amplitude and phase noise in nano-scale rf circuits reza navid may 14, 2007
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Amplitude and Phase Noise Amplitude and Phase Noise in Nano-scale RF Circuitsin Nano-scale RF Circuits
Reza Navid Reza Navid
May 14, 2007May 14, 2007
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CMOS Scaling Since Early 70sCMOS Scaling Since Early 70s
100
1,000
10,000
100,000
1,000,000
10,000,000
100,000,000
1,000,000,000
1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
0.01
0.1
1
10
100
Today, 45nm technology node is available for commercial production design.Today, 45nm technology node is available for commercial production design.Several other nano-scale devices are also becoming available.Several other nano-scale devices are also becoming available.
4004 Intel Processor2,250 10-MOSFETs
386 Intel Processor275,000 1-MOSFETs
Pentium IV Intel Processor169,000,000 90n-MOSFETs
Ch
ann
el L
eng
th (
Mic
ron
)
Nu
mb
er o
f M
OS
FE
Ts
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Scaling Problem at Nanometer ScalesScaling Problem at Nanometer Scales
Reliability: Mismatch:
Intrinsic Gain:
Small output resistance Low intrinsic gain
Noise:
Short-channel MOSFETs are noisier that Long-channel ones
Physical lengthPhysical length
Ro Long-channel prediction
1986 Year19991994 1996
Dra
in N
oise
leve
l
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Phase Noise
ffo f
of
LNA Noise
f
Noise in RF ReceiversNoise in RF Receivers
Electrical noise strongly impacts the overall performance.Electrical noise strongly impacts the overall performance.
LNA
LO
Mixer
Input Noise Output Noise
TransmissionTransmission No SignalNo Signal
ff s sf
f f
so ff
IF Filter
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OutlineOutline
• Amplitude Noise in MOSFETNoise in MOSFETsPhysical and Compact ModelsNoise Performance of Ballistic MOSFETs
• Jitter and Phase Noise in OscillatorsIndirect Noise Characterization Using Phase NoiseTime-Domain Formulation of Phase NoiseExperimental Results
• Directions for Further Research
• Conclusions
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OutlineOutline
• Amplitude Noise in MOSFETNoise in MOSFETsPhysical and Compact ModelsNoise Performance of Ballistic MOSFETs
• Jitter and Phase Noise in OscillatorsIndirect Noise Characterization Using Phase NoiseTime-Domain Formulation of Phase NoiseExperimental Results
• Directions for Further Research
• Conclusions
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Noise Sources in MOSFETsNoise Sources in MOSFETs
• There are two noise sources in a MOSFET:Drain current noise (ind)Induced gate noise (ing)
Drain
Source
Gate
1/f noise
White noise
We study the white noise part of the drain noise in saturation.We study the white noise part of the drain noise in saturation.
ing Cgsgg gmvgs go ind
• 1/f Noise: Unknown origin, believed to be due to traps
Gate
Source
Drain
• Gate Noise: Carrier fluctuations
coupled to gate through Cgs
2ngi 2gsC
2ndi
f f
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dR
RkTvn d4d 2
dx
Classical MOSFET Noise FormulationClassical MOSFET Noise Formulation
• Classical long-channel formulationImpedance Field Method [Van Der Ziel, 1970]:
Divide the channel into small piecesCalculate noise of each piece (assuming equilibrium noise)Integrate (assuming independence)
It accurately predicts noise in long-channel MOSFETs.It accurately predicts noise in long-channel MOSFETs.
N+ N+
GS D
Noise transfer Noise transfer function (Impedance)function (Impedance)
2
22 d
dxZ
vi nnd
L
x
ndnd ii0
22 d
3/2,42 dond gkTi
dR
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Deficiency of the Long-Channel ModelDeficiency of the Long-Channel Model
Several methods are proposed to study this excess noise.Several methods are proposed to study this excess noise.
Long-channel prediction
1986 Year
2.9
7.9
Jindal (0.75m)
Abidi (0.7m)
1999
Scholten (0.35m)1.1
1994
Triantis (0.7m)
1996
3.3
0.67
Tedja (1m)
• Excess noise has been reported for 20 years now:
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Excess Noise in Short-Channel FETsExcess Noise in Short-Channel FETs
• Researchers have tried to explain excess noise:Local heating effects [Traintis, 1996]Hydrodynamic simulations [Goo, 1999, Jungemann 2002] Montecarlo analysis [Jungemann, 2002]…
We present a model based on ballistic MOSFET model.We present a model based on ballistic MOSFET model.
Usual approach
Model revision
Long-Channel FETsLong-Channel FETsToday’s FETs, 50% Today’s FETs, 50%
BallisticBallistic Ballistic FETsBallistic FETs
Long-Channel Model:Long-Channel Model:IIndnd=4=4kTkTggdodo
Short-Channel Short-Channel Model: Model: IIndnd=4=4kTkTshshggdodo
Model revision
Our approach
Ballistic Mode:Ind=2qId
• MOSFETs are moving towards ballistic limit.
