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Transcript of Noise02s Raf
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Rafael J. Betancourt-Zamorahttp://www.betasoft.org/
May 16, 2002
Noise Tutorial:
Low-frequency CMOSAnalog Design
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Noise Tutorial: Low-frequency CMOS Analog Design
2002, Rafael J. Betancourt-Zamora http://www.betasoft.org/
Outline
Goals
Noise Overview
Resistor Noise Sources
MOSFET Noise Sources
Noise of Common Amplifier Topologies
Examples
Summary
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Noise Tutorial: Low-frequency CMOS Analog Design
2002, Rafael J. Betancourt-Zamora http://www.betasoft.org/
Grasp the importance of noise performance in low-frequency
instrumentation design
Understand the types of noise present in integrated resistorsand MOS devices.
Understand the noise trade-offs of different circuit topologies
Perform simple noise analysis
Goals
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Noise Tutorial: Low-frequency CMOS Analog Design
2002, Rafael J. Betancourt-Zamora http://www.betasoft.org/
Outline
Goals
Noise Overview
Resistor Noise Sources
MOSFET Noise Sources
Noise of Common Amplifier Topologies
Examples
Summary
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Noise Tutorial: Low-frequency CMOS Analog Design
2002, Rafael J. Betancourt-Zamora http://www.betasoft.org/
t
V t( )
P x( )
FUZZ 6
Random process with zero mean
Instantateous amplitude is unpredictable
Average noise power can be measured (variance)
What does it look like?
WHITE NOISE (GAUSSIAN DISTRIBUTION)
m 0=
Vrms
=
STANDARD DEVIATION
VARIANCE
MEAN
2
Vrms
2
=f
Vrm s2
Hz
Noise Power Spectral Density(Normalized Noise Power)
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Noise Tutorial: Low-frequency CMOS Analog Design
2002, Rafael J. Betancourt-Zamora http://www.betasoft.org/
Types of Noise
THERMAL
SHOT
FLICKER
thermal excitation of charge carriers
fluctuations in dc current flow through junctions
traps in semiconductors
f
Vrm s2
Hz
f
Vrm s2
Hz
f
Arms
2Hz
1 f
Vrms2
f---------- 4kTR=
Irms2
f----------- 2qIDC=
Vrms2
f-------------
Kf VDC2
f--------------------=
, V2/Hz
, A2/Hz
, V2/Hz
k= 1.38 x 10-23J/K
q= 1.6 x 10-19C
T= Temperature, K
Kf= Flicker coefficient
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Noise Tutorial: Low-frequency CMOS Analog Design
2002, Rafael J. Betancourt-Zamora http://www.betasoft.org/
Resistor Thermal Noise
Vn2
f------ 4kTR= , V2/Hz
R
* R
Vn2 4kTRfn=
Vn2
In2 4kT
R
---------------- fn=
In2
, V2 , A2
NOISE DENSITY
NOISE POWER
In2
f-------
4kTR
----------------= , A2/Hz
1k@ 25 C
nV Hz
pA Hz
4.05
4.05
fn = NOISE BANDWIDTH
Integrate noise PSD over frequency to arrive at total noise power.
For white noise, multiply PSD by noise bandwidth.
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Noise Tutorial: Low-frequency CMOS Analog Design
2002, Rafael J. Betancourt-Zamora http://www.betasoft.org/
Noise Bandwidth
NOISE BW
Noise bandwidth is defined for a brickwall transfer function
Noise bandwidth is not the same as 3dB bandwidth
ff3dB fn
Avo2
Avo2
fn Avf( )2
0
df=
No. Poles
1
2
3
2nd-order BPF
fn2--- f3dB=
fn 1.22 f3dB=
fn 1.16 f3dB=
fn2--- f3dB=
Avf( )
2
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Noise Tutorial: Low-frequency CMOS Analog Design
2002, Rafael J. Betancourt-Zamora http://www.betasoft.org/
kT/C Limit
C
R
*
Vn2
Vo2
fn2--- f3dB=
f3dB1
2RC---------------=
fn1
4RC-----------=
Vo2 4kTRfn= , V2
}
Vo2 4kTR 1
4RC-----------
=
Vo2 kT
C------=
Total noise power is independent of R
Capacitor is noiseless, but accumulates noise from resistor
This fundamental limit is important for sampled systems
, V2
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Noise Tutorial: Low-frequency CMOS Analog Design
2002, Rafael J. Betancourt-Zamora http://www.betasoft.org/
Combining Noise Sources
R1
*R2Vn1
2 In22
R2
*Vn2
2
R1+R2
* Vn1
2Vn2
2+
R1 In12
R1||R2In1
2In2
2+
For uncorrelated noise sources, just add the noise powers.
