UIo

ut(A

)

simplecascode

22

Cascode Current Mirror (cont.)

Minimum headroom voltage

tnGSb VVV −= 2 GSb VV 2=

23

Low-Voltage Cascode Current Mirror

Modified of Cascode CM for Low-Voltage (Wide-Swing) Operation

212

21121

21121

121112

2121

:saturationin M1

:saturationin M2

tntnGS

tnGStnGSGS

tnGSbtnGSGS

tnGSGSbtnGSGSbA

tnGSbtnbGSX

VVVVVVVV

VVVVVVVVVVVVVVV

VVVVVVV

≤−⇒+≤−+⇒

+≤≤−+⇒−+≥⇒−≥−=

+≤⇒−≥=

212

211 )(

effefftnbout

GStnGSb

VVVVVVVVV

+=−≥⇒

+−=

24

Low-Voltage Cascode Current Mirror (cont.)

Biased by a diode-connected transistor

LW

nLW

LW

nLW

LW

LW

LW

LW

25

242

31

)1(1

1

+=

=

=

=

=

IREF Iout

+

-

Vout

M3M1

M4M2

I1

Vb

M5

5215

5

42

31

1

)1( and

)1(

2 Then,

.Let

tneffefftneffb

effeff

effeffeff

LW

OXn

REFeffeffeff

REF

VVVVVnV

VnV

nVVVCIVVV

II

++=++=

+=

==

===

=

µ Inaccuracy due toBody effectSome margin is necessary to ensure saturation.⇒ Reduce the aspect ratio for M5.

25

Low-Voltage Cascode Current Mirror (cont.)

Design for short-Channel Devices

26

Regulated Drain Current Mirror

27

Supply-Independent Bias

Supply-Dependent BiasingResistive Bias

Example

golden referencecurrent

VDD

IREF

M1 M2

Iout

VDD

IREF

M1 M2

IoutR1

DD

1

2

11

V tosensitive

)/()/(

/1⇒

+∆

=∆LWLW

gRVI

m

DDout

28

Supply-Independent Biasing (cont.)

Using MOSFET only

tppOXp

REFtn

nOXn

REFDD V

LWCIV

LWCIV −++=

)/(2

)/(2

µµ

29


Supply-Independent Biasing

Example for Long-channel devices

22

21

)11(1)(

2effect.body eNeglect th

)(2

)(2

KRCI

RIVKCIV

CI

BNLW

OXnout

BouttnNL

WOXn

outtn

NLW

OXn

out

−=

++=+

µ

µµ

VDD

RB

M1

M3

M2

M4

K(W/L)N (W/L)N

(W/L)P (W/L)P

IoutIout

VDD

M1 M2

M3 M4

(W/L)N (W/L)N

(W/L)P K(W/L)P

RB

30


Short-Channel Device

31


Using feedback to increase the output resistance of MOSFET

32


Improved circuit

33

Outline


34

Common-Source Amplifier

Common-Source Amplifier

+

-VIN

M3 M2

M1CL

RIN

Vout

VDD

Ibias

Rout

outR

212

21 //

dbdbL

dsdsout

CCCCrrR

++==

++≅++=

++≅

++++≅

−=

−

21121

222111

112

211113

10

1)1)(1()(

)()]1([1

ppppp

gdgsgsgd

gdmp

gdoutoutmgdgsindB

outmv

sssssD

CCCCCCCg

CCRRgCCR

RgA

ωωωωω

ω

ω

)(

)()]1([where

1)1(

222111

21111

21 1

1

CCCCCCRRb

CCRRgCCRa

bssasRg

VV

gdgsgsgdoutin

gdoutoutmgdgsin

gC

outm

in

out m

gd

++=

++++=

++

−−=

35

Common-Source Amplifier (cont.)

Miller’s Theorem

Miller Capacitance

-3dB Frequency open-circuit time constant method

Y

Y1

+V1-

+V2-

Y1

+V1-

+V2-

I1 I1I2 I2

K=V2/V1

222122

111211

)11()(

)1()(

YVYK

VYVVI

YVYKVYVVI

=−=−=

=−=−=

neglected)(usually )11(

Capacitor)(Miller

)1()1(

11

11

111

10

gdgdright

gdoutm

gdoutmgdleftM

outmv

CCK

C

CRg

CRgCKCCRgAK

≈−=

≈

+=−==−==

YK

Y

YKY

)11(

)1(

2

1

−=

−=

)(][11

213 CCRCCRCR rightoutMgsin

iii

dB +++≈≅

∑−ω

36

Source Follower

Source-Follower

No voltage gainLow output resistanceNot suffering from Miller effect ⇒ better frequency responseExhibiting large amounts of overshoot and ringing under certain conditions

+

-VIN

M3 M2

M1

CL

Rin

Vout

VDD

IbiasRout

Vin

Vout

Rin

Cgs1

Cgd1

gm1Vgs1 gs1Vs1

rds1

rds2 C2

+Vgs−

Vin

Vout

Rin

Cgs1Cgd1gm1Vgs1

R2 C2

+Vgs−

212

1212 )/1(||||

dbsbL

sdsds

CCCCgrrR

++==

1

/1)()/1(||

2111

110

11

211112

<+++

==

≅+++== −

dsdssm

moutmv

mdsdssmmout

gggggRgA

ggggggRR

37

Common-Gate Amplifier

Common-Gate Amplifier

The gain is slightly less than that of the common-source amplifier.Since the gate of the transistor is ac ground, it does not suffer from Miller effect.

⇒ Frequency response is superior to that of CS amplifier.

