7-things that we should know about op-amp design

1

7-things that we should know about Op-amp DesignNatsem India Design’s Pvt. Ltd.

2

7-things that we should know about Op-amp Design

T. SrinivasStaff EngineerData Converters Group.

3

National Semiconductor Corporation Confidential7-things that we should know about Op-amp DesignData Converters Group, India.

Objective

• Op-amp is a fundamental part of Analog Circuit Design.

• Our aim is to increase your familiarity with Op-amp Design and…

Fear of Op-amp In Analog Circuit Design Course Design Systems

4


Contents

1. Small Signal Model of MOSFET.2. Current Mirrors.3. Gain Bandwidth Product of an Op-amp.4. Stability of an Op-amp.5. Slew-rate of an Op-amp.6. Offset of an Op-amp.7. Noise of an Op-amp.

Conclusion

5


1. Small Signal Model of MOSFET.

THGSDSDSTHGSn

DS

THGSDSDSTHGSnDS

VVVifVVVL

WKI

VVVifVVDSVVL

WKI

)1(2

22

D

S

GTriode Region:

Saturation Region:

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 1 2 3 4

VGS [V]

IG [A

]

0.0E+00

1.0E-04

2.0E-04

3.0E-04

4.0E-04

5.0E-04

6.0E-04

7.0E-04

0 1 2 3 4

VGS [V]

IDS

[A]

0.0E+00

5.0E-06

1.0E-05

1.5E-05

2.0E-05

2.5E-05

3.0E-05

3.5E-05

4.0E-05

4.5E-05

5.0E-05

0 0.5 1 1.5 2 2.5 3

VDS [V]

IDS [A]

VGS1

VGS2=VGS1+0.1

VGS3=VGS2+0.1

6



Regions of OperationStrong inversion

VGS> VTH

Weak inversionVGS < VTH

Triode regionVDS < VGS -VTH

SaturationVDS > VGS -VTH

CTatmVq

kTVt

eeL

WII VtVnVtVSODS

DSGS

0

//

278.25

1

DSDS

THGSoxDS VVVVL

WCI

2

22 THGS

oxDS VV

LWCI

7



• For Designing Amplifiers, MOSFET Operating in Saturation Region is preferred [IDS depends on Input!].

• To achieve -100dB THD Vin < (VGS- VTH)*40V.

• The small signal model that we show is valid for MOSFET in Saturation Region and for Vin<< VDSAT.

THGSDSDSTHGSn

DS

THGSDSDSTHGSnDS

VVVifVVVL

WKI

VVVifVVDSVVL

WKI

)1(2

22

D

S

GTriode Region:

Saturation Region:

2m1X

2

mXConst.

2

22 inn

inTHDCnTHDCn

DS VL

WKVVVL

WKVVL

WKI

D

S

GVin

VDC

VGS=VDC+Vin

8



• This signal model is sufficient for first-cut hand calculations.

22 THDC

nDS VV

LWKI

VDS = VDD – IDS*R

D

S

G

VDC

R

VDD

VDC + vin

VDS = VDD – IDS*R – Iin*R inDC Vgm

inTHDCn

I

THDCn

inDS VVVL

WKVVL

WKiI*

2

2

R

g m*V

in

vout= - gm*vin*RG

S

D

vin

RgvvAC m

in

outGain *

OXGSDSDS

DSds WLCc

IIVr

32&1

CGS rds

Eff

9



Intrinsic Gain

rDs

g m*V

in

vout= - gm*vin*rDS

G

S

D

vin

LWV

Lwhere

V

Ig

I

VVL

WKrgGain

DSAT

DSAT

DS

m

DS

THGSn

DSm

&1)(

1

*

D

S

G

• To Increase Gain reduce VDSAT or increase length of MOSFET.

