Design and Calibration Techniques for SAR and Pipeline ADCs
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1 Erik Jonsson School of Engineering & Computer Science Design and Calibration Techniques for SAR and Pipeline ADCs Yun Chiu Erik Jonsson Distinguished Professor Texas Analog Center of Excellence University of Texas at Dallas
2 Course Outline Principles of Multistep A/D Conversion Architectural Redundancy Error Mechanisms and Digital-Domain Calibration Error-Parameter Identification PRBS Test-Signal Injection (sub-adc, sub-dac, input) Two-ADC Equalization (ref.-adc, split-adc, ODC) Energy Efficiency and Trend Summary IN2P3, 5/20/15-2- Y. Chiu
3 Course Outline Principles of Multistep A/D Conversion Architectural Redundancy Error Mechanisms and Digital-Domain Calibration Error-Parameter Identification PRBS Test-Signal Injection (sub-adc, sub-dac, input) Two-ADC Equalization (ref.-adc, split-adc, ODC) Energy Efficiency and Trend Summary IN2P3, 5/20/15-3- Y. Chiu
4 What is A/D Conversion? ref CT, CA in out DT, DA Analog Input Digital Output f s V Vin t N Vin nt FS s LSB = =, Dout n = = 2 N 2 VFS t=nt s Quantization = division + normalization + truncation V FS is the Full-Scale range of ADC determined by V ref. IN2P3, 5/20/15-4- Y. Chiu
5 Quantization Error (or Noise) N = 3 D out N is large V in >>, V in is active ε is uniformly distributed P ε V FS V FS 2 V in 1/ /2 0 /2 ε - ε 2 2 / σ ε = ε dε = 12 - /2 "Random" quantization error is usually regarded as noise. Ref. [1] IN2P3, 5/20/15-5- Y. Chiu
6 Flash ADC Exhaustive Search V FS V i Strobe f s Massive parallelism Very fast Encoder D out Reference ladder consists of 2 N equal size resistors Input is compared to 2 N -1 reference voltages Throughput = f s 2 N -1 comparators Complexity = 2 N Flash ADC is rarely used for beyond 6-8 bits due to complexity. IN2P3, 5/20/15-6- Y. Chiu
7 Long Division (Decimal Case) = 183 r 3 Dividend Divisor Quotient Remainder Step 1: 1 st bit Step 2: 2 nd bit Step 3: 3 rd bit IN2P3, 5/20/15-7- Y. Chiu
8 Quantization (Binary Case) N = 3, FS = 1000, = 1000/8 = 125, V in = 735 D = o V in = 1,0,1 r 110 Vin LSB QN Do Step 1: 1 st bit Step 2: 2 nd bit Step 3: 3 rd bit The procedure is also known as "binary search". IN2P3, 5/20/15-8- Y. Chiu
9 Successive-Approximation (SAR) ADC SAR = 1 comparator + 1 DAC + digital logic IN2P3, 5/20/15-9- Y. Chiu
10 Binary Search MSB Cycle 0.735V N = 3, FS = 1 V, = V, V in = V 0.5V... Sampling V X = V i 0.5V; if V X > 0, MSB = 1, keep current V X V X ; otherwise, MSB = 0, restore V X V X + 0.5V; IN2P3, 5/20/ Y. Chiu
11 Binary Search MSB-1 Cycle 0.235V N = 3, FS = 1 V, = V, V in = V 0.25V... Sampling V X = V X 0.25V; if V X > 0, MSB-1 = 1, keep current V X V X ; otherwise, MSB-1 = 0, restore V X V X V; IN2P3, 5/20/ Y. Chiu
12 Binary Search MSB-2 Cycle 0.235V N = 3, FS = 1 V, = V, V in = V 0.125V... Sampling V X = V X 0.125V; if V X > 0, MSB-2 = 1, keep current V X V X ; otherwise, MSB-2 = 0, restore V X V X V; IN2P3, 5/20/ Y. Chiu
13 Quantization (Binary) Modified N = 3, FS = 1000, = 1000/8 = 125, V in = 735 D = o V in = 1,0,1 r 110 Vin LSB QN Do Step 1: 1 st bit Step 2: 2 nd bit Step 3: 3 rd bit Always use the same divisor but amplify the residue. IN2P3, 5/20/ Y. Chiu
14 Algorithmic (Cyclic) ADC Fixed comparison threshold (V FS /2) + 1-b DAC + Residue Amplifier Modified "Binary Search" IN2P3, 5/20/ Y. Chiu
15 Bit Cycles V o V FS b j =0 b j =1 0 V FS /2 V FS V X Comparison if V X < V FS /2, then b j = 0; otherwise, b j = 1 Residue generation V o = 2 (V X -b j V FS /2) IN2P3, 5/20/ Y. Chiu
16 Pipelined ADC Algorithmic ADC loop unrolled pipeline enables high throughput IN2P3, 5/20/ Y. Chiu
17 Presentation Outline Principles of Multistep A/D Conversion Architectural Redundancy Error Mechanisms and Digital-Domain Calibration Error-Parameter Identification PRBS Test-Signal Injection (sub-adc, sub-dac, input) Two-ADC Equalization (ref.-adc, split-adc, ODC) Energy Efficiency and Trend Summary IN2P3, 5/20/ Y. Chiu
18 What happens with circuit offsets? Ideal RA offset CMP offset V o V o V o V FS b=0 b=1 V FS b=0 b=1 V os V FS b=0 b=1 V os 0 V FS /2 V FS V i 0 V FS /2 V FS V i 0 V FS /2 V FS V i D o D o D o 0 V FS /2 V FS V i V FS /2 V i 0 V FS 0 V FS /2 V FS V i Nearly zero tolerance on circuit offset errors!! IN2P3, 5/20/ Y. Chiu