Short-Channel Model: Ind=ks(2qId)
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OutlineOutline
• Amplitude Noise in MOSFETNoise in MOSFETsPhysical and Compact ModelsNoise Performance of Ballistic MOSFETs
• Jitter and Phase Noise in OscillatorsJitter and Phase Noise in OscillatorsIndirect Noise Characterization Using Phase NoiseTime-Domain Formulation of Phase NoiseExperimental Results
• Directions for Further Research
• Conclusions
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-4
-2
0
2
4
Phase Noise in OscillatorsPhase Noise in Oscillators
• Device noise leads to frequency fluctuations.Example: Ring Oscillators
Phase noise characterizes the frequency fluctuations.Phase noise characterizes the frequency fluctuations.
Ou
tpu
t
t
ffo
I
t
Time Domain
Ph
ase
No
ise
Frequency Domain
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Phase Noise: Phase Noise: Formulation and MeasurementFormulation and Measurement
• Phase noise definition: PSD of signal divided by power
Hard to formulate
Easy to measure PN
(d
Bc/
Hz)
fo ffo+f
• Phase noise measurement helps estimate device noise:
This method is most suitable for formulation of phase noise in This method is most suitable for formulation of phase noise in switching-base oscillators.switching-base oscillators.
• Need accurate formulation for specific oscillators.Time-domain phase noise analysis method
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Time-Domain Phase Noise AnalysisTime-Domain Phase Noise Analysis
• Formulation of phase noise:1) Calculate jitter2) Calculate phase noise using jitter-phase-noise relationships
TTiiTTjj has necessary andhas necessary and sufficient sufficient
information for phase noise calculation.information for phase noise calculation.
• Jitter characterization:
T2Ti
T1
With white noise(presented here)
i-j0
2oT
ji TT
With colored noise(presented elsewhere)
i-j0
2oTji TT
Without low-frequency poles
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Jitter in Switching-Based Oscillators (1)Jitter in Switching-Based Oscillators (1)
• Switching-based oscillators: Energy-injecting elements act like ideal switches.
Calculate jitter during each switching; Add them up to find total jitter.Calculate jitter during each switching; Add them up to find total jitter.
vC
in C R
vref
Ideal noise-free switch
Passive noisy network
vout
vC voutin in
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Jitter in Switching-Based Oscillators (2)Jitter in Switching-Based Oscillators (2)
• Calculation procedure:Calculate voltage variance at the switching time.Divide by the square of voltage slope to get jitter.
This is suitable for switching-based oscillators.This is suitable for switching-based oscillators.
2
222
0 0
)(
2
)2
(
2 )( ,d d )()()(
)2
(
S
tvTeiie
C
etv C
o
t t
nnRC
RC
t
CRC
t
vC
in C R
vrefvc
t
2vc
2vc2T
Slope=Svref
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-120
-100
-80
-60
-40
-20
0
-1.E+06 -5.E+05 0.E+00 5.E+05 1.E+06
Jitter-Phase-Noise Relationships (1)Jitter-Phase-Noise Relationships (1)
• If all covariance terms are zero [Navid, 2005],
Phase noise has peaks around odd harmonics, as expected.Phase noise has peaks around odd harmonics, as expected.
The 1st harmonic
PN
(dB
c/H
z)
f (Hz)
The 3rd harmonic
f (Hz)
-120
-100
-80
-60
-40
-20
0
-1.E+06 -5.E+05 0.E+00 5.E+05 1.E+06
0
222
21
2220
22
22
cos2
cosh
24cosh
2cos
4cosh
4sinh)(
TT
Tf
TTT
TfPN
oo
oo
o
Variance of one period
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-180
-160
-140
-120
-100
-80
-60
-40
-20
0
1.E+00 1.E+02 1.E+04 1.E+06 1.E+08 1.E+10
Jitter-Phase-Noise Relationships (2)Jitter-Phase-Noise Relationships (2)
• It can be approximated by a Lorentzian Function.Consistent with the results for sinusoidal signals [Herzel, 1999]
Jitter-phase-noise relationship for nonzero jitter covariance is Jitter-phase-noise relationship for nonzero jitter covariance is presented elsewhere [Navid, 2004].presented elsewhere [Navid, 2004].
Lorentzian
Exact phase noise• Usually:
PN
(dB
c/H
z)
f (Hz)
2
223
23
)(
ooo
oo
ffTf
TffPN
23ooo Tfff
2
23
)( f
TffPN oo
off
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Phase Noise in Ring OscillatorsPhase Noise in Ring Oscillators
• Time-domain phase noise analysis:Treat invertors as ideal switches.Use long-channel noise formulation.
On State:
Off State:
I og/1
dog/1dokTg4
dokTg3
8
A B
Use time-domain jitter analysis for switching-based oscillators.Use time-domain jitter analysis for switching-based oscillators.
