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Analysis and Modeling of Neural-Recording ADC

Mentors:Wolfgang Eberle

Vito Giannini

Progress Update: Summer Internship

Vaibhav Karkare

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Design Constraints for ADC

Constraints on ADC for neural recording not well defined in literature– Need to formulate constraints based on end result of the processing

Spike-sorting process [3]

3

Strategy for Defining Specifications

Sample neural data– Read from Neuralynx format

into Matlab– Quantized and converted back

into Neuralynx format

Osort software used for spike sorting [4]– Only known hardware-friendly

clustering algorithm

Two clustering accuracy metrics are defined– Difference being inclusion of

detection errors and false alarms [5]

Sample Neural Data

Spike-Sorting

Non-ideal quantizer

Spike-Sorting

Compare classification

results

Bird’s eye view of analysis approach

4

Number of bits needed

Most previous analysis calculates number of bits based on electrode thermal noise [6]

– Making quantization noise equal to thermal noise degrades SNR by up to 3 dB

– Thermal noise is uncorrelated with data while quantization noise is not

Knee of the curve lies around 9 bits– Reasonable assumption for

the ADC

– Matches commonly used number for ADC design in neural recording systems

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Clustering Accuracy vs. DNL

Non-monotonic behavior of curves precludes identification of clear trend– Need for statistical averaging

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CA Over Multiple DNL profiles

The mean classification accuracy is not a strong function of DNL– Indicates that the design of the ADC can sacrifice some DNL in favor

of savings in power / area

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Variance of Accuracy

Higher DNLs also lead to higher variance in classification accuracy– Non-monotonic nature implies more averaging is needed

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Conclusions: Part 1

Summary of this work:– Created automated simulation setup for evaluation of impact of

quantization error on spike-sorting results

– Initial results point towards classification accuracy being a weak function of DNL

– DNL around 1.5 LSB can be tolerated without significantly affecting classification accuracy

– Higher DNLs lead to lower classification accuracy and higher variance in classification results

Future Work:– Simulation over larger number of DNL profiles and large number of

data sets is required to establish validity of results

– Similar analysis can be performed to include other non-idealities in analog front-end

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SAR ADC: Architecture

Operation governed by passive charge sharing

Size of capacitor array dictated by matching requirements and size of unit capacitor

Architecture of SAR ADC [7]

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Ideal Case Model

Comparator makes decisions using voltage difference

Model ADC using charge conservation– Solve for differential and common mode voltages

1

1 1 2

1

2 2 1

1

( ) ( ) (A.1)2

( ) ( ) (A.2)2

( 2)

2

ifi i i i i i i i

DDeq cm arr eq f arr f f

ifi i i i i i i i

DDeq cm arr eq f arr f f

i i iDDeq f arri

f i ieq arr

VC V SC V C V C V V

VC V SC V C V C V V

C V SC VV

C C

1

1

(A.3)

(A.4)

i icm cm cm

i i ieq eq arr

V V V

C C C

(A.5)

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Symmetric Array Parasitics

1

1

1

2 (A.3)

2

(2 2) (A.4)

2

2 (A.5

i i i iDD DDeq f arr ti

f i i ieq arr t

i i iDDeq cm ti

cm i ieq t

i i i ieq eq t arr

C V SC V SC VV

C C C

C V C VV

C C

C C C C

)

1

1 1 2

1

2 2 1

( ) ( ) ( ) ( ) (A.1)2

( ) ( ) ( ) ( ) (A.2)2

ifi i i i i i i i i i

DD DDeq cm arr t eq t f arr f f

ifi i i i i i i i i i

DD DDeq cm arr t eq t f arr f f

VC V SC V u S C V C C V C V V

VC V SC V u S C V C C V C V V

Solution to the above system of simultaneous linear equations gives:

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Effect of Symmetric Parasitics

Common mode drift with each conversion step– Due to top and bottom plate capacitances charged to different values– Can affect comparator decisions

Gain error in ADC characteristics– Assuming parasitics are proportional to array capacitance

