A/D Converter Figures of Merit and Performance Trends
Boris Murmann Stanford University
Definition
2
FIGURE OF MERIT
A numerical quantity based on one or
more characteristics of a system or
device that represents a measure of
efficiency or effectiveness
First Known Use of FIGURE OF MERIT
Circa 1865
A/D Converter Characteristics
3
Resolution Conversion Rate
Power Dissipation
Input Impedance
Supply Rejection
Yield
Common-Mode Rejection
Die Area
Aperture Bandwidth
Metastability Rate
Process Feature Size
Practical ADC FoMs Must Be Simple
4
Resolution Conversion Rate
Power Dissipation
Input Impedance
Supply Rejection
Yield
Common-Mode Rejection
Die Area
Aperture Bandwidth
Metastability Rate
Process Feature Size
FoM
Typical FoM Usage
An FoM is just one entry in larger comparison table that intends to tell the whole story
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[Miyahara, ISSCC 2014]
FoM Construction
The FoM should reflect the design tradeoffs in a fair and realistic manner
Conversion Rate ↔ Power Dissipation
Resolution ↔ Power Dissipation
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Resolution Conversion Rate
Power Dissipation
? ?
Conversion Rate ↔ Power Dissipation
In an ideal world, the power dissipation is directly proportional to the conversion rate
Physics: Power = Energy/Time
To first order, this is also a reasonable baseline assumption for ADCs
ADCs: Power = Energy Conversion Rate
To second order, ADC power scales superlinear with conversion rate
Hard to capture analytically in a simple FoM
Deal with this in practice by comparing only ADCs with similar conversion rates
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Resolution ↔ Power Dissipation
This tradeoff is much harder to quantify and depends on what limits the underlying circuits
First order results for different limiting mechanisms
Matching: Power grows 8x per added bit
Thermal noise: Power grows 4x per added bit
Process CV2: Power grows 2x per added bit
Which trade-offs should be used in an ADC FoM?
Looking at experimental data gives clues
Typically use peak Signal-to-Noise-and-Distortion Ratio (SNDR) as a proxy for resolution
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10 20 30 40 50 60 70 80 90 100 11010
-14
10-12
10-10
10-8
10-6
SNDR [dB]
AD
C E
nerg
y =
P/f
s [J]
Experimental Data (1997-2004)
B. Murmann, "ADC Performance Survey 1997-2014," [Online]. Available: http://web.stanford.edu/~murmann/adcsurvey.html
2x per 6dB
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Experimental Data (1997-2009)
B. Murmann, "ADC Performance Survey 1997-2014," [Online]. Available: http://web.stanford.edu/~murmann/adcsurvey.html
10
10 20 30 40 50 60 70 80 90 100 11010
-14
10-12
10-10
10-8
10-6
SNDR [dB]
AD
C E
nerg
y =
P/f
s [J]
10 20 30 40 50 60 70 80 90 100 11010
-14
10-12
10-10
10-8
10-6
SNDR [dB]
AD
C E
nerg
y =
P/f
s [J]
Experimental Data (1997-2014)
4x per 6dB
“Thermal Slope”
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B. Murmann, "ADC Performance Survey 1997-2014," [Online]. Available: http://web.stanford.edu/~murmann/adcsurvey.html
Observations
In 2004, the leading edge across all SNDR showed a 2x per bit tradeoff
A FoM that encapsulates this slope was justifiable at that time
In 2014, the situation is different
Leading edge designs with SNDR > 50dB show a 4x per bit tradeoff
Suggests that a larger fraction of recent designs is truly limited by noise, not process technology
Need to consider carefully which FoM is appropriate