A B
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Phase Noise in Ring Oscillators (cont.)Phase Noise in Ring Oscillators (cont.)
• Using jitter-phase-noise relationships [Navid, 2005]:
oddo
o fP
kT
vNCf
kTT
min22
2 33.733.7
2
min22
33.733.7
f
f
P
kT
fNCv
kTffPN o
dd
o
Very simple equations, but how accurate?Very simple equations, but how accurate?
Dynamic Power2
min ddovNCfP
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Phase Noise in Ring OscillatorsPhase Noise in Ring Oscillators
Lmin m
fosc MHz
PNmeas. dBc/Hz
PNmin.
dBc/HzPN dB
2.00 232 -118.5 -119.7 1.2 2.00 115 -126.0 -128.0 2.0 0.53 751 -114.0 -115.4 1.4 0.39 850 -112.6 -114.6 2.0 0.36 931 -111.7 -113.8 2.1 0.32 932 -112.5 -114.2 1.7 0.32 869 -112.2 -114.6 2.4 0.28 929 -112.3 -114.3 2.0 0.25 898 -112.0 -115.9 3.9 0.25 959 -110.9 -115.5 4.6 0.25 1330 -111.5 -116.7 5.2
The difference is only a few dB; it increases in short-channel devices.The difference is only a few dB; it increases in short-channel devices.
• Measured results form Hajimiri, JSSC 1999 compared to our formulation:
ff=1MHz=1MHz
Lmin (m)
PN
(dB
)
2
min
33.7
f
f
P
kTfPN o
0
1
2
3
4
5
6
0 0.5 1 1.5 2 2.5
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Oscillators for Noise CharacterizationOscillators for Noise Characterization
The unsymmetrical ring oscillator is only one of many possibilities.The unsymmetrical ring oscillator is only one of many possibilities.
• Need an oscillator with predictable phase noise, not necessarily low phase noise: an unsymmetrical ring oscillator.
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The Unsymmetrical Ring OscillatorThe Unsymmetrical Ring Oscillator
Fabricated in National Semiconductor’s 0.18Fabricated in National Semiconductor’s 0.18m CMOS process.m CMOS process.
• Chip photo:
OSC3, L=.54m
OSC2, L=.38m
OSC1, L=.18m
Ring oscillators for Ring oscillators for functionality testfunctionality testMIM MIM
CapacitorsCapacitors
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MOSFET Noise CharacterizationMOSFET Noise Characterization
The oscillator with longer transistors has better spectral purity.The oscillator with longer transistors has better spectral purity.
• Frequency spectrum of the oscillators:
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MOSFET Noise Characterization (Cont.)MOSFET Noise Characterization (Cont.)
Oscillator with Longer transistors has 7dB smaller phase noise.Oscillator with Longer transistors has 7dB smaller phase noise.
• Phase noise of the oscillators:
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Device Noise ParametersDevice Noise Parameters
Extracted device noise parameters are consistent with our prediction.Extracted device noise parameters are consistent with our prediction.
• Device noise parameters can be extracted from phase noise data.
Long-channel Long-channel predictionprediction
OSC3OSC3OSC1OSC1
Full shot Full shot noisenoise
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Further Research on Phase NoiseFurther Research on Phase Noise
• Time-domain phase noise analysis:
Jitter/phase noise calculation for various oscillators/PLL systems.
Vb
PFD Charge Pump
:N
VCOLoopFilter
Fref
• Indirect device noise characterization for Nanotubes and Nanowires:
Ring oscillators built with these devices are already available (Z. Chen et al, Science 24 March 2006).
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Noise for Device EngineeringNoise for Device Engineering
• Non-equilibrium noise carries unique device informationDevice engineering based on noise characterization
Examples:Examine carrier transport using noise data
Nano-tubes, Nano-wires, MOSFETs, …
Design new devices based on noise measurement Bio-analytical devices
Use noise data to improve existing devices and build new ones.Use noise data to improve existing devices and build new ones.
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Other Scaling ProblemsOther Scaling Problems
Reliability: Mismatch:
Intrinsic Gain:
Small output resistance Low intrinsic gain
Noise:
Short-channel MOSFET are noisier that Long-channel ones
Ro Long-channel prediction
1986 Year19991994 1996
Dra
in N
oise
leve
l
Physical lengthPhysical length
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ConclusionsConclusions
• Efficient CMOS analog design calls for a careful study of noise in MOSFETs, which has been a mystery for two decades.
• Time domain phase noise analysis method accurately predicts the phase noise in switching-based oscillators.
• Device noise can be characterized through phase noise measurement, facilitating process characterization.
• Noise can be useful.
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AcknowledgmentAcknowledgment
This work is supported under an SRC customized research project from Texas Instruments and
MARCO MSD center.
We would like to thank National Semiconductor Inc. for the fabrication of test chips.