19 Over-range & Under-range Comparators V o V o V FS b j =0 b j =1 V FS b j =0 b j =1 B j+1 =2 B j+1 =1 B j+1 =1 V FS /2 V FS /2 B j+1 =0 B j+1 =0 0 V FS /2 V FS V i 0 V FS /2 V FS V i B j+1 =-1 D o D o V FS /2 V FS V i 00 0 V FS /2 V FS V i 1 CMP 3 CMPs IN2P3, 5/20/ Y. Chiu
20 Redundancy (a.k.a. DEC or RSD) Original w/ Redundancy V o V o V FS b=0 b=1 b=-1 b=0 b=1 b=2 0 V FS /2 V FS V i 0 V FS /2 V FS V i 4-level (2-bit) DAC required instead of 2-level (1-bit) DAC IN2P3, 5/20/ Y. Chiu
21 Complementary Analog-Digital Information V o V FS b j =0 b j =1 V FS /2 0 V FS /2 V FS D o bit 1 FS 0 V FS /2 V FS V i V i B j+1 =2 B j+1 =1 B j+1 =0 B j+1 =-1 Max tolerance of comparator offset is ±V FS /4 simple comparators Key to understand redundancy: Vo b j =0 2 V V V= i b FS o j IN2P3, 5/20/ Y. Chiu
22 From 1-bit to 1.5-bit Architecture ½ FS ½ bit 1-bit No redundancy Vo b =0 2 IN2P3, 5/20/ Y. Chiu
23 From 1-bit to 1.5-bit Architecture ½ bit ½ FS ½ bit ½ FS Vo b =0 2 Vo b =0 2 IN2P3, 5/20/ Y. Chiu
24 From 1-bit to 1.5-bit Architecture Vo b =0 2 Vo b =0 2 Center the two thresholds optimal symmetric offset tolerance IN2P3, 5/20/ Y. Chiu
25 The 1.5-bit Architecture V =2V - b-1 V o i R 3 decision levels ENOB = log 2 3 = 1.58 Max tolerance of comparator offset is ±V R /4 An implementation of the Sweeny-Robertson-Tocher (SRT) division principle The conversion accuracy relies on the loop-gain error, i.e., the gain error and nonlinearity A 3-level DAC is required Can the same technique be applied to SAR? Ref. [2] IN2P3, 5/20/ Y. Chiu
26 1.5-bit Multiplier DAC (MDAC) Φ 2 V i Φ 1 C 1 Φ 1 C 2 -V R /4 A V o V R /4 Φ 1e -V R 0 V R Decoder Φ 2 V o C C C Vi b 1 V R 1 C C 1 V =2 V - b-1 V o i R 2X gain + 3-level DAC + subtraction all integrated Can be generalized to n.5-bit architectures IN2P3, 5/20/ Y. Chiu
27 2.5-bit Multiplier DAC (MDAC) Φ 2 Φ 1 C 1 V R V o V i b=0 b=1 b=2 b=3 b=4 b=5 b=6 Φ 1 C 2 V R /2 V R 1 V R 6 Φ 1 C 3 0 V i 6 CMP s b Φ 1 C 4 -V R /2 A V o -V R Φ 2 Φ 1e 0 V R Decoder Φ 2 Φ 2 -V R -5V R /8-3V R /8 -V R /8 V R /8 3V R /8 5V R /8 V R V =4 V - b-3 V o i R 4X gain + 7-level DAC + subtraction all integrated IN2P3, 5/20/ Y. Chiu
28 Residue Transfer Function (2.5b MDAC) V o V R V R /2 b=-3 b=-2 b=-1 b=0 b=1 b=2 b=3 overflow range 0 normal range -V R /2 -V R V R V R 1 V R 2 V R 3 V R 4 V R 5 V R 6 underflow range V i Only half of the internal dynamic range is used under ideal condition! IN2P3, 5/20/ Y. Chiu
29 With comparator offset V o V R V R /2 b=-3 b=-2 b=-1 b=0 b=1 b=2 b=3 overflow range 0 normal range -V R /2 -V R V R V R 1 V R 2 V R 3 os V R 4 V R 5 V R 6 underflow range V i IN2P3, 5/20/ Y. Chiu
30 Internal Redundancy V o V R V R / overflow range 0 normal range -V R /2 -V R V R V R 1 V R 2 V R 3 V R 4 V R 5 V R 6 underflow range V i Comparator and amplifier offsets tolerated by internal redundancy. IN2P3, 5/20/ Y. Chiu
31 How does Redundancy work in SAR? Binary search is efficient, but displays zero error tolerance. IN2P3, 5/20/ Y. Chiu
32 Binary Search Revisited +FS in -FS X When everything is ideal IN2P3, 5/20/ Y. Chiu
33 Binary Search w/ Dynamic Error +FS in -FS X Settling error, comparator hysteresis etc. IN2P3, 5/20/ Y. Chiu
34 Overlapping Search Ranges +FS 1111 X in FS 0000 Results indicate decision trajectory, no longer binary-coded. IN2P3, 5/20/ Y. Chiu
35 Redundancy of Sub-binary Search +FS in -FS X Dynamic errors absorbed by redundancy. IN2P3, 5/20/ Y. Chiu
36 SAR Redundancy Redundant conversion consumes more bit cycles, but can recover intermediate decision errors. Redundancy can be exploited to expedite conversion progress or to save power. DAC levels (matching) still need to be accurate. (will come back to this later ) IN2P3, 5/20/ Y. Chiu
37 Presentation Outline Principles of Multistep A/D Conversion Architectural Redundancy Error Mechanisms and Digital-Domain Calibration Error-Parameter Identification PRBS Test-Signal Injection (sub-adc, sub-dac, input) Two-ADC Equalization (ref.-adc, split-adc, ODC) Energy Efficiency and Trend Summary IN2P3, 5/20/ Y. Chiu
38 Pipelined ADC Errors (I) 1.5b MDAC Capacitor mismatch Op-amp finite-gain error and nonlinearity Charge injection and clock feed-through (S/H) Settling error V =2 V -d V o i R V o C1 C2 C2 t fs Vi dv C1C2 C1C2 C1 C1 A V A V o /H R o IN2P3, 5/20/ Y. Chiu