M3 M2

M1 CL

Vout

VDD

Ibias

RS

+

-VIN

Vbias

rin

Rout

1

1

1

1

12

11111

1

1

111

1

)2 ,For ( )1(11

dsL

m

inS

in

s

out

in

s

in

out

mindsL

ds

L

mdssm

Ldsin

dsL

dssm

s

out

gGg

rRr

VV

VV

VV

grrR

rR

ggggRgr

gGggg

VV

+×

+≅=

≈=+≅++

+=

+++

=

38

Cascode Amplifier

Cascode Amplifier

Folded-Cascode Amplifier⇒ improving input range

M5

M2

M1

CL

Vout

VDD

Ibias

Rin

+

-VIN

Vbias

Ron

M3

M4

M6Rop

outmv

oponout

dsdsmop

dsdsmon

RgA

RRRrrgRrrgR

−=

=

≅≅

0

433

122

||

LoutdB

outin

CR

RR

1.resistanceoutput large its todue poleoutput by the

dominantususally isfrequency 3dB- the,For

3 ≈

<<

−ω

39

Differential Amplifier

Differential Pair

M1 M2

iD1 iD2

2.5VvI1

iB

40

Differential Amplifier (cont.)

Current Mirror Load -- Large-Signal Analysis

I∆+ I∆−I∆+

SSI0

↓↓

0

0=outV

↓

)( 21 ininout VVfV −=

IISS ∆−2 IISS ∆+

2

IISS ∆−2

↑

)( 21 ininout VVfV −=

IISS ∆+2 IISS ∆−

2

IISS ∆+2

SSI 0

↑↑

DDout VV =

SSI

M1, M3, M4: offM2, M5: deep triode

M2: offM4: deep triode

41


I/O Characteristic

Vout vs. VDD

↑

↓

↑

Fout VV =circuit, symmetricFor

42


Small-Signal Analysis Asymmetric Swings due to the Load

Calculation of Gm

1

121 22

min

outm

inmin

min

mout

gviG

vgvgvgi

−==

−=−−=

43


Calculation of Rout

Overall Gain

4or1XI

42

42,143

32,1

//

//122

ooout

o

X

o

X

o

X

om

o

XX

rrR

rV

rV

rV

rg

r

VI

≈

+≈++

=

outR 2C

23

10

422

42

1

//

CR

RgACCCC

rrR

outdB

outmv

dbdbL

dsdsout

≈

≈++=

=

−ω

biasMds

biasMds

biasLW

OXnm

Ir

Ir

ICg

44

22

1

2

2

λ

λ

µ

=

=

=+

-Vin

Vout

M1 M2

M4M3

Ibias

CL

44


Single-Ended vs Differential Amplifier

For given device dimension, this circuit requires half of the bias current to achieve the same gain as a differential pair. However, advantages of differential operation often outweigh the power penalty.

)//( 211 oomv rrgA −=

45


Power-Supply Rejection Ratio (PSRR)

PSRR+

PSRR-

+ −

VB1

Vo

M1

M3 M4

M2

M5

VDD

VSS

CL

1/gm3

2ro2

i

vo

i ro4

vdd

CL

Loop

p

vd

pdd

odd

Crr

sAA

svvA

)//(1

/1

/11

42

0

=

+=

+==

ω

ω

ω0|| 1 v

dd

ddd A

AAPSRRA ==⇒= +

mismatches toduemainly ||

0

⇒∞→=

==

−ss

d

ss

oss

AAPSRR

vvA

46

Systematic Design Approach

Parameter Domains for Characterizing Amplifier Performance

Degrees of Freedom: 2Small-signal parameter domain

Natural design parameter domain

Alternate parameter domain

L

momv C

gGBrgA =−= 1

, om rg

DOXn

D

OXnv ILW

CGB

ILWC

A /2

/2

=

−=

λµ

λµ

EBLDDEBv V

PCV

GBV

A

=

−=

2 12λ

,/ DILW

, EBVP

47

Systematic Design Approach (cont.)

Design Equations

+−

voutVCM

vd/2 -vd/2

VB

VDD

M1 M2

M5MB

IB

M3 M4

1 : α

CL

3(min)

15(max)

15

1

1

11

11111

1

12

1121

111

142

52,15

tan180

)1(2)(

1)(

2))()((

)(

)()1(2

)(1//

)1(22 )1( Let

EBout

EBEBDDout

EBL

D

p

t

LEBDDLEB

D

L

EBLW

oxn

L

mpvt

Loutp

EBpnEBLW

oxnpn

EBLW

oxnoutmv

pn

DD

Dpndsdsout

DD

DDBDDBD

VVVVVV

GBVCISR

PM

CVVP

CVI

CVC

CgAGB

CR

VVCVCRgA

PV

IrrR

VPIIIVPII

=

−−=

==

−≈

+====×≈=

=

+=

+==

++

=+

==

+==⇒+=⇒=

−

ωω

ααµωω

ω

λλµλλµ

λλαα

λλ

αααα

tpSGptnGSnEB VVVVV +−= or :bias Excess

48


Input Common-Mode Range (CMR)

CMR+For M5 in the saturation region,

CMR-For M1 in the saturation region,

11515

5(min)5

tpEBEBDDSGEBDDCM

EBSD

VVVVVVVV

VV

−−−=−−=

=

+

13313

3111111

tptnEBtpGSCM

GStpDGtpSGSD

VVVVVV

VVVVVVV

++=+=

=+≥⇒+≥

−

49


Spread Sheet Method

3.31E+029.06E+013.85E+061.65E+043.51E+083.92E+019.10E+010.25 0.25 0.15 10.0 3.00E-03

1.10E+029.06E+011.28E+064.96E+041.17E+083.92E+019.10E+010.25 0.25 0.15 10.0 1.00E-03

1.10E+029.10E+011.28E+064.96E+047.02E+073.47E+015.46E+010.25 0.25 0.25 10.0 1.00E-03

SR(V/us)PMfp1 (Hz)RoutGB (Hz)Avo(dB)AvoVBE5VEB3VEB1αP

L=1µm, W=10µm, VDS=0.825V and ID=100uA

-0.754Vtp0.105λp4.24E-05μpCox2.5E-12CL

0.57Vtn0.0415λn1.23E-04μnCox3.3VDD

6.24E+021.07E+028.66E+028.26E-048.26E-050.25 2.90 0.07 2.15

2.08E+023.57E+012.89E+022.75E-042.75E-050.25 2.90 0.07 2.15

2.08E+023.57E+011.04E+022.75E-042.75E-050.25 2.80 0.07 2.05

(W/L)5(W/L)3(W/L)1ID5IBVout(min)Vout(max)Vicm(min)Vicm(max)

