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Dispositivos Semiconductores
Dispositivos Semicoductores - DIEC/UNS
Basics
• RMS value:
T
1 2
2
2
Vn (rms )  E (v ) 
v
(
t
)
dt

T1  T2 T1
• Mean value:
T
1 2
V  E (v ) 
v(t )dt

T1  T2 T1
• Variance σ2 (standar dev. σ)
 2  E (v 2 )  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 3V  45V
216
– Noise has to be less than half
LSB (less significant bit)
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
Vn (rms)  4kTRB
– 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
k=1.38e-23 V2/ (Hz-Ω-K)
Dispositivos Semicoductores - DIEC/UNS
Shot Noise
• Due to the discrete nature of charge
flow
I n (rms)  2 q I DC B
– q = 1.6 e-19
• Shot noise is Gaussian and White
– Formula assumes no correlation in
charges (good for diodes, not for
metallic conductors)
Dispositivos Semicoductores - DIEC/UNS
Shot Noise
• Relative percentage of noise
increases when current decreases
I n (rms)  2 q I DC B
Percentage of In with respect to current (normalized
to B=1)
-2
10
• Example:
-3
10
– Idc=1A, In=57nA (0.000006%)
– Idc=1uA, In=3.42pA (0.006%)
– Idc=1pA, In=56fA (5.6%)
-4
10
– B=10Khz
-5
10
-6
10
-9
10
-8
10
-7
10
-6
10
-5
10
-4
10
-3
10
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
Vn (rms)  vn B
• For a resistor
vn (rms )  4kTR
V / Hz
v 2 n (rms )  4kTR
V 2 / Hz
• Two uncorrelated noise sources are added:
v  va2  vb2
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
 VS2 
SNR  10log10  2 
 Vn 
• Noise figure of an amplifier
– Ratio of the output of a real amplifier to a perfect amplifier
 4kTRS  vn2 

vn2 
NF  10log10 
  10log10 1 

4
kTR
4
kTR
S
S 



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:
Vn (rms)  4kTRB
• Maximum resistor value for
22.5µV noise is:
Rmax  3.1M 
Dispositivos Semicoductores - DIEC/UNS
Noise model of an amplifier
• Noiseless transistor
• Noise is modelled with:
– current noise source
– voltage noise source
• Input-referred equivalent
noise:
ea (rms)  en2  (in Rs )2
• Circuits are solved using small-signal models
• The noise sources depend on the transistor type, model and bias
conditions
– Bipolar
– JFET
– MOS
Dispositivos Semicoductores - DIEC/UNS
Bipolar transistor noise
2(kT )2
en  4kTrbb  2qI r  4kTrbb 
qI c
2
2N5087
in  I b
2
2
c e
 Johnson noise in the base resistance
 Shot noise in Ib
 Collector current shot noise across the
base-emitter junction equivalent resistance
(Ic/Vt)
 1/f noise in rbb also manifest
 Some 1/f of Ib through rbb (noticeable at
high currents)
Dispositivos Semicoductores - DIEC/UNS
Bipolar transistor noise
 Total values of noise are
determined from the small
signal model
 Dominant source of noise
depends on Rs
 Equivalent input voltage and current
noise for an npn 2N5087 transistor
Dispositivos Semicoductores - DIEC/UNS
Motivation: Flash AD Converter
• Suppose a Bandwith B=10Khz
• Using a bipolar input amplifier
with I=1mA:
– Input voltage noise:
Vn (rms)  2
nV
 10 Khz  0.2V
Hz
– Input current noise:
Vn (rms)  2
pA
 3.6M  10 Khz  600V
Hz
(12 bits)
Dispositivos Semicoductores - DIEC/UNS
JFET transistor noise
 voltage noise is the Johnson noise of the
channel resistance
en  4 KT
2
2
; gm  I D
3g m
 Shot noise from leakage current
 This current and the noise increase
with temp and VDG
in  3.2 1019 I G B
Dispositivos Semicoductores - DIEC/UNS
2
Motivation: Flash AD Converter
• Suppose a Bandwith B=10Khz
• Using a 2N3954 FET input
amplifier with I=1mA:
– Input voltage noise:
Vn (rms)  10
nV
 10 Khz  1V
Hz
– Input current noise:
Vn (rms)  0.5
fA
 3.6M  10 Khz  0.15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
en 2  4 KT
2
; gm  I D
3g m
• Flicker noise
– Effects of Si-SiO2 interface
traps on carriers
– Proportional to area
Total input noise. Orbit 1.2µm process
 Kf  1
en  

C
W
L
 ox
f
2
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.
Dispositivos Semicoductores - DIEC/UNS