10



Intrinsic Bandwidth

CGSrDs

g m*V

in

G

S

D

vin

Iin

Iout

223

***

LV

Cg

gCvgIoutCvI

requirednotisMOSFETIIWhen

DSAT

GS

mT

mGST

inmGSinin

outin

Gain-Speed Product = LL

223

• To Increase Bandwidth increase VDSAT or decrease the length of MOSFET.

11


1. Small Signal Model of MOSFET.Gain

0

100

200

300

400

500

600

700

800

900

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

VDSAT[V]

Gai

n

Bandwidth

0.00E+00

2.00E+10

4.00E+10

6.00E+10

8.00E+10

1.00E+111.20E+11

1.40E+11

1.60E+11

1.80E+11

2.00E+11

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

VDSAT[V]

Ban

dwid

th (r

ad/s

ec)

Gain-Bandwidth Product

0.00E+00

1.00E+12

2.00E+12

3.00E+12

4.00E+12

5.00E+12

6.00E+12

7.00E+12

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

VDSAT[V]

GB

W (r

ad/s

ec)

L=0.5um

L=1.0um

L=1.5um L=0.5um

L=1.0um

L=1.5um

L=0.5um

L=1.0um

L=1.5um

12



211 ||* DSDSm rrgGain

Example 1:VDD

VinVDC

VOUT

M1

M2 g m2*

0

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

2.2 2.3 2.4 2.5 2.6 2.7 2.8

VDC[V]

G

rDS1

g m1*

Vin

S

vin

rDS2

AC Gain vs. DC Gain

0

5

10

15

20

25

30

35

-0.3 -0.2 -0.1 0 0.1 0.2 0.3

Vin [V]

Gai

nDC Gain

AC Gain

13


2. Current Mirrors.

Not Again. It doesn’t make any sense.

These are the Basic Building Blocks of Analog IC design.

VDD

10uAVOUT

M2M1

10uA

0uA0V

10uA1V

0uA

Let (W/L)1=(W/L)2 VT=0.8V, gDS=0

VOUT = 0.0V IDS2 = 0VOUT = 0.1V IDS2 = 7.5uAVOUT = 0.2V IDS2 = 10uAVOUT = 1.0V IDS2 = 10uA

Let (W/L)2=2*(W/L)1

VOUT = 1.0V IDS2 = 20uA

VOUT = 0.0V IDS2 = 0VOUT = 0.1V IDS2 = 6.75uAVOUT = 0.2V IDS2 = 9uAVOUT = 1.0V IDS2 = 9uA

M2

VDD

10uAVOUT

M1

gDS1=1e-6 S & gDS2=0;

1uA

9uA

1V

If gDS1 = gDS2 =1e-6;

IOUT=10uA VOUT= ???

VOUT=2V IOUT=???

14


2. Current Mirrors.

Small Signal AnalysisVDD

10uAVOUT

M2M1

rIN rOUT

g m2*

Vin

g m1*

Vin

G

rDS1

S

vin rDS2rIN

VOUT

rOUT

111 mDSmIN gggg

= 0

2DSOUT gg

Due to CGS we have a Pole Hereg m

2*V

in

g m1*

Vin

G

rDS1

S

vin rDS2

VOUT

CGS1 CGS2

221

1 T

GSGS

m

CCgPole

15


2. Current Mirrors.

Better Current Mirror Large Output resistance.VDD

VOUT

M1

M2

M3

M4

V1

V2

V1

1. M1 – M3 is the Current Mirror.

2. M4 – M2 helps in achieving high resistance.

3. Requires high turn on voltage. VOUT > V1+VDSAT2

122 .. DSDSmOUT rrgr

V1=VGS3

V2=VGS3 + VGS4

VDD

1. M1 – M3 is the Current Mirror.

2. M4 – M2 helps in achieving high resistance.

3. VOUT > V3 + VDSAT2 > 2*VDSAT

122 .. DSDSmOUT rrgr

VOUT

M1

M2

M3

M4M5

I1 I1

V1

V2

V3 V3

V1=VGS3

V2=VGS5

V3=V2 – VGS4 > VDSAT

16


2. Current Mirrors.

Wide Swing Current Mirror.There are Two Questions that we should answer.