For correlated sources use:
Vo2
Vn12
Vn22
2cVn1Vn2+ +=
c 1 CORRELATION COEFFICIENT
SERIES PARALLEL
Vo2 4kT R1 R2+( )fn= Io
24kT 1
R1-------
1
R2-------+( )fn=
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Noise Tutorial: Low-frequency CMOS Analog Design
2002, Rafael J. Betancourt-Zamora http://www.betasoft.org/
Resistor Flicker (1/f) Noise
f
Vn2
Hz1 f Vnf
2
f-------
Kf
VDC2
f---------------------= , V
2/HzTHERMAL
fc
fff Vnf2 Kf
VDC2
f---------------------
fL
fH
df K
f VDC
2 fH
fL-----
ln= =
Vo2 4kTRfn K
f VDC
2 fHfL------
ln+=
TOTAL RESISTOR NOISE
, V2
Constant noise power per decade
fc
defines 1/fcorner frequency where
flicker noise is equal to thermal noise.
Vnf2
2.3Kf VDC2= FORfH/fL= 10
fL fH
, V2
ASSUMES
fn fc
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Noise Tutorial: Low-frequency CMOS Analog Design
2002, Rafael J. Betancourt-Zamora http://www.betasoft.org/
Noise Index
Vnf2
VDC2
-------------
DEC
Kf VDC2 10( )ln
VDC2
----------------------------------------------------- 2.3Kf= =
Normalize 1/fnoise per Volt, per decade of frequency
Can express 1/fnoise PSD and fcin terms of NI
NI 2.3K
f
10 6
= , V/V/decade
Vnf2 NI
2VDC
2
2.3 10 12
-----------------------------
1
f---= , V2/Hz
fc
NI2
VDC2
2.3 10 12
4kTR--------------------------------------------------=
, Hz20log(NI)
poly
pdiff
ndiff -10dB
-5dB
-15dB
[Motchenbacher93]
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Noise Tutorial: Low-frequency CMOS Analog Design
2002, Rafael J. Betancourt-Zamora http://www.betasoft.org/
Outline
Goals
Noise Overview
Resistor Noise Sources
MOSFET Noise Sou rces
Noise of Common Amplifier Topologies
Examples
Summary
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Noise Tutorial: Low-frequency CMOS Analog Design
2002, Rafael J. Betancourt-Zamora http://www.betasoft.org/
Noise Sources in a MOSFET
*
Vnf2 Ind2
*
Vng2DRAIN THERMAL NOISE
FLICKER NOISE
GATE THERMAL NOISE
Vng2
f-------- 4kTRG 3=
Ind2
f------- 4kTgm=
, V2/Hz
, A2/Hz
={{2/3, long channel
2-3, short channel
Rds = 1/gm
Long Channel
Saturation
due to limited channel conductance
can be neglected with good layout
Vnf2
f-------
Kf
WLCoxf-------------------= , V
2/Hz Kf 1.2 10
24= V2 FFOR NMOS
[Razavi01]
SPICE
Inf2
f------
Kf
IDCAF
LEFF2
Coxf-----------------------= , A
2/Hz
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Noise Tutorial: Low-frequency CMOS Analog Design
2002, Rafael J. Betancourt-Zamora http://www.betasoft.org/
Input-referred Noise
*
Vnf2 Ind2
*
Vni2
Ini2
Define equivalent input voltage andcurrent noise sources.
MOSFET input current noise sourcecan be neglected at low frequencies.