39 Pipelined ADC Errors (II) 2.5b MDAC DAC bit-encoding scheme d j d j, d j, d j, d j = d j,1 + d j,2 + d j,3 V j C1 C2 C C = dj, 1 + dj,2 + dj,3 Vr + Vj + 1 C C C C A C V j+1 IN2P3, 5/20/ Y. Chiu
40 RA Gain Error and Nonlinearity R o o R i R R R R R R i R IN2P3, 5/20/ Y. Chiu
41 RA Gain Error and Nonlinearity R o o R i R R R R R R i R Raw accuracy is usually limited to bits w/o error correction. IN2P3, 5/20/ Y. Chiu
42 RA Gain Error and Nonlinearity R o o R i R R R R R R i R Raw accuracy is usually limited to bits w/o error correction. IN2P3, 5/20/ Y. Chiu
43 The Basic Idea of Digital Calibration ADC Digital Computation Unknown System System Inversion Calibration = efficient digital processing to undo certain analog errors e.g., SC amplifier: Analog soln: Vo C Vi C2 βa match C 1 and C 2 make βa very large Digital soln: any constant C 1 and C 2 any constant A is fine IN2P3, 5/20/ Y. Chiu
44 Two Essential Components of Dig. Cal. 1. A digital-domain technique (e.g. equation) to recover accurate analog information from raw digital output Treat analog precision or linearity only Neglect small consequence on SNR A CL - C C2 βa =# 2. An algorithm to identify the error parameters Foreground vs. Background techniques IN2P3, 5/20/ Y. Chiu
45 Linear MDAC Correction Analog residue function: C1 C2 C3 C 4 + C A V j,1 j,2 j,3 j = d + d + d Vr + Vj+ 1 C C C C Normalized residue function: Vj C1 C2 C3 Vj+1 C 4 + C A = dj,1 + dj,2 + dj,3 + Vr C C C Vr C Vj 1 Vj Vj+1 1 = dj,1 + dj,2 + dj, 3 + = dj + V 4 V 4 4 V 4 r Digital representation: D = d β + d β + d β + D α j j,1 j,1 j,2 j,2 j,3 j, 3 j+1 j = k d β + D α j,k j, k j+ 1 r j r ideal residue function error parameters: { α j, β j,k } IN2P3, 5/20/ Y. Chiu
46 Bit-Weight (Radix) Correction For 1-b or 1.5-b MDAC: D =D 1 in j j j+1 j+1 j+2 j+2 j+1 j j-1... =...+ d β + d β + d β +... α α α =...+d jγj+d j+1γj+1+d j+ 2 γj weighted sum of ALL bits! (bit weight or radix error) Alternatively, D =D 1 in dj dj+1 dj+2 = j j + 1+ j+1 j j+ 2 j d+ j dj j d j+1+ dj+1 j+1 d j+2+ dj+2 j+2 = j j+1 j segmental offset IN2P3, 5/20/ Y. Chiu
47 Bit-Weight (Radix) Correction d 1 =-1 d 1 =0 d 1 =1 d 1 =-1 d 1 =0 d 1 =1 d 1 =-1 d 1 =0 d 1 =1 D o D o D o -V R V i V R -V R V i V R -V R V i V R 1.5b MDAC residue nonlinearity radix error: needs multiplication segmental offset: addition only IN2P3, 5/20/ Y. Chiu
48 Nonlinear MDAC Correction Analog representation: V j V V C1 C2 C3 C 4 + = dj, 1 + dj,2 + dj,3 Vr + Vj+ 1 C C C Normalized analog representation: C1 C2 C3 V C 4 + C A = dj,1 + dj,2 + dj,3 + C C C Vr C j j+1 r C A V C j+1 V j+1 Digital representation: D dj,1 β j,1 + dj,2 β j,2 + dj,3 βj,3 D m dj,k β j,k + Dj+1 αj,m = +f j j+1 k m error parameters: { α j,m, β j,k } Next problem: how to determine {α j,m, β j,k } precisely? IN2P3, 5/20/ Y. Chiu
49 Let s try to push this Correcting nonlinearity: "Give me a place to stand on, and I will move the Earth " L Drawn 0.15μm V DD 1.2V Corrected w/ 9th-order power series -70 dbfs Archimedes, 200 BC IN2P3, 5/20/ Y. Chiu
50 On nonlinear correction Memory-less polynomial computation is efficient A few coefficients fits/predicts full-range nonlinearity (requiring digital multipliers and adders mostly) Caveat 1: coefficients depend on signal statistics! Caveat 2: coefficients depend on PVT variations! Piecewise-linear or lookup table can be useful Memory, digital power, and cost Complexity and convergence time (esp. tracking speed in background mode) Solution needs to be practical after all IN2P3, 5/20/ Y. Chiu
51 SAR Redundancy Forms (I) +FS Vin -FS Radix: 0 3/8 1/8 9/32 3/ Unit-Element DAC Best matching Arbitrary decision threshold arbitrary radix each bit DAC resolution slightly higher Binary-to-Thermo encoder (slow) Ref. [3] IN2P3, 5/20/ Y. Chiu
52 SAR Redundancy Forms (II) +FS Vin -FS Radix: 0 1/2 1/4 1/2 3/ Binary DAC Good matching Periodic redundancy non-uniform radix selective bits SAR logic slightly more complex Can also use UE DAC Ref. [4] IN2P3, 5/20/ Y. Chiu
53 SAR Redundancy Forms (III) +FS Vin -FS Radix: Sub-binary DAC Poor matching Uniform redundancy uniform radix each bit Simple layout, simple SAR logic (fast) Cannot use UE DAC Must calibrate DAC Ref. [5] IN2P3, 5/20/ Y. Chiu