1) How should we generate V2.

2) We know V3 = VDSAT, what is the exact value of ‘’.

VDD

VOUT

M1

M2

M3

M4M5

I1 I1

V1

V2

V3 V3

0.00E+00

1.00E+07

2.00E+07

3.00E+07

4.00E+07

5.00E+07

6.00E+07

0 0.5 1 1.5 2

Alpha

Resi

stan

ce (o

hms)

= 1.5 is fine

If M1 – M4 are of same size, for = 1.25, (W/L)5 = 1/5 (W/L).

1/5 (W/L)

W/L

W/L

W/L

W/L

W/L

17


2. Current Mirrors.

Example 2:

VDC

R

VDD

Vin

VOUT

RgGain m *Replace the R with MOSFET and Build an

1) Amplifier with Gain = 50

2) Amplifier with Gain of 3 (Kn=3*Kp).

VDD

Vin

VOUT

M1

M2M3

21

1

DSDS

m

gggGain

1) If gm=100*gDS Gain = 50.

2) Gain varies with Process.

VDD

Vin

VOUT

M1

M2

2

1

m

m

ggGain

1) If (W/L)2=(W/L)1 Gain = 3.

2) Gain varies with Process.

18


2. Current Mirrors.

Example 3:VDD

M2 (W/L)=2

M3 (W/L)=1

M4 (W/L)=1

10uA

20uA

150uA

M1 (W/L)=???

VGS4 + VGS3 = VGS2 + VGS1

(W/L)1 = 15.

The above loop formed by Gate-Source voltages is known as Trans-linear loop.

VDD

M2 2*(W/L)

M1 (W/L)

(a) (b)

MB1 (W/L)

MB1 (W/L)

VOUT = ?10uA

VOUT will near to VDD

M2 in Triode region

M1 in Saturation Region

19


3. Gain Bandwidth Product of an Op-amp.

1st order Low Pass FilterR

C

VIN VOUT

RCtINOUT

ININ

INOUT

eVtV

thenInputstepDCs

VVIf

sVsRC

sV

/1)(

,

)(1

1)(

-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

1 10 100 1000 10000 100000

freq

mag(VOUT)

Phase (VOUT)

0

0.2

0.4

0.6

0.8

1

1.2

3.00E-03 3.20E-03 3.40E-03 3.60E-03 3.80E-03 4.00E-03

time(sec)

[vol

ts]

VIN

VOUT

sec/1ln1)(

)()(

radTs

BW

VTsVV

OUT

OUTOUT

20



Op-amp in Feed-back.

+ -VIN VOUT

GBWAs

A0

0

1

)()(

11

)(

)(

11

11)(

)(

0

2

..

10

0

00

0

GBWAifVtV

eA

AVtV

thens

VsVIf

AFor

GBWsA

AsVsV

INOUT

Source

GBWt

Source

INOUT

ININ

IN

OUT

sec/1ln1 radTs

GBW

Amplifier GBW required to settle in the given time (Ts) and with in given error ().

21



Example 4:

+ -VIN VOUT

GBWAs

A0

0

1

Design a Amplifier with Gain of 4, operating at 100MHz and it should settle with 10-bit accuracy for a full-scale output of 1V.

99975.0

9995.02111

1

21

11..

0

0

2

1

SourceSource

eA

ASource

GBWt

Source

sec510025.04 nTsMHzfGain CLK

GHzGBWdBKA

184160

22


4. Stability of an Op-amp.

• We use simple design technique to deal with stability issues.

• This approach is sufficient to deal with most of the circuits and systems.

VIN = 1V

VOUT

I Designed an Oscillator.

Phase Margin is not enough.

Poles are not in the right location.

Lets Change some W/L’s and see.