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R. H. Walden, “Analog-to-digital converter survey and analysis”, IEEE J. Select. Areas Commun., April 1999
Popular FoMs
Walden FoM1
2x per bit
Schreier FoM2 (DR)
4x per bit
Ignores distortion
Schreier FoM3 (SNDR)
4x per bit
Includes distortion
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1 R. H. Walden, “Analog-to-digital converter survey and analysis”, IEEE J. Select. Areas Commun., Apr. 1999 2 R. Schreier and G. C. Temes, Understanding Delta-Sigma Data Converters, Wiley, 2005 3 A.M.A. Ali, et al., "A 16-bit 250-MS/s IF Sampling Pipelined ADC With Background Calibration," JSSC, Dec. 2010
𝑭𝒐𝑴𝑺,𝑫𝑹 = 𝑫𝑹 + 𝟏𝟎𝒍𝒐𝒈𝑩𝑾
𝑷
𝑭𝒐𝑴𝑺 = 𝑺𝑵𝑫𝑹 + 𝟏𝟎𝒍𝒐𝒈𝒇𝒔/𝟐
𝑷
𝑭𝒐𝑴𝑾 =𝑷
𝒇𝒔 ⋅ 𝟐𝑬𝑵𝑶𝑩 𝑬𝑵𝑶𝑩 =
𝑺𝑵𝑫𝑹 − 𝟏𝟕𝟔
𝟔. 𝟎𝟐
State-of-the-Art FoM Lines
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B. Murmann, "ADC Performance Survey 1997-2014," [Online]. Available: http://web.stanford.edu/~murmann/adcsurvey.html
10 20 30 40 50 60 70 80 90 100 11010
-14
10-13
10-12
10-11
10-10
10-9
10-8
10-7
SNDR [dB]
AD
C E
nerg
y =
P/f
s [J]
ISSCC & VLSI 1997-2014
FoMS = 173dB
FoMW
= 5fJ/conv-step
104
105
106
107
108
109
1010
1011
130
135
140
145
150
155
160
165
170
175
180
185
fs [Hz]
FoM
S [dB
]FoMS vs. Conversion Rate (2014)
–10dB per
decade
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B. Murmann, "ADC Performance Survey 1997-2014," [Online]. Available: http://web.stanford.edu/~murmann/adcsurvey.html
FOMS computed
for fin near fs/2
FoMS vs. Conversion Rate (2009)
16
B. Murmann, "ADC Performance Survey 1997-2014," [Online]. Available: http://web.stanford.edu/~murmann/adcsurvey.html
104
105
106
107
108
109
1010
1011
130
135
140
145
150
155
160
165
170
175
180
185
fs [Hz]
FoM
S [dB
]
FoMS vs. Conversion Rate (2004)
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B. Murmann, "ADC Performance Survey 1997-2014," [Online]. Available: http://web.stanford.edu/~murmann/adcsurvey.html
104
105
106
107
108
109
1010
1011
130
135
140
145
150
155
160
165
170
175
180
185
fs [Hz]
FoM
S [dB
]
13 dB
60x
Limits?
We have seen spectacular FoM improvements over the past decade – when will this come to an end?
High frequency asymptote of FOMS (60x improvement)
Process fT has scaled roughly 10x over last decade
The rest must have come from better design
Asymptote shift will continue as long as technology improves, and we find ways to improve design
Low frequency asymptote of FOMS (13dB improvement)
Much has been written about limits of ADC energy
A reasonably well-accepted limit is given by the energy of a class-B switched capacitor circuit
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𝑷
𝒇𝒔 𝒎𝒊𝒏
= 𝟖𝒌𝑻 ⋅ 𝑺𝑵𝑹 ⇒ 𝑭𝑶𝑴𝑺 = 𝟏𝟗𝟐𝒅𝑩
104
105
106
107
108
109
1010
1011
130
140
150
160
170
180
190
200
fs [Hz]
FoM
S [dB
]FOMS Limits?
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B. Murmann, "ADC Performance Survey 1997-2014," [Online]. Available: http://web.stanford.edu/~murmann/adcsurvey.html
192 dB Close to impossible
186 dB Realistic bound?
Summary
FoMs must be simple to be useful
Consequences
FoMs do not tell the whole story, one must consider all relevant aspects of a design (table)
The tradeoffs hardcoded into a FoM are based on assumptions that may not always apply
FoM usage
Compare only designs with similar conversion rates and resolutions
FoMS is preferred for designs with SNDR > 50dB
FoMW still has its place for low-resolution designs
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