Time-Interleaved ADCs - Theory and Design -...

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Time-Interleaved ADCsTheory and Design

Manar El-Chammas

Texas Instruments

December 11, 2011

Who am I?

Received B.E. from A.U.B. in 2004

Received Ph.D. from Stanford University in 2010I Thesis: “Background calibration of timing-skew in time-interleaved

ADCs”I Ph.D. Advisor: Boris MurmannI Research interests: Integrated circuits, background calibration, low

power design

Currently working at Texas Instruments (Dallas, TX) on high-speeddata converters

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Tutorial objectives

To understand the theory and operation of time-interleaved ADCsand how to design them

At the end of this tutorial, you will have a toolbox to analyzetime-interleaved ADCs with and a starting point from which todesign one

�� ��Stop me whenever you have questions

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A broad-stroke outline

Overview of data converters

The time-interleaved ADC

Quantitative analysis of time-varying errors

Design of time-interleaved ADCs

Calibration

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Part I

Overview of Data Converters

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Introduction

Data converters important part of signal chain

[Slide taken from B. Murmann notes]

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Data converter applications

Consumer electronicsI Video and audioI Digital camerasI Automotive systems

Communication systemsI Wireless infrastructureI Ethernet

Computing and controlI Storage mediaI Feedback systems

InstrumentationI Medical equipmentI Oscilloscopes

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Examples

Agilent oscilloscope

Published in ISSCC 2003

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Examples

1 kS/s ADC for medical implants

Published in ESSCIRC 2010

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Examples

TI ADC used in wireless infrastructure

Published in ISSCC 2010

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Reference books

Principles of Data Conversion System Design, Behzad Razavi

Data Converters, F. Maloberti

CMOS Data Converters for Communications, Mikael Gustavsson et al.

Understanding Delta-Sigma Data Converters, Richard Schreier et al.

Data Conversion Handbook, Analog Devices Inc.

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Analog-to-digital conversion

Definition

The conversion from a continuous-time signal to a discrete-timerepresentation

ADCIN OUT

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Analog-to-digital conversion

Analog-to-digital conversion consists of two operations ...

Sampling

Quantization

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Sampling and quantization

Sampling

(Discretizing in time)

Quantization

(Discretizing in amplitude)

[Murmann notes]

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Sampling and quantization

Most common approach is to discretize uniformly in both time andamplitude

These two concepts alone can fill an entire semester ...

For more on these, see reference books

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Types of ADCs: the flash ADC

Flash ADC has 2B − 1 comparators

Extremely fast with limited resolution

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Types of ADCs: the pipeline ADC

Pipeline ADCs have moderate speed and high resolution

[Image from B. Murmann notes]

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Types of ADCs

SAR

Sigma-delta

Algorithmic

Single-slope

Time-to-digital

... references previously mentioned discuss most of these

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Part II

The Time-Interleaved ADC

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Introduction to time-interleaved ADCs

Definition

An ADC that cycles through a set of N sub-ADCs, such that the aggregatesample-rate is N times the sample-rate of the individual sub-ADCs

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Introduction to time-interleaved ADCs

0(t)

x(t) y[n]

ADC0

ADC1

ADCN-1

1(t)

N-1(t)

. . .

.

Sub-ADCs tend to be identical

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Back in 1980 ...

William Black, Ph.D. thesis“High Speed CMOS A/Dconversion techniques”

Published “Time-InterleavedConverter Arrays”

[Black 1980]�� ��This “high speed” technique was for a 7-bit 2.5 MHz ADC

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... 30 years later

Time-interleaved ADCs are still a serious research area

Multi-GHZ ADCs are the normI Agilent, 2003: 80-way interleaved 20 GS/sI Fujitsu, 2009: 4-way interleaved 56 GS/sI Nortel, 2010: 16-way interleaved 40 GS/s

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How exactly does it work?

Intuitive in the time-domain

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First ADC samples the signal ...Example of Two Interleaved Sub-ADCs

12

x(t) y[n]

ADC0

ADC1

x(t)

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Second ADC samples the signal ...Example of Two Interleaved Sub-ADCs

13

x(t) y[n]

ADC0

ADC1

x(t)

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And again, first ADC samples the signal ...Example of Two Interleaved Sub-ADCs

14

x(t) y[n]

ADC0

ADC1

x(t)

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Time-domain analysis

Each sub-ADC output is (ignoring quantization)

yi [n] = x ((nN + i)Ts) (1)

where Ts is sampling period, N is interleaving factor, andi = 0, ...,N − 1

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Time-domain analysis

0(t)

x(t) y[n]

ADC0

ADC1

ADCN-1

1(t)

N-1(t)

. . .

