IEEE International Sytnposium on Circuit and System 2003 Tutorial Guide

4. Analog Adaptive Filters

Duration: Half Day

Tutorial Presenter: ' o Prof. A. Chan Carusone, University of Toronto, Canada

Who Should Attend: Researchers and designers of digital communication transceivers. This includes people working either at the circuit level (analog, digital, or mixed signal) or the system level. The material would also be of interest to adaptation algorithm researchers.

Abstract: Adaptation is used whenever a Filter's parameters must track poorly controlled or time varying conditions. At low speeds, adaptive filtering is easily and efficiently performed using digital circuits. However, analq filters are preferable when high speed, low power operation is required and moderate linearity can be tolerated. In these cases, the combination of flexibility and performance offered by analog adaptive filters can be an enabling technology. This tutorial will provide a overview of the area, including the algorithms, architectures, and circuits.

I n the first part of the tutorial, analog filter structures suitable for adaptation are presented. Both analog discrete time (transversal, transpose, IIR) and continuous time (Laguerre and ladder filters) filter structures are covered including first order circuit designs.

The second part of the tutorial is a discussion of adaptation strategies suitable for analog filters. The traditional LMS algorithm has several problems when applied to analog adaptive filters. Algorithmic and circuit techniques for combating these problems will be discussed. Alternative adaptation algorithms will also be presented.

Finally, the third part of the tutorial brings together material presented in the first two sections by focusing on practical applications of analog adaptive filters. Both established applications and ongoing research areas wilt be considered including magnetic storage read channels, Ethernet transceivers, coaxial cable channels, backplanes, chip-tochip connections, and optical communications. We shall see how the applications dictate the designers' choice of adaptation strategy, filter structure and circuit implementation.

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IEEE Internalional Symposium on Circuit and System 2003 Tutorial Guide

Time Table

Tutorial 4: Analog Adaptive Filters

13:30 Analog filter structures suitable for adaptation; analog discrete time (transversal, transpose, IER) and continuous time (Laguerre and ladder filters) filter structures; first order circuit designs

~~ ~ ~ ~

14:30 Adaptation strategies for analog filters; algorithmic and circuit techniques

15:OO Coffee break

15:30 Alternative adaptation algorithms

16:OO Practical applications of analog adaptive filters; magnetic storage read channels, Ethernet transceivers, coaxial cable channels, backplanes, chip- to-chip connections, and optical communications

17:OO Close

18:OO Welcome reception

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IEEE International Symposium on Circuit and System 2003 Tutorial Guide

REEE Ink Symposium Circuits & Systems Tutorial:

Analog Adaptive Filters May 25,2003

T. Chan Carusqne University of Toronto

Dept. of Electrical & Computer

1

/--

Outline I I Motivation

2. Adaptive Filter Introduction

3. Adaptation algorithms

a) LMS adaptation b) LMS variations c) Dc offset effects in

the LMS algorithm d) Alternative (non-

LMS) adaptation algorithms

4. Filter structures & implementations

a> Discrete time b) Continuous time

a) Co-axial cable b) Magnetic storage c) High-speed ethernet d) Chip-to-chip

communications e) Optical Fibre

5. Applications

Slide 2 of 100

IEEE Intemational Symposium on Circuit and System 2003 I u t o m w i d e

Digital Communications

Why bother with adaptive filters at all? Channel impairments are unknown & time-varying

- 10 - Slide 3 of 100 Anem Adaplrve Mers

Fmf T. Chan C a r u m . Universrly ofTomnto

Equalization e A communication channel changes the shape

of pulses passing through it > Intersymbol interference (ISI)

Channel, H(s) Equalizer, 1/H(s)