*
Vni2
Vnd2
f--------
Ind2
f------- gm
2 4kTgm
---------------------= = , V2/Hz
INPUT-REFERRED DRAIN NOISE
TOTAL INPUT-REFERRED NOISE
Vni2
f-------
4kTgm
---------------------
Kf
WLCoxf-------------------+= , V
2/Hz
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Noise Tutorial: Low-frequency CMOS Analog Design
2002, Rafael J. Betancourt-Zamora http://www.betasoft.org/
1/f Corner Frequency
4kTgm
---------------------
Kf
WLCoxfc----------------------=
f
Vn2 Hz
1 f
THERMAL
fc
fff
Defines where flicker noise is equal to thermal noise.
Need to increase transistor area to reduce flicker noise.
fc
Kfgm4kTWLCox---------------------------------------=
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Noise Tutorial: Low-frequency CMOS Analog Design
2002, Rafael J. Betancourt-Zamora http://www.betasoft.org/
Outline
Goals
Noise Overview
Resistor Noise Sources
MOSFET Noise Sources
Noise of Common Ampl i fier Topolog ies
Examples
Summary
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Noise Tutorial: Low-frequency CMOS Analog Design
2002, Rafael J. Betancourt-Zamora http://www.betasoft.org/
Current Source
In1
2
I1
VBIAS
In12
f------- 4kTgm=
Neglected flicker noise of M1
Need to minimize output current noise
Minimize gmfor low noise
Vo2
Vo2
f
--------In1
2
f
------- ro2
= , V2/Hz
, A2/Hz
VDD
M1
Vo2
f-------- 4kTgmro
2= , V
2/Hz
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Noise Tutorial: Low-frequency CMOS Analog Design
2002, Rafael J. Betancourt-Zamora http://www.betasoft.org/
Common Source
RL
VDD
M1
InL2
*
Vnf2 In12
Vo2
Vi
Neglected output conductance of M1
Maximize gm, RL, and transistor area for low noise
For a differential pair, double the noise
Vni2
f-------
4kTgm
---------------------
Kf
WLCoxf-------------------
4kT
gm2RL
----------------------+ += , V2/Hz
In12
f------- 4kTgm= , A
2/Hz
InL2
f---------
4kTRL----------------= , A
2/Hz Vnf
2
f-------
Kf
WLCoxf-------------------= , V
2/Hz
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Noise Tutorial: Low-frequency CMOS Analog Design
2002, Rafael J. Betancourt-Zamora http://www.betasoft.org/
Source Follower
M1
In22
Vo2
*
Vn12
VDD
Vi
VBIAS
M2
Neglected flicker noise of M2
VERY NOISY, AVOID
Vni2
f-------
Vn12
f--------
In22
f-------
1gm1--------------- ro1
2ro2
2|| ||
2
Av
2---------------------------------------------------------------------------+= , V2/Hz
Vn12
f--------
4kTgm1---------------------
Kf
WLCoxf-------------------+= , V
2/Hz
In22
f------- 4kTgm= , A
2/Hz
Av
1WHERE
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Noise Tutorial: Low-frequency CMOS Analog Design
2002, Rafael J. Betancourt-Zamora http://www.betasoft.org/
Common Gate
In12
Vo2
VBIAS
M1
RL
VDD
InL2
Vi
Neglected output conductance of M1
Define equivalent input voltage and current noise sources
Input noise current cannot be ignored
Transfers load current noise to the input
InL2
f--------- 4kT
RL----------------= , A
2/Hz
In12
f------- 4kTgm= , A
2/Hz
Ini2
f-------
4kTR
L
----------------gm
2Kf
WLCoxf-------------------+= , A
2/Hz
Vni2
f-------
4kTgm
---------------------4kT
gm2RL
----------------------
Kf
WLCoxf-------------------+ += , V
2/Hz
Rs = 1/gm
(neglecting
body effect)
*
Vnf2
Vnf2
f-------
Kf
WLCoxf-------------------= , V
2/Hz
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Noise Tutorial: Low-frequency CMOS Analog Design
2002, Rafael J. Betancourt-Zamora http://www.betasoft.org/
Cascode
Vo2
VBIAS
M1
RL
VDD
InL2
*
Vn12
Vi
In22M2
Vn12
f--------
4kTgm1---------------------
Kf