.

Output multiplexer combines these streams such that

y [n] = yi

[n − i

N

]where i = n mod N (2)

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Frequency-domain analysis

This is less intuitive ...

Can take the discrete-time Fourier transform (DTFT) of the(upsampled) sub-ADC outputs and the time-interleaved ADC output

In theory, ...

Y (f ) =N−1∑i=0

Yi (f ) (3)

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Frequency-domain analysis

Assume you have an input signal with the following DTFT

0 0.2 0.4 0.6 0.8 1

0

0.2

0.4

0.6

0.8

1

|X(f

)|

f

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Frequency-domain analysis

The resulting (upsampled) sub-ADC output DTFT will be

0 0.2 0.4 0.6 0.8 1

0

0.05

0.1

0.15

0.2

0.25

|Y0(f

)|

f

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Frequency-domain analysis

Replicas have different phases for each of the sub-ADCs

When summed, the phases cancel each other out

You will get the same spectrum as the input

0 0.2 0.4 0.6 0.8 1

0

0.2

0.4

0.6

0.8

1

|Y(f

)|

f

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Time-varying errors

In theory, theory and practice are the same.

In practice, they are not.

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Time-varying errors

Ideally, a time-interleaved ADC can be blackboxed into a singlemonolithic ADC

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Time-varying errors

Offset

Gain

Timing skew

(Bandwidth)

0(t- 0)

x(t) y[n]

ADC0

ADC1

ADCN-1

1(t- 1)

N-1(t- N-1)oN-1

GN-1

o1

G1

o0

G0

. . .

.

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Time-varying errors

Ideal

-1 0 1 2 3 4 5 6 7 8 9 10

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

x(t)

Offset

-1 0 1 2 3 4 5 6 7 8 9 10

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

x(t)

Gain

-1 0 1 2 3 4 5 6 7 8 9 10

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

x(t)

Timing Skew

-1 0 1 2 3 4 5 6 7 8 9 10

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

x(t)

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Sources of errors

PVT (Process, voltage, temperature) variations

Current flow, layout nonidealities, mismatch in stray capacitance, etc.

�� ��All of these will limit your ADC performance

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Offset mismatch

Each sub-ADC ideally digitizes x(t)

yi [n] = x ((nN + i)Ts) (4)

Each sub-ADC actually digitizes x(t) + oi

yi [n] = x ((nN + i)Ts) + oi (5)

oi is different for each sub-ADC

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Frequency-domain effects

0 0.2 0.4 0.6 0.8 1

0

0.05

0.1

0.15

0.2

0.25|Y

0(f)|

f

The DTFT of the sub-ADC changes because of these offsets

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Frequency-domain effects

0 0.2 0.4 0.6 0.8 1

0

0.5

1

|Y(f

)|

f

The DTFT of the ADC has spurs at frequencies i · fs/N

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Gain mismatch

Each sub-ADC ideally digitizes x(t)

yi [n] = x ((nN + i)Ts) (6)

Each sub-ADC actually digitizes Gix(t)

yi [n] = Gix ((nN + i)Ts) (7)

Gi is different for each sub-ADC

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Frequency-domain effects

0 0.2 0.4 0.6 0.8 1

0

0.05

0.1

0.15

0.2|Y

0(f)|

f

The DTFT of the sub-ADC changes because of these gain differences

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Frequency-domain effects

0 0.2 0.4 0.6 0.8 1

0

0.2

0.4

0.6

0.8|Y

(f)|

f

The DTFT of the ADC has replicas at frequencies fin − i · fs/N

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Timing skew

Each sub-ADC ideally digitizes x(t)

yi [n] = x ((nN + i)Ts) (8)

Each sub-ADC actually digitizes x(t − τi )

yi [n] = x ((nN + i)Ts − τi ) (9)

τi is different for each sub-ADC

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Frequency-domain effects

0 0.2 0.4 0.6 0.8 1

0

0.05

0.1

0.15

0.2

0.25|Y

0(f)|

f

The DTFT of the sub-ADC changes because of timing skew

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Frequency-domain effects

0 0.2 0.4 0.6 0.8 1

0

0.2

0.4

0.6

0.8

1|Y

(f)|

f

The DTFT of the ADC has replicas at frequencies fin − i · fs/N

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Some notes

Gain and offset mismatch are “static” errors

Impact independent of input frequency

But ... what if gain is a function of frequency? (which it is)

And ... what if the gain transfer function varies? (which it will)

You have bandwidth mismatch ...