Challenges: only linear channels, H(s), can be equalized generally requires amplification, hence, noise

channel H(s) may not be known a priori enhancement

3 M a k e equalizer adaptive

Analcg Adeplrvs FiNers Slide 4 of 100 Pmf. T. Chan Caruume. Universlhi Dl Tomnlo

IEEE International Symposium on Circuit and Systcm 2003 Tutorial Guide

Echo Cancellation Full duplex: transmit and receive over the same channel Some transmit signal leaks into receive path due to imperfect hybrid circuits

e Echo canceller output should mimic the echo signal

Integrated Circuit

- - - - - I - - - - - - - - - - - -

* Challenges: similar to equalizer

Analog Adaptive Fillers Prof. t. Chan Camsone. Universiw oiToronta

Slide 5 of 100

\ Crosstalk Cancellation e transmit signal from neighboring channel

leaks into receive path Crosstalk canceller mimics the coupling path -

q 2 x = - o -a-----------

Integrated Circuit 1 4 -

Ansbg Adanim Frlfsrs Pmf T. Chan Carusone, University of Toronto

Slide 6 of 100

IEEE International Symposium on Circuit and Svslem 2003 Tutorial Guide

\ Digital Communications

f

Why bother with analog adaptive filters? 8 Case #I: Very high speed required 3 A/D conversion not possible or practical

Q Case #2: Moderate linearity & low power required s Possible power savings resulting from reduction in

s Improvement may be debateable as CMOS process A/D resolution and/or DSP required

technologies scale

AoaiDg Adaptive Filters Prof. T. Chan Carusone. Unlvsrslty of Toronto Slide 7 of 100

Digital Communications

Example #I : Adaptive equalization of I O + Gbls data 1

1 O+ G bls Digital Digital CDR, rJTH-H-1 Channel Decoding, etc.

B A/D must operate at I O + GSamples/sec with several bits accuracy 3 huge power consumption 3 may not even be feasible, especially in CMOS

A n a l ~ g Adaptwe finer5 pmr 1. Chan Carusone, Unwersityof TorDnlO

Slide 8 of 100

TEE€ International Symposium an Circuit and System 2003 Tutorial Guide

7

Digital Communications

L

9 bit AGC +

N D - Anti-aliasing -+ filter I

Example #I : Adaptive equalization of 1 O+ Gb/s data rjyH;H-l 10+ Channel Gb/s Equalizer Analog Decoding Demux &

a no need for AID may be implemented at the transmitter

Analog Adaptive Fiitars Slide 9 of 100 Pmf. T Chan CaruSone. University of Toronto

Analog vs. Digital Adaptive Filters

Example #2: Signal conditioning in Gigabit ethernet From other transminers

/ 1

o Lots of high-speed DSP 3 power-hungry e Considerable anafag front end still required o 9-bit A/D design is challenging

/-

\ Analog Adaptwe Fifisrs Prof T Cnan Camwoe. uoivetolty of rorirnCo Slide 10 of 100

. . . lEEEI?t?mational Symposium on L!rcuit and system LUG; 1-

-3 AGC +

Anti-aliasing filter f

Analog Adaptive FMers Prof T. Chan Carusone. University of Toronto

Slide 11 of 100

Outline

I. 2. 3. 4. 5.

Motivation Adaptive Fi Iter Introduction Adaptation algorithms Filter structures & implementations Applications

AnSIOg Adaplivs Fillers Slide 12 of 100 Prof T. Chan Caruvlne Unwerrily of Toronto

IEEE International Symposium on Circuit and System 2003 Tutoriat Guide

f-

Adaptive Filter Introduction

Adaptive Fil tel

Adaptive filter has input U and output y e The filter has programmable parameters, p (e.g. transfer

function coefficients, location of poles, zeros, etc.. .) e The filter’s “desired” or “ideal” output is known, d o Adaptation algorithm adjusts p to minimize the power in the

error, e = d - y

Slide 13 of 100

/

Adaptive Filter Introduction

Adaptive

Alternate interpretation: 5. Adaptation algorithm adjusts p so that y is the

best possibte estimate of d

IEEE lnternational Symposium on Circuit and System 2Nf3 i uwm C%kk

Transmitter

System Identification Model

Decision- 2 Receiver

' Channel , Adaptive Making d

Filter, H

Adaptive , Filter, H

U b

e I

noise

System IO be d Define: U = filter input ' identified, G - y = fitter output d = desired output e = error in output with respect to desired output = (d -y)

i; After convergence, H will match G as closely as possible 2 can then use H as a model for G (a.k.a. "model matching")