50

Outline


51

Ideal Opamps and Applications

Ideal Opamp

Open Loop

∞→∞→

→∞→

BWARR

o

id

0-

+

VoutVin-

Vin+

Rid Ro

A

)( −+ −= ININOUT VVAV

−

+VINVOUT VIN

VOUT

L+

L-

slope=A

52

Ideal Opamps and Applications (cont.)

Close Loop with Negative Feedback

Inverting amplifier

Finite open-loop gain

−

+

R1

R2

VINVOUTvirtual

short 1

2

21

RR

VV

RV

RV

IN

OUT

OUTIN

−=⇒

−=

−

+

R1

R2

VINVOUT

AVOUT− A

RRR

RV

VR

VA

V

RA

VV

IN

OUT

OUTOUTOUT

IN

/)1(1

1

1

21

2

21

++×−=⇒

−=

+

.0 feedback, negative and For =−∞→

=−

−+

−+

ININ

OUTININ

VVAA

VVV

53

Ideal Opamps and Applications (cont.)

Non-inverting amplifier

Difference amplifier

−

+VIN

VOUT

R2

R1

1

2

21

1RR

VV

RVV

RV

IN

OUT

OUTININ

+=⇒

−=

−

−

+VIN

VOUT

R2

R1

AVV OUT

IN −

ARRR

RV

VR

VA

VV

RA

VV

IN

OUT

OUTOUT

INOUT

IN

/)1(1

1)1(

)()(

1

21

2

21

++×+=⇒

−−=

−−

Finite open-loop gain

−

+

V1VOUT

R2

R1

R3

R4

V2

)(

, and For

)1(

121

2

4231

11

22

1

2

43

4

VVRRV

RRRR

VRRV

RR

RRRV

OUT

OUT

−=

==

−++

=

54

Stability

General ConsiderationsBasic negative-feedback system

Example

1. anddependent in frequency is Assume)()( :gain Loop

)(1)()(

≤=

+=

βββ

βsHsL

sHsHs

XY

−

+VIN

VOUT

R2

R1

.11 ,1 If

/)1(1

1)1()/(11

/11

1

2

1

21

2

21

1

RR

VVA

ARRR

RAA

AV

VRR

R

IN

OUT

IN

OUT

+=≈>>

+++=

+=

+=⇒

+=

ββ

ββ

ββ

55

Stability (cont.)

Barkhausen’s Criteria for oscillation

Example

δω

ω

ωωωωω

ω

+=⇒=

=⇒

=−⇒=∠

−++

−=

+++

−=+

+−=

2/ 1|)(|

1

0)/(1180)()]/(1[3

/1)(

)/(13/1)1()(

120

0

000

12

12

1

2

RRjLRC

CRCRjLCRCRj

RRjL

sCRsCRRR

ZZZ

RRsL

sp

p

o

.at oscillates system The180)(

1|)(|

00

0

ωω

ω

⇒−=∠

=ojL

jL

56

Stability (cont.)

Bode plot of loop gain for unstable and stable system

o180−ω dB0ω

o180−ω

phase excess 180)(

gain excess 1|)(| if unstable, is System

0

180o

o

−<∠

>−

dBjL

jL

ω

ωo

o

180)(

1|)(| if stable, is System

0

180

−>∠

<−

dBjL

jL

ω

ω

(PX)point crossover phase :(GX)point crossover gain :

180

0

o−ωω dB

57

Stability (cont.)

Time-domain responses versus the pole locationstjjp pppp )exp( ωσωσ +⇒+=

RHP polesUnstable with growing amplitudes

Imaginary polesUnstable with constant-amplitude oscillation

LHP poles ⇒ stable

58

Stability (cont.)

One-pole systemLoop Locus

00 )1( ωβAp +−=

])1/[(11)(

/1)(

00

0

0

0

0

ωββ

ω

AsA

A

sXY

sAsH

+++

=

+=

⇒unconditional stable

59

Stability (cont.)

Multipole SystemsTwo-pole system

21

221

01

2102

21

2121

2102

21212,1

210212

210

021

0

21

0

4)(1

0)1(4)(

2

For

2)1(4)()(

)1()(

)/1)(/1()(

)/1)(/1()(

pp

pp

pppp

pp

pppppp

pppp

pp

pp

pp

A

A

pp

Ap

AssA

AssAs

XY

ssAsH

ωωωω

β

ωωβωω

ωω

ωωβωωωω

ωωβωωωω

βωω

ωω

−=⇒

=+−+⇒

+−==

+−+±+−=

++++=

+++=

++=

⇒still unconditional stable

60

Stability (cont.)

Three-pole system

Additional poles (and zeros) impact the phase to a much greater extend than they do the magnitude.If the feedback factor decreases, the circuit becomes more stable because the gain crossover move toward the origin while the phase crossover remains constant.

↓β

61

Stability (cont.)