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Some notes ... continued

Timing skew is not a “static” errorSampling Error Due to Timing Skew

Skew

Error Error

x(t)

Ideal Sampling

Point

Actual Sampling

Point

SkewIdeal

Sampling Point

Actual Sampling

Point

x(t)

t t

18

“Fast” signals suffer more sampling error due to timing skew than “slow” signals

“Fast” signals suffer more sampling error due to timing skew than“slow” signals

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Why is timing skew such a problem?

ADCs are generally uniform sampling systems

What if two consecutive samples aren’t at times nTs and (n + 1)Ts?

I If the deviation is random, you have jitterI If the deviation is deterministically time-varying because you are

interleaving, you have timing skew

I Timing skew becomes jitter as N →∞

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How much of a problem is timing skew?

Interleave N B-bit sub-ADCs

Input signal is sinusoid with frequency fin

στ =

√(N

N − 1

)·(

1

22B

)·(

2

3(2πfin)2

)(10)

[Jenq 1988]

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How much of a problem is timing skew?

0.1 1 102

3

4

5

6

7

8

AD

C R

esol

utio

n [B

its]

Standard Deviation of Skew [ps]

fin

= 2 GHz

fin

= 4 GHz

fin

= 8 GHz

fin

= 16 GHz

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Sources of timing skew

Vout1

Vin

Vout2

0 0.2 0.4 0.6 0.8 10

0.5

1

1.5

2

2.5

3

3σ T

imin

g Sk

ew [

ps]

Normalized Power

Threshold mismatch causes delay change

Rule: Halve deviation with four-fold increase in power (Pelgrom’sequation)

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Sources of timing skew

Vout1

Vin

Vout2

C

C+ C

0 2 4 6 8 10 12 14 160

2

4

6

8

∆ C / C [%]

3σ T

imin

g Sk

ew [

ps]

Trace RC differences cause delay change

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Sources of timing skew

Phas

e G

ener

ator

To Sub-ADC

Vin

Vin

To Sub-ADC

Can easily have over 10 ps skew [Agrawal 2008]

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Part III

Quantitative Analysis of Time-Varying Errors

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Errors exist. What can we do?

Step 1: Quantify error you can tolerate

Step 2: Define your design space

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The sinusoidal approach

Most ADC simulated with a sine wave input

Allows you to define dynamic performance metrics

I Fundamental tone and harmonicsI SFDR: Spurious free dynamic rangeI SNR: Signal to noise ratioI SNDR: Signal to noise and distortion ratio

Can do the same for time-varying errors

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Bounds on time-varying errors (part 1)

Bound on offset

σo =

√(N

N − 1

)·(

A2

3 · 22B

)(11)

Bound on gain

σg =

√(N

N − 1

)·(

2

3 · 22B

)(12)

Bound on timing skew

στ =

√(N

N − 1

)·(

2

3 · 22B · (2πfin)2

)(13)

[Jamal 2001]

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Examples

5-bit ADC with input amplitude A = 1 and N = 2I σo = 25 mVI σg = 3.6 %I στ = 1

175·fin(e.g. fin = 100 MHz, στ ≈ 57 ps)

12-bit ADC with input amplitude A = 1 and N = 2I σo = 0.2 mVI σg = 0.028 %I στ = 1

22,000·fin(e.g. fin = 100 MHz, στ ≈ 0.5 ps)

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Bounds on time-varying errors (part 2)

In real-world applications, ADCs don’t sample sine waves

Many systems are broadband

Tx Rx Data OutData In

Channel

High-Speed Serial Link

5�� ��Using a sine wave at Nyquist will overdesign your system

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Cost of overdesign

More chip area

More power

Longer design cycle

More $$$

Use minimum-mean square error to derive more realistic bounds

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“Best-fit” approach

y [n] = xo [n] + e[n] (14)

xo [n] is the “best-fit”

xo [n] = G x (nTs − τ) (15)

