ch11b_noiseinmosfet

7/24/2019 ch11b_NoiseInMOSFET

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Sam Palermo

Analog & Mixed-Signal Center

Texas A&M University

ECEN474: (Analog) VLSI Circuit DesignFall 2012

Lecture 12: Noise


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Announcements

HW3 due Wednesday Oct 24 Todays office hours are from 4-5:30

Reading Razavi Chapter 7

2


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Agenda

Noise Types Noise Properties

Resistor Noise Model

Diode Noise Model

MOSFET Noise

Filtered Noise

OTA Noise Example

3


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Noise Significance

Why is noise important? Sets minimum signal level for a given performance

parameter

Directly trades with power dissipation and bandwidth

Reduced supply voltages in modern technologiesdegrades noise performance

4

( )2

2/

=

noise

noisesigV

VddPPVdd

SNRPowerSignal

Noise is often proportional to kT/C Increasing capacitance to improve noise performance

has a cost in increase power consumption for a givenbandwidth


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Interference Noise

Interference Man-Made Noise Deterministic signal, i.e. not truly random

Could potentially be modeled and predicted, but practically this may behard to do

Examples

Power supply noise Electromagnetic interference (EMI)

Substrate coupling

Solutions

Fully differential circuits

Layout techniques

Not the focus of this lecture

Unless the deterministic noise is approximated as a random process

5


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Inherent Noise

Electronic or Device Noise Random signal

Fundamental property of the circuits

Examples

Thermal noise caused by thermally-excited random motion of carriers

Flicker (1/f) noise caused by material defects

Shot noise caused by pulses of current from individual carriers insemiconductor junctions

Solutions

Proper circuit topology

More power!!!

Is the focus of this lecture

6


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Noise Properties

Noise is random

Instantaneous noise value is unpredictable and thenoise must be treated statistically

Can only predict the average noise power Model with a Gaussian amplitude distribution

Important properties: mean (average), variance,power spectral density (noise frequency spectrum)

7

[Johns]


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RMS Value

If we assume that the noise has zero mean(generally valid)

RMS or sigma value is the square-root of thenoise variance over a suitable averaging time

interval, T

8

( ) ( )21

0

21

T

nrmsn dttvT

V

Indicates the normalized noise power, i.e. if

vn(t) is applied to a 1resistor the averagepower would be

( )( )2

2

1 rmsn

rmsn

n VV

P =

=


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Signal-to-Noise Ratio (SNR)

Quantified in units of dB

9

powernoise

powersignallog10SNR

( )

( )

( )

( )

( )

=

rmsn

rmsx

rmsn

rmsx

V

V

V

VSNR log20log10

2

2

2

rmsx

VofpowernormalizedwithsignalaFor


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Thermal Noise Spectrum

The power spectral density (PSD) quantifies howmuch power a signal carries at a given frequency

Thermal noise has a uniform or white PSD

10

The total average noise power Pnin a particularfrequency band is found by integrating the PSD

( )=2

1

f

f

n dffPSDP

( ) fnffnPn

== 0120

:spectrumnoisewhiteFor


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Thermal Noise of a Resistor

The noise PSD of a resistor is

11

( )

(K)etemperaturabsolutetheisTandconstantBoltzmanntheiskwhere

kTnfPSD 40==

The total average power of a resistor in agiven frequency band is

( ) fkTffkTkTdfPf

f

n === 444 122

1

Example: f=1Hz Pn=4x10-21W=-174dBm


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Resistor Noise Model

An equivalent voltage or current generatorcan model the resistor thermal noise

12

fkTRRPV nRn == 42 f

R

kT

R

PI nRn ==

42

Recall the PSD is white (uniform w/frequency)

[Johns]


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Noise Summation

13

( ) ( ) ( )

( ) ( ) ( )[ ]

( ) ( ) ( ) ( ) ( )

++=

+=

+=

T

nnrmsnrmsnrmsno

T

nnrmsno

nnno

dttvtvT

VVV

dttvtvT

V

tvtvtv

0

21

2

2

2

1

2

0

2

21

2

21

2

1

Same procedure applies to noise current

summing at a node


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Correlation

Last term describes the correlationbetween the two signals, defined by thecorrelation coefficient, C

14

( ) ( )

( ) ( )

( ) ( ) ( ) ( ) ( )rmsnrmsnrmsnrmsnrmsno

rmsnrmsn

T

nn

VCVVVV

VV

dttvtvTC

21

2

2

2

1

2

21

0

21

2

1

++=

=

Correlation always satisfies -1C1 C=+1, fully-correlated in-phase (0)