Phase Margin

|)(|log20(PM)Margin Gain 180)((PM)Margin Phase

180

0

o

o

−−=

+∠=ω

ωjL

jL dB

o

o

180)(

1|)(| if stable, is System

0

180

−>∠

<−

dBjL

jL

ω

ω

Small PM Large PMpeaking large 5.11|)(|

)175exp(1/1

)(/11/1

)(1)()(

5180)((PM)Margin Phase

)175exp()(

175)(

0

00

00

0

0

0

⇒=

+=

+=

+=

=+∠=

−=⇒

−=∠

βω

βω

βωβ

ωω

ω

ωβ

ω

dB

dBdB

dBdB

dB

dB

dB

jXY

j

jLjHjHj

XY

jL

jjH

jL

o

oo

o

o

62

Stability (cont.)

45° phase margin

peak %03 3.1|)(|

707.0293.0/1

)135exp(1/1)(

45180)((PM)Margin Phase

)135exp()( 135)(

0

0

0

00

⇒=

+=

+=

=+∠=

−=⇒−=∠

βω

ββω

ω

ωβω

dB

dB

dB

dBdB

jXY

jjj

XY

jL

jjHjL

o

oo

oo

63

Stability (cont.)

Closed-loop time response for various phase margin

PM=60°, ⇒negligible frequency peaking⇒little ringing and fast settling

Example: unity-gain buffer (large-signal step response)

βω 1|)(| 0 =dBj

XY

Optimum value

(W/L)=50 µm /0.6µmft=150 MHzPM=65°Nonlinearity of the circuit causes the variation of the poles and zeros during transient.

64

Practical Design Parameters

ssssddddcmcmOSdvout vsAvsAvsAVvsAV )()()())(( ++++=

Gain and bandwidth (gain-bandwidth product)Phase margin Slew rate and settling timeOffset voltageCommon-mode range (CMR)Common-mode rejection ratio (CMRR)Power-supply rejection ratio (PSRR)

||cm

v

AACMRR =

||

||

ss

v

dd

v

AAPSRR

AAPSRR

=−

=+

65

Practical Design Parameters (cont.)

Linear Settling Timedue to the finite unity-gain frequency of the opamp

+ A(s)

β

Vin Vout

Vstep

ττ

τ

6.9 accuracy 0.1% 4.6 accuracy 1%

)1()(

)( )()(

: Response Step

/

⇒⇒

−=

=⇒=

−tstepout

stepinstepin

eVtvs

VsVtuVtv

occurs. limiting rate-slew no , If

| 0

SlopeSR

Vdt

dVSlope stept

out

>

== = τt

CL

ttp

pp

ssAsAsA

ssAω

AsAsA

βωββ

ωωω

ωωω

+≅

+=

≈<<<<

≈+

=

/111

)(1)()(

:gain loop-Closed

.)( ,For

) :(Note )/1(

)(

:opamp dcompensate pole-dominant a of modelorder -first Simple

1

10t1

0

tCLA βωτ

ωβ

≅=≅∴1 and 1 3dB-0

66

Practical Design Parameters (cont.)

Example: Opamp Gain and Unity Gain Frequency for an ADC

β

β

ββ

ββ

β

1

1

2

(0.5LSB) 2

11

)11(1)/(11

111

+

+

>

<

−≈

+=

+=

N

OL

NOL

OL

v

OL

OLCL

A

A

A

A

AAA

MHzfMHzf

fNtNf

ft

VVAN

CCCC

C

tCLK

CLKsettle

tCLK

settle

Nv

FI

FI

F

572 100

)1(44.0)1(11.0 ,2

1 If

(84dB) / 22 12

5.0 ,For 142

=⇒=

+=⋅

+>=

=>⇒=

==+

=

+

β

β

β

settlesettle

N

t

t

NN

settle

Nt

t

tdB

tfinaloutout

tN

tf

t

e

eVv

settle

⋅+

=⋅

>

=⋅<

<∆

==

−=

+

++

+−

−

−

βπβ

βωτ

ωβωω

τ

τ

τ

)1(11.02

2ln

2ln2ln

21 ,

2 within settle To

opamp) offrequency gain -unity :(

11

)1(

1

11

1/

3

/,

67

Telescopic Opamp

Design Equations

75(min)

319(max)

19

1

1

11

11111

1

162

42

162

42

111

62

42

162

42

866244

92,19

tan180

)1(2)(

1

)(4

)(/4

)()1(4

)(2

)(||)()1(22

)1( Let

EBEBout

EBEBEBDDout

EBL

D

p

t

LEBDDLEB

D

L

EBLW

oxn

L

mpvt

Loutp

EBEBnEBpDEBnEBp

EBDoutmv

EBnEBp

DD

DEBnEBp

dsdsmdsdsmout

DD

DDBDDBD

VVV

VVVVV

GBVCISR

PM

CVVP

CVI

CVC

CgAGB

CR

VVVIVVVIRgA

VVPV

IVV

rrgrrgRV

PIIIVPII

+=

−−−=

==

−≈

+====×≈=

=

+=

+==

++

=+

=

≅+

==⇒+=⇒=

−

ωω

ααµ

ωω

ω

λλλλ

λλαα

λλ

αααα

vout

VB

VDD

M1 M2

M9MB

M3 M4

1 : α

CL

V1 V2

VB1

VB2

M5 M6

M7 M8

EBD

EBDdsm λVI

VIrg 1 /2==

λ

68

Folded-Cascode Opamp

Design Equations

-

+Vin

Q1 Q2

Ibias

VB1Vout

Q9Q10

Q6 Q5

Q7Q8

VB2

CL Rout

consuming more powerwider ICMRslightly larger output swing

10863

113

3

10

10883166

~ :swingOutput

1

)(||)]||([

effeffeffeffDD

GSeffbtneffDD

LoutdB

outmv

dsdsmdsdsdsmout

VVVVV

VVCMRVVVCMRCR

RgArrgrrrgR

+−−

+=−+−=+

≅

≅≅

−ω

69

Folded-Cascode Opamp (cont.)

