an accurate pll behavioral model for fast
TRANSCRIPT
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Department ofDepartment of ElectricalElectrical Engineering Engineering EElectronic lectronic DDesignesign AAutomation Laboratoryutomation LaboratoryNational Central University
2007/10/12
An Accurate PLL Behavioral Model for Fast An Accurate PLL Behavioral Model for Fast Monte Carlo Analysis under Process VariationMonte Carlo Analysis under Process Variation
Authors : *Chin-Cheng Kuo, Meng-Jung Lee, I-Ching Tsai,Chien-Nan Jimmy Liu, and Ching-Ji Huang
Department of Electrical Engineering National Central University, Taiwan (R.O.C.)
* : speaker
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OutlineOutline
IntroductionBottom-up Behavioral ModelingModified Sensitivity AnalysisExperimental ResultsConclusions
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Process Variation EffectsProcess Variation Effects
In deep-submicron technology, impacts of device parameter variation become major factors limiting circuit performance
Process variation aware analysis is necessary in the early design stage (re-design↓)
Monte Carlo Simulation (MCS) is often usedStatistical analysisMuch random data for analysisMany simulation times → time-consuming
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Traditional Statistical AnalysisTraditional Statistical AnalysisTransistor-level Monte Carlo Simulation (MCS)Based on the statistical models of transistor parameters from IC foundry
High accuracyLong simulation time
HSPICE Monte Carlo
Analysis(circuit performance)
Device variation
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Hierarchical Statistical AnalysisHierarchical Statistical AnalysisSolve the speed issue of traditional MC analysis Response Surface Methodology (RSM) technique
Regression-based methodNumeric statistical results
HSPICE MCS
complicated
simple
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Regression Cost of RSMRegression Cost of RSM1st-order RSM :
2nd-order RSM :
Number of training samples is at least 4 times greater than the number of unknown coefficients
Even if a simplified algorithm is used
Example: If k =4 1st RSM : 5 unknown coefficients �20 training samples 2nd RSM : 15 unknown coefficients � 60 training samples
kk XaXaXaaY ++++= ...22110
ref: Xin Li, Jiayong Le, Pileggi, L.T., Strojwas, A., “Projection-based performance modeling for inter/intra-die variations”, ICCAD, 2005.
∑∑∑= ==
++=k
i
k
jjiij
k
iii XXaXaaY
1 110
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Our TargetsOur Targets
HSPICE MCS
Pure RSM-based
Our *BMCS
Regression cost N/A Worse
Accuracy Better Based on complexity Good
Better
Worse
Good
Good
Good
Simulation time Worse
Observability(waveforms)
Better
Hierarchical Statistical Analysis
*BMCS: Behavioral Monte Carlo Simulation
*SE - like analysis
efficient PLL behavioral model
Developed methods
*SE: Sensitivity Analysis
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Sensitivity Analysis (SSensitivity Analysis (SEE))Delay under process variation :
Use sensitivity analysis (SE) to reflect the process variation effects in behavioral parameters
Can save considerable regression time for complicated curve fitting
Disadvantage: Traditional sensitivity analysis may have larger error at analog blocks
We propose modified sensitivity analysis for analog circuits, without extra simulation cost
ii
ddidd x
xTTxTT Δ×∂∂
≈−Δ=Δ 0)(Td0 : Nominal delay
: Delay sensitivity to deviceparameter xii
d
xT∂∂
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Behavioral MCSBehavioral MCS
Behavioral Monte Carlo Simulation (BMCS) Analyze process variation effects at behavioral levelSimulation results include detailed output waveforms and performance shift
The accuracy of the behavioral models is the most critical issue in BMCS-based approaches
Directly affect the statistical resultsIdeal top-down model is not suitableUse bottom-up modeling method to extract actual circuit properties to improve the accuracy
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Our BMCS FlowOur BMCS Flow
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OutlineOutline
IntroductionBottom-up Behavioral ModelingModified Sensitivity AnalysisExperimental ResultsConclusions
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Characterization ModeCharacterization ModeCharge pump PLLOnly one extraction pattern Automatically consider parasitic and loading effectsCan extract all required characteristic parameters from simulation results
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PFD & FDPFD & FDPhase frequency detector and Frequency dividerCharacteristic parameters:
delay time� transition time and reset time for PFD
typical PFD structure PFD output responses
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CP & LFCP & LFCharge Pump and Loop FilterCharacteristic parameters:
Source current (IUp) & current mismatch (IUp - IDn)Impedance of LF Equivalent switch on/off time
C1
C2