Analog Adapiive Fiiers Prof. T. rhan Cams". U n m W of T O " Slide 15 of 100

Example: Equalization ,.+ noise

Q Desired output, d = transmitted waveform :: Must have access to the transmitted data at the receiver in

order to generate e (e.g. training sequence) Similar to the system identification problem except the system to be identified, G = (channel)-'

Anelog Adaplim Wsrs PmL T. Chan Carusone, Universlly of Tomnlo

Slide 16 of 100

IEEE Intemalional Symposium on Circuit and Syslcm 2003 Tutorial Guide

d . Transmitter

Decision=Directed Equalization

Deciwon- 2 Receiver

, Making Adaptive ’ ,‘ Filter, H Channel

noise

e Instead, may use receiver’s decisions as the “desired” signal ‘i. “Decision-directed” operation ;i Assumes fairly low bit error rate (BER) > May use training sequence at the start to decrease BER,

then switch to decision-directed

Anslog Adaptrm filfers Slide 17 of 100 Pruf. T. than Cawsoone. Unlventy of Toronto

Adaptive Pre-emphasis noise

f y Decision- 2

Receiver

> Channel Making “

e (Theoretically) it does not matter what’order you apply the adaptive filter and the channel

i Sometimes it is beneficial to apply adaptive filtering at the transmitter: “Pre-emphasis” (usually high frequency components are amplified/emphasized prior to transmission)

Slide 18 of 100 An- Adaptwe fillers Pmf. T. Chan Carusone. unwamly ol T-IO Slide 18 of 100 An- Adaptwe fillers Pmf. T. Chan Carusone. unwamly ol T-IO

IEEE International Symposium on Circuit and System 2003 I utorial Crude

/ Example: Echo Cancellation

n

I Canceller I I+

e

8 Recall: U = filter input y = filter output d = desired output e = error in output with respect to desired output = ( d - y )

Analog Adaptwe Filters Pmf. T. Cnan Carusone. UnNWS%y d Tomnlo Slide 19 of 100

/- \ Example: Crosstalk Cancellation

(P Recall:

Crosstalk Cancelier

U = filter input y = filter output d = desired output e = error in output with respect to desired output = (d-yJ I

Slide 20 of 1 OD mnaicg ndapuve Finers Pmt T Cnan Carusone, University 01 Toronto

Tuiorial Guide [EEF Intmaliond Symposium on Circuit and System 200:

f -

Outline

I . 2. 3.

4. 5.

Motivation Adaptive Filter Introduction Adaptation a lgori t h ms a) LMS adaptation b) L M S variations c) Dc offset effects in the LMS algorithm d) Alternative (non-LMS) adaptation algorithms

Filter structures & implementations Applications

Analog Adaplive filters Slide 21 of 100 Pmf. T. Chan Carusone. University of Tomnto

Gradient Descent Adaptation

I parameter case:

dE[e’] < O :. Ap > 0

0 p determines the rate of adaptation: larger p 3 faster convergence P

Slide 22 of I00 I An&g Adaptwe F ~ h m Prof. T Chan Cardsone. UnNerslty of Tomnto

IEEE lntemat~onal Symposium on Circuit and System 2003 Tutorial Guide

Gradient Descent Adaptation - - .-

Multiple parameters: Each is updated independently (simultaneously) depending on its own partial derivative

o e.g. 2 parameters:

I ) L ‘I 1

A

f

Analq Adapirvs Flllnsrs Slide 23 of 100 Prof. T. Chan Carusone. Untversily 01 Tomnto

f- \ Gradient Descent Adaptation

p must also be chosen to ensure stability

€ [ e ’ ]

\ p underdamped, but still stable

P

- Airaim Adaphvs Fillers Prof. T. Chan Carusone. University of Tomnto

Slide 24 of 100

IEEE International Symposium on Circuit and System 2003 Tutorial Guide

Gradient Descent Adaptation a Usually, is chosen conservative

w 1 ! 7 for smooth “overdamped convergence

p overdamped 3 smooth convergence p critically damped 3 requires a knowledge of ETe‘l vs. p (not

usially availablej

Slide 25 of 100 Amkg Adaptwe Fib6 Prof. T. Chan Catusone. University of Toronto

/ Gradient Descent Adaptation

pmax = maximum p for which adaptation is still stable

P will depend upon the shape of the performance surface “shallow” bowl larger pmax since the slope SE[&(k)]/Sp is always smaller

4 - 3 - 2 - 1 0 1 2 3 4

Slide 26 of 100 A m h g Adaptha Fitem Pmf T. Chen Carusone. Universltv olTomnto

~~~ ._ Tutonal Guide IEEE International Symposium on Circuit and System 2003

\ Gradient Descent Adaptation f

With multiple parameters, must choose p conservatively for worst-case (steepest) para meter

e In this case, using the same p for both parameters results in a p that is slower than necessary for p 1

n /'I

A n a I ~ g Adaptive Fitem Prof. T. Chan Carusone. University of Tomnta

Slide 27 of 100

' Gradient Descent Adaptation

How can we calculate x [ e 2 ) a p ?

some period of time, To

+ Ap ) and (p - Ap)

> Operate filter at (p + Ap) and (p - Ap ) for

r Average e* over To to estimate E[e2] at (p

AP > Problem: only becomes accurate for

large To = slowlinaccurate

Analog Adaptive hners Prof T Chan Carusone. Universily of Tomnto

Slide 28 of 100

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IEEE International Symposium on Circuit and System 2003 Tutorial Guide

LMS Algorithm

a How can we calculate a~[2I/dp? > Assume that E[e2(k)] = e2(k)

9 0 is the "gradient signal" for parameterp 3 Substitute this back into general gradient

descent method:

LMS Algorithm Problem: What is the effect of the approx: SE[e2(k)]/Sp = -24? After convergence, SE[g(k)lISp = 0 but -2eQ + 0

~ 1 ~ 2 1

e So, &(k) # 0 and parameters "bounce" around their optimal values

1 5 I

P

Tutonal Guide IEEE International Symposium on Circuit and System 2003

LMS Algorithm Exception: If the adaptive filter can be made to match the “target” exactly 3 y = d 3 e = 0 3 -2e4 = 0 3 Ap(k) = O

I I

a?‘--- o w i m w a m m m

Never occurs in practice

Ere’

LMS Algorithm e e

The amount of “bounce” can be reduced by decreasing p The amount of bounce is the “misadjustmenf‘

E[e2

PI <Pz

P P

Slide 32 of I00 Analog Adap!h wlars Pml. 1. Chan C a m e . Unrverwty d Toronto

[EEE International Symposium on Circuit and System 2003 Tutorial Guide

LMS Algorithm + Tradeoff between speed and accuracy of

convergence in choice of p

LMS Algorithm Compromise can be reached by employing “g ea r-s h ifti ng ” approach

I Decrease p at t = 200

d 0.5

50 i o 0 1 5 0 230 300 2?Q al € 0.1

e 0.6

Slide 34 of 100

m a 0.4 -

50 I oa 150

A m k g A d a u h Fineta PmC T. Chan Carum*. Univsmiy of Tomnto

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lEEE International Slmposlum on Circuit and System 2003 Tuturial Guide

Obtaining Gradient Signals ~

