Dispositivos Semicoductores - DIEC/UNS Ruido Dispositivos Semiconductores.

Dispositivos Semicoductores - DIEC/UNS

Ruido

Dispositivos Semiconductores


Basics

• RMS value:

• Mean value:

• Variance σ2 (standar dev. σ)

2

1

2 2

1 2

1( ) ( ) ( )

T

n

T

V rms E v v t dtT T

2

11 2

1( ) ( )

T

T

V E v v t dtT T

2 2( ) ( )E v E v


Basics

• Gaussian distribution– Has a probability density

function:


Motivation: Flash AD Converter

• A 3-volts 16 bits ADC (analog to digital converter)– One bit is equivalent to

– Noise has to be less than half LSB (less significant bit)

16

345

2

VV

22.5 V


Noise definition and sources

• Noise: random noise of a physical (often thermal) origin

• Types: – Johnson (white)– Shot noise– Flicker noise (1/f)


Johnson (thermal) noise

• Product of thermal energy kT

• Flat frequency spectrum– Same noise power in each

hertz of bandwith: White– Gaussian distribution

• In a resistance

– Where k is Boltzmann’s constant (4kT=1.62 x 10e-20 V^2/Hz-Ω)

• Example: a 10K resistor in a 10Khz bandwith has 1.3uV

( ) 4nV rms kTRB

k=1.38e-23 V2/ (Hz-Ω-K)


Shot Noise

• Due to the discrete nature of charge flow

– q = 1.6 e-19

• Shot noise is Gaussian and White– Formula assumes no

correlation in charges (good for diodes, not for metallic conductors)

( ) 2n DCI rms q I B


• Relative percentage of noise increases when current decreases

• Example:

– Idc=1A, In=57nA (0.000006%)

– Idc=1uA, In=3.42pA (0.006%)

– Idc=1pA, In=56fA (5.6%)

– B=10Khz

Shot Noise

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-6

10-5

10-4

10-3

10-2

( ) 2n DCI rms q I B Percentage of In with respect to current (normalized to B=1)

I [amps]


Flicker Noise

• Excess noise found in many occasions in nature– Flow of Nile– Speed of ocean currents– Intensity of classical music– Wind blow

• Spectrum 1/f• For resistor, depends

heavily on materials, geometry, etc. – Carbon comp. 0.1µV – 3.0µV– Carbon film 0.05μV – 0.3μV– Metal 0.02µV – 0.2µV– Wire wound 0.01µV – 0.2µV

– (rms μV over 1 decade)


Interference

• Interfering signal or stray pickup is also noise• Spectrum and characteristics depend on

interfering signal– Ex. 50Hz pickup has constant amplitude and fixed

frequency– Car ignition noise have broad spectrum– Radio and TV signals– Mechanical vibrations

• Effect minimized by shielding and filtering


Noise Density

• Measured noise depends on bandwith

• RMS Noise density vn

• For a resistor

• Two uncorrelated noise sources are added:

2 2

( ) 4 /

( ) 4 /

n

n

v rms kTR V Hz

v rms kTR V Hz

( )n nV rms v B

2 2a bv v v


Example

• R1=1M, R2=100K in series– vn1= 0.12μV

– vn2= 40nV

– vnt= 0.135 μV


Signal to noise ratio (SNR)

• Relation between signal and noise in db

• Noise figure of an amplifier– Ratio of the output of a real amplifier to a perfect amplifier

2

10 210log S

n

VSNR

V

2 2

10 10

410log 10log 1

4 4S n n

S S

kTR v vNF

kTR kTR


Example

• Two series resistors and source signal 1mV– SNR = ?

• Amplifier (2N6483 Jfet, Id=100μA) with en= 7nV/√Hz– NF = ?



• Suppose a Bandwith B=10Khz

• Single resistance noise is:

• Maximum resistor value for 22.5µV noise is:

( ) 4nV rms kTRB

max 3.1R M


• Circuits are solved using small-signal models• The noise sources depend on the transistor type, model

and bias conditions– Bipolar– JFET– MOS

Noise model of an amplifier

• Noiseless transistor• Noise is modelled with:

– current noise source– voltage noise source

• Input-referred equivalent noise:

2 2( ) ( )a n n se rms e i R


Bipolar transistor noise 2N5087

bn Ii 22

2 2 2( )4 2 4n bb c e bb

c

kTe kTr qI r kTr

qI

Johnson noise in the base resistance

Collector current shot noise across the base-emitter junction equivalent resistance (Ic/Vt)

Some 1/f of Ib through rbb (noticeable at high currents)

Shot noise in Ib

1/f noise in rbb also manifest


Bipolar transistor noise

Equivalent input voltage and current noise for an npn 2N5087 transistor

Total values of noise are determined from the small signal model

Dominant source of noise depends on Rs




• Using a bipolar input amplifier with I=1mA: – Input voltage noise:

– Input current noise:

( ) 2 10 0.2n

nVV rms Khz V

Hz

( ) 2 3.6 10 600n

pAV rms M Khz V

Hz

(12 bits)


JFET transistor noise

BIi Gn192 102.3 D

mn Igm

gKTe ;3

242

voltage noise is the Johnson noise of the channel resistance

Shot noise from leakage current

This current and the noise increase with temp and VDG




• Using a 2N3954 FET input amplifier with I=1mA: – Input voltage noise:

– Input current noise:

( ) 10 10 1n

nVV rms Khz V

Hz

( ) 0.5 3.6 10 0.15n

fAV rms M Khz V

Hz

(21 bits)


Comparison of discrete devices

Current noise Voltage noise

Bip

Bip


MOS noise

• Thermal noise– Channel resistance

• Flicker noise– Effects of Si-SiO2 interface

traps on carriers– Proportional to area

2 1fn

ox

Ke

C W L f

2 24 ;

3n Dm

e KT gm Ig

Total input noise. Orbit 1.2µm process


References

• Horowitz and Hill, The Art of Electronics, 1989, Cambridge Univ. Press• Randall L. Geiger, Phillip E. Allen, N. Strader, VLSI. McGraw Hill, 1990. • Paul R. Gray, Robert G. Meyer, Analyis and Design of Analog Integrated

Circuits. John Wiley and Sons, 3rd edition, 1993. • M. Adlerstein, Andreas G. Andreou, “Noise Measurement, Internal

Report,” Johns Hopkins University, 2005.

Dispositivos Semicoductores - DIEC/UNS Ruido Dispositivos Semiconductores.

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