Efficient ADC Testing Condition
with Histogram Method
Yujie Zhao, Anna Kuwana, Shuhei Yamamoto, Yuto Sasaki,
Haruo Kobayashi, Takayuki Nakatani, Kazumi Hatayama
Keno Sato, Takashi Ishida,
Toshiyuki Okamoto, Tamotsu Ichikawa
Division of Electronics and Informatics
Gunma University
ROHM Semiconductor
Dec. 3, 2020
4th International Conference on Technology and Social Science
2/25
Outline
• Objective
• ADC Test with Histogram Method
• Input Sine Wave and Sampling Frequency
Relationship in ADC Histogram Test Method
Sine Wave Histogram and Waveform Missing
Metallic Ratio and Prime Number Ratio
• Conclusion
3/25
Outline
• Objective
• ADC Test with Histogram Method
• Input Sine Wave and Sampling Frequency
Relationship in ADC Histogram Test Method
Sine Wave Histogram and Waveform Missing
Metallic Ratio and Prime Number Ratio
• Conclusion
4/25
Background
2020/12/4
IoT(Internet of Things)
High quality & Low cost test is required
The application of digital signal and
analog signal conversion is very
extensive.
Analog signal
(sound, light)
Digital signal
(Binary number)
5/25
Research Objective & Approach
Analog-to-Digital Converter (ADC)
Linearity Test
Test cost is proportional to test time
the low-sampling-rate high-resolution ADC
● low-speed sampling
● high-resolution
take a long time
Increasing the sampling efficiency
Propose “short-time” Relationship Between Input Frequency and Sampling Frequency
This Work
6/25
Outline
• Objective
• ADC Test with Histogram Method
• Input Sine Wave and Sampling Frequency
Relationship in ADC Histogram Test Method
Sine Wave Histogram and Waveform Missing
Metallic Ratio and Prime Number Ratio
• Conclusion
7/25
■Histogram method (Ramp wave input)
7
Highly linear ramp signal generation is difficult
ADC output histograms for all bins are equal if
ADC is perfectly linear
t
Ramp wave
ADC
DUT
001010011100101110111
Output
Code
Number
of Samples
INL
DNL
Conventional Linearity Testing 1
DNL
INL
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Conventional Linearity Testing 2
8
■Histogram method(Single sine wave input)
High accuracy sine wave can be generated
using an analog filter
The number of samples is small
around the middle of output codes
t
Sine wave
Sine wave
GeneratorBPF ADC
DUT
Output
Code
Number
of Samples
INL
DNL
f
Remove
DNL
INL
9/25
DNL & INL
9
001 010 011 100 101 110 111
Output
Code
Number
of Samples
DNL
Important testing for ADCs
DNL : Difference between an actual step width
and the ideal value
INL : Deviation from ideal conversion line
k
i
iDNLkINL1
)()(
10/25
Outline
• Objective
• ADC Test with Histogram Method
• Input Sine Wave and Sampling Frequency
Relationship in ADC Histogram Test Method
Sine Wave Histogram and Waveform Missing
Metallic Ratio and Prime Number Ratio
• Conclusion
11/25
Repetitive waveform sampled with asynchronous
Sampling CLK
Measured waveform
Compose a 1-period waveform0
50
100
150
200
250
0 128 256 384 512 640 768 896 1024N
um
ber
of
Sam
ple
s
Output Code
Probability Distribution Function
𝑝 𝑣 =1
𝜋𝐴2−𝑣2
The sampled histogram
is compared with
the PDF.
The histogram is
measured, DNL and INL
are calculated.