Nontrivial to solve in the general sense

Solvable for WSS and WSCS signals [El-Chammas 2009]

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Intuition

Gai

n (G

)

Skew (t)

Gai

n (G

)

Skew (t)

Find vector that minimizes distance to sub-ADC vectors

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Wide-sense stationary

Definition

A signal is wide-sense stationary (WSS) if its mean and autocorrelation arenot a function of time

m(t1) = m(t2) = m (16)

R(t1, t1 + τ) = R(t2, t2 + τ) = R(τ) (17)

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Calculate the MSE

f (G , τ) = E[e[n]2

]− E [e[n]]2 (18)

Remember:

e[n] = y [n]− xo [n] (19)

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Calculate the MSE

f (G , τ) =

(G 2P +

P

N

N−1∑i=0

G 2i − 2

G

N

N−1∑i=0

Gi R(τi − τ) +1

N

N−1∑i=0

o2i

)−

1

N2

(N−1∑i=0

oi

)2

(20)

(work your “write” arm muscles and derive this)

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Calculate the “best-fit” parameters

�� ��Minimize f (G , τ)

Differentiate with respect to G and τ and set to zero

G =1

NP

N−1∑i=0

GiR(τ − τi ) (21)

τ = arg maxτ

N−1∑i=0

GiR(τ − τi ) (22)

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Mismatch or quantization limited?

SNRf =P

f (G , τ)≷

3

2· 22B = SNRQ (23)

f (G , τ) ≶2 · P

3 · 22B(24)

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Effect of timing skew

Impact on timing skew is different than previously shown

Assume oi = 0 and Gi = 1

1

P

N−1∑i=0

R(τ − τi ) ≥ N

√SNRQ − 1

SNRQ(25)

Let’s make one more assumption: the autocorrelation is second orderdifferentiable

R(τ) ≈ R(0) +����XXXXR ′(0)τ +

R ′′(0)

2τ2 (26)

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Effect of timing skew

στ ≤

√(N

N − 1

)·(

2

3 · 22B

)·(

1

|R ′′(0)|

)(27)

Function of three parameters (N, B, and R ′′(0))

M. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 71 / 158

More on autocorrelation intuition

Autocorrelation related to speed of signal

t

x(t)

R(t)

t

t

x(t)

R(t)

t

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Importance of signal statistics

R(τ) = sinc(2fcτ) (28)

R ′′(0) = −1

3(2πfc )2 (29)

If you had used sine wave analysis, you would overconstrain thevariance of τ by 3

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Importance of signal statistics

Same applies to more realistic signals (e.g. WSCS)

If timing skew is a problem, then improve your design space byknowing your system

Sidenote: this viewpoint also extends to nonlinearities and jitter (Seee.g. [Gupta 2006] and [Da Dalt 2002])

M. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 74 / 158

Questions?

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Part IV

Design of Time-Interleaved ADCs

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The coolest ADCs from the past 10 years

Agilent, 2003, ISSCC

Terranetics, JSSC 2006

Nortel, ISSCC 2010

Fujitsu, OFC 2010

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Interleaving 80 pipeline ADCs

20 GS/s 8 bit ADC

Correct for gain, offset, and timing skew [Poulton 2003]

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Interleaving 4 pipeline ADCs

1 GS/s 11 bit ADC

Correct for gain and offset [Gupta 2006]

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Interleaving 16(0) SAR ADCs

40 GS/s 6 bit ADC

Correct for gain, offset, and timing skew [Greshishchev 2010]

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A 56 GS/s ADC

56 GS/s 8 bit ADC and interleaved 4x80 ADCs [Dedic 2010]

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Choosing the design space

You have: input signal statistics + bit resolution + application space

Calculate acceptable bounds on time-varying errors

Choose sub-ADC architecture (beyond scope of tutorial)

Choose interleaving factor

Design clocking network

Deal with time-varying errors�� ��Looks simpler than it is

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Sub-ADC architecture

Extremely low end resolution and high end resolution choice is easyI Flash ADCs for 3 bitsI Sigma-Delta for 24 bits

SAR, pipeline, ...

