Digitally Assisted A/D Conversion- Trading off Analog Precision for Computing Power

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1 Digitally Assisted A/D Conversion- Trading off Analog Precision for Computing Power UCB IC-Seminar November 25, 2002 Boris Murmann Prof. Bernhard E. Boser

2 Outline Motivation Research Overview Analog Errors and Digital Correction Correction Parameter Estimation Prototype IC Summary

3 Demand for High Performance ADCs Source: Analog Devices Increasing number of applications use sophisticated DSP

4 Modern Application 4 Million Transistors 50% P tot (ADC only) Baseband Processor [Thomson et. al., ISSCC 2002]

5 Research Plan Goals: o Reduce power consumption of high performance ADCs o Improve compatibility with fine line technology Approach: o Relax analog domain precision o Recover ADC accuracy in digital domain

6 Outline Motivation Research Overview Error Analysis and Digital Correction Calibration Technique Experimental Results Conclusion

7 Research Vehicle: Pipelined ADC V in S/H STAGE 1 STAGE N-1 STAGE N R bits (e.g. R=1) V in A/D D/A - 2 R V res res V D D=0 D=1 Predominant topology for wide performance range: bits, MHz V in

8 Relax Analog Precision? V in A/D D/A - 2 R V res D Digital correction helps tolerate large sub A/D errors [Lewis, 1987] Digital calibration removes D/A and linear gain error by adjusting digital weights [Karanicolas, 199]

9 Relax Analog Precision? V in - 2 R V res A/D D/A D Digital correction helps tolerate large sub A/D errors [Lewis, 1987] Digital calibration removes D/A and linear gain error by adjusting digital weights [Karanicolas, 199] Remaining burden: Fast, highly linear gain element 50-70% of total pipeline ADC power is consumed by interstage amplifiers

10 Conventional Gain Element E.g. [Kelly, ISSCC 2001] Electronic feedback linearizes, stabilizes High gain requirement costs headroom and/or additional stages power penalty Semiconductor technology trend: Decreasing VDD and low intrinsic device gain!

11 Precision Amplifier Alternatives Low loop gain Open loop Power Precision Sensitivity Power Precision Sensitivity

12 Research Overview V D Digital Post- D raw corrected in ADC Processor Aspects: Analog domain errors (1 st and 2 nd order) Digital correction mechanism Error measurement and tracking

13 Outline Motivation Research Overview Analog Errors and Digital Correction Correction Parameter Estimation Prototype IC Summary

14 Precision Requirements V in STAGE 1 STAGE i V resi STAGE i+1 STAGE N V ini A/D D/A - 2 Ri ε i V resi A/D Backend B bits Residue errors must be < ½ LSB of backend converter E.g. -bit Stage1 in 12-bit converter 9-bit backend ε 1 <0.1%

15 Basic Amplifier Considerations 1.5 R R 1 Diff. Pair TF Tangent V o 0.5 V i I SS Vo/(ISS*R) V 2 V i dsat max =? Vi/Vdsat Example: Simplest possible topology What fraction of transfer function should be used?

16 Transfer Function Nonlinearity V V = I SS R V β V β V 2 1 V 8 V 1 V 128 V 0 i i i i dsat dsat 2nd order (Device Mismatch) dsat dsat rd order 5th order (Gain Compression) 5... Linearity Error [%] nd order (0.5% mism.) rd order 5th order 0.1% Vi/Vdsat rd order error unavoidable 5 th and higher order error small for V imax 0.5V dsat Desirable to neglect high order terms Design implications?

17 Design Example V ˆ in = V ref A/D D/A - Vˆ x V! ref = 0. 5 V R 2 2 R dsat V ˆ = V res ref V ref R Vˆ V x dsat mv 1V mv 500 mv 1V 125 mv 250 mv mv 125 mv (headroom, g m /I D ) Simple diff. pair practical for stage resolution R>2 Third order error model sufficient in this case

18 Pipeline Stage Model a V x a 2 V x 2 V in a 1 A/D D/A - V os V res D 2 R How can we correct errors digitally?

19 Offset Pushthrough a V x a 2 V x 2 V in a 1 V os A/D D/A - V res -V os D Input referred converter offset, does not harm linearity Equivalent sub-a/d offset can be addressed with digital RSD arithmetic [Lewis, 1987]

20 Gain Error Pushthrough a V x a 2 V x 2 V in 2 R /a 1 a 1 A/D D/A - V res D

21 Gain Error Pushthrough a V x a 2 V x 2 V in 2 R /a 1 a 1 A/D D/A - V res a 1 /2 R D Correct digital weight of sub-conversion [Karanicolas, 199] Results in (often) tolerable input referred gain error

22 Second Order Cancellation V x V res a 1 a 2 V x 2 a V x V res b1 b V x V x s b 0? If a 0: ) ( ) ( s x b s x b b x a x a x a + + = + + = = = = : a a s a a a a a b a a a b a b With