Bias Currents and Slew Rate

Ibias2/2

Ibias1

2/21 biasbias II −

offIbias2

Ibias11biasI

0

2/21 biasbias II >

L

bias

CISR 1=

offIbias2

Ibias11biasI

21 biasbias II −121 2 biasbiasbias III <≤

L

bias

L

biasbiasbias

CI

CIIISR 2211 )(

=−−

=

12 biasbias II ≤

Case 1

Case 2

70


Purposes for Q11 and Q12Q11 and Q12 are turned off during normal operation and almost have no effect on the opamp.Q11 and Q12 act as clamp transistors to prevent the drain voltages Q1 and Q2 from having large transients where they change from their small-signal voltages to voltages very close to the negative power-supply voltage. Thus, the opamp can recover more quickly following a slew-rate condition.Increase the slew-rate performance of the opamp:

L

bias

biasbiasbias

CISR

III

2

121 2

=

<≤

71


Design Example

95.3 19.6 9.5 3.3 9.5 74.4 W/L

126.26 75.76 12.63 12.63 12.63 63.13 ID (µA)

M11M9M3M7M5M1

14.69 0.50 2.80 -0.50 2.10 7.58 126.26 10.05 79.34

Rout (MΩ)VominVomaxCMR-CMR+SR (V/µs)IB (µA)GB (MHz)Avo (dB)

Calculation Results:

0.250.250.250.250.250.2

VEB11VBE9VEB3VBE7VEB5VEB1

Set VEB to calculate the performance.

0.20.51075

αP (mW)GB (MHz)Avo (dB)

Specification:

LDDEB CVVPGB

1)1( α+=

])([4

752

1 EBnpnnEBpEBvo VVV

Aαλκλλαλ +++

=

VDD

Vbias-n

Vcasc-n

Vcasc-p

Vbias-p

IB

(1+α)IB/2

M11

M1 M2

M3

M5

M7

M9M10

M8

M6

M4

VOUTVIN- VIN+

72

Gain Boosting

Increasing the Output Impedance by Feedback

Gain Boosting in Cascode Stage1221 oomout rrgAR ≈122 oomout rrgR ≈

regulated cascode23(min)

1223311

12233 )(

effGSout

oomommoutmv

oomomout

VVVrrgrggRgA

rrgrgR

+=−≈−=

≈

73

Gain Boosting (cont.)

Gain Boosting for Differential Cascode Stage

352(min) effGSISSout VVVV ++=

74


Folded-Cascode Circuit Used as Auxiliary Amplifier

311(min)

11(min),

effeffISSout

effISSYX

VVVV

VVV

++=

+=

1223311

13315

13111195771

151

)()//()]//([

oomommoutmv

oomoutmout

oomooomout

outm

rrgrggRgArrgRgR

rrgrrrgRRgA

−≈−=≈

≈=

75


Gain Boosting Applying to Signal and Load Paths

In contrast to two-stage opamps, where the entire signal experiences the poles associated with each stage, in a gain-boosted opamp, most of the signal directly flows through the cascode devices to the output. Only a small error component is processed by the gain-boosting amplifier and slowed down.

76

Fully-Differential Opamps

The Need for Common-Mode Feedback Circuits

.2/ toequal defined, wellare levels mode-commonouput andinput The

DSSDD RIV −

changes. tageoutput vol largein result may rs transistoNMOS and PMOSin currents the

between Mismatches defined. not well are levels mode-commonouput andinput The

)//)(( NPNPout RRIIV −=

−

+

Vin−

Vin+

Vout+

Vout−−

+ )( −+−+ −=− ininvoutout VVAVV

77

Continuous-Time CMFB Circuits

Common-Mode Feedback (CMFB) Circuits

Common-mode feedback with resistive sensing

78

Continuous-Time CMFB Circuits (cont.)

Common-mode feedback using source followersNote: R1 and R2 or I1 and I2 must be large enough to ensure that M7 or M8 is not starved at a large output swing.

Sensing and controlling output CM level

79

SC CMFB Circuits

Switched-capacitor CMFB circuit

more accurately defined CM level

off :modeion Amplificat

on :modeReset

1

7,62,1

57,61

SVV

VVVS

GSCC

GSGSCM

=

+=⇒

CMGSCCout

GSCMCC

VVVVSVVVS

≈+=⇒

−=⇒

52,15,4

62,15,4,1

on :modeion Amplificat on :modeReset

80

SC CMFB Circuits (cont.)

Another example

)(

)(2)(2))((20)()(

0

))((

))(( :

)()(

)()( :

,12

1,2,

1212

22

22

2

11

11

1

biascmcmoutSC

Scntrl

SC

Ccntrl

biascmScntrlcmoutCcntrlcmoutSC

cntrloutSC

cntrloutSC

biascmScntrloutC

biascmScntrloutC

VVVCC

CVCC

CV

VVCVVCVVCCQQQQ

QQ

VVCCQ

VVCCQ

VVCVVCQ

VVCVVCQ

+−+

++

=⇒

−+−=−+⇒

=−+−⇒

=∆+∆⇒

−+=

−+=

−+−=

−+−=

−−++

−+

−−

++

−−

++

φ

φ

)( ,For ,12 cntrlbiascmcmoutcntrlcntrlcntrl VVVVVVV −−===

VCM

φ1φ2

φ1φ2

CS CC

VCM

φ1φ2

φ1φ2

CSCC

Vcntrl

Vbias

VOUT+ VOUT−

81

Two-Stage Opamps

Two-Stage CMOS Opamp with Output Buffer

Equivalent Circuit for Uncompensated Opamp (without Cc and M16)

767

421

// //

dsdsIImmII

dsdsImmI

rrRggrrRgg

====

82

Two-Stage Opamps (cont.)