54 Sub-binary DAC Construction Hard-coded in analog form No B2T encoder Simple layout V i V DAC DAC V X d 0 D o d N-1 e.g., Radix = 1.86 C N-1 C N-2 C N-3 C N-4 C N-1 C N-2 C N-3 C N-4 Ref. [5] IN2P3, 5/20/ Y. Chiu
55 Sub-binary DAC Transfer Function 2 N D o Redundant region MSB = 0 N = 14 2 N Do MSB = 1 V i 0 V L V H FS = V H = V L Note: only one transition edge shows up May 20, IN2P3 Summer IN2P3, 5/20/ Y. Chiu
56 Sub-binary DAC Quantization Vi d o = V N-1 C j 2dj -1 j=0 Cj = N-1 j=0 FS w j 3 2d -1 Q =V C 2d -1 DAC R j j j=0 V i 3 j=0 C j j V i V DAC d 3 = 1 C 3 C DAC Radix = 1.86 d 2 = 0 C 2 V X d 0 d N-1 d 1 = C 1 C C Ref. [5] C 0 C 0 D o d 0 = 1 IN2P3, 5/20/ Y. Chiu
57 Sub-binary DAC Digital Correction V i d o = = VFS N-1 j=0 w j 2d -1 j w j = bit weights N raw = 14 N net = 12 Do do Next problem: how to determine {w j } precisely? IN2P3, 5/20/ Y. Chiu
58 Presentation Outline Principles of Multistep A/D Conversion Architectural Redundancy Error Mechanisms and Digital-Domain Calibration Error-Parameter Identification PRBS Test-Signal Injection (sub-adc, sub-dac, input) Two-ADC Equalization (ref.-adc, split-adc, ODC) Energy Efficiency and Trend Summary IN2P3, 5/20/ Y. Chiu
59 Error-Parameter Identification Techniques (BG) With PRBS test-signal injection (dither) Sub-ADC injection (comparator dither) Sub-DAC injection (DAC dither) Input injection (Independent Component Analysis) With two-adc equalization (test signal free) Reference-ADC equalization (training sequence) Split-ADC equalization (blind) Offset double conversion (ODC) (blind, single ADC) Parameter extraction is what the game is all about IN2P3, 5/20/ Y. Chiu
60 Recent BG Digital Calibration Techniques PRBS injection (Dither) T(n) V in ADC x(n) Adaptive DPP y(n) e(n) Temes [6,7], Lewis [8], Galton [9,10] Two-ADC equalization V in ADC 1 x 1 (n) Adaptive DPP y 1 (n) Adaptive ADC 2 x 2 (n) DPP y 2 (n) e(n) Lewis [11], Chiu [12], McNeill [13] IN2P3, 5/20/ Y. Chiu
61 PRBS Test-Signal Injection IN2P3, 5/20/ Y. Chiu
62 Comparison of PRBS Injection Techniques Sub-ADC injection considered as dynamic comparator offset, no removal needed higher sub-adc resolution (injection and ADC matching not req d) works only with busy input Sub-DAC injection needs to be removed in digital output higher sub-dac resolution (injection and DAC matching req d) can work with quiet input Input injection (sub-dac + sub-adc) needs to be removed in digital output No impact on sub-adc or sub-dac resolution works only with busy input IN2P3, 5/20/ Y. Chiu
63 PRBS Test-Signal Injection (Sub-ADC Injection) IN2P3, 5/20/ Y. Chiu
64 Sub-ADC Injection Comparator Dither residue path D 1 T=0 In steady state, analog gain (G 1 ) and digital gain (G 1-1 ) cancel exactly. 2 -k ¼ to avoid overflow in residue output. No need to match injection scaling factor (2 -k ) to the sub-adc thresholds. IN2P3, 5/20/ Y. Chiu
65 Sub-ADC Injection Comparator Dither d 1 =1 d 1 =2 V R V R /2 ¼ bit ½ bit V R /2 -V R typ. k = 2 Converge@ D 1 T=0 In steady state, analog gain (G 1 ) and digital gain (G 1-1 ) cancel exactly. 2 -k ¼ to avoid overflow in residue output. No need to match injection scaling factor (2 -k ) to the sub-adc thresholds. IN2P3, 5/20/ Y. Chiu
66 Exploiting Internal Redundancy Ref. [14] Input falling in shaded region randomly sees one of two RTF s dithering. Decision threshold needs not to be accurate or matched to each other. Digitization outcome is independent of PRBS when ADC is ideal!! IN2P3, 5/20/ Y. Chiu
67 Identifying Residue Gain Error Segmental offset : D 1= 1 d+d 1 1δ1+ 1 d 1 2+ d If V 1 { region 1 } and T = +1, D 1 = D ideal; if T = -1, D 1 = Dideal - δ1 If V 1 { region 2} and T = +1, D 1 = D ideal +δ 1; if T=-1, D 1 =Dideal IN2P3, 5/20/ Y. Chiu
68 Identifying Residue Gain Error Calculating correlation: 1 1 D 1T = Dideal - Pr V 1{ region 1 } -D Pr V 1{ region 2 } ideal 1 ideal = δ1pr V 1{ region 1 } δ1pr V 1{ region 2 } = δ1 Pr V 1 { region 1 or 2 } 2 D -δ D +δ ideal LMS learning: δ n+1= δ n+μd ntn D δ removedt Correlation reveals information about segmental offset. Exact size of shaded region is not important (only affects Pr(.)). Key observation: if ADC is ideal, D 1 must be uncorrelated to T. IN2P3, 5/20/ Y. Chiu