23


4. Stability of an Op-amp.Two-Stage Amplifier

VN VP

VDD

M1 M2

M3 M4

M5

I1 I2

VOUT

CC

CL

Poles

g mi. v I

N

g dsi

sC1

g mo.

v1

g dso

sCL

v1sCC VOUTvIN

55

514221

;;;

DSdsommo

GSDSDSdsimmmi

ggggCCgggggg

)(.)(

)()(

)()()(.)(

)()(

112

112

1

CCCCCCsCgsggsCgg

sVsV

CCCCCCsCgCCgCCgsggsCgg

sVsV

CLCLCmodsidso

Cmomi

IN

OUT

CLCLCmoCdsoLCdsidsidso

Cmomi

IN

OUT

V V*gm5

VOUTVOUT=0

24


4. Stability of an Op-amp.Two-Stage Amplifier

C

mo

CLL

mo

C

mi

dsodsi

momi

IN

OUT

momi

CLCL

mi

C

mo

C

dsodsi

CLCL

dsodsi

Cmo

mo

C

dsodsi

momi

IN

OUT

Cgz

CCCCCgf

Cgf

ggggAWhere

ffAs

fAs

zsA

sVsV

ggCCCCCCAs

gCAs

gCsA

ggCCCCCCs

ggCgs

gCs

gggg

sVsV

111

210

21

02

1

0

10

11020

0

112

&/

,,1

1

)()(

)(1

1

1

1

)()(

VIN

VOUT

21

02

1

0

10

1

1

ffAs

fAs

zsA

VP

VN

Op-amp in Feedback should be stable.

25


4. Stability of an Op-amp.Two-Stage Amplifier- Condition for Maximally flat response.

VIN

VOUT

21

02

1

0

10

1

1

ffAs

fAs

zsA

VP

VN

21

2

1

0

0

21

02

1

0

0

01

..1

11)(

)(

1

1&:1

ffs

fsA

AsVsV

ffAs

fAs

AA

AFrequencyHighVeryatisZAssumeCase

IN

OUT

Equate it to 2nd order Butterworth equation.

C

mi

C

mi

L

mo

nn

nn

CgBandwidthand

Cg

Cg

ffffwfw

ws

ws

ffs

fs

.2.2

.2.11;

.12

21

1

..1

1

1221

2

1

2

21

2

1

CLL

mi

C

mo CCCg

Cg

fz

*55

*5 21

To satisfy Assumption, We use the following rule of thumb.

26


4. Stability of an Op-amp.

Example 5:

VIN

VOUT

21

02

1

0

0

1ffAs

fAs

A

VP

VN

Design a Amplifier with Gain of 2, operating at 1MHz and when 1V input is applied output should settle with in 2V ± 2mV. [A0=1e7]

sec/663.27**2

sec/663.2731

1ln1

sec5.01,5.02

12

1

radefCgf

radeeTsC

gf

TsMHzfGain

L

mo

C

mi

CLK

0.0

0.5

1.0

1.5

2.0

2.5

0.0E+00 1.0E-07 2.0E-07 3.0E-07 4.0E-07 5.0E-07

Time [sec]

Out

[V]

-6.0E-03

-5.0E-03

-4.0E-03

-3.0E-03

-2.0E-03

-1.0E-03

0.0E+00

1.80 1.90 2.00 2.10 2.20 2.30 2.40 2.50

Mx [f2=Mx*beta*f1)

Erro

r[V]

27


5. Slewrate of an Op-amp.

VIN = 2V

VOUT = 2V

VDD = 5V

M1 M2

M3 M4

M5

I1 I2

VOUT

CC

CL

2V2V

4V

VIN = 3V

3V2V

3.8

3V3V

4V

2V

3V

VOUT = 3V

Linear system

Slew-rate limited

1V

2V

3V

A Slew-rate limited system will cause non-linearity.

28



• Often in switched capacitor circuits, output stage current limitation leads to op-amp slewing.

• In continuous time circuits where we have to drive resistor loads, output stage current limitation leads to non-linearity.