Sine Wave Histogram
12/25
A large amount of data is required to reproduce the waveform Test time: long
Waveform Missing
𝑻𝑪𝑳𝑲
TSIG
Waveform Missing occurs in
Special ratio(TCLK and Tsig)
Sampling CLK
Measured waveform
13/25
𝛼 = 1,1
2,1
3,2
3,⋯ ,
1
6,⋯
Τ1 6
1
Τ1 1024
CLK
sig
Waveform Missing
𝑓𝐶𝐿𝐾 ≈1
𝛼𝑓𝑠𝑖𝑔𝑓𝐶𝐿𝐾 ≫ 𝑓𝑠𝑖𝑔
𝑓𝐶𝐿𝐾 ≈ 𝑓𝑠𝑖𝑔
Yuto Sasaki, Yujie Zhao, Anna Kuwana and Haruo Kobayashi, "Highly Efficient Waveform Acquisition Condition in
Equivalent-Time Sampling System", 27th IEEE Asian Test Symposium, Hefei, Anhui, China (Oct. 2018)
Special ratio
TCLK and Tsig , 𝑓𝐶𝐿𝐾 and 𝑓𝑠𝑖𝑔
14/25
Waveform Missing
Normal situation Waveform Missing
15/25
Golden Ratio
Golden Ratio: 𝐥𝐢𝐦𝒏→∞
𝑭𝒏
𝑭𝒏−𝟏= 𝟏. 𝟔𝟏𝟖𝟎𝟑𝟑𝟗𝟖𝟖𝟕𝟒𝟗𝟖𝟗𝟓 = 𝝋
The most beautiful ratio
16/25
Yuto Sasaki, Yujie Zhao, Anna Kuwana and Haruo Kobayashi, "Highly Efficient Waveform Acquisition Condition in
Equivalent-Time Sampling System", 27th IEEE Asian Test Symposium, Hefei, Anhui, China (Oct. 2018)
Τ1 𝜑
CLK
Golden ratio 𝝋
𝒇𝑪𝑳𝑲 = 𝝋 × 𝒇𝒔𝒊𝒈𝝋 = 1.6180339887…
Golden Ratio
17/25
Outline
• Objective
• ADC Test with Histogram Method
• Input Sine Wave and Sampling Frequency
Relationship in ADC Histogram Test Method
Sine Wave Histogram and Waveform Missing
Metallic Ratio and Prime Number Ratio
• Conclusion
18/25
Metallic ratio
Golden Ratio: 𝐥𝐢𝐦𝒏→∞
𝑭𝒏
𝑭𝒏−𝟏= 𝟏. 𝟔𝟏𝟖𝟎𝟑𝟑𝟗𝟖𝟖𝟕𝟒𝟗𝟖𝟗𝟓 = 𝝋
n Decimal
0 1
11 + 5
21.6180339887… Golden ratio ∅
2 1 + 2 2.4142135623… Silver ratio
33 + 13
23.3027756377… Bronze ratio
4 2 + 5 4.2360679774…
… …
n𝑛 + 𝑛2 + 4
2
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Histogram of Saw wave
𝑇𝑠𝑖𝑔
ℎ𝑖 𝑘 =𝑀
𝑁, 𝑘 = 1,2,3, . . . , 𝑁ideal value error 𝑒 𝑘 =
𝑁 ∙ ℎ 𝑘
𝑀− 1
ideal value ℎ𝑖 𝑘 =
𝑀
𝑁
Output Code
Number of
Samples
Total number of samples is M and
ADC resolution(the number of the histogram) is N.
ℎ 𝑘
20/25
ADC Resolution 3Bit N = 8, Increase MRMS
Number of Samples M
Root-Mean-Square of the errors between the actual and ideal histograms 𝑅𝑀𝑆 =
σ ⅇ 𝑘2
𝑁
21/25
RMS between the actual and ideal
Resolution N
RMS
Total number of samples M = 2048, Increase resolution N. Compare RATIO
22/25
RMS of Prime Number RatioRMS
Most of the RMS results are not as good as Metallic ratio.
Total number of samples M = 2048, Increase resolution N. Compare RATIO
Resolution N
𝒇𝑪𝑳𝑲 = 𝒇𝒔𝒊𝒈 × 𝑹𝑨𝑻𝑰𝑶
23/25
RMS results within a range(1~4)
0
500
1000
1500
2000
2500
3000
3500
1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4
RMS
RatioTherefore, we calculated the RMS within
a certain range (1~4) to find a good ratio.
RMS minimum point
Total number of samples M = 2048, Resolution 8Bit N=256
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Outline
• Objective
• ADC Test with Histogram Method
• Input Sine Wave and Sampling Frequency
Relationship in ADC Histogram Test Method
Sine Wave Histogram
Random Sampling and Waveform Missing
Metallic Ratio and Prime Number Ratio
• Conclusion
25/25
Conclusion
25
Find a ratio that is more efficient and has a
smaller RMS like the golden ratio
next issue
Golden ratio sampling
Efficiency: Highest
Sampling frequency: low
Metallic ratio sampling
Efficiency: Good
Sampling frequency: High
Prime number ratio sampling
Efficiency:Not Good
Sampling frequency: High