DC gain:

Frequency Response Without Compensation

Due to the square-law nature, ωp1 and ωp2 are usually quite closed to each other.⇒ Phase margin is significantly less than 45°.⇒ The opamp must be compensated before used in a closed-loop configuration.

)1)(1()(

1' 1'

'2

'1

21

pp

vov

IIIIp

IIp

ssAsA

CRCR

ωω

ωω

++=

==

)(tan)(tan)(

])(1][)(1[|)(|

'2

1'1

1

2'

2

2'1

ppv

pp

vov

jA

AjA

ωω

ωωω

ωω

ωω

ω

−− −−=∠

++=

321

883

2

1

)/(

vvvvo

mLmv

IImIIv

ImIv

AAAAgGgA

RgARgA

××=+≈

−=

−=

83

Compensation

With Compensation Capacitor (Cc)

zero) (RHP

)(

1])1[(

1

z

2

21

C

mII

CICIIIII

CmIIp

CIImIIIICvIp

Cg

CCCCCCCg

CRgRCCAR

=

++≅

≅+−

≅

ω

ω

ω

)(tan)(tan)(tan)(

)1)(1(

)1()(

2

1

1

11

21

ppzv

pp

zvo

v

jA

ss

sAsA

ωω

ωω

ωωω

ωω

ω

−−− −−−=∠

++

−=

Translating the dominant pole toward origin to improve stability

Pole splitting as a result of Miller compensation

84

Compensation (cont.)

Effect of RHP zeroUnity-gain frequency and gain-bandwidth product

'1pω '2pω1pω2pω

product)bandwidth -(gain

1)( )( , Since

frequency.gain -unity Find

11

1

1

1t

CgA

AjAs

AsA

C

mpvot

t

pvotv

p

vovp

==⇒

==⇒≈>>

ωω

ωω

ω

ω

ωω

85


Effect for the output stage

gmIvd RI

+vd-

gmIIvo1 RII

+vo1-CI

gm8(vo2-vo)

rds8

+vo2-

CII

gm9vo1 rds9

vo

CC

CL

gmIvd RI

+vd-

gmIIvo1 RII

+vo1-CI

CII

CC gm9vo1-gm8vo2vo+

vo2-

RIII CL

o

9 1 8 2

o2

1 2

8

9

8 8

9 9

Find zero by setting v =0.

Using node equation at v , one can obtain1( ) [ ( ) ] 0

1( ) [ ( ) ] 0

1[(1 ) ] 0

m o m o

mII C o C II oII

mmII C C II

m II

m mC II mII z

m m II

g v g v

g sC v s C C vR

gg sC s C Cg R

g gs C C g sg g R

⇒ =

− + + + =

⇒ − + + + =

⇒ − + + + = ⇒ = −

8

9

8

9

1

(1 )

mmII

m II

mC II

m

ggg R

g C Cg

+

− +

zero) (LHP

1,For 98

II

mII

II

IImII

z

mm

Cg

CR

gs

gg

−≈+

−=

=

86


Lead Compensation (Rz)

Several ways to choose RZ:Taking RZ=1/gmII, one can eliminate the RHP zero.Let ωz=ωp2 to cancel the nondominant pole.However, ωp2 is often not known a priori.Let ωz=1.2ωt to increase the phase margin.

frequency)gain -(unity

)(

1

1

10t

1z

3

C

mIpv

CZg

IZp

CgA

CR

CR

mII

≅≅

−=

=

ωω

ω

ω

)(

1])1[(

1

2

21

CICIIIII

CmIIp

CIImIIIICvIp

CCCCCCCg

CRgRCCAR

++≅

≅+−

≅

ω

ω

87


Other approaches to Remove RHP zeroEliminating forward signal feedthrough

88


Indirect Current Feedback

zero) (LHP zC

mcg

Cg

=ω

89


Indirect feedback compensation without additional power dissipation

90

Design Equations

Slew rate

First-stage gain

Second-stage gain

Gain-bandwidth

First pole

Second pole

Zero (RC=1/gm7)

SRI

CD

C

= 5

)(2

)||(425

14211 λλ +

−=−=

D

mdsdsmV I

grrgA

A g r rg

IV m ds dsm

D

2 7 6 77

7 6 7

2= − =

−+

( || )( )λ λ

ωtm

C

g

C= 1

ωp

V C ds dsA C r r1

2 2 4

1≅

( || )

ωpm m

L

g

C C

g

C27

1 2

7≅+

≅

ωZ → ∞↓(↑)1/2(↑)1/2RHP Zero↑

↑CL↑

↓↑SR ↑

↓(↑)1/2(↑)1/2ωt ↑

↑(↑)1/2↑↑(↑)1/2(↓)1/2(↓)1/2AV ↑

CCL7W7(W/L)6L3,4W3,4L1,2(W/L)1,2ID6ID5

CZg CRmII

)(1

1z −=ω

Positive CMRVcm(max)=VDD-VSD5(sat)-VSG1

Negative CMRVcm(min)=VSS+VGS3+VTp

Positive output swing Vout(max)=VDD-VSD6(sat)-VGS8

Negative output swingVout(min)=VSS+VDS9(sat)

Power dissipationPdiss=(ID5+ ID6+ ID8+ ID10+ ID11)( VDD- VSS)

91

Design Equations (cont.)