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Sub-ADC architecture

10-6

http://www.stanford.edu/~murmann/adcsurvey.html

10-8

10-7

10-10

10-9

s [Jou

les] fJ100

conv-step2ENOBs

PFOMf

10-11

10

P/f s

FlashPipelineSAR

1 766 02

SNDR[ dB] .ENOB.

20 30 40 50 60 70 80 90 100 11010

-13

10-12

SARSigma-DeltaOther

SNDR [dB]

[Image from Murmann class notes]

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Interleaving can lower power*

Lessons from parallel processing [Horowitz 2006]

* at the expense of complexity, area, and headache

M. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 85 / 158

Interleaving can lower power

[Maloberti 2008]

11-bit ADC at 100 MS/s needs ∼ 15 mW

At 800 MS/s needs ∼ 700 mW

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Interleaving can lower power

3 4 5 6 7 8 9 10 11 12

30

35

40

45

50

55

60

65

70

75

Interleaving Factor

Pow

er [

mW

]

Increasing fs will force you to hit a technological wall

True even in the smallest ADC element - the comparator

M. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 87 / 158

Clocking network

Phase Generator

0(t) 1(t) N-1(t)

Phase Generator

0(t) 1(t) N-1(t)

Input Clock

Sub-ADC Clocks

. . . . . . . .

t

0(t)

1(t)

2(t)

N-1(t)

Ts

Ts

Ts

Need to provide N clocks to sub-ADCs

Ideally offset by Ts

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Clocking network

Phase locked loops and delay locked loops

Can use frequencies lower than sub-ADC sample rates

M. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 89 / 158

Clocking network

Clock-gating

Use full-rate clocks and control sub-ADC clock with digital logic (e.g.[Louwsma 2008])

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Clocking network

Shift registers (e.g. [Gao 2008])

M. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 91 / 158

Time-varying errors?

You’ve chosen your sub-ADC architecture

and your interleaving factor

and designed your clocking network

How do you deal with time-varying errors?

Two approaches: correct by design or correct with calibration

M. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 92 / 158

Approach 1: by design

voffset ≈3√WL

mV /µm (30)

Pelgrom’s Model

12-bit ADC, 1 Vp−p requires less than 0.3 mV offset

WL > 100µm2

In 65 nm CMOS, W > 1.5 mm ...

M. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 93 / 158

Approach 1: by design

There exist analog offset-minimization techniques for amplifiers andcomparators

[Suarez 1975]

Most of these are extremely old

M. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 94 / 158

Approach 1: by design

Trimming

Dynamic techniques: auto-zeroing or chopping

[Makinwa 2002]

M. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 95 / 158

Approach 1: by design

Introduce redundancy

[Ginsburg 2008]

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Approach 1: by design

Introduce redundancy

[Ginsburg 2008]

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Alternative approach for offset and gain

Correct with calibration

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Some design techniques for timing skew

Timing skew problem exists between track-and-holds

Use a front-end sampler

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Front-end sampler

[Poulton 1987]

M. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 100 / 158

Front-end sampler

Possible Solution: Hide Timing Skew

28

S. Gupta et al, “A 1-GS/s 11-bit ADC With 55-dB SNDR, 250-mW Power Realized by a High Bandwidth Scalable Time-Interleaved Architecture “, IEEE JSSC, Dec. 2006, vol. 41, pp. 2650 - 2657

Add a sampler to the ADC front-endAdd a sampler to the ADC front-end and use a full-rate clock

M. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 101 / 158

Front-end sampler

Possible Solution: Hide Timing Skew

29

Add a sampler to the ADC front-end and use a full-rate clockAdd a sampler to the ADC front-end and use a full-rate clockto hold the input every clock period

M. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 102 / 158

Front-end sampler

Possible Solution: Hide Timing SkewPossible Solution: Hide Timing SkewPossible Solution: Hide Timing Skew

Sub-ADC clocks have some margin for errorSub-ADC clocks have some margin for error

Requires a full-rate clock and a sampler Requires a full-rate clock and a sampler that can settle fast enoughthat can settle fast enough

3131M. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 103 / 158

Front-end sampler

[Gupta 2006]

M. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 104 / 158

Use a better clocking scheme

Front-end samplers have limited application

[Louwsma 2008]

