an analysis of stochastic self-calibration of tdc …...–cycles of ring oscillators –number of...
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![Page 1: An Analysis of Stochastic Self-Calibration of TDC …...–Cycles of ring oscillators –Number of stages –Phase difference of ring oscillators 16 Kobayashi Lab @ Gunma University](https://reader033.vdocuments.net/reader033/viewer/2022041919/5e6b43b87f31a13cd8257dd0/html5/thumbnails/1.jpg)
Kobayashi Lab @ Gunma University
The 22nd Asian Test Symposium, Yilan, Taiwan, R.O.C
The 22th IEEE Asian Test Symposium (ATS’13) , Yilan, Taiwan, Nov. 20, 2013
An Analysis of Stochastic
Self-Calibration of TDC Using
Two Ring Oscillators
Kentaroh Katoh, Yuta Doi, Satoshi Ito, Haruo Kobayashi,
Ensi Li, Nobukazu Takai, Osamu Kobayashi
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Kobayashi Lab @ Gunma University
The 22nd Asian Test Symposium, Yilan, Taiwan, R.O.C
Contents
• Background
– Motivation
– TDC
– Abstract of Stochastic Calibration
– Aim of Study
• Preliminaries for Simulation
• Simulation Results
• Conclusion
2
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Kobayashi Lab @ Gunma University
The 22nd Asian Test Symposium, Yilan, Taiwan, R.O.C
Motivation
3
Advanced CMOS Process
Variation Timing Errors
Serious Timing-Related
Problems
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Kobayashi Lab @ Gunma University
The 22nd Asian Test Symposium, Yilan, Taiwan, R.O.C
TDC for solution of timing-related problems
4
TDC (Time to Digital Converter)
Examples of Timing-Related Problems
Jitter of High-Speed Serial Interface
Delay Fault of Logic Circuit
Solution
On-Chip Delay Measurement
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Kobayashi Lab @ Gunma University
The 22nd Asian Test Symposium, Yilan, Taiwan, R.O.C
TDC (Time to Digital Converter)
• An On-Chip Delay Measurement Circuit
• Time Interval Digital Value
• Consists of CMOS digital elements
can be embedded in advanced VLSI
5
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Kobayashi Lab @ Gunma University
The 22nd Asian Test Symposium, Yilan, Taiwan, R.O.C
Basic TDC
6
t TDC Code t TDC Code
0 < t < τ1 10000000 τ4 < t < τ5 11111000
τ1 < t < τ2 11000000 τ5 < t < τ6 11111100
τ2 < t < τ3 11100000 τ6 < t < τ7 11111110
τ3 < t < τ4 11110000 τ7 < t 11111111
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Kobayashi Lab @ Gunma University
The 22nd Asian Test Symposium, Yilan, Taiwan, R.O.C
Problems of TDC
7
Advanced CMOS Process
Variation Delay Variation of Buffers
Non-linearity Characteristics Problem
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Kobayashi Lab @ Gunma University
The 22nd Asian Test Symposium, Yilan, Taiwan, R.O.C
Problems of TDC (Cont.)
8
t TDC Code t TDC Code
0.0 < t < 1.2 10000000 3.9 < t < 4.9 11111000
1.2 < t < 2.3 11000000 4.9 < t < 5.7 11111100
2.3 < t < 3.0 11100000 5.7 < t < 7.0 11111110
3.0 < t < 3.9 11110000 7.0 < t 11111111
t TDC Code t TDC Code
0.0 < t < 1.0 10000000 4.0 < t < 5.0 11111000
1.0 < t < 2.0 11000000 5.0 < t < 6.0 11111100
2.0 < t < 3.0 11100000 6.0 < t < 7.0 11111110
3.0 < t < 4.0 11110000 7.0 < t 11111111
0
2
4
6
8
0 2 4 6 8T
DC
Co
de
t
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Kobayashi Lab @ Gunma University
The 22nd Asian Test Symposium, Yilan, Taiwan, R.O.C
Problems of TDC (Cont.)
