Dispositivos Semicoductores - DIEC/UNS
Ruido
Dispositivos Semiconductores
Dispositivos Semicoductores - DIEC/UNS
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
Dispositivos Semicoductores - DIEC/UNS
Basics
• Gaussian distribution– Has a probability density
function:
Dispositivos Semicoductores - DIEC/UNS
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
Dispositivos Semicoductores - DIEC/UNS
Noise definition and sources
• Noise: random noise of a physical (often thermal) origin
• Types: – Johnson (white)– Shot noise– Flicker noise (1/f)
Dispositivos Semicoductores - DIEC/UNS
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)
Dispositivos Semicoductores - DIEC/UNS
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
Dispositivos Semicoductores - DIEC/UNS
• 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]
Dispositivos Semicoductores - DIEC/UNS
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)
Dispositivos Semicoductores - DIEC/UNS
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
Dispositivos Semicoductores - DIEC/UNS
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
Dispositivos Semicoductores - DIEC/UNS
Example
• R1=1M, R2=100K in series– vn1= 0.12μV
– vn2= 40nV
– vnt= 0.135 μV
Dispositivos Semicoductores - DIEC/UNS
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
Dispositivos Semicoductores - DIEC/UNS
Example
• Two series resistors and source signal 1mV– SNR = ?
• Amplifier (2N6483 Jfet, Id=100μA) with en= 7nV/√Hz– NF = ?
Dispositivos Semicoductores - DIEC/UNS
Motivation: Flash AD Converter
• Suppose a Bandwith B=10Khz
• Single resistance noise is:
• Maximum resistor value for 22.5µV noise is:
( ) 4nV rms kTRB
max 3.1R M
Dispositivos Semicoductores - DIEC/UNS
• 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
Dispositivos Semicoductores - DIEC/UNS
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
Dispositivos Semicoductores - DIEC/UNS
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
Dispositivos Semicoductores - DIEC/UNS
Motivation: Flash AD Converter
• Suppose a Bandwith B=10Khz
• 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)
Dispositivos Semicoductores - DIEC/UNS
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
Dispositivos Semicoductores - DIEC/UNS
Motivation: Flash AD Converter
• Suppose a Bandwith B=10Khz
• 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)
Dispositivos Semicoductores - DIEC/UNS
Comparison of discrete devices
Current noise Voltage noise
Bip
Bip
Dispositivos Semicoductores - DIEC/UNS
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
Dispositivos Semicoductores - DIEC/UNS
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.