C=-1, fully-correlated out-of-phase (180)

C=0, uncorrelated (90)


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Uncorrelated Signals

For two uncorrelated signals, the mean-squared sum is given by

15

( ) ( ) ( )

anglesrightatvectorsweretheythoughasAdd

2

2

2

1

2

rmsnrmsnrmsno VVV +=

For two fully correlated signals, the mean-squared sum is given by

( ) ( ) ( )( )

vectors)(alignedlinearlyaddvaluesRMS

iprelationshphasebydeterminedisSign

2

21

2

rmsnrmsnrmsno VVV =


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Noise Example #1: Two Series Resistors

The noise of the two resistors is uncorrelated orstatistically independent, so C=0

16

( ) ( ) ( ) ( ) ( )rmsnrmsnrmsnrmsnrmsn vCvvvv 2122

21

2 2++=

( ) ( ) ( ) ( ) fRRkTvvv rmsnrmsnrmsn +=+= 212

2

2

1

2

4

Always add independent noise sources usingmean squared values

Never add RMS values of independent sources


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TAMU-ELEN-474 2009 Jose Silva-Martinez

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Lets compute the output voltage: Apply superposition (noise sourcesare small signals, you can use small signal models)!

2n1nin0 v2R1R

1Rv

2R1R

2Rv

2R1R

2Rv

+

+

+

+

+

=

But noise is a random variable, power noise density has to be used rather than voltage; then

the output referred noise density (noise in a bandwidth of 1 Hz) becomes

2kTR42R1R

1R1kTR4

2R1R

2Rv

v2R1R

1Rv

2R1R

2Rv

22

2

n0

2

2n

2

2

1n

2

2

n0

+

+

+

=

+

+

+

=

+

vin-

vn1

vn2

R1

R2

v0

Noise Example #2: Voltage Divider

Above is what you do for deterministic signals,

but we cannot do this for the resistor noise

( ) ( ) ( )fvsHfv xfjsx

xTon

22

2

2

,

==

:CaseGeneral


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Diode Noise Model

Shot noise in diodes is caused by pulses of currentfrom individual carriers in semiconductor junctions

White spectral density

18

Where q=1.6x10-19C and ID

is the diode DC current

[Johns]


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- 19 -

Thermal Noise

=> Spectral Density of the thermal noise drain current (CMOStransistor biased @ linear region)

DS

2d

R

kT4i =

( )DSTGSoxDS

VVVL

WC

1R

Resistor

Transistor

in1

2=4kT/R1

R1

2di

substrate

P+ P+

S G D

N

N+

B

Channel


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- 20 -

[ ] [ ]DSTGSox2

d VVVL

WCkT4i

=

f

White Noise

2di

DSR

kT4

Low current noise => W/L => gmor go

@ Saturationm

DS

o g

3

2

R

1g =

( ) ( )TGSox2d VV

L

WC

3

kT8i

=m2d kTg

3

8i =

@ Triode region


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MOSFET 1/f (Flicker) Noise

Caused by traps near Si/SiO2interface thatrandomly capture and release carriers

21

( )fWLC

gKfi

ox

mFd

22 =

KFis strongly dependent on the technology


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1/f Noise Corner Frequency

This is the frequency atwhich the flicker noisedensity equals the

thermal noise density

22

==

=

W

I

I

g

LCkT

K

WL

g

CkT

Kf

gkTfWLC

gK

D

D

m

ox

Fm

ox

Fco

m

coox

mF

1

44

42

For a given gm/ID(which sets ID/W), theonly way to reduce fcois to use longerchannel devices


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- 23 -

2di

Thermal Noise gsmd Vgi =

2gs

2m

2d Vgi =

Flicker Noise

Output and input referred noise

Current noise is the real one

Referred to the input

m

2gseq

g

kT

3

8V =

Veq2

Voltage noise representation is an

artifact to facilitate system analysis

fWLC

gKi

ox

mFd

22 =

=

=

fWLC

Kv

gfWLC

gKv

ox

Feq

mox

mFeq

11

1

2

2

22


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- 24 -

Equivalent input referred voltage noise

2eqV

2m

2df

2dth2

eqg

iiV

+=

fWLC

K

g

kTV

ox

F

m

eq

11

3

82 +=

( ) =BW

2

eqtotaleq df)f(vRMSV

Equivalent input referrednoise voltage means that all

current noise sources are

accounted as drain

current and represented

by an equivalent noise

voltage at transistor gate


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- 25 -

NOISE COMPONENTS (values provided are for a 0.8 m technology)

M1

veq2

id2

2

f/1

2

th

2

eq vvv +=

dffWLC

Kdf

g

kT

3

8v

OX

F

m

2

eq +=

)PMOS(Hzm/V10x5.0

)NMOS(Hzm/V10x8.9C

K

29

29

OX

F

=

=

FOR LOW-FREQUENCY APPLICATIONS,

WHEREIN 1/F NOISE IS DOMINANT,

PMOS DEVICES MUST BE USED.