10 b, 1.35 GS/s

Transistor threshold limitation

M. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 105 / 158

Part V

Calibration

M. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 106 / 158

Approach 2: use calibration

Straightforward for offset and gain

Not as trivial for timing skew

M. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 107 / 158

Calibration = estimation + correction

Definition

Estimation: An approximation of the value or extent of something

Definition

Correction: The action or process of correcting something

M. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 108 / 158

Types of calibration

Digital vs. mixed-signal

Foreground vs. background

M. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 109 / 158

Digital calibration

Adaptive FilterADC0

ADC1

y0[n]y0[n]

y1[n]

x(t)

~

~

Digital

Backend

y1[n]

Detection

Adaptive Filter

M. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 110 / 158

Mixed-signal calibration

ADC0

ADC1

y0[n]

y1[n]

x(t)

Digital

Backend

Detection

M. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 111 / 158

Foreground calibration

InputOutput

Test

M. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 112 / 158

Foreground calibration

Input No OutputTest

Detection

M. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 113 / 158

Background calibration

Input Output

Detection

M. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 114 / 158

Offset and gain“almost” solved problem

Still a research topic

But ... there is a popular solution

M. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 115 / 158

Correcting offset

Estimation ...oi ∝

∑j

Di ,j (31)

Correction ...Di ,j = Di ,j − oi (32)

M. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 116 / 158

Correcting gain

Estimation ...Gi ∝

∑j

(Di ,j )2 (33)

Correction ...Di ,j = Di ,j/Gi (34)

M. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 117 / 158

Example 1 (1998)

[Fu 1998]

M. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 118 / 158

Example 1 (1998)

[Fu 1998]

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Example 1 (1998)

10-bit, 40 MS/s, two-way interleaved ADC [Fu 1998]

M. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 120 / 158

Example 2 (2001)

[Jamal 2001]

M. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 121 / 158

Example 2 (2001)

[Jamal 2001]

M. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 122 / 158

Example 3 (2007)

[Oh 2007]

Makes use of pilot tones in OFDM systems

M. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 123 / 158

Example 3 (2007)

[Oh 2007]

M. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 124 / 158

Example 3 (2007)

[Oh 2007]

6-bit, 200 MS/sM. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 125 / 158

And timing skew?

Still ongoing research

No single winner

M. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 126 / 158

Example 1 (2001)

[Jamal 2001]

Requires fractional delay filter

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Example 1 (2001)

[Jamal 2001]

M. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 128 / 158

Example 2 (2003)

[Poulton 2003]

M. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 129 / 158

Example 2 (2003)

[Poulton 2003]

M. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 130 / 158

Example 2 (2003)

Foreground calibration

Apply pulse train with fast edges

Use FFT to measure phase delay of T/H

Adjust time delay

Rinse and repeat

[Poulton 2003]

M. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 131 / 158

Example 3 (2005)

[Elbornsson 2005]

Digital and background calibration

Uses cost function based on input statistics

M. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 132 / 158

Example 3 (2005)

[Elbornsson 2005]

Use inverse DTFT to reconstruct signal using timing estimation

Update timing estimation with cost function (i.e. has cost functiondecreased or increased?)

Requires bandlimited signal (common limitation to many blindcalibration algorithms)

M. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 133 / 158

Example 4 (2008)

[Haftbaradaran 2008]

M. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 134 / 158

Example 4 (2008)

[Haftbaradaran 2008]

M. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 135 / 158

Example 4 (2008)

[Haftbaradaran 2008]

Has 0.86 ps delay change (on average)

M. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 136 / 158

Example 4 (2008)

[Haftbaradaran 2008]

M. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 137 / 158

Example 5 (2010)

[Huang 2010]

6-bit 16 GS/s flash ADC

M. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 138 / 158

Example 5 (2010)

[Huang 2010]

M. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 139 / 158

Example 5 (2010)

[Huang 2010]

Change capacitive load on delay cells (similar to [Poulton 2003])

M. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 140 / 158

Example 6 (2010)

[El-Chammas 2010]

5-bit 12 GS/sAdd extra channel (used 1-bit ADC in implementation)M. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 141 / 158

Example 6 (2010)

M. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 142 / 158

Example 6 (2010)

Maximize correlation between extra ADC and each sub-ADC byadjusting delay cell

M. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 143 / 158

Example 6 (2010)

Adjust delay cell load (around 0.3 ps resolution)

M. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 144 / 158

Example 6 (2010)

Several hundred milliseconds for initial convergence

M. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 145 / 158

Example 7 (2011)

[Payne 2011]

12 bit 1GS/s ADCCorrect gain and offset in DSPCorrect timing skew and bandwidth in analog

M. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 146 / 158

And many more ...