69 PRBS Test-Signal Injection (Sub-DAC Injection) IN2P3, 5/20/ Y. Chiu
70 Sub-DAC Injection DAC Dither residue path Dˆ 2 Converge@ ˆ 2 D T=0 In steady state, analog gain (G 1 ) and digital gain (G -1 1 ) cancel exactly. 2 -k ¼ to avoid overflow in residue output, DAC adds 2 bits minimum. Injection bit scaling factor (2 -k ) must match to the sub-dac unit elements. IN2P3, 5/20/ Y. Chiu
71 Sub-DAC Injection DAC Dither d 1 =1 d 1 =2 V R V R /2 ¼ bit ½ bit V R /2 Dˆ 2 -V R Converge@ typ. k = 2 In steady state, analog gain (G 1 ) and digital gain (G 1-1 ) cancel exactly. 2 -k ¼ to avoid overflow in residue output, DAC adds 2 bits minimum. Injection bit scaling factor (2 -k ) must match to the sub-dac unit elements. ˆ 2 T=0 DIN2P3, 5/20/ Y. Chiu
72 Signal-Dependent DAC Dither PRBS Injection Table V j (V R ) T = +1 T = ⅜ 0 0 -⅜ -⅛ 0 V R -⅛ ⅛ -½ V R ½ V R ⅛ ⅜ -V R 0 ⅜ PRBS only injected when input falls within the shaded region. Extra comparators needed to instrument the SD dither. Ref. [15] IN2P3, 5/20/ Y. Chiu
73 Opportunistic DAC Dither Vres/VR V =4V -V D res in R Vres/VR V =4V -V D+PN res in R Gap 0 4Vin - VR D'+PN, Vin V V res = 4Vin - VR D, o.w. Vres/VR V th V th V th Gap 1 0 th V in /V R V in /V R -2 When redundancy is not ample, blind injection requires large DR. Without additional comparators, detecting V th vicinity is difficult. IN2P3, 5/20/ Y. Chiu
74 Exploiting Comparator Metastability DFF Q+ Q- Ready Comparator resolving time T 0 V in -V th small V in -V th large Metastable output Q+, Q- Q+, Q- Ready=1 Time Normal output Ready=0 0 V in -V th Time Comparator resolving time indicates proximity of input. Proximity detector also functions as metastabilty detector/resolver. IN2P3, 5/20/ Y. Chiu
75 12b 160MS/s CMOS Prototype (40nm) (5b + 8b) synchronous two-step pipelined SAR architecture. First-stage capacitor weights identified w/ opportunistic DAC dither. IN2P3, 5/20/ Y. Chiu
76 Die Photo Clock Sub- & ADC1 PN Gen. Sub- ADC2 300μm Sub- ADC3 Sub- ADC4 Sub- ADC5 139μm Integrator + DAC MDAC1 MDAC2 MDAC3 MDAC4 40nm low-leakage CMOS process (active area = 0.042mm 2 ) Ref. [16] IN2P3, 5/20/ Y. Chiu
77 Measured ADC Dynamic Performance 90 Fs = 160MHz after cal. 90 Fin = 25MHz after cal Fin = 80MHz Fs = 160MHz db 70 db SNDR SFDR Fin [MHz] 60 SNDR SFDR Fs [MHz] IN2P3, 5/20/ Y. Chiu
78 Power Consumption Ref. [16] Analog 1.1V 2.8mW (53.6%) Digital 1.1V 2.2mW (42.2%) Total power is 4.96mW at 160MS/s operation. IN2P3, 5/20/ Y. Chiu
79 PRBS Test-Signal Injection (Input Injection) IN2P3, 5/20/ Y. Chiu
80 Direct Input Injection Algorithm works reliant on the independence b/t input and T. Multi-parameter extraction is possible by Independent Component Analysis. IN2P3, 5/20/ Y. Chiu
81 Independent Component Analysis (ICA) 1 o i D o =αd+β 1 D2-kT 2 ICA Algorithm Only two parameters need to be identified. Hérault-Jutten (HJ) stochastic de-correlation: α = α -μ g D g T n+1 n α 1 o 2 β = β -μ g D g T n+1 n β 2 o 1 In our simulation, we picked g 1 (x) = x and g 2 (x) = x 3. Ref. [17] IN2P3, 5/20/ Y. Chiu
82 Simulation Results H-J Learning Trajectory Before ENOB= After ENOB= / Typical learning pattern of the H-J algorithm Steady-state coefficient fluctuation causing low-level spurs IN2P3, 5/20/ Y. Chiu
83 ICA extended to nonlinear treatment Error model: 2 3 V = f V a +a V +a V +a V +... o i 0 1 i 2 i 3 i Update equations: j b n+1 =b n -μ D n T n j =1,...,5 j j j o Ref. [17] IN2P3, 5/20/ Y. Chiu
84 An ICA Approach for SAR Calibration Digital Post-Processing ˆd T: PRBS dˆ i T ICA recovers 2X speed at the cost of slower convergence. ALL bit weights {w j } are learned simultaneously! IN2P3, 5/20/ Y. Chiu
85 Prototype SAR ADC w/ ICA Sub-binary DAC Ref. [18] IN2P3, 5/20/ Y. Chiu
86 Prototype SAR ADC w/ ICA ICA Ref. [18] 90nm CMOS, 0.05mm 2 12b, 50MS/s in BG mode ( )mW power (45fJ/step) CICC Best Paper Award IN2P3, 5/20/ Y. Chiu
87 Measurement Results Dynamic Performance SFDR / SNDR [db] SFDR w/ cal. SNDR w/ cal. SFDR w/o cal. SNDR w/o cal. ENOB [bit] f in [MHz] Learning Curve Gear shifting helps stabilize the steady-state fluctuations. IN2P3, 5/20/ Y. Chiu
88 Two-ADC Equalization IN2P3, 5/20/ Y. Chiu