23 Use of Digitized Residue V in STAGE 1 STAGE i V resi STAGE i+1 STAGE N b V x V ini - b1 V resi A/D D resi A/D D/A b 0 -b 0 D Compensate error using digital backend representation of residue Add 1-2 bits to backend to reduce quantization error

24 Third Order Correction b V x b 1 V res A/D - b V x D res

25 Third Order Correction V res b 1 A/D b V x - e(v res ) D res 0 : cos 1 cos 1 2 ) ( 1 1 < = + = b b p with p V p V V e res res res π

26 Third Order Correction b V x V res b 1 A/D D res - D' res e(d res ) Single-parameter correction function can be precomputed and stored in look-up table (ROM) Small ROM size achievable through continuous data compression methods

27 Complete Digital Correction V in A/D D/A - V res a 1 V x +a 2 V x2 +a V x A/D D res p 2 D' res e(d' res ) - D'' res p 1 p D a p1 p2 p R a a 2 a a a 1 How can we measure parameters in digital domain?

28 Outline Motivation Research Overview Analog Errors and Digital Correction Correction Parameter Estimation Prototype IC Summary

29 Calibration Concept Classical Approach: Problem: V in A/D D out Chip Temp. Power-Up Idle Test Signal Param. Calibration Circuit Bad time to calibrate! Calibrate now? Time Correction parameters depend on temperature, etc. Classical foreground calibration unfeasible Need continuous background calibration during normal A/D operation

30 Key: Two-Residue Pipeline Stage V in A/D D/A - V res SHIFT D Vres/Vref 0 Vres/Vref Vi/Vref Vi/Vref Add: Digital SHIFT signal, redundant A/D and D/A states Can carry out conversion on red or black segments

31 Digitized Segment (a 2 =0) no calibration: h 1 <h 2 perfect calibration: h 1 =h 2 Dres (0...2 B -1) h 1 h 2 Dres (0...2 B -1) h 1 h Vi/Vref Vi/Vref Idea: Measure h 1, h 2 and force difference to 0 How to measure without interrupting A/D operation? Solution: Statistics based measurement

32 Distance Estimation (1) Dres (0...2 B -1) "Red" with Prob. 1/2 "Black" with Prob. 1/2 Input Samples V in (k) For each input sample fair coin toss [independent of V in (k)] decides red/black

33 Distance Estimation (2) Dres (0...2 B -1) q CH ref (q) f(v in (k)) v q v in Simple input model: stationary random process Count # of codes q in black channel cumulative histogram CH ref (q)

34 Distance Estimation () Dres (0...2 B -1) h CH(j+m) CH(j) CH(j-m) H* CH ref (q) f(v in (k)) Place counter array in red channel v q After n samples, find red count that is closest to CH ref (q) Distance Estimator H* v in

35 Distance Estimation (4) Dres (0...2 B -1) f(v in (k)) h CH(j+m) CH(j) CH(j-m) H* CH ref (q) Can show: lim E( H*) h n var( H*) F ( v n q ) 2 f ( v q 2B ) 2 F(v q ) v q v in Estimation fails if signal not busy around v q Detectable!

36 LMS Loop V ini V resi STAGE i A/D D resi b - D' res Update rate: f s /n e(d' res ) p Distance Estimation H 1 H 2 - Accum. µ Accumulator forces average H 2 -H 1 to zero Tradeoff: Residual variance of p vs. tracking time constant Straightforward extension to track p 1, p 2

37 Tracking Time Constant Avg. Time Const. [msec] N Converter Resolution [bits] τ Example : k = B = N f AVG s = 100MHz k 2 2 f ε s 2B Confidence Backend res. Sampling rate ε = 0.5 LSB precision [bits] Example: N bit converter with -bit Stage1, uniform input distribution Must address/attenuate potentially faster variations in analog domain

38 On-Chip Temperature Variations µp Temperature Map [Najm, EEdesign 01/09/01] Local g m R replica bias Solutions: Local replica biasing Rule of thumb, d=200µm: T remote / T local >10, τ=100µs Keep distance to hot spots, common centroid layout

39 Outline Motivation Research Overview Analog Errors and Digital Correction Correction Parameter Estimation Prototype IC Summary

40 Note: Slides were removed due to prepublication restrictions. Please Refer to my publication at ISSCC 200 for a deatialed description of the prototype.

41 Potential Deep sub-µm: P analog P digital P saved Multi-stage calibration Topological optimization Vision: 12b, 200MHz ADC in 0.1µm Net savings 70% possible!

42 Summary Open loop amplification o o Reduces ADC power consumption Improves deep sub-µm compatibility Resulting analog errors o o Slow -> statistics based digital calibration Fast -> analog domain techniques Demonstrated feasibility through 12b, 75MSa/sec prototype IC Future Work: Optimized deep sub-µm implementation

43 Acknowledgements High Speed Converter Group, Wilmington, MA o Katsu Nakamura, Sudhir Korrapati, Dan Kelly, Larry Singer, Will Yang, Doug Mercer, Richard Schreier, Steve Reine,... ADSiV San Jose ADBrk Berkeley

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