Problem: How can we obtain $? 3 Depends upon the filter structure

e m pro yed : ’ Adapt only zeros while keeping poles fixed 3 “adaptive linear combiner” (usual case) Adapt poles and zeros 3 “adaptive I IR filtering” (challenging!)

A m l q Adaptive Fiiiers Slide 35 of 200 PtoI. T. Cnan Carusone. Umversiry of Toronlo

\ Adaptive Linear Combiner (ALC)

U -

I

e Each block, gi, represents a fixed LTI system Adapted parameters are the coefficients, pi Changing pi's only effects the filter‘s zeros (not the poles) 3 always stable

0 Overall impulse response & transfer function from U

to J’:

V

h’

h (k ) = P,g,(k)+. . . + P N ~ , ( k ) = Pig;(’) i=l

A’

H ( z ) = piGi (z ) i=l /

Analog Adaplive Aners Pml T Cmn Carusone. Universlly 01 Toronto

Slide 36 of 100

lEEE International Symposium on CircujI and System 2003 Tutorial Guide

Adaptive Linear Combiner

Problem: How can we obtain $?

LMS for ALC Y z -

Slide 37 of 100

Adaptive linear Combiner

p(k + l ) = j?(+ Zp(R)T(k )

Matrix notation:

Let, 5 = E[e'l Note : 5 = &)is the "performance surface"

Let, *) = cmin, where j5 * are the optimal A ,C coefficients

It can be shown that: &E)= cmh + 6 - jj *)R(jj- F*r

Where R is the NxNstate correlation matrix:

5 is a N-dimensional paraboloid R, = E[Xi(k)*Xj(k)]

Slide 38 of $00

. I ulorial buicie IEEE lntematlonal Symposium on Circuit and System 2003

f Adaptive Linear Combiner 0 The shape of &I) is related to the state

CO rrel a t ions, E[xi(k)x,( k)] independent states 3 a “round bowl” 3 fast convergence of all parameters Dependent states 3 “ill-conditioned” performance surface = poor convergence e.g. 2 parameters with highly dependent states:

Slide 39 of 100

tf \ Adaptive Linear Combiner

a ALCs have several advantages: J Stability of the filter is guaranteed because

the pole locations are fixed J The MSE is a parabolic function of the

parameters; hence, there is onfy one local minimum; stability of the adaptation procedure is guaranteed using a gradient descent algorithm (such as LMS)

+, required for LMS adaptation J Relatively easy to obtain the gradient signals,

Slide 40 of 100

Tutorial Guide IEEE International Symposium on Circuit and Systcm 2003

Analog Transversal Filters

Example: Analog transversal filter GI(=)= X = 1 G,(z) = 7 4 - - z - I G , v ( . z ) = ~ - ~ x , v - -N+I

e N-parameter FIR filter

Slide 41 of 100 Analog Adaptive hkrs Prof. T. Chan Carusone. University Of Toronto

/ Analog Transversal Filters

e

P The states are uncorrelated LMS adaptive transversal filter:

If u(k) is white, ~ [ ~ ( k ) u ( k - i ) ] = o , v i + o a E [ x , ( k ) x , ( k ) j = O , vi+,

Slide 42 of 100 Analog Adaplm fimm Pmi T ChanCamma. Univsrslty ofTomnm

IEEE lntcmational Symposium on Circuit and System 2003 I u r o r ” k

( Adaptive IIR Filtering ___ ~~ ~ ~~

o In general, one may adapt the zeros and

J May provide better performance with fewer

x Poles may become unstable x Convergence to the optimum filter parameters

poles of a filter

ad a pted pa ram eters

is not guaranteed using gradient descent techniques (e.g. the LMS algorithm)

for LMS adaptation x More difficult to obtain the gradient signals, $,

Analcg Adaptwe Filfsrs Pmf. T Chan Carusone. UniversiIy o l Toronto

Slide 43 of 100