89 Two-ADC Equalization Techniques Reference-ADC equalization Slow-Fast two-adc architecture to accomplish accuracy and throughput simultaneously using adaptive equalization Two (different) ADC s needed, subject to skew error without SHA Split-ADC equalization Two almost identical ADC s employed for blind equalization Two ADC s needed, subject to skew error without SHA Offset double conversion (ODC) Self-equalization by digitizing every sample twice with opposite DC offsets injected to the input Single ADC with modified timing in background mode Conversion throughput halved in background mode IN2P3, 5/20/ Y. Chiu
90 Two-ADC Equalization (Reference-ADC) IN2P3, 5/20/ Y. Chiu
91 Reference-ADC Equalization Ref. [11,12] Concept inspired by adaptive equalization in digital comm. receivers Divide-and-conquer approach to achieve analog speed and accuracy IN2P3, 5/20/ Y. Chiu
92 EQZ of Time-Interleaved ADC Array 1X Ref. ADC D r Digital Cal. Ф r ADC 1 ADF 1 D 1 V in T/H 1X Ф 1 Ф Ф DLL Ф 1 ADC 10 D 10 ADF 10 Ф 10 Ф 10 ALL paths are aligned to the unique ref. ADC after equalization. IN2P3, 5/20/ Y. Chiu
93 Prototype 10-way TI-ADC Array Die photo Performance Comparison time of publication) Time CMOS Process Speed [MS/s] SFDR [db] FoM [fj/step] ISSCC µm ISSCC µm VLSI08 65nm ISSCC µm The 2009 DAC/ISSCC Student Design Contest Award Ref. [5] IN2P3, 5/20/ Y. Chiu
94 ADC Array EQZ Measured Spectra SNDR=31.2dB SFDR=33.0dB HD3 2fs/10 4fs/ SNDR=46.7dB SFDR=65.2dB After Cal SNDR=42.2dB SFDR=60.5dB Ref. ADC fs/10 3fs/ HD HD frequency [MHz] frequency [MHz] frequency [khz] (f s = 600MS/s, f in = 7.8MHz, A in = 0.9FS, 16k samples) IN2P3, 5/20/ Y. Chiu
95 Two-ADC Equalization (Split-ADC) IN2P3, 5/20/ Y. Chiu
96 Split-ADC Equalization Ref. [13] V o ADC A V i V o ADC B V i Blind equalization w/o reference possible by offsetting the RTFs Fast convergence due to zero-forcing equalization IN2P3, 5/20/ Y. Chiu
97 Zero Forcing ε = d B d A ε = 0 d B d A d B d A V in V in Error observation Radix correction Zero-forcing EQZ IN2P3, 5/20/ Y. Chiu
98 Two-ADC Equalization (Offset Double Conversion) IN2P3, 5/20/ Y. Chiu
99 Offset Double Conversion (ODC) for SAR Digital Post-Processing ODC enables zero-forcing self-equalization. ALL bit weights {w j } are learned simultaneously! IN2P3, 5/20/ Y. Chiu
100 How to determine Bit Weights? Is the transfer curve shift-invariant? IN2P3, 5/20/ Y. Chiu
101 How to determine Bit Weights? Is the transfer curve shift-invariant? IN2P3, 5/20/ Y. Chiu
102 How to determine Bit Weights? Is the transfer curve shift-invariant? IN2P3, 5/20/ Y. Chiu
103 How to determine Bit Weights? Shift-invariant ONLY when the transfer curve is completely linear! Non-constant difference b/t D + and D reveals bit weight information. IN2P3, 5/20/ Y. Chiu
104 Prototype SAR ADC w/ ODC Sub-binary DAC ODC Aux. DAC Ref. [19] V X CLK CMP n Ready CLK C 13 C 1 C 0 C 0 C C 13,d C 6,d CMP p d 13 d 1 d 0 +V R V R SAR Logic ACLK V in 0.13µm CMOS, 0.06mm 2 12b, 45MS/s in FG mode 3mW power (36.3 fj/step) Most read JSSC article Nov IN2P3, 5/20/ Y. Chiu
105 Measurement ADC Spectra (BG Mode) 0-20 SNDR = 60.2dB SFDR = 66.4dB THD = -61.7dB 0-20 SNDR = 70.7dB SFDR = 94.6dB THD = -89.1dB Before Cal. After Cal. db -60 db Freq [MHz] Freq [MHz] IN2P3, 5/20/ Y. Chiu
106 Convergence Time (BG Mode) e [LSB] e [LSB] e [LSB] Number for samples x Number for samples x Number for samples x MS/s 1ms IN2P3, 5/20/ Y. Chiu
107 Comparison with 12b ADCs 10 1 (@ time of publication) FoM (pj/conv. step) MS/s 45MS/s Year Total Power: 3.0mW Active area (mm 2 ) mm Year IN2P3, 5/20/ Y. Chiu
108 Summary of Dig. BG Cal. Techniques Method Parameter Test signal Injection point Reference DNC + GEC { β j,k, α j,m } multi PRBS sub-dac [9,10,20-24] Split capacitor { j } 1 PRBS sub-dac [25,26] Sig.-dep. dither { γ j } 1 PRBS sub-dac [15,16] GEC + SA { γ j } 2 PRBS sub-adc [27,28] Statistics { α j,m } 1 PRBS sub-adc [29,30] Fast GEC { γ j } 1 PRBS sub-adc [31] ICA { γ j }, { α j,m } 1 PRBS input [17,18,32,33] Ref. ADC { β j,k, α j,m } n/a n/a [5,11,12,34-36] Virtual ADC { β j,k, α j,m } offset sub-dac [37,38] Split ADC { α j,m } n/a n/a [13,39] { β j,k, α j,m } n/a n/a [40] ODC { γ j } offset input [19] { β j,k, α j,m } offset input [41] References are furnished at the end of the slides. IN2P3, 5/20/ Y. Chiu