VIN = 2V

1

2

1 2

VOUT

VIN = 2V

Output Stage current limited

Output Stage can supply huge current

29



• Class-AB output stage should be used when driving resistor loads and some switched capacitor circuits.

• Class-AB input stage can be employed to reduce power.

VPVN

VDD = 5V

M1 M2

M3 M4

M11

I1

VOUTCC

CL

I2 I2

M6

M5

CC

M7M8

M9 M10

M12

Two-stage op-amp with class-AB output stage

30



Design Considerations for Slewrate (Switched capacitor Circuits).

.2

&)(

DifffullyforVVgI

GBWSR

CgGBW

CISRSlewrate

DSATDSAT

m

C

m

C

TCLK

TCLK/2

TSettleTSlew

settleslewCLK

CLKCLK TTT

fT

2&1

SRVTthenTTif

swingoutputMaximumVTSR

SWGCLKCLKslew

SWGslew

22

.

1ln1

2)1(

1ln1

GBWT

GBWT

CLK

settle

DSAT

SWG

DSAT

SWG

DSATSWG

VV

VV

getweVGBW

SRngsubstitutiVSR

GBWThus

1ln

1ln11

31



Example 6:1 2

1

2 1

VIN

VOUT

2

1 CL

CS

CF

VDD = 5V

M1 M2

M3 M4

I1

I2 I2

M6M5

M7 M82.5V

Design a Amplifier with Gain of 2 for 10-bit ADC, operating at clock frequency of 1MHz with a Maximum input amplitude of 1V. Assume CF=1pF and CL=1pF.

32



Example 6:

CL

CF

CPCS

vIN

vOUT

gm*v

1

g DS

v1

FSP

FPSLLeff

FSP

F

m

Leff

m

F

F

S

IN

OUT

CCCCCCCC

CCCCWhere

gC

s

gCs

CC

svsv

)(&

1

1

)()(

Leff

F

settle

F

m

Leff

m

ptIN

ININ

CC

TGBWiserrorwithsettletorequiredGBW

CgzGBW

CgpWhere

ezp

CFCSVtVoutthen

sVSvIf

.1ln

.1''

&.

11)()( .

33


5. Slewrate of an Op-amp.Example 6:

MHze

GBWusVe

SRthususT

mVVAssume

pFCpFCmADCbitVVVInpMax

pFCCAssumepFCCGain

CLK

DSAT

FS

SWG

LeffPFS

1365.0*517.0**2

7*3&/2.85.0*483.0

2487.0&1

483.066.612.7

66.6100

;3/11,297.010,21.

6.10,2*22

6

What is this

-1.0E-03-9.0E-04-8.0E-04-7.0E-04-6.0E-04-5.0E-04-4.0E-04-3.0E-04-2.0E-04-1.0E-040.0E+00

0 0.2 0.4 0.6 0.8 1

Vin [V]

Erro

r in

Out

put [

V]

34


5. Slewrate of an Op-amp.Example 6:Op-amp Can’t supply Infinite current.

vIN

CL

CF

CPCS

vOUT

gm*v

1

g DS

v1

MHzGBWusVSRnewThusV

VCCC

CCVV

CLVCFVknowWeat

CPAssume

SWG

INFSL

FSINOUT

14&/953.04.24.02

4.0||

||)0(

0)(,0)(,0

;0

2

-3.0E-04

-2.5E-04

-2.0E-04

-1.5E-04

-1.0E-04

-5.0E-05

0.0E+00

0 0.2 0.4 0.6 0.8 1Vin [V]

35


5. Slewrate of an Op-amp.Example 7:

Below op-amp should be designed for a Slewrate of 6V/us, what should be the input stage tail current if the op-amp is folded cascode op-amp.

‘VIP, VIN’ forms fully differential signals (2VPP) with ‘VCM’ as common mode.

VCM=1V

VIP

VIN

10pF

10pF

1pF

1pF

Parasitic Caps.

Minimum Tail Current = 12uA.