Nonlinear Settling Time: due to slew-rate limitingSlew Rate: the maximum rate that output can change

Offset VoltageRandom offset: due to device mismatches resulting from process variations. ⇒employing matching layout techniqueSystematic offset: due to design error

C

D

C

D

C

CcC

out

CI

CI

CI

dtdV

dtdVSR

15(max)

max

2===≅

≡teffttpSG

DLW

OXpmg

C

VVVSR

ICgCt

m

ωω

µω

11

111

)(

,)(2 and Since 1

=+=

==

7

7

3

3

374343

521

)/()/(

mirror.current a toequivalent is M7 and M3. , Since

.2/,For

LWI

LWI

VVVVVVIII

VV

DD

GSGSDSDSGSGS

DDD

inin

=⇒

⇒====

=== −+

5

6

4

7

76

6

6

5

5

)/()/(2

)/()/(

and)/()/(

M6),and(M5mirror current for theAlso

LWLW

LWLW

IILW

ILW

I

DD

DD

=⇒

=

=

occurs. limiting rate-slew no , If

| 0

SlopeSR

Vdt

dVSlope stept

out

>

== = τ

92

Design Equations (cont.)

Alternate Design Equations

])(1][)[(4

)(11

))()(()()(

)(2

)(2

))()(()(

)/2()1(

)/2(1

)(/211

)(1// and

)(1//

)1( . and Let

8712321

8

2882

188

8883

772

12

1121

1111

82

21

89

989988

776

142

521529516

EBpnEBEBpnvvvvo

EBpn

EBLW

oxnpnEBLW

oxn

EBLW

oxnoutmv

EBpnIImv

EBpnEBLW

oxnpn

EBLW

oxnImv

pnEB

DD

pnEBD

DpnEBDdsdsmout

DpndsdsII

DpndsdsI

DDDDDDD

VVVAAAA

V

VCVCVCRgA

VRgA

VVCVCRgA

VPV

VI

IVIgggR

IrrR

IrrR

IVPIIII

λλλλ

λλ

µλλµµ

λλ

λλµλλµ

λλααα

λλ

λλ

λλλλ

αααα

+++=××=

++=

++==

+=−=

+=

+=−=

++++

=++

=

++=

++=

+==

+==

++=⇒==

GBVCISR

PM

gR

Cg

CR

gxg

Cg

CCg

CVVP

CVI

CVC

Cg

EBC

D

p

t

z

t

p

t

mout

L

m

Loutp

mmtz

gs

m

III

mp

CEBDDCEB

D

C

EBLW

oxn

C

mt

15

3

11

2

1

8

83

17

8

772

1211

1

111

tantantan90

)1( 1)1(2.1 2.1

)1(2

)(

==

−

−

−≈

≈≈≈

−=⇒=

≈+

≈

++==

=≈

−−−

ωω

ωω

ωω

ω

ωω

ω

αα

µω

93

Comparison

Comparison

94

Cascode-Cascade Opamp

1

9

29

z

3

99

992

11995753311

11

11

952

32

111995753311

11111199

11

512

175312

1311

1

119

9

575313

1

1

)1(

))1((

11 )1(

1

1)1(

)1(8)()(

)1(2

)()(8

)()(8

12)/2/()/2/(

12//

)1(2)1(

EBCDDC

B

CZEBDD

CZLp

CCZ

m

IZp

EBLDDLEB

B

L

m

CICLLI

Cmp

CDD

EBEBEB

vop

EBCDDCEBC

m

pnEBEBnEBpEBEBEBEBEB

EBEBEBEB

oo

m

moomoo

mvo

DDBDD

VGBCV

PCISR

CRP

VVCRC

CCRg

CR

VCVP

CVI

Cg

CCCCCCCg

CVVVVP

AGB

VCVP

CVI

CgGB

VVVVVVVV

IIVI

VIIVIIVI

ggg

gggggggA

IVIVP

×=+

==

−+

=+

−=−

=

−=

+−=−=−≈

++−≅

+++

−=−=

+===

++=

++=

++=

++=

+=+=

α

αα

ω

ω

ω

αααω

αλλλλλλω

α

λλλλλλλλλλ

λλλλλλ

αα

VDD

VSS

Vin+

M2M1

M3 M4

M5

Vin−

M8

Cc

M6

Cc

M9

Vo+

CL

Vo−

CL

M7 M10

M11 M12M13

95

Low-Voltage Opamp

CMOS Technology

96

Low-Voltage Opamp (cont.)

Input Common-Mode Range of a Differential Input Stage

For Vsat=0.3V, VDD(min)=0.9VVDD=1.5V and Vtn1=0.7V, Vicm(max)=1.9V and Vicm(min)=1.3V

)(51(min)

1)(3(max)

)(5)(1)(3

)(511)(3(min)

satDSGSicm

tnsatSDDDicm

satDSsatDSsatSD

satDSGStnsatSDDD

VVVVVVV

VVV

VVVVV

+=

+−=

++=

++−=

97


Parallel NMOS and PMOS Differential Input Stage

Effective input transconductance

1)(5

1)(5

SGPsatSDPDDonp

GSNsatDSNonn

VVVV

VVV

−−=

+=

98


Constant gm Differential Input Stage Using Current Compensation

.4 ,For

. ,For

.4 ,0For

)(2

)()(Let

)(2

)(2

bnDDicmonp

bpnonpicmonn

bponnicm

pnmT

POXpNOXn

pPOXpmP

nNOXnmN

IIVVV

IIIVVV

IIVV

IIgL

WCL

WC

IL

WCg

IL

WCg

=<<

==<<

=<<

+=

==

=

=

β

µµβ

µ

µ

99

MOS Switches in Low-Voltage Design

Pass Transistors

100

MOS Switches in Low-Voltage Design (cont.)

Problem for the switch

Use transmission gate.Larger layout areaIt may not turned on for low voltage.

Increase gate voltage to 2.3V.

101


Charge Pumps (Voltage Generators)

102


Charge-Pump Clock Driver

Nonoverlapping clock generation circuit

103


Bootstrap circuit and switching device.