109 Presentation Outline Principles of Multistep A/D Conversion Architectural Redundancy Error Mechanisms and Digital-Domain Calibration Error-Parameter Identification PRBS Test-Signal Injection (sub-adc, sub-dac, input) Two-ADC Equalization (ref.-adc, split-adc, ODC) Energy Efficiency and Trend Summary IN2P3, 5/20/ Y. Chiu
110 ADC Figure-of-Merit (FoM) Walden FoM: FoM W P Joule ENOB 2BW 2 Conversion - Step "Energy Efficiency" Schreier FoM: ENOB 2BW 4 FoMS 10log10 db P P: power consumption ENOB: effective number of bits BW: min{f s /2, ERBW} ERBW: effective resolution BW Walden FoM is intuitive but penalizes noise/matching-limited designs. Schreier FoM is more fair to high dynamic range designs. IN2P3, 5/20/ Y. Chiu
111 Performance, Efficiency, and Power Performan ce =2BWα ENOB HzStep Performance = Speed SNR α/2 Energy Efficiency P J α/2 2BW α ENOB Step Note: Performance Efficiency ENOB P =2BW α = Power ENOB 2BW α α=2-4 IN2P3, 5/20/ Y. Chiu
112 Performance Efficiency (PE) Chart 1E+17 1E+16 Constant performance Performance = 2 BW 3 ENOB 1E+15 1E+14 (log scale) 1E+13 1E+12 1E+11 1E+10 Constant efficiency 1E+09 1E-18 1E-17 1E-16 1E-15 1E-14 1E-13 1E-12 (log scale) X Y = Power α=3 Energy Efficiency = Power/(2 BW 3 ENOB ) IN2P3, 5/20/ Y. Chiu
113 PE Chart: Pipelined ADC (<2005) 1E+15 1E+14 Pipeline (<2005) Performance 1E+13 1E+12 10W 1E+11 1W 10μW 100μW 1mW 10mW 100mW 1E+10 1E-16 1E-15 1E-14 1E-13 1E-12 1E-11 Efficiency ISSCC & VLSI data IN2P3, 5/20/ Y. Chiu
114 PE Chart: Pipelined ADC ( ) 1E+15 Pipeline (<2005) 1E+14 Pipeline ( ) Performance 1E+13 1E+12 10W 1E+11 1W 10μW 100μW 1mW 10mW 100mW 1E+10 1E-16 1E-15 1E-14 1E-13 1E-12 1E-11 Efficiency ISSCC & VLSI data IN2P3, 5/20/ Y. Chiu
115 PE Chart: Pipelined ADC ( ) 1E+15 Pipeline (<2005) 1E+14 Pipeline ( ) Pipeline ( ) Performance 1E+13 1E+12 10W 1E+11 1W 10μW 100μW 1mW 10mW 100mW 1E+10 1E-16 1E-15 1E-14 1E-13 1E-12 1E-11 Efficiency ISSCC & VLSI data IN2P3, 5/20/ Y. Chiu
116 PE Chart: SAR ADC (<2005) 1E+15 1E+14 SAR (<2005) Performance 1E+13 1E+12 10W 1E+11 1W 10μW 100μW 1mW 10mW 100mW 1E+10 1E-16 1E-15 1E-14 1E-13 1E-12 1E-11 Efficiency ISSCC & VLSI data IN2P3, 5/20/ Y. Chiu
117 PE Chart: SAR ADC ( ) 1E+15 SAR (<2005) 1E+14 SAR ( ) Performance 1E+13 1E+12 10W 1E+11 1W 10μW 100μW 1mW 10mW 100mW 1E+10 1E-16 1E-15 1E-14 1E-13 1E-12 1E-11 Efficiency ISSCC & VLSI data IN2P3, 5/20/ Y. Chiu
118 PE Chart: SAR ADC ( ) 1E+15 SAR (<2005) 1E+14 12b,160MS/s 5mW SAR ( ) SAR ( ) Performance 1E+13 1E+12 10W 1E+11 1W 10μW 100μW 1mW 10mW 100mW 1E+10 1E-16 1E-15 1E-14 1E-13 1E-12 1E-11 Efficiency ISSCC & VLSI data IN2P3, 5/20/ Y. Chiu
119 PE Chart: Both ADCs (<2014) 1E+15 1E+14 Industry ADCs Pipeline (<2005) Pipeline ( ) Pipeline ( ) SAR (<2005) SAR ( ) SAR ( ) Performance 1E+13 1E+12 University ADCs 10W 1E+11 1W 10μW 100μW 1mW 10mW 100mW 1E+10 1E-16 1E-15 1E-14 1E-13 1E-12 1E-11 Efficiency ISSCC & VLSI data IN2P3, 5/20/ Y. Chiu
120 PE Chart: Both ADCs (<2014) 1E+15 1E+14 ADI TI KENET NSC BCM Agilent Pipeline (<2005) Pipeline ( ) Pipeline ( ) SAR (<2005) SAR ( ) SAR ( ) Performance 1E+13 OSU IMEC 1E+12 NCTU NCKU OSU AKM Panasonic MIT Michigan Fujitsu ADI 10W 1E+11 EUT 1W 10μW 100μW 1mW 10mW 100mW 1E+10 1E-16 1E-15 1E-14 1E-13 1E-12 1E-11 Efficiency ISSCC & VLSI data IN2P3, 5/20/ Y. Chiu
121 To conclude Thank you for your attendance! IN2P3, 5/20/ Y. Chiu
122 Bibliography 1. W. R. Bennett, "Spectra of quantized signals," Bell Syst. Tech. J., vol. 27, pp , Jul S. H. Lewis et al., "A 10-b 20-MS/s analog-to-digital converter," JSSC, vol. 27, Mar F. Kuttner, "A 1.2-V 10-b 20-Msample/s nonbinary successive approximation ADC in 0.13-μm CMOS," in ISSCC, C. C. Liu et al., "A 10b 100MS/s 1.13mW SAR ADC with binary-scaled error compensation," in ISSCC, W. Liu et al., "A 600MS/s 30mW 0.13μm CMOS ADC Array Achieving Over 60dB SFDR with Adaptive Digital Equalization," in ISSCC, T. Sun, A. Wiesbauer, and G. C. Temes, "Adaptive compensation of analog circuit imperfections for cascaded delta-sigma ADCs," in ISCAS, P. Kiss et al., "Adaptive digital correction of analog errors in MASH ADC s Part II: Correction using test-signal injection," TCAS2, vol. 47, Jul D. Fu, K. C. Dyer, S. H. Lewis, and P. J. Hurst, "A digital back-ground calibration technique for time-interleaved analog-to-digital converters," JSSC, vol. 33, Dec