EE610: CMOS AnalogEE610: CMOS Analog Circuits

EE610: CMOS AnalogEE610: CMOS Analog Circuits

L3: MOS Models-3 (5th Aug. 2013)

B. MazhariDept of EE IIT Kanpur

G-NumberB. Mazhari, IITK76

Dept. of EE, IIT Kanpur

Why does sound quality of my audio system degradeat high volume?g


V V

Distortion

Vin V0

Vin= a0 sin wt

V0= b0 + b1 sin ωt + b2 sin 2ωt + b3 sin 3ωt + ……….

1001

22

bbHD 100

1

33

bb

HD

22 bb100

......

1

32

bbb

THD


Example

20 10 inin VkkVV

V = a sin ωtVin = a0 sin ωt

tka

tkaka

V 2cos20

sin20

20

0

20

0 2020

20 5100

20/kaHDTHD 0

0

02 5100 a

kaHDTHD


How do we measure the speed of a transistor?


Unity Gain Frequency

VDD

ig=igoSin(t)

VSS

1gain current at which Frequency dii


0;0 dsvsbvgi

C Cgd

Gig

id

D

Cgd

Gids

Cgsgmbvbs

D

CgsCgb

S

gmvgs

dgmvgs

Cdb

roCgs

Cgb CsbS

S

B

ggbgdgsg vCCCji )( d m gsi g v

( )d mg gs gd gb

i gi j C C C

1

( )mg

C C C

mg 1 ( )m Ngf V V

( )g gs gd gbi j C C C ( )T gs gd gbC C C


gbgdgs

mT CCC

2 ( )2 2

m NT GSQ THN

gs

gf V VC L

Example

58.1 10 ; 4.1 ; 0.43m gs gdg C fF C fF g g

1 2.82

mT

d b

gf GHzC C C

2 gs gd gbC C C


How small a voltage can this amplifier amplify ?

10k ohms

1

100 ohms

Vin1 Vo

in


Noise Model

Noise analysis of circuits is commonly carried out in analog circuits.

Each resistor and diode and transistor is a source of noise.

To do the analysis, we need noise models for these elements.

Si i lt d t ll i it d th iSince noise voltages and currents are small in magnitude, theirinfluence on the circuit can be obtained through small signal analysisof the circuit. As a result, the noise voltages and currents can be addedof the circuit. As a result, the noise voltages and currents can be addedto the small signal mode described earlier.

There are several different kinds of noise sources that can be found insemiconductor devices. Perhaps the most important is the ThermalNoise


Noise

10k ohms 10k ohms

Example

1100 ohms

100 ohms

12

Vo1 Vo2

21 Trmse e dt

T

0T

Rms noise due to sum of two uncorrelated noise sources e1 and e2 will be

2 2 21 2 1 2 1 2

0 0 0 0

1 1 1 1( )T T T T

rmse e e dt e dt e dt e e dtT T T T

0 0 0 0T T T T

2 2 2 21 1T Te e dt e dt e e


1 2 1 20 0

rms rms rmse e dt e dt e eT T

Thermal noise results from random motion of charge carriers within aconductor or a semiconductor as result of presence of scattering centerswithin the element.

II


Any resistor can be modeled as a noise free resistor in series with a rmsnoise voltage source as shown below:

R eNR

fkTRen .4~

f is the bandwidth over which noise is measured. The thermal noiseitself has a uniform spectral density and is called white noise.

For 1 , 1 , 100nR M f MHz e V


The thermal noise can also be represented as resistor in parallel with anoise current source:

R RR

iN.)4(~ fRkTin

N

Example: Noise AnalysisExample: Noise AnalysisR

vO

RvIN

The output voltage will have a componentdue to applied input voltage and a componentdue to noise generated by the resistors


due to noise generated by the resistors.

Ren1

vO

RvIN

e0.5o in onv v v

en2

Th i t ib ti d t h i t b f dThe noise contributions due to each resistor can be foundseparately and then added up in rms manner afterwards to

bt iG-NumberB. Mazhari, IITK

90

obtain von.