Noise density (V2/Hz)

f

Vn2

Thermal

Flicker

Corner frequency

Spice model


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Filtered Noise

Noise output spectral density is a function only of themagnitude of the transfer function, and not its phase

With multiple uncorrelated noise sources, combinedoutput is also uncorrelated

26

( )fvni2 ( ) ( ) ( )

( ) ( ) ( )fvfjAfv

fvfjAfv

nino

nino

2

2 222

=

=

( )fvn2

1

( )fvn2

2

( )fvn2

3

( )fvno2 ( ) ( ) ( )fvfjAfv ni

i

ino

2

3,2,1

22 2=

=

[Johns]

[Johns]


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First-Order RC Circuit Example

27

What is the total output noise power?

[Razavi]


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First-Order RC Circuit Example

28

( ) ( )

( ) ( ) ( )

( )C

kT

C

kTfRC

C

kTv

xx

dx

CRf

kTR

v

kTRCRf

fvfjAfv

sRCs

v

vsA

f

f

out

out

Rout

R

out

=

==

=+

+=

+==

+==

=

=

02

22tan

2

tan1

41

4

441

12

1

1

0

12

1

2

0

2222

2

2222

222

Using

sfrequenciealloverintegratePowerNoiseTotalcalculateTo

[Razavi]


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- 29 -

Noise is generated by R but integrated noise is function of C (??)

( ) ( )

=

+=0

2

24

1

1

C

kTdfkTR

RCvtotal

+

vin

-

vn R

v0

C

Thermal

noise

f

f(log)

f(log)

4kTR

RC2

1

-2

To get more insight, lets have a closer look on the operations!

Notice that:

When R increases thermal noiseincreases too but the corner

frequency decreases, leading to a

constant area under the curves!


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Noise Bandwidth

The noise bandwidth is equal to the frequencyspan of a brickwall filter having the same outputnoise rms value

30

( )C

kT

RC

kTRBv

B

dfvBv

n

pn

non

=

==

=

=

2

1

2

4

2

2

0

0

22

0

OutputNoiseTotal

:derivationslidespreviouswithValidating

filterorder-firstaFor

[Razavi]


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- 31 -

Output referred noise: Take advantage of SYMMETRIES!

id1

IB

M1 M1

0.5id1

ioutVX

M2 M2 Output referred current noise density

Superposition: Every transistor contributes;

consider one at the time.

Analysis: You can use standard circuit analysis

techniques but at the end of the day you have to

consider POWER.

Output noise density: Each noise component

represent the RMS value of random uncorrelated

noise! Then add the power noise components

1m

2

1out kTg38i =

0.5id1

Noise injected into the common-source

node equally splits into the two branches


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- 32 -

Output referred noise: Take advantage of SYMMETRIES!

IB

M1 M1

id2

ioutVX

M2 M2

Output referred current noise density due to the P-

type devices:

Left hand side transistor:

Right hand side transistor

22

22

238 mdout kTgii =

Noise due to the current source is mainly

common-mode noise

id2

Noise injected into the common-source

node equally splits into the two branches

Id~0

22

238 mout kTgi =


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- 33 -

Output and input referred noise

id1

IB

M1 M1

v1

id2

ioutVX

M2 M2

Output referred current noise density

+

= 2m1m2

out kTg3

82kTg

3

82i

Input referred noise density (V2/HZ)

In this case, noise due to the current source is

mainly common-mode noise

Be careful because this is not always the case!

v2

+

=

1m

2m

1m1m

2

eq,ing

g

g

kT

3

82

g

kT

3

82v


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- 34 -

Integrated Input referred noise

id1

IB

M1 M1

v1

id2

ioutVX

M2 M2

=

+

=

BW

2

eq,inRMS

1m

2m

1m1m

2

eq,in

dfV)V(Noise

g

g

g

kT

3

82

g

kT

3

82v

Input referred noise level (volts)

v2

Input referred thermal noise density (V2/Hz)

Example: for thermal noise, the noise level becomes

(assuming a single-pole system)

+= BWg

gg

kTVNoisem

m

m

RMS2

113

16)(1

2

1

4kT16x10-21coul.V( )BWg

g1

g

kT8)V(Noise

1m

2m

1m

RMS +I should advise you to use:


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