Extract from Vctrloutput waveform
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VCOVCOVoltage-controlled oscillatorLinear VCO model
Simpler approachCharacteristic parameters: Vmin , fmin ,Vmax , fmax , KVCO
(V2, f2)
Kvco(V1, f1)
(Vmin, fmin)
(Vmax, fmax)
Vctrl [V]
fout [Hz]
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SSEE Analysis for Process VariationAnalysis for Process Variation
Find the relationship of behavioral parameters under device parameter variation
Just for timing parameters in our behavioral model
Delay change under width variation :
Extract the sensitivity value ( ):
Extend to be a process variation aware model:
WdT ΔΔ ,
WTE dS Δ_,
constantW
TW
TS WdWd
WTE d=
ΔΔ
≈∂
∂= ΔΔ
Δ,,
_,
oxdtd
dd
TTEoxVTEt
LTEWTEdoxtd
STSV
SLSWTTVLWT
ΔΔ
ΔΔ
×Δ+×Δ+
×Δ+×Δ+=ΔΔΔΔ
_,_,
_,_,0
),,,(
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OutlineOutline
IntroductionBottom-up Behavioral ModelingModified Sensitivity AnalysisExperimental ResultsConclusions
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Current Variation in CPCurrent Variation in CPDrain current of MOS in saturation region:
Current variation ratio under Vt variation:
2)(2 tGS
ox
nD VV
LW
TI −=
εμ
Sensitive analysis (SE)
SE may not suitable
[ ]
22
2
2
2 '
11
)()(
)()()(
⎟⎠⎞
⎜⎝⎛ Δ−=⎟⎟
⎠
⎞⎜⎜⎝
⎛−
Δ−=
⎟⎟⎠
⎞⎜⎜⎝
⎛−
Δ−−=
−Δ+−
≅Δ
=Δ
kV
VVV
VVVVV
VVVVV
IVIVratio
t
tGS
t
tGS
ttGS
tGS
ttGS
D
tDt
Only need to find k
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Our Method vs. Traditional SOur Method vs. Traditional SEE
Same extraction timeMore accurate: more similar to the HSPICE results
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Modeling Strategy for VCO (1/3)Modeling Strategy for VCO (1/3)VCO transfer curve under length variationTraditional SE method:
, _ΔΔ
= =ΔE f L L
fS constant
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Modeling Strategy for VCO (2/3)Modeling Strategy for VCO (2/3)
Consider Vctrl effects:
VCOLL Kslope
ffVV+
−−=
ΔΔ
'min
'1
1min,
VCOLL Kslope
ffVV+−
+=Δ
Δ
'2
'max
2max,
minf
L = 0Δ
outf
ctrlV
1fΔ
1V
maxf
L < 0 Δ
minfΔ'
minf
'maxf
2fΔ
2V 0max,V0min,V
LV Δmax,
LV Δmin,
'1f
'2f
1min
max2
min 1, _ , _
max, _ , _
2
;
;
E L E L
E L E L
f f
f f
L L
L L
f fS S
f fS S
Δ Δ
Δ Δ
Δ Δ= =
Δ ΔΔ Δ
= =Δ Δ
_ _2 1, ,
2 1
( )E f L E f LL
L S S
V Vε Δ Δ
Δ
Δ × −=
−
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Modeling Strategy for VCO (3/3)Modeling Strategy for VCO (3/3)
W L V Toxtφ φ φ φ φΔ Δ Δ ΔΔ = + + +=>
Our modified SE
_ min,
_ max,
_ min,
min
max
min
, _
,
,
,
,
, [ ]
( )
)
(
( ) -
( , )L
L
L L
E f L ctrl
E f L ctrl E f L ctrl
E f L ctrl
if
if
V t V
L V V t V
S
S S
S V t V ε
Δ
Δ
Δ Δ
Δ
Δ Δ
Δ
≤
Δ ≥=
+ ×
, otherwise
⎧⎪⎪⎨⎪⎪⎩
min
min,
max,
, _
min
max
, _
, _
2
2
2
( )
, ( )
[ ( ) -
( ) ,
( )
( )
ctrl
L
L
E f L
E f L ctrl
L E f L ctrl
L S if V t V
L S if V t V
L S V tt
t
t
π
π
π
φΔ
Δ
Δ
Δ
Δ Δ
Δ ≤
Δ ≥
Δ
×
= ×
× +
( ){ }min, ] , L L otherwiseV dtεΔ Δ×
⎧⎪⎪⎨⎪⎪⎩ ∫
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Experimental ResultsExperimental ResultsCharge pump PLL with TSMC RF 0.18μm processUse Verilog-A language to describe our PLL modelSimulation environment: Analog Artist (Cadence)
HSPICEOur model
No process variation: Vctrl waveform
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Process Variation ExperimentsProcess Variation Experiments
HSPICE Monte Carlo
Analysis(output performance)
Device variationBehavioral
Monte Carlo Simulation
(output performance)
WΔ
LΔ
tVΔ
oxTΔ
Comparison100 runs
(Any Distribution)
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Our BMCS vs. HSPICE MCSOur BMCS vs. HSPICE MCS
*Corr. Coe. : Correlation Coefficient
Corr. Coe. = 0.999
VVlocklock
Corr. Coe. = 0.991
TTsettlesettle
*Perfect match: points on the red line(slope = 1)
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100 Runs MC Simulation Results100 Runs MC Simulation Results
Standard Deviation (St. Dev.)
1st RSM+ BMCS
Trad. SE+ BMCS
Modified SE+ BMCS HSPICE
Mean 0.993 -0.1% -0.1% 0.1%32.4% 2.9%
1.9%-0.8%-6.1%0.7%-1.8%
2.0%-6.1%-6.1%63.6%-3.5%
5.9%2.2%-0.5%-7.6%-2.9%-2.4%
0.0363.4490.57312.21.36
Worst 16.6 16.4 16.7 17.0�34.27
2.43
0.993 0.995 0.994St. Dev. 0.045 0.035 0.034
Mean 3.441 3.438 3.374St. Dev. 0.541 0.572 0.576
Mean 12.4 12.4 13.2St. Dev. 2.29 1.41 1.40
Extraction time (hrs) 8.57 8.57 N/ASimulation time (hrs) 2.51 2.64 598.54
Jitterpk-pk(ps)
Vlock(V)
Tsettle(μs)
Use same PLL behavioral model (ours)
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ConclusionsConclusions
Use accurate behavioral model to perform fast MC analysis for process variation (BMCS)
Our modified sensitivity analysis saves considerable regression cost for complicated curve fitting
Handle any distribution of device parameter variation
Include detailed output waveforms and behavior shift, not some statistical numbers only (well observability)
Reduce the simulation time for MC analysis from several days to several hours
Retain high accuracy
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Thanks for your attention !!!