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Asymmetric Array Parasitics

1

1 1 2

1

2 2 1

( ) ( ) ( ( ) ( ) ) ( ) (A.1)2

( ) ( ) ( ( ) ( ) ) ( ) 2

ifi i i i i i i i i i i

DD DDeq cm arr t eq t b f arr f f

ifi i i i i i i i i i i

DD DDeq cm arr t eq t b f arr f f

VC V SC V u S C V C u S C u S C V C V V

VC V SC V u S C V C u S C u S C V C V V

(A.2)

Separate terms for Vif1 and Vi

f2 , solve for Vi

f1 and Vif2

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Effect of Parasitic Mismatch

Dependence of O/P on absolute single-ended voltage leads to DNL– Differential Voltage now depends on absolute voltage values

across parasitics– Estimated DNL of up to 3 LSB for 10% parasitics (with extreme

mismatch in top and bottom plate cap)

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Modeling Junction Capacitances

In this analysis we focus on the non-linear S-D drain capacitances– Gate capacitances are expected not to significantly impact the

linearity of the ADC

0 (1 / )

Fit to simulated data gives:

0.7

0.37

mR Fj j

F

C C V

m

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Polynomial Approximation

Diode equation leads to non-integer exponents– Equations do not easily converge with numerical methods

Use polynomial fit instead – Fits equally well with monotonic characteristics over range of interest

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Modeling with Junction Parasitics

We have two equations in two variables and 5th order

( )Q C V dV

Re-write charge conservation with non-linear capacitors

Need to use numerical methods– Unique solution does not exist

– The initial condition is derived by solving the equation without parasitic junction capacitances

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Effect of Junction Parasitics

Even with symmetric parasitic values the non-linearity of the junction caps leads to DNL in the ADC– Junction caps are charged to different voltages

– ADC with 1.04 m switch for 60 fF capacitor has DNL contribution of 0.3 LSB due to parasitic junction capacitors

– DNL contribution dependent on ratio between array capacitor and switch size

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Conclusions: Part 2

Summary of this work:– Modeled the effect of non-linearities on static characteristics of ADC

– Matlab model integrated with existing model which also includes comparator mismatch and thermal noise

– Parasitics of array capacitance lead to a CM drift

– Mismatch in parasitic capacitances leads to DNL

– Junction capacitances lead to DNL even when switches are perfectly symmetric

Future Work:– Validation of model with Cadence simulations

– Modeling dynamic non-idealities of ADC

– Combining Part 1 and Part 2 to have a application-specific optimized ADC

– Check out for options to better performance of previous ADC using trends shown by models

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References/AcknowledgmentsREFERENCES

[1] B. Murmann, “ADC Performance Survey 1997-2009”, [Online] Available: http://www.stanford.edu/~murmann/adcsurvey.html

[2] B.Razavi, “Principles of Data Conversion System Design”, IEEE Press, 2005

[3] V. Karkare, S. Gibson, and D. Markovic, “A 130 W, 64-Channel Spike-Sorting DSP Chip”, ASSCC, Nov’09

[4] U. Reutishauser, E. Schuman, and A. Mamelak, “Online detection and sorting of extracellularly recorded action potentials in human medial temporal lobe recordings in vivo”, JNM, May’05

[5] S. Gibson, J.W.Judy, and D. Markovic, “Comparison of Spike-Sorting Algorithms for Future Hardware Implementation”, EMBC, Aug’08

[6] M.Chae, et. al., “Design Optimization for Integrated Neural Recording Systems”, JSSC, Sep’08

[7] J. Craininckx and G. Van der Plaas, “A 65fJ/Conversion-Step 0-to-50 MS/s 0-to-0.7 mW 9b Charge Sharing SAR ADC in 90nm Digital CMOS”, ISSCC, Feb’07

ACKNOWLEDGMENTS

Wolfgang Eberle, Vito Gianniani, Dejan Markovic, Sarah Gibson, and Ivan Gligorijevic.

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Questions / Comments?