Noise in Circuits

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NOISE IN CIRCUITS

MOHAMMAD A MAKTOOMIM.TECH (CSD: 2011-2013)

ELED,AMU


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Noise: Definition & Classification

EXTERNAL noise: Outside Interference- Even between different part of circuit

(Electric & Magnetic interaction throughparasitic capacitor/ inductor)

Everything except the desirable ones !


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Contd

External noise: periodic, intermittent, orrandom

- Present, even if we could manage to remove allexternal noise !

- Always random- due to random phenomena likethermal agitation of electrons in resistors/ randomEHP generation/recombination in semiconductors.

INTERNAL noise: INHERENT NOISE


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It limits minimum signal that can beprocessed/detected

The noise level of a circuit directly tradeswith power dissipation and speed

In most circuits, low noise dictates the useof large capacitors and/or large gm whichmeans high power dissipation

But, Why do we care???


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BASIC CONCEPTS

RMS value:

T is some suitable averaging interval. is mean-square value= average power

dissipated by xn(t) in 1 resistor.

NOISE SUMMATION: if the noise are

uncorrelated then superposition holds forpower -

1/ 2

2

0

1( )

T

n nX x t dt

T

2

nX

2 2 2 2

1 2 1 2

0

1[ ( ) ( )]

T

n n n n nX x t x t dt X X

T


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SPECTRAL DENSITY

Power spectral density (PSD) shows howmuch power signal caries at a particularfrequency.

Expressed as or !

Total (mean) power is, then

2/V Hz /V Hz


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Noise Type: A brief description

THERMAL NOISE

Result of random motion of electrons in

conductor due to thermal effectsWhite spectral density

Proportional to absolute temperature

Also known as Johnson or Nyquist noise


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THERMAL NOISE

r= NO NOISE (just in model) rb= NOISY (parasitic material resistance)

(Pure) Capacitor, Inductor= No thermal Noise

Purely reactive elements do not generate Noise !

NOT associated with resistor symbol !


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SHOT NOISE

Occurs in pn Junction

Result of discrete movement of chargeacross the barrier when current flowsthrough it.

White noise

Thermal noise is independent of biascurrent, Shot noise is not !


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FLICKER NOISE

Least understood noise!

Found in all active devices (occurs onlywhen dc current flows)

Due to carrier traps in semiconductorand released (randomly)

Spectral density proportional to 1/f

,hence the other name- 1/f noise.


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NOISE in Resistor

Thermal noise is major source

PSD: V2/Hz

K= Boltzmann Const T= Temeperature in kelvin

Could be modeled in Norton or Thevenin

form

2( ) 4RV f KTR


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Noise in Resistor

Spectrum is white !

Practically, White only up to 100THz(then drops)


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Input-referred noise

A1 :noiseless As A1increases, outputNoise will also increasewrong conclusion, as itequally amplifies the signal.Hence the notionof input-referrednoise.


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An Example

Evaluate: output noise and input referred

noise over DC to 1KHz

(1)

(2) Vout(f)= =

2

2 4 4( ) 18.26 24

10 1R

KT KT AI f E

K K Hz

1 .1018.26 24( )

1 10

k kE

k k

3.88 9

VE

Hz


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Mean-power:

RMS output noise = 122.67nV Input referred noise= 122.67nV/

=1.35uV

12 2 2

0

( ) (3.88 9 ) .1k

out out

VV V f df E kHz

Hz

1( )1 10

k

k k


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SPICE SIMULATION


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NOISE in DIODES

SHORT noise is major source

Model: A current source in parallel toincremental resistance

PSD: 2 ( ) 2d d

I f qI

d

d

KTr

qI

2/A Hz


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NOISE IN BJTs

Due to Shot noise of Base and collectorcurrent

Flicker noise of base current

Thermal noise of base resistance

Common practice is to model all noise by

two equivalent sources at the base:2 1( ) 4 ( )

2i b

m

V f KT r g

2

2( ) 2 (

( )

CBi B

IKII f q I

f f


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NOISE IN MOSFET

Dominant source is Flicker and Shot noise Flicker Noise Modeled by a voltage source in series

with gate:

K is device dependent parameter (lower for PMOSthan NMOS as their majority carrier is less likelyto be trapped) Large area device has low flicker noise !

Thermal noise due to resistive channel In saturation, modeled by a drain to source current

of

2( )

g

ox

KV f

WLC f

2 2( ) 4 ( )

3d mI f KT g


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Models could be simplified by

Dividing current by in referring

Back to input as voltage sourceOr vice versa. [ ]

2

mg

d m gsi g v


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Opamp Model

Modeled by three uncorrelated

Noise sources as shown.

In CMOS opamp, Current sourcesmay be ignored, at low frequencies


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SUMMARY of Noise

Models


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EXAMPLE-1

An opamp Circuit


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Integrate, and add.


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EXAMPLE-2

Common-source stage

2 2 2

,

2 4(4 . )

3

n out m m D

ox D

K KTV KT g g R

C WLf R

2V

Hz

Resistors thermal noiseMOS thermal & flicker noise


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EXAMPLE-3

Common-emitter

Evaluate optimum

IC, to minimize

Equivalent input

Noise

Assume:

Collector shot noise dominate input noise voltage

Base current shot noise dominates input noise current


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Given assumptions mean


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Differentiate and equate to zero to obtain,


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Conclusion

Discussed various terminology

Discussed Various noise mechanism

Discussed noise models of variouselements

Some examples were discussed

SPICE simulation discussed


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References

John and Martin, Analog Integrated Circuit Design

John Wiley & Sons, India, 1997

Baker, R J, CMOS Circuit design, layout and

simulation, John Wiley & sons, India, 2005 Razavi, B, Design of Analog CMOS Integrated

Circuits, TMH, India, 2002

Voss, 1/f(flicker noise): A brief review,33rd Annual Symposium on Frequency Control.

1979, pn,40-46


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Noise in Circuits

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