9
t TDC Code t TDC Code
0.0 < t < 1.2 10000000 3.9 < t < 4.9 11111000
1.2 < t < 2.3 11000000 4.9 < t < 5.7 11111100
2.3 < t < 3.0 11100000 5.7 < t < 7.0 11111110
3.0 < t < 3.9 11110000 7.0 < t 11111111
t TDC Code t TDC Code
0.0 < t < 1.0 10000000 4.0 < t < 5.0 11111000
1.0 < t < 2.0 11000000 5.0 < t < 6.0 11111100
2.0 < t < 3.0 11100000 6.0 < t < 7.0 11111110
3.0 < t < 4.0 11110000 7.0 < t 11111111
0
2
4
6
8
0 2 4 6 8
TD
C C
od
e
t
0
2
4
6
8
0 2 4 6 8
TD
C C
od
e
t
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Kobayashi Lab @ Gunma University
The 22nd Asian Test Symposium, Yilan, Taiwan, R.O.C
Basics of stochastic calibration
• Stochastic Calibration
Applied Histogram Method
• Stochastic Time Interval is launched from
• start and stop input
10
2
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Kobayashi Lab @ Gunma University
The 22nd Asian Test Symposium, Yilan, Taiwan, R.O.C
Basics of stochastic calibration
• Stochastic Calibration
Applied Histogram Method
• Stochastic Time Interval is launched from
• start and stop input
11
5
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Kobayashi Lab @ Gunma University
The 22nd Asian Test Symposium, Yilan, Taiwan, R.O.C
Basics of stochastic calibration
• Stochastic Calibration
Applied Histogram Method
• Stochastic Time Interval is launched from
• start and stop input
12
8
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Kobayashi Lab @ Gunma University
The 22nd Asian Test Symposium, Yilan, Taiwan, R.O.C
Basics of stochastic calibration
13
• When Distribution of time interval is uniform
• Each length of each bin is convergent
in proportion to relative delay of each buffer
1.2 1.1
0.7
0.9 1.0 0.8
1.3
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Kobayashi Lab @ Gunma University
The 22nd Asian Test Symposium, Yilan, Taiwan, R.O.C
Basics of stochastic calibration 2
• Time interval following uniform dist.
• Two ring oscillators with no correlation
• Generate time interval following uniform
dist. with low extra area
• Apply two ring oscillators as generator of
time interval
14
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Kobayashi Lab @ Gunma University
The 22nd Asian Test Symposium, Yilan, Taiwan, R.O.C
Stochastic calibration architecture [10]
15
Upper ring oscillator
Lower ring oscillator
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Kobayashi Lab @ Gunma University
The 22nd Asian Test Symposium, Yilan, Taiwan, R.O.C
Calibration and design parameters
• Calibration Parameters
– Probability of convergence
– Time required for convergence
depend on
• Design Parameters
– Cycles of ring oscillators
– Number of stages
– Phase difference of ring oscillators
16
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Kobayashi Lab @ Gunma University
The 22nd Asian Test Symposium, Yilan, Taiwan, R.O.C
Aim of study
• For top-down design of calibration
• designer need relation between calibration
parameters and design parameters
• Analyze relation between calibration
parameters and design parameters to get
guideline of calibration design
17
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Kobayashi Lab @ Gunma University
The 22nd Asian Test Symposium, Yilan, Taiwan, R.O.C
Contents
18
• Background
– Abstract
– TDC
– Abstract of Stochastic Calibration
– Aim of Study
• Preliminaries for Simulation
• Simulation Results
• Conclusion
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Kobayashi Lab @ Gunma University
The 22nd Asian Test Symposium, Yilan, Taiwan, R.O.C
Definition of cycles of two ring oscillators
19
Upper Ring Oscillator
Lower Ring Oscillator
T0
T1
d
Initial differential
delay
T0 > T1
Beginning of
calibration
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Kobayashi Lab @ Gunma University
The 22nd Asian Test Symposium, Yilan, Taiwan, R.O.C
Definition of DNL
20
2
1
2
1
STGSTG N
i ij
ij
N
i i
iij
b
b
T
Tdnl
|)|,|,max(| )(1 2 jNjj MEASdnldnlDNL
dnlij:differential non-linearity error of i-th stage after j-th
sampling
DNLj: differential non-linearity error after j-th sampling
Ti :Delay of buffer of i-th buffer
bij :Length of bin of i-th stage after j-th sampling
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Kobayashi Lab @ Gunma University
The 22nd Asian Test Symposium, Yilan, Taiwan, R.O.C
Definition of required measurement for
convergence
• NE(TDC, T0, T1, d, DNL) : Number of
required measurement for convergence of
TDC within target DNL when cycles of upper
and lower ring oscillator are T0 and T1.