WLCoxf-------------------+= , V
2/Hz
InL2
f---------
4kT
RL
----------------= , A2/Hz
Neglected output conductance of M1
M2s noise contribution is negligible at low frequencies
Capacitance at M1s drain increase noise at high frequencies
Vni2
f-------
4kTgm1---------------------
Kf
WLCoxf-------------------
4kT
gm12
RL
--------------------------+ += , V2/Hz
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Noise Tutorial: Low-frequency CMOS Analog Design
2002, Rafael J. Betancourt-Zamora http://www.betasoft.org/
Outline
Goals
Noise Overview
Resistor Noise Sources
MOSFET Noise Sources Noise of Common Amplifier Topologies
Examples
Summary
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Noise Tutorial: Low-frequency CMOS Analog Design
2002, Rafael J. Betancourt-Zamora http://www.betasoft.org/
Variable Resistor
(1-k)RTIn2
2
kRT In12
Vo
Vi
(1-k)RT
In2
kRT
Vo
Req= k(1-k)RTWORST CASE
k= 0.5Req=RT/4
In2
f
------- 4kT
Req----------------= , A
2/Hz
In2
f-------
16kTRT
---------------------= , A2/Hz
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Noise Tutorial: Low-frequency CMOS Analog Design
2002, Rafael J. Betancourt-Zamora http://www.betasoft.org/
Inverting Operational Amplifier Filter
R1 * R2 *
C
*
Vn12
Vn22
Vo
Vi
Vna2
-
+
Negligible input noise current
Ignore 1/f noise
Low frequency operation
where
Vni2
f------- Vn1
2 Vn22
Avi2
--------+=
Avi
R2
R1-------=
1. SHORT Vna
2. SHORT Vi
Vni2
f------- Vna
2 A
vni2
Avi2
------------
Vna2
1 R1
R2-------+
2
= =
Avni
1 R2
R1-------+=
3. APPLY SUPERPOSITION
Vni2
f------- Vn1
2 Vn22
Avi2
--------+ Vna2
1 R1
R2-------+
2
+=
FOR LARGE GAIN, R2 >> R1
Vni2
f------- Vn1
2 Vn22
Avi2
--------+ Vna2
+= , V2/Hz
fn2---
1
2R2C----------------- 1
4R2C-------------= =
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Noise Tutorial: Low-frequency CMOS Analog Design
2002, Rafael J. Betancourt-Zamora http://www.betasoft.org/
Outline
Goals
Noise Overview
Resistor Noise Sources
MOSFET Noise Sources Noise of Common Amplifier Topologies
Examples
Summary
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Noise Tutorial: Low-frequency CMOS Analog Design
2002, Rafael J. Betancourt-Zamora http://www.betasoft.org/
What We Learned
Thermal noise and flicker noise are the major sources of headachesfor low-noise, low frequency instrumentation design in CMOS.
Noise bandwidth is not the same as 3dB bandwidth.
Capacitors are noiseless, but they can accumulate noise.
Resistors can have flicker noise, but only when there is current flow.
NOISE IN GENERAL
NOISE IN MOSFETS
Need to increase transistor area to reduce flicker noise.
Current source: Minimize gmfor low noise current
Common source: Maximize gm, RL, and transistor area for low noise
Source follower: VERY NOISY, AVOID Common gate: Transfers load current noise to the input. Input noise
current cannot be ignored.
Cascode: Cascode transistor noise contribution is negligible at lowfrequencies.
N i T i l L f CMOS A l D i
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Noise Tutorial: Low-frequency CMOS Analog Design
2002, Rafael J. Betancourt-Zamora http://www.betasoft.org/
1. P.H. Garret, Analog I/O Design: Acquisition, Conversion,Recovery,Reston Publishing, Reston, VA, pp. 264, 1981.
2. D.A. Johns, K. Martin Analog Integrated Circuit Design,John Wiley & Sons, pp. 706, 1997.
3. C.D. Motchenbacher, J.A. Connelly, Low Noise ElectronicSystem Design,John Wiley & Sons, pp. 422, 1993.
4. B. Razavi, Design of Analog CMOS Integrated Circuits,McGraw-Hill, pp. 684, 2001.
References