E. J. Siragusa and I. Galton, "Gain error correction technique for pipelined analogue-to-digital converters," Electronics Letters, vol. 36, I. Galton, "Digital cancellation of D/A converter noise in pipelined A/D converters," TCAS2, vol. 47, Mar X. Wang, P. J. Hurst, and S. H. Lewis, "A 12-bit 20-MS/s pipelined ADC with nested digital background calibration," in CICC, Y. Chiu, C. W. Tsang, B. Nikolic, and P. R. Gray, "Least mean square adaptive digital background calibration of pipelined analog-to-digital converters," TCAS1, vol. 51, Jan J. McNeill, M.C.W. Coln, B. J. Larivee, ""Split ADC" architecture for deterministic digital background calibration of a 16-bit 1-MS/s ADC," JSSC, vol. 40, Dec H. S. Fetterman et al., "CMOS pipelined ADC employing dither to improve linearity," in CICC, IN2P3, 5/20/ Y. Chiu
123 Bibliography 15. Y.-S. Shu and B.-S. Song, "A 15b linear, 20MS/s, 1.5b/stage pipelined ADC digitally calibrated with signaldependent dithering," in VLSI, Y. Zhou, B. Xu, and Y. Chiu, "A 12b 160MS/s synchronous two-step SAR ADC achieving 20.7fJ/step FoM with opportunistic digital background calibration," to appear in VLSI, Y. Chiu, S.-C. Lee, and W. Liu, "An ICA framework for digital background calibration of analog-to-digital converters," Sampling Theory in Signal and Image Processing (STSIP), vol. 11, no. 2-3, W. Liu, P. Huang, and Y. Chiu, "A 12-bit 50-MS/s 3.3-mW SAR ADC with background digital calibration," in CICC, W. Liu, P. Huang, and Y. Chiu, "A 12bit 22.5/45MS/s 3.0mW 0.059mm 2 CMOS SAR ADC achieving over 90dB SFDR," in ISSCC, P. C. Yu et al., "A 14b 40MS/s pipelined ADC with DFCA," in ISSCC, E. J. Siragusa and I. Galton, "A digitally enhanced 1.8V 15b 40MS/s CMOS pipelined ADC," in ISSCC, A. Panigada and I. Galton, "Digital background correction of harmonic distortion in pipelined ADCs," TCAS I, Sep A. Panigada and I. Galton, "A 130mW 100MS/s pipelined ADC with 69dB SNDR enabled by digital harmonic distortion correction," in ISSCC, K. Nair and R. Harjani, "A 96dB SFDR 50MS/s digitally enhanced CMOS pipeline A/D converter," in ISSCC, H.-C. Liu, Z.-M. Lee, and J.-T. Wu, "A 15b 20MS/s CMOS pipelined ADC with digital background calibration," in ISSCC, J.-L. Fan, C.-Y. Wang, and J.-T. Wu, "A robust and fast digital background calibration technique for pipelined ADCs," TCAS I, Jun J. Li and U.-K. Moon, "Background calibration techniques for multistage pipelined ADC s with digital redundancy," TCAS II, Sep IN2P3, 5/20/ Y. Chiu
124 Bibliography 28. J. Li et al., "0.9V 12mW 2MSPS algorithmic ADC with 81dB SFDR," in VLSI, B. Murmann et al., "A 12b 75MS/s pipelined ADC using open- loop residue amplification," in ISSCC, J. Keane et al., "Background interstage gain calibration technique for pipelined ADCs," TCAS I, Jan R. Massolini, G. Cesura, and R. Castello, "A fully digital fast convergence algorithm for nonlinearity correction in multistage ADC," TCAS II, May S.-C. Lee, B. Elies, and Y. Chiu, "An 85dB SFDR 67dB SNDR 8OSR 240MS/s SD ADC with nonlinear memory error calibration," in VLSI, Y. Zhou and Y. Chiu, Digital calibration of inter-stage nonlinear errors in pipelined SAR ADC, in MWSCAS, C. Tsang et al., "Background ADC calibration in digital domain," in CICC, D. Stepanovic and B. Nikolic, A 2.8GS/s 44.6mW time-interleaved ADC achieving 50.9dB SNDR and 3dB effective resolution bandwidth of 1.5GHz in 65nm CMOS, in VLSI, B. Xu and Y. Chiu, Background calibration of time-interleaved ADC using direct derivative information, in ISCAS, B. Peng et al., "A virtual-adc digital background calibration technique for multistage A/D conversion," TCAS II, Nov B. Peng et al., "A 48-mW, 12-bit, 150-MS/s pipelined ADC with digital calibration in 65nm CMOS," in CICC, J. McNeill et al., "Split-ADC digital background correction of open-loop residue amplifier nonlinearity errors in a 14b pipeline ADC," in ISCAS, S. Sarkar, Y. Zhou and Y. Chiu, "PN-assisted deterministic digital calibration of split two-step ADC to over 14-bit accuracy," to appear in MWSCAS, B. Peng et al., "An offset double conversion technique for digital calibration of pipelined ADCs," TCAS II, Dec B. Murmann, "ADC Performance Survey ," [Online]: IN2P3, 5/20/ Y. Chiu
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