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Department of Electrical and Computer Engineering
Successive Approximation ADCs
Vishal Saxena
Boise State University
(vishalsaxena@boisestate.edu)
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Successive Approximation ADC
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Data Converter Architectures
1 word/OSR*Tclk
1 level/Tclk
Resolution
[Bits]
1 bit/Tclk
20
Integrating
Partial word/Tclk
Oversampling
15
Successive Approximation
1 word/Tclk
Algorithmic
Subranging
Pipeline
Folding & Interpolating
Interleaving
Flash
10
5
Nyquist
Oversampling
0
1k
10k
100k
1M
10M
100M
1G
10G
100G
Sample Rate [Hz]
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Successive Approximation ADC
VX
Vi
b1
VDAC
bN
•
•
Do
Shift
Register
Binary search over DAC inputs
•
N*Tclk to complete N bits
•
successive approximation register or SAR
High accuracy achievable (16+ bits)
•
•
...
...
DAC
Relies on highly accurate comparator
Moderate speeds (typically 0.1-10 MHz parts)
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Binary Search Algorithm
VDAC
VX
Vi
Vi
VFS
b1
VDAC
bN
...
...
DAC
Do
VFS
2
Shift
Register
0
1
MSB
0
0
1
1
Tclk
•
DAC output gradually approaches the input voltage
•
Comparator differential input gradually approaches zero
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0
LSB
t
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Binary Search Algorithm contd.
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High Performance Example
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Charge Redistribution SAR ADC
Φ1e
VX
SAR
8C
4C
2C
C
C
Do
VR
Φ1
Φ1
Φ1
Φ1
Φ1
Vi
•
4-bit binary-weighted capacitor array DAC (aka charge scaling DAC)
•
Capacitor array samples input when Φ1 is asserted (bottom-plate)
•
Comparator acts as a zero crossing detector
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Charge Redistribution (MSB)
Φ1e
VX
SAR
8C
4C
2C
C
C
Do
VR
Φ1
Φ1
Φ1
Φ1
Φ1
Vi
•
Start with C4 connected to VR and others to 0 (i.e. SAR=1000)
Vi 16C =  VR - VX  C4 - VX  C3 +C2 +C1 +C0   VX 
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VR  8C - Vi 16C VR

- Vi
16C
2
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Comparison (MSB)
VX
1
0
Sample
t
1
MSB
MSB TEST : VX 
VR
 Vi
2
•
If VX < 0, then Vi > VR/2, and MSB = 1, C4 remains connected to VR
•
If VX > 0, then Vi < VR/2, and MSB = 0, C4 is switched to ground
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Charge Redistribution (MSB–1)
Φ1e
VX
SAR
8C
4C
2C
C
C
Do
VR
Φ1
Φ1
Φ1
Φ1
Φ1
Vi
•
SAR=1100
Vi 16C   VR  VX  12C  VX  4C  VX 
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VR 12C  Vi 16C 3
 VR  Vi
16C
4
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Comparison (MSB–1)
VX
1
2
0
Sample
t
1
MSB
0
MSB -1 TEST :
VX 
3
VR  Vi
4
•
If VX < 0, then Vi > 3VR/4, and MSB-1 = 1, C3 remains connected to VR
•
If VX > 0, then Vi < 3VR/4, and MSB-1 = 0, C3 is switched to ground
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Charge Redistribution (Other Bits)
Φ1e
VX
SAR
8C
4C
2C
C
C
Do
VR
Φ1
Φ1
Φ1
Φ1
Φ1
Vi
•
SAR=1010, and so on…
Test completes when all four bits are determined w/ four charge
redistributions and comparisons
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After Four Clock Cycles…
VX
1
2
3
4
0
Sample
t
1
MSB
0
0
1
LSB
•
Usually, half Tclk is allocated for charge redistribution and half for
comparison + digital logic
•
VX always converges to 0 (Vos if comparator has nonzero offset)
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Summing-Node Parasitics
Φ1e
CP
Vos
SAR
8C
4C
2C
C
C
Do
VR
Φ1
Φ1
Φ1
Φ1
Φ1
Vi
•
If Vos = 0, CP has no effect eventually; otherwise, CP attenuates VX
•
Auto-zeroing can be applied to the comparator to reduce offset
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SAR ADC Considerations
•Power efficiency – only comparator consumes DC power
•Conversion rate typically limited by finite bandwidth of RC network
during sampling and bit-tests
•For high resolution, the binary weighted capacitor array can become
quite large
•E.g. 16-bit resolution, Ctotal~100pF for reasonable kT/C noise contribution
•If matching is an issue, an even larger value may be needed
•E.g. if matching dictates Cmin=10fF, then 216Cmin=655pF
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SAR ADC Considerations contd.