Adaptive HR Filtering “ Mu It i - m od a I” pe rfo r m a n ce surface Steady-state parameters depend upon the initial conditions No guarantee that you will converge to the optimal parameters Note: For ALC, you are guaranteed a (N- dimensional) parabolic performance surface 3 “unimodal”

P

Anakq Adaptwe Fillers P d . T. Chan C~NSRW. University of Toronto

Slide 44 of 100

IEEE International Symposium on Circuit and System 2003 Tutorial Guide

/--

Adaptive I1R Filtering

a Problem: How can we calculate 4 for an llR filter parameter?

P Adaptive fitter, H

?Y

8P

y = b * hb, +[other t e m that don’t depend on b] = p .a * hbv + .:. = p . u * h , , * h b + . . .

.. - U * h,, * hby

Aoalog A d s p m Filters Slide 45 of 100 Prof. T. chan Cawsons. University of Toronto

/

Adaptive 1IR Filtering Example:

IEEE International Symposium-on Circuit and System 2003 'I uioritll tiuide

LMS Algorithm Implementation I

o LMS update rule can be implemented using either analog or digital circuits

9 For digital filters, use digital LMS:

Slide 47 of 100

/- \ LMS Algorithm lmplementation

e For analog filters, analog implementation may seem naturalhbvious:

AnRQ Adapnvs hnem Slide 48 of 100 Pmt T. Chm Cawisone. University of Tomnb

IEEE International Symposium on Circuit and System 2003 Tutorial Ciuide

-

f- \ LMS Algorithm Implementation

Problem: dc offsets on the gradient and error signals hinder the adaptation z always present on analog signals

Analog AriapfAm Fdters Prof. T. Chan Carusone, UnivemydTomnto

Slide 49 of 1 DO

/- \ LMS Algorithm Implementation

Solution: dc offsets on the error signal can be eliminated by a dc tap

3 Other sources of offset remain

w DC tap

Slide 50 of 100 A & C $ 7 A ~ F i H 6 K Piof. T. Chan Cenrsme. U n i v e m Or Twonla

IEEE InternarionaI Symposium on Circuit and System 2003 Tutorial Guide

f- \ LMS Algorithm Implementation

Solution: use digital adaptation a Problem: too much hardware!

0 U

Analog Filter

Ar&u~Ad@rmFiRurs Slide 51 of 100 Prof. T. Chan Canrume. University of Tamnb

/f \ L M S Algorithm Implementation

o Solution: use simplified adaptation algorithms 0 Any monotonic function can be applied to e or

$i and still movep, in the correct direction

LMS: p , ( k + l ) = p i ( k ) + 2 p e ( k ) - & t ) Sign-data LMS: p i ( k + l ) = p i (k)+2pe(k) -sgn(#j (k) )

Sign - error LMS : pi (k + 1) = pi@)+ 2~ - sgn(e(k)) - #i ( k ) Sign -sign LMS: pi (k+l )= p i (k )+2~ . sgn(e (k ) ) . sgn(~ i (k ) )

An&g A d a m RU~I'S Slide 52 of 100 pmt T. than Carusme. Univef€ilydTomnto

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Tutorial Guide lEEE lntemational Symposium on Circuit and System 2003

1 f LMS Algorithm Implementation I

I "i. Much simpler hardware

I LMS

\ SS-LMS

. 4 & c g ~ w t e r s Pmf. T. Chan Carusone. Unwersity of Toronto

Slide 53 of 100

LMS Algorithm Implementation

a

a

PI

Problem: slower adaptation and risk of instability Example: Gradient estimates for LMS & SS-LMS

Side 54 of 100

IEEE lntcmational Symposium on Circuit and System 2003 Tutorial Guide

\ Alternate Adaptation Algorithms

Example #I: look at transitions and adjust the amount of high-freq boost in the equalizer for,

zero overshoothndershoot [Everitt '981 certain maximum slope [Shoval '951

enough

TOO

boost

Equalizer

1- Channel

Slide 55 of 100

Alternate Adaptation Algorithms e

e

Due to these difficulties, some people have implemented other adaptation approaches Example #2: Look at relative attenuation of highllow frequencies and program equalizer to compensate for the difference