A. M. Abo and P. R. Gary, "A 1.5-V, 10-bit, 14.3-MS/s CMOS Pipeline Analog-to-Digital Converter,” IEEE Journal of Solid-State Circuits, vol 34, May 1999.

104

Switched-Opamp

Design concept

Input structure

Switchable opamp

Switched-capacitor biquad

Switched-opamp biquad

Switched-capacitor integrator

J.Crols and M.Steyaert, “Switched-opamp: An approach to realize full CMOS switched capacitor circuits at very low power supply voltages,” IEEE J. Solid-State Circuits, vol. 29, pp. 936-942, Aug. 1994.

105

Switched-Opamp

Example: Fully-Differential Switched-Opamp MDAC

M. Waltari and K.A.I. Halonen, “1-V 9-bit pipelined switched-opamp ADC” IEEE J. Solid-State Circuits, vol. 36, pp. 129-134, Jan. 2001.

106

Outline


107

Layout Considerations

Differences Between Layout and CircuitThe differences are mainly due to the following reasons:

These effects are not very substantial for digital systems; but they may have a significant impact on the accuracy of analog circuits and must be avoided or compensated.

Lateral diffusion Etching under the protection

Boundary dependent etchingError in the pattern size due to

Tri-dimensional effects

108

Layout Considerations (cont.)

Absolute and Relative Accuracy

109


Layout of an analog MOS transistorPoor layout and its equivalent circuit

Correct Layout

Metal profile with multi-contacts and only one contact

110


Layout of a wide transistorPoor layout

Correct layout (split into several parallel transistors)

⇒ Reducing Csb and Cdb

111


Layout of Matching TransistorsSources causing transistor mismatches

Gradient effect existing in the fabrication processTo minimize the effect, two transistors that must be matched to each other should be placed very close.For wide transistors, layout techniques to improve matching must be employed.

112


MOS Matching Model

WLAWLAV VT

t

2

2

2

22

)(

)(

β

ββσ

σ

=∆

=∆

113


Errors in Matched MOS Transistor Pairs

2

2

222

222

2

2

2

)()/(

1)()(

)()()()(

ββσσσ

σβ

βσσ

∆+∆=∆

∆+∆

=∆

IgVV

VI

gI

I

mtGS

tm

DS

DS

VTm

mt

m

AA

IgV

Ig βσ

ββσ

=⇒∆=∆ )( )()()( 222

2

114


115


Layouts of a Differential Pair

Normal layout

Inter-digitized layout Common-centroid layout

116


Orientation of transistorsPoor layout of transistors with different orientation

Boundary dependent etching Compensation of boundarydependent etching with dummy elements

117


Layout or Resistors

Layout of two matched resistors

sq)/(resistor sheet :

2

Ω

+=

s

scont

RWLRRRW

L

118


Resistance is temperature-dependent.Matched resistors should be arranged with their centroids placed

symmetrical with respect to the power devices.

Resistor realized by well diffusion

119


Layout of Capacitors Cross-section and layout of a capacitor

perimeter. on the depends Matching

)(2)2)(2('

: Undercut)(2

⇒−=

+−×≈−−=

+=×=

×=

xPALWxLW

xLxWA

LWPLWA

At

Cox

oxε

120


Layout of ratioed capacitors

Capacitors with non-integerMultiple of unit capacitorMatched capacitor with

common-centroid symmetry

121


Layout of Analog CellsGuidelines

Use transistors with the same orientation.Minimize the source or the drain contact area by stacking transistors.Respect the symmetries that exist in the electrical network as well as in the layout to reduce offset.Use low resistive paths when a current needs to be carried.Shield critical nodes.

Example: two-stage Opamp

Placement of transistors in a stacked fashion

122


Corresponding layout

Use of dummy transistors in the placement of transistors

123


Digital Noise CouplingCapacitive couplings

Analog lines routed parallel to the digital lines

Crossing between analog lines and clocks

Separation to reduce horizontal coupling

Dummy line for horizontal shielding

124


Coupling through the substrateUsing well-shielding

Noise Injection through the power supply

digitalanatot

totanatot

IIIdt

dILIRIRV

+=

++=∆

log

log211

40

125


Reduce R1: keeping the digital and analog sections as separate as possible and merging them at the place very close to the supply pad.If possible, use separate pads for the analog and digital section.

When extra pins are available, separate pins for the analog and digital supply should be used.Place the supply pins in the middle of the frames.

126


Floor Planning of Mixed-Signal BlocksGeneral guidelines

Put the analog critical components as far as possible from the digital elements.Make the connections to the critical nodes as short as possible.Avoid crossing between the analog biasing lines and digital busses.

Path of bias and supply lines for basic analog cells

Typical floorplan of an SC filter

127


Typical floorplan of a fully-differential SC filter

Typical floorplan of a mixed-signal chip

128


Block Diagram Layout of a Pipelined ADC

129


Decoupling Capacitors in a Mixed-Signal Chip

130

References

R. J. Baker, CMOS: Circuit Design, Layout, and Simulation, IEEE Press, 2005.P. E. Allen and D. R. Holberg, CMOS Analog Circuit Design, Oxford University Press, Inc., 2002. B. Razavi, Design of Analog CMOS Integrated Circuits, McGraw-Hill, Inc., 2001.D. A. Johns and K. Martin, Analog Integrated Circuit Design, John Wiley & Sons, Inc., 1997. J. E. Franca and Y. Tsividis, eds., Design of Analog-Digital VLSI Circuits for Telecommunications and Signal Processing, Prentice-Hall, 1994.

Documents

Analog and Mixed-Signal Design for SOCweng/courses/IC... · design architecture will be required to extend the trend for lower supply voltages for mixed-signal applications. An alternative