There are many more approaches for timing skew calibration

Some require energy free bands, and others don’t

Some use fractional delay filters, and others tune delay with delay cells

There is much research in both the estimation and correction blocks

M. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 147 / 158

Current time-interleaved ADCs

15 20 25 30 35 40 45 50 55 6010

−1

100

101

102

103

104

Ene

rgy

[pJ]

SNDR [dB]

ADCsFOM=1 pJ/conv−stepFOM=0.1 pJ/conv−step

ADCs faster than 1 GS/s (published in ISSCC and VLSI)

M. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 148 / 158

Current time-interleaved ADCs

15 20 25 30 35 40 4510

0

101

102

103

Ene

rgy

[pJ]

SNDR [dB]

Other ADCsThis WorkFOM=1 pJ/conv−step

ADCs faster than 10 GS/s

M. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 149 / 158

Making sense of the noise

Can either minimize mismatch through careful design and layout

Or can use calibration

“Optimal” type of calibration is application and system dependent

Be careful of throwing everything at the digital backend

A lot of room for future research

M. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 150 / 158

Making sense of the noise

What are some common themes?

Some operations are better done in digital

Others are better in analog

Co-optimization of calibration and circuit design

M. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 151 / 158

Summary

Time-interleaved ADCs important in pushing performance

Time-varying errors set performance limitations

System-level analysis improves design space specifications (e.g.mismatch constraints and ADC architecture)

Calibration techniques extremely useful in compensating for errors

M. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 152 / 158

Questions

Email: manar@ti.com, manar.chammas@gmail.com

M. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 153 / 158

Thank you

M. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 154 / 158

References

R.E. Suarez, P.R. Gray, and D.A. Hodges, “All-MOS Charge RedistributionAnalog-to-Digital Conversion Techniques–Part II,” IEEE Journal of Solid-State Circuits,vol. sc-10, no. 6, pp. 379-385, Dec. 1975

W. Black and D. Hodges, “Time Interleaved Converter Arrays,” IEEE Journal ofSolid-State Circuits, vol. 15, no. 6, pp. 1022-1029, Dec. 1980

K. Poulton, J. Corcoran, and T. Hornak, “A 1-GHz 6-bit ADC System,” IEEE Journal ofSolid-State Circuits, vol. 22, no. 6, pp. 962-970, Dec. 1987

Y.-C. Jenq, “Digital Spectra of Nonuniformly Sampled Signals: Fundamentals andHigh-Speed Waveform Digitizers,” IEEE Transactions on Instrumentation andMeasurement, vol. 37, no. 2, pp. 245-251, June 1988

D. Fu, K.C. Dyer, S.H. Lewis, and P.J. Hurst, “A Digital Background CalibrationTechnique for Time-Interleaved Analog-to-Digital Converters,” IEEE Journal ofSolid-State Circuits, vol. 33, no. 12, pp. 1904-1911, Dec. 1998

S. Jamal, “Digital Background Calibration of Time-Interleaved Analog-to-DigitalConverters,” Ph.D. dissertation, U.C. Davis, Davis, CA, 2001

N. Da Dalt, M. Hareneck, C. Sandner, and A. Wiesbauer, “On the Jitter Requirements ofthe Sampling Clock for Analog-to-Digital Converters,” IEEE Transactions on Circuits andSystems I: Fundamental Theory and Applications, vol. 49, no. 9, pp. 1354-1360, Sept.2002

M. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 155 / 158

References

K. Makinwa, “Dynamic Offset-Cancellation Techniques,” Smart Sensor Systems, 2002

K. Poulton, R. Neff, B. Setterberg, B. Wuppermann, T. Kopley, R. Jewett, J. Pernillo, C.Tan, and A. Montijo, “A 20 GS/s 8 b ADC with a 1 MB Memory in 0.18 µm CMOS,” inProceedings of IEEE International Solid-State Circuits Conference, vol. 1, Feb. 2003, pp.318-496