•Comparator offset Vos introduces an input-referred offset ~
(1+CP/ΣCj)*Vos
•CP in general has little effect on the conversion (VX→0 at the end of the
search)
•however, VX is always attenuated due to charge sharing of CP
•Binary search is sensitive to intermediate errors made during search –
if an intermediate decision is wrong, the digitization process cannot
recover
•DAC must settle into ±½ LSB bound within the time allowed
•Comparator offset must be constant (no hysteresis or time-dependent
offset)
•Non-binary search algorithm can be used (Kuttner, ISSCC’02)
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SAR ADC Considerations contd.
•Commonly used techniques
•Implement "two-stage" or "multi-stage" capacitor network to reduce array
size [Yee, JSSC 8/79]
•Split DAC or C-2C network
•Calibrate capacitor array to obtain precision beyond raw technology
matching [Lee, JSSC 12/84]
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SAR ADC Speed Estimation
• Model RC network when VIN is charged
• Replace switches with R’s
• Assume switches are sized proportional to capacitors
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SAR ADC Speed Estimation contd.
• Speed limited by RC time constant of capacitor array and switches
• For better than 0.5 LSB accuracy
• Sets minimum value for the charging time T
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Recap: Advantages of SAR ADC
•
Mostly digital components
•
good for technology scaling
•No linear, high precision amplification is required
• fast, low power
•Minimal hardware
•1 comparator is needed
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SAR Evolution
•Digital friendly architecture in scaled CMOS has renewed interest in
SAR innovation
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Limitations of Synchronous SAR
•Cost
•High-speed internal clock needed 
•Speed Limitation
•Worst-case cycle time 
•Margin for clock jitter 
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Asynchronous SAR Concept
•Self-timed Asynchronous comparisons
•Master clock used for synchronizing with the sample rate
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How much comparison time is saved?
•Conv. time between sync. and async. SAR, assuming regenerative
comparator is used.
•It varies with residue voltage profile
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Asynchronous SAR ADC Concept
•
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Asynchronous SAR ADC Concept
• Dynamic to save power and generate ready signal
• Reset switches for fast recovery
• Ready signal is generated by NAND gate!
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Monotonic Capacitor Switching
•Monotonic switching procedure
•Input-common mode voltage
gradually converges to ground
•Exploit differential configuration
•Asynchronous comparisons
•Switching energy reduced by
81%
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Monotonic Capacitor Switching contd.
•
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Monotonic Capacitor Switching contd.
•Conventional switching
procedure
•Monotonic switching procedure
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Monotonic Capacitor Switching contd.
•
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Loop-unrolled SAR ADC
•Use N comparators for
each bit of conversion
•“loop unrolling”
•Asynchronous individual
comparisons
•1.25Gbps 6-bit
•Serial links application
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Loop-unrolled SAR ADC contd.
•High speed comparator
•IDAC for offset cancellation
•Metastability detection
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Time Interleaving
• Sampling rate scale
proportionally to the number of
interleaved channels
• Calibration is required for interchannel mismatch
• Relaxed clock distribution
• For example:
• 8bit 56GS/s
• 320 of 175MS/s SAR
(Fujitsu)
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90GS/s 8bit with 64x Time Interleave
• Two comparators ping pong in two consecutive conversions
implemented in 32nm SOI
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Title
•Text
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References
1.
2.
3.
Rudy van de Plassche, “CMOS Integrated Analog-to-Digital and Digital-to-Analog
Converters,” 2nd Ed., Springer, 2005..
Y. Chiu, Data Converters Lecture Slides, UT Dallas 2012.
B. Boser, Analog-Digital Interface Circuits Lecture Slides, UC Berkeley 2011.
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