36


6. Offset of an Op-amp.

1. Systematic Offset:

20uA 100uA

VDD = 5V

M1 M2

M3 M4

M5

VOUT

CC

CL

5.3u/1.5u10*15u/1.5u

15u/1.5u

10uA 10uA

2.5V

Case 1: VDSAT and Length of M3-M4 & M5 are same.

Offset=48uV

Case 2: VDSAT of M3-M4 & M5 is same but Length is different

Offset=715uV

10*5u/0.5u40*15u/1.5u

Case 3: Length of M3-M4 & M5 is same but VDSAT is different

Offset=718uV

0.00E+00

1.00E-04

2.00E-04

3.00E-04

4.00E-04

5.00E-04

6.00E-04

7.00E-04

8.00E-04

Case1 Case2 Case3

37



2. Random Offset : Due to Process Variations

100uA

VDD = 5V

M1 M2

M3 M4

M5

VOUT

CC

M6 M7

V4

V2

V5

V7

20uA

Process steps like Photolithography, Etching and Deposition are not uniform.

Values of V1,V2, V3 depends on the sigma of the process. Normally they will be in the order of ‘mV’.

Proper layout [Common-Centroid Layout, proximity matching] techniques can reduce the mismatch, thus Offset.

Can a designer play a role in reducing the over-all Offset.

38




V5=(gm7*V7/gm5)

V7

100uA + gm7*V7

VDD = 5V

M1 M2

M3 M4

M5

VOUT

CC

M6 M7

20uA

VIN

Input Referred Offset Due to: VB2 & V5

100uA

VIN + V5/A1

5

775

1

*1

m

m

gg

VVA

OffsetreffredInput

39



2. Random Offset : Due to Process VariationsInput Referred Offset Due to: V2 & V4

2

442 *

m

m

ggVVOffsetreffredInput

VDD = 5V

M1 M2

M3 M4

M5

VOUT

CC

M6 M7

V4

20uA

VIN

10uA + gm4*V4

VIN+(gm4/gm2)*V4

40




2

442

75

75

12

442

*

1*

m

m

mm

m

ggVVOffsetreffredInputTotal

VggV

AggVVOffsetreffredInputTotal

Design M1-M2 (Differential Pair) and M3-M4 (Current Mirror) Carefully.

• Decrease gm4 (For given ‘I’ Increase VDSAT for Current Mirrors).

• Increase gm2 (For given ‘I’ Decrease VDSAT for Differential pair).

To reduce V2 and V4, use Large devices (Large L and Large W). Mismatch is inversely proportional to the Area of the MOSFET.

)(mVBWLAVX

41


7. Noise of an Op-amp.

Types of “Noise”• Interference

– Cross talk, Clock Coupling…– Supply Noise.Taken Care by proper design (Shielding,

Differential circuits, etc…)

• Device Noise– Thermal Noise (Fundamental).– Process related (1/f noise).

42



Thermal Noise:• Dissipative elements (resistors, MOSFET’s, …)• Random fluctuations of v(t) of i(t).• White noise with zero mean.

Resistor MOS Noise (Strong inversion)

*

R

22 4 VfkTRvn

2nv

2ni

22

22

3838

AfkTgi

AfgggkTi

mn

mbdsmn

43



kT/C Noise (Resistor):

rms

out

nout

n

VCkT

CkTRCRC

CRkTVout

f

RCf

RCkTRffVVout

RCkTRfv

sRCfV

HzVkTRv

222tan.2

21

124)(

114)(

11)(

/4

0

12

2

02

22

2

0

2

22

22

22

R

*

R2

nv

C C

2outv

100n

F

1K 100K

Case 1: Case 2:

1.0E-14

1.0E-13

1.0E-12

1.0E-11

1.0E-10

1.0E-09

1.0E-08

1.0E-07

1.0E-06

1.0E-03 1.0E-01 1.0E+01 1.0E+03 1.0E+05 1.0E+07

Freq [Hz]

Noi

se D

esni

sty

[V-s

qrt(

Hz)

]

100n

F

1K

100KTotal Noise=200nV

44



kT/C Noise (Op-amp):VDD = 5V

M1M2

M3 M4

M5

VOUT

CC

MB1 MB2

VPVN in1

2 in22

in42in3

2

Noise Analysis is Similar to offset Analysis

We can neglect the noise due to M5 & MBX.

Assume gm1=gm2 & gm3=gm4

Calculating the input referred noise.

HzVgg

gmkTv

g

kTg

g

kTg

g

kTg

g

kTgv

HzVkTgi

m

mn

m

m

m

m

m

m

m

m

n

mn

/113

16

38

38

38

38

/38

2

1

32

22

4

22

3

22

1

22

22

22

vn2

45



kT/C Noise (Op-amp):

vn2

A(s) Vout

1

32

1

1

3

12

0

22

2

1

1

3

12

22

2

1341

4

13

161)(

1

13

161

)(1)()(

m

m

C

m

C

m

m

m

m

C

m

m

mn

gg

CkTVout

gC

gg

gkT

ffVoutVout

gC

gg

gkT

vsA

sAfVout

1

0

0

1)(

m

C

gCAs

AsA

For =1, CC=10pF and gm1=gm3=80uS

Noise at the output VoutRMS=32uV.

1/f - noise is suppressed by assigning kf=0

1.0E-11

1.0E-10

1.0E-09

1.0E-08

1.0E-07

1.0E-06

1.0E-05

1.0E-04

10 100 1000 10000 100000 1000000 1E+07 1E+08 1E+09

freq [Hz]

Out

put N

oise

Des

nity

[V/s

qrt(H

z)]

Output Noise

Total Noise=40uV

Caution: RHS Zero is neglect for calculations, for a poor design it will increase the total output - noise drastically.

46



1/f Noise (‘Fake’ Noise):

• Caused by traps in semiconductor material– Due to contamination or crystal defects

• Has a 1/f power spectral density

• Figure of Merit is called ‘Kf’ and Kf=A/ToxB.• Kf is process dependent.• For TOX>900A, NMOS(Kf) > PMOS(Kf). So PMOS is less

noisy.

2fi

lo

hi

OX

Dff

f OX

DffTOTAL

OX

Dff

ff

CI

LK

ff

CI

LK

i

ff

CI

LK

i

hi

lo

ln222

22

47



1/f Noise (‘Fake’ Noise):

1.0E-11

1.0E-10

1.0E-09

1.0E-08

1.0E-07

0.01 0.1 1 10 100 1000 10000

freq (Hz)

Nois

e De

ssity

[A/s

qrt(H

z)]

1V

1V

W/L

W/L=35u/1u

W/L=70u/2u

W/L=140u/1u

Kf=1.36e-27, IDS=500uA

flo=1Hz, fhi=1MHz, Tox=1250A

W/L=140u/1u

nArmsiff

CI

LK

i fTOTALlo

hi

OX

DffTOTAL 65ln2

2

IRMS=40nA

48


CONCLUSION

• I hope the topics covered would be useful as a starting point and help you to extend the concepts to system level issues.

• I express my gratitude to following people:– Inventors of Google.– My Professors at IIT Madras.– For Natsem India and RVCE.– For SANYO Japan.

49


About Author

Area of Interest:Analog/Mixed-signal Integrated Circuit Design, with focus on Data converters.

Education:M.Tech, Microelectronics and VLSI Design, IIT Madras, Chennai, 2001.B.Tech, Electronics & Communications, S.V University, Tirupati, 1999.

Work Experience Associated with SANYO LSI, India (Feb ‘01 - April ‘05). Associated with Natsem, India (May ‘05 - Present).

Design Experience:Multi-stage rail-to-rail operational amplifiers, Switched capacitor Circuits.Architectures for 20-bit/24-bit ADC/DAC.

7-things that we should know about op-amp design

Documents

amp designt

amp designnatsem india

avgs vig achart500000000000

our aim is

small signal model of