J. Elbornsson, F. Gustafsson, and J.-E. Eklund, “Blind Equalization of Time Errors in aTime-Interleaved ADC System”, IEEE Transactions on Signal Processing, vol. 53, no. 4,pp. 1413-1424, Apr. 2005

S. Gupta, M. Inergield, and J. Wang, “A 1-GS/s 11-bit ADC with 55-dB SNDR, 250-mWPower Realized by a High Bandwidth Scalable Time-Interleaved Architecture,” IEEEJournal of Solid-State Circuits, vol. 41, no. 12, pp. 2650-2657, Dec. 2006

M. Horowitz, “Scaling, Power and the Future of CMOS,” Workshop on On- and Off-ChipInterconnection Networks for Multicore Systems, Stanford, CA, Dec. 2006

Y. Oh and B. Murmann, “A Low-Power, 6-bit Time-Interleaved SAR ADC Using OFDMPilot Tone Calibration,” in Proceedings of IEEE Custom Integrated Circuits Conf., SanJose, CA, Sep. 2007, pp. 193-194

B. Ginsburg and A. Chandrakasan, “Highly Interleaved 5b 250 MS/s ADC withRedundant Channels in 65nm CMOS,” in Proceedings of IEEE International Solid-StateCircuits Conference, vol. 1, Feb. 2008, pp. 240-610

M. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 156 / 158

References

A. Haftbaradaran and K.W. Martin, “A Background Sample-Time Error CalibrationTechnique Using Random Data for Wide-Band High-Resolution Time-Interleaved ADCs,”IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 55, no. 3, pp. 234-238,Mar. 2008

S. Louwsma, A. van Tuijl, M. Vertregt, and B. Nauta, “A 1.35 GS/s, 10 b, 175 mWTime-Interleaved AD Converter in 0.13 µm CMOS,” IEEE Journal of Solid-State Circuits,vol. 43, no. 4, pp. 778-786, Apr. 2008

X. Gao, E. Klumperink, and B. Nauta, “Advantages of Shift Registers Over DLLs forFlexible Low Jitter Multiphase Clock Generation,” IEEE Transactions on Circuits andSystems II: Express Briefs, vol. 55, no. 3, pp. 244-248, Mar. 2008

F. Maloberti, “High-Performance Data Converters: Trends, Process Technologies andDesign Challenges,” IEEE Asia Pacific Conference on Circuits and Systems, vol. 1, Nov.2008, pp. 12-16

M. El-Chammas and B. Murmann, “General Analysis on the Impact of Phase-Skew inTime-Interleaved ADCs,” IEEE Transactions on Circuits and Systems I: Regular Papers,vol. 56, no. 5, pp. 902-910, May 2009

A. Agrawal, A. Liu, P. Hanumolu, and G.-Y. Wei, “An 8×5 Gb/s Parallel Receiver WithCollaborative Riming Recovery,” IEEE Journal of Solid-State Circuits, vol. 44, no. 11, pp.3120-3130, Nov. 2009

M. El-Chammas (TI) Time-Interleaved ADCs Dec. 2011 157 / 158

References

Y. Greshishchev, J. Aguirre, M. Besson, R. Gibbins, C. Falt, P. Flemke, N. Ben-Hamida,D. Pollex, P. Schvan, and S.-C. Wang, “A 40 GS/s 6b ADC in 65nm CMOS,” inProceedings of IEEE International Solid-State Circuits Conference, vol. 1, Feb. 2010, pp.390-391

I. Dedic, “56 GS/s ADC Enabling 100GbE,” OFC 2010

B. Murmann, EE315B 2010 Class Notes, Stanford University,

C.-C. Huang, C.-Y. Wang, and J.-T. Wu, “A CMOS 6-bit 16-GS/s Time-Interleaved ADCwith Digital Background Calibration,” in VLSI Circuits Symposium, Digest of TechnicalPapers, June 2010, pp. 159-160

M. El-Chammas and B. Murmann, “A 12-GS/s 81-mW 5-bit Time-Interleaved Flash ADCWith Background Timing Skew Calibration,” in VLSI Circuits Symposium, Digest ofTechnical Papers, June 2010, pp. 157-158

R. Payne, et al., “A 12b 1GS/s SiGe BiCMOS Two-Way Time-Interleaved Pipeline ADC,”in Proceedings of IEEE International Solid-State Circuits Conference, vol. 1, Feb. 2011,pp. 182-183

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