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Kobayashi Lab @ Gunma University
The 22nd Asian Test Symposium, Yilan, Taiwan, R.O.C
Calculation of NE
22
Measure Delay
Update Histogram
NE = 0
DNLNE < DNL ?
j < NMAX ? NE++
N
N
Y
Y
Fail
Success
NMAX: Maximum Iteration time
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Kobayashi Lab @ Gunma University
The 22nd Asian Test Symposium, Yilan, Taiwan, R.O.C
Definition of convergent probability
• Convergent probability PE(DNL): Probability
of success of calibration within a pre-
defined error DNL when calibration is
performed multiple times
23
0.100/)( CALSCALE NNDNLP
NSCAL: Times of which calibration is success
NCAL: Execution times of calibration
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Kobayashi Lab @ Gunma University
The 22nd Asian Test Symposium, Yilan, Taiwan, R.O.C
Definition of prime cycles
• A prime cycle c is defined as follows
24
npc 10/
p: prime number
n: number of figures of the fraction part
1 3 9 1
n = 2
Prime number
1 3 9 1
Prime cycle
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Kobayashi Lab @ Gunma University
The 22nd Asian Test Symposium, Yilan, Taiwan, R.O.C
Contents
25
• Background
– Abstract
– TDC
– Abstract of Stochastic Calibration
– Aim of Study
• Preliminaries for Simulation
• Simulation Results
• Conclusion
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Kobayashi Lab @ Gunma University
The 22nd Asian Test Symposium, Yilan, Taiwan, R.O.C
Experiments
• Design Parameters
– Cycles of two ring oscillators (T0, T1) VS
• Convergent probability (PE)
• Required measurement time to convergent (NE)
– Initial differential delay (d) VS
• Required measurement time to convergent (NE)
– Bit length of each counter
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Kobayashi Lab @ Gunma University
The 22nd Asian Test Symposium, Yilan, Taiwan, R.O.C
Experimental setup
• Buffer delay is set to 1 (unit delay)
• Varied 100 TDCs (TDC0-TDC99) are
constructed
• Variation is 10% of buffer delay following
gaussian distribution
• Maximum delay measurement times:NMAX=214
• Number of figure of fraction: n=2
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Kobayashi Lab @ Gunma University
The 22nd Asian Test Symposium, Yilan, Taiwan, R.O.C
Cycle of two ring oscillators (T0, T1) Spec.