lEEE lntemationd SympoSiUm on Circuit arid System 2003 Tutorial Guide

\ /+-

Alternate Adaptation Algorithms ~~

Example #3: “Zero-Forcing” algorithm [Lucky, ’651

d Does not require access to gradient signals

x Does not minimize mean-squared error causes noise enhancement

Slide 57 of 100

f l \ Alternate Adaptation Algorithms e Example #4: Dither parameters and look for

correlated changes in the output squared error [Chan Carusone, ’021

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I UlOflal u m IEEE International Symposium on Circuit and System 2003

f- Outline 1. Motivation 2. Adaptive Filter Introduction 3. Adaptation algorithms 4. Filter structures & implementations

a) Discrete time i. Transversal ii. Other

b) Continuous time i. Transversal ii. Cascade of biquads ,

iii. Ladder

5. Applications

Slide 59 af 100

r Discrete Time Filters

a Discrete-time basic building blocks: 1. Delay stage 2. Multiply or Programmable Gain 3. Summation Example: Tra nsve rsa I F i I te r

Slide 60 of 100 AmIw Adaprrve FiNers Pml T. Chan Carusone, Univenity dTomnto

IEEE International Symposium on Cumit and System 2003 Tutorial Guide

c Discrete Time Filters

I. Delay stage: sample and hold circuits e Based on holding a voltage on a

capacitor:

“Tcac k” Wold’’

T I T -

Slide 61 of 100

/- Analog Filter Implementation

o Can create a delay-line using this approach:

CTk Ck CTk Clk

T - T T T I

Slide 62 of 100

- .. IEEE International Symgosium on Circuit and System 2003 Tutond tiuide

Discrete Time Filters

2. Programmable Gain: can be realized by varying the size of the holding capacitors

P If capacitors are digitally programmable, gain can be digitally programmable [Gomez, ’931

Discrete Time Filters 2. Programmable Gain: alternately, can

multiply 2 analog quantities together via a Gilbert cell

> Requires the filter parameter value to be an analog voltage [Kiriaki, ’971

Slide 64 of t O O

Discrete Time Filters

2. Programmable Gain: can use a multiplying dig ital-to-analog converter, M DAC

xi 1 Voltage

Reference

Digital parameter value, p

Slide 65 of 100

r Discrete Time Filters

3. Summation: easiest and fastest way is to use current signals, then simply tie them together

Slide 66 of 100 AnalcgMaJweFih W. T . CMn Carusorm. Unmlsrty d Tomto

Analog Transversal Filter

Straightforward implementation:

I z 1 I

Problems: DC offsets, noise, etc. introduced by each S/H accumulate as the signal progresses along the chain Each S/H must operate at the full sampling rate

Slide 67 of 100 L

Anakq4dapbmFillers Pmf. T. (%an Camsme. Unrvarvly dtmb

Analog Transversal Filter f-

Slide 68 of 100 L

Analoa A d a p t h t i t e n Pmf. T. Chan Cawme. LJnivers3ty dTwonto

Solution: rotating tap weights [Haque '771, [Ah uj a '791

Tap Might Shift Register

P:V

e Problem: at high speed, the dynamic power consumption of shifting the tap coefficients around becomes large

I I \

e

.

IEEE International Symposium on Circuit and System 2003 Tutorial Guide

/-

Analog Transversal Filter

Solution: rotating switch matrix [Sonntag '951

-

Problem: mismatch between different S/Hs show up as fixed pattern noise at the output

I :-

I Pi

:I A m Adaptive H h Slide 69 of 100 Pmf. T. Chan Canrsone. Umemily d T m b

Analog Transversal Filter I e Solution:

master S/H at front