RvON1

RvON2

ReN1

21

1N

ONeV R 2

22

NON

eV

eN2

22 22

21)( ONON VVrmsvoltagenoiseTotal

osfkTRvoltagenoiserms .2

For R = 1M and Oscilloscope bandwidth of 50MHz , rms noisevoltage = 0 64mV


voltage = 0.64mV.

Besides thermal noise, there is another kind of noise called Shot Noisethat is commonly found in semiconductor devices. This noise occurswhenever carriers have to cross a potential barrier

How many holes cross the

x potential barrier?

p


Shot Noise occurs whenever carriers have to cross a potential barrierlik i PN j ti di d Bi l J ti T i tlike in PN junction diodes or Bipolar Junction Transistors

The noise results from the fact that the number of carriers that are ableThe noise results from the fact that the number of carriers that are ableto cross the barrier are random in nature. This results in fluctuation incurrent which can be expressed asp

- + +-

Noiseless diode

-

-

- +

+

+

+

+

+-

-

-

2 2ni qI f

- + +-

V(x)

in

n

AMHzfcurrentmAforin

1811~ x


nA18

ICE B C

C

2nc Ci qI f

10kiC

1 1 18nc Ci for I mA f MHz nA

180on nc Cv i R V

I; CV m C m

IA g R gkT q

k i ll ld likG-NumberB. Mazhari, IITK

94

To keep noise small, we would like tokeep RC and IC small but it reduces gain !

There is another noise component called Flicker Noise which resultsfrom random variations in carrier density caused by charge trapping andde-trapping. It can be expressed as:

FAFf Iki2

1 f If

i .1

Because the spectral density of this noise goes as ~1/f, it is also called1/f noise

2~ne

fen

1~2

Hznv (Pink noise)

20

fn

White noise

G-NumberB. Mazhari, IITK95ff0 = 30Hz

White noise

Since noise voltages and currents are small, they can be represented aspart of small signal model as shown below

ids

g v r

G D

iithgmbvbs

gmvgs ro i1/f

S

B

The capacitances are not shown for simplicity.


p p y

NOISE MODEL OF A MOSFET

The noise in a MOSFET comes from thermal noise due to channelresistance and flicker noise due carrier trapping at the oxide interface.

Thermal Noise:

fgkTi mther 32.4~

Flicker Noise:2

kF m

flik gi

Flicker Noise: kerflic AFox eff eff

if C W L

1A 25 210k V F1FA 25 210 .Fk V F


The shot noise due to gate leakage or diode leakage currents is relativelysmall and so is neglected.

V 3 3V

RD i

VDD= 3.3VRD = 100K

Noise analysisD iRd

i i

vogmvgs

VG= 1.2V

2/1 VO+vo

vgsro

ith iflickervin

thon th Dv i R ker

kerflic

on fic Dv i R Rdon Rd Dv i R

2ker22 flicRdth G-NumberB. Mazhari, IITK

98

kerflicon

Rdon

thonon vvvv

V = 3 3V

Amplifier Analysis

V 3 3V

VDD= 3.3VRD = 100K

VOVDD= 3.3V

RD = 100K VG= 1.2V2/1

VG= 1.2V

2/1 VO+vo dc

vin

RD

vo

vSmall-signal

ro

vin

vgs

gmvgs


You mean I can operate a MOSFET like a BJT???


SubthresholdThe Subthreshold region refers to a region of device operation g g pwhere GS THNV V in NMOS

kTDSVqkTNTHNVGSVq

effW )(

/kTVF kTNqVGS

I kTDSVqkTNeff

effDOD ee

LW

II 1. ,/ qkTVFor DS kTND eI

The subthreshold region is NkTdVS G 32G-NumberB. Mazhari, IITK

101

e subt es o d eg o scharacterized by subthreshold slopedefined as

NqId

SD

G 3.2log10

The transconductance of a MOS is related to subthreshold slope:p

113.2

DSDSm I

SIVTNgkTN

qV

D

GS

eI DSDS II

I bth h ld i MOS t lik BJT

D

In subthreshold region, MOS acts like a BJT

V V: BE TV VC SCBJT I I e

TGS VVSDS eIIMOS :

The advantage of MOS is that it offers almost infinite input


The advantage of MOS is that it offers almost infinite inputimpedance. Its disadvantage is that current levels are low.

Do I need to memorize model equations for both NMOSqas well as PMOS Transistors?


PMOS

GD

G

BSiO2 S

Poly

++ +

DB S

P+N+ P+

N-Silicon


Pmos made in an N-well

SiOPoly Poly

SiO2

N+ N+P+ P+ P+N+

P Silicon P Silicon

N-well

P-Silicon P-Silicon

pmos and nmos made side-by-side


Differences with respect to NMOS

-ved

IDSPoly

gnd-ve

DS

P+ P+N+ +++++++

N-Silicon

VGS is negative ; Threshold voltage VTP is negative


VDS is negative ; IDS is negative

D D -

+

G G

+

-

++

SS

+- -

S ++

G -

SDPDSN II

D-

SGPGSN VV SDPDSN VV


SDPDSN

Transformations

VV VV VV SGPGSN VV SDPDSN VV SBPBSN VV

THPTHN VV SDPDSN II

]1[)( 2N VVVI ]1[)(2

2

2

P

DSnTHNGSN

DS VVVI

]1[)(2

2SDpTHPSG

PSD VVVI


Why is small signal model of PMOS identical to that ofNMOS?NMOS?

Cgd

DGidsgmbvbs

gmvgs

Cdb

ro

S

Cgs

C b

gmbvbs

B

CsbSCgb


B

]1[)( 2DSTHNGS

NDS VVVI

]1[)(

]1[)(2

2P

DSnTHNGSDS

VVVI

VVVI

]1[)(2

2SDpTHPSG

PSD VVVI

sdsd m sg mb sb

vi g v g v sd m sg mb sbo

i g v g vr

same as NMOSdsds m gs mb bs

vi g v g vr

or


Small Signal Model

Cgd

DG

gmvgs ro

DGids

Cgsgmbvbs

gmvgs

Cdb

ro

SCgb CsbSgb

B

THPSGQ

SDQm VV

Ig

2SDQp

o Ir

1


THPSGQ VV SDQp

We have so far discussed simple MOS models which are suitable for ‘hand-analysis’ of circuits. For more accurate prediction of circuit characteristics using circuit simulation more accurate MOS models are requiredrequired.

SPICE and its various variants are the most popular circuit simulation p ptool. In SPICE, there are a number of MOS models that are available including Level-1, level-2, Level-3, BSIM1, BSIM2, BSIM3, BSIM4 etc.

Level 1 model is the simplest and is basically similar to the large signalLevel-1 model is the simplest and is basically similar to the large signal model that we have described earlier. A popular model for submicron devices is BSIM3 model.


BSIM3 : Berkeley Short Channel IGFET (Insulated gate Field Effect) Model


99!



Comparison

VDS = 3.3V

KP 100 A/V2


KPN=100 A/V2

400.0u

500.0u

KP = 85uA/V^2 VGS = 3.2

300.0u

400.0uLevel-1

200.0u

BSIM3

VGS = 2.2

100.0uBSIM3

VGS = 1.2

0.00 0.60 1.20 1.80 2.40 3.000.0u

ID(M3) (A)V(V2)

ID(M1) (A)VGS=3.3Volts


( )

We can make the fit better for 3.3V but then the fit for lower voltageswould not be good.

375.0uKP = 65 uA/V^2

Level-1

300.0u BSIM3

150 0u

225.0uLevel-1

75.0u

150.0uBSIM3

0.00 0.60 1.20 1.80 2.40 3.000.0u

ID(M3) (A) ID(M1) (A) VGS=3.3VoltsID(M3) (A)V(V2)

ID(M1) (A)


A good fit for all voltages is not possible because the equations in thetwo models are different!

VDS = 3.3V

KP 75 A/V2


KPN=75 A/V2

Output Resistance

VGS = 1.2V


λN=0.015 V-1

V = 1 8VVGS = 1.8V

Output Resistance is not constant in saturation but increases with drain


Output Resistance is not constant in saturation but increases with drain-source voltage


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EE610: CMOS AnalogEE610: CMOS Analog Circuits