• T0 > T1
• Evaluate in following three cases
– Case 1 : Both T0 and T1 are prime cycles
– Case 2 : T0 is multiple of T1
– Case 3 : Arbitrary values of T0 and T1
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Kobayashi Lab @ Gunma University
The 22nd Asian Test Symposium, Yilan, Taiwan, R.O.C
Cycle of two ring oscillators (T0, T1) Spec. 2
• Parameter set up
– NSTG : 8 16 32 64 128
– Upper ring oscillator cycle T0 is fixed to Tp0
– Lower ring oscillator cycle T1 is swept up from Tmin to Tmax
– DNL 1/1,024
– Calibrate multiple times and calculate PE and NE
– Initial differential delay d 0
29
NSTG Tmin Tmax Tp0
8 2 12 11.93
16 2 18 17.89
32 2 36 35.93
64 2 68 67.93
128 2 132 131.87
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Kobayashi Lab @ Gunma University
The 22nd Asian Test Symposium, Yilan, Taiwan, R.O.C
Simulation Sequence
30
NSCAL += NSCAL(TDCi) NCAL += NCAL(TDCi)
Calculate NE(TDCi)
i = 0 NSCAL=0 NCAL=0 NE=0
i < 99 ? i++
N
Y
Calculate PE= NSCAL/NCAL× 100.0
Update NEmin,NEmax
NE += NE(TDCi)
Calculate NE ave= NE/NCAL
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Kobayashi Lab @ Gunma University
The 22nd Asian Test Symposium, Yilan, Taiwan, R.O.C
Cycle of two ring oscillators (T0, T1) Spec. 3
• Convergent probability PE spec.
31
Case NSTG
8 16 32 64 128
Case 1 100.0 100.0 100.0 100.0 100.0
Case 2 0.0 0.0 0.0 0.0 0.0
Case 3 38.6 43.9 56.4 75.8 78.5
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Kobayashi Lab @ Gunma University
The 22nd Asian Test Symposium, Yilan, Taiwan, R.O.C
Cycle of two ring oscillators (T0, T1) Spec. 4
• Required Measurement Time NE spec.
32
NE Case NSTG
8 16 32 64 128
NEmin Case 1 367 517 605 772 802
Case 2 0 0 0 0 0
Case 3 359 464 640 731 984
NEave Case 1 633.1 1,060.0 1,509.6 1,976.3 2,323.3
Case 2 0 0 0 0 0
Case 3 648.7 1,052.4 1,303.8 1,724.8 1,911.7
NEmax Case 1 798 1,597 3,178 6,324 10,000
Case 2 0 0 0 0 0
Case 3 3,427 10,000 10,000 6,381 10,000
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Kobayashi Lab @ Gunma University
The 22nd Asian Test Symposium, Yilan, Taiwan, R.O.C
Initial differential delay specification
• Parameter setup
– T0 Tp0, T1 2.11 fixed
– d is swept up from 0 to T0
– NEave is calculated
– DNL = 1/128, 1/256, 1/512, 1/1,024
33
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Kobayashi Lab @ Gunma University
The 22nd Asian Test Symposium, Yilan, Taiwan, R.O.C
Initial differential delay specification
• Result
34
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Kobayashi Lab @ Gunma University
The 22nd Asian Test Symposium, Yilan, Taiwan, R.O.C
Bit length of each counter
• Calculate bit length of each counter with
the following equation assuming 10%
variation
• DNL 1/1,024
35
STGECNT NNL /1.1log2
NSTG 8 16 32 64 128
LCNT 9 10 9 7 7
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Kobayashi Lab @ Gunma University
The 22nd Asian Test Symposium, Yilan, Taiwan, R.O.C
Conclusion
• Analyze the relation between calibration
parameters and design parameters
• Analyze not with mathematical analysis but
with computer simulation higher accuracy
• Get the following two conclusions
– Both of the frequencies of the two ring oscillators
should be the prime frequencies
– When both of the frequencies are the prime
frequencies, we estimate the required number of
the times of measurement from the target DNL.
36
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Kobayashi Lab @ Gunma University
The 22nd Asian Test Symposium, Yilan, Taiwan, R.O.C
Questions
• Q.プロセスばらつきを考慮しなかったのはなぜか?
• A.本研究は設計者への設計ガイドラインを目的としており,特に設計パラメータとキャリブレーション特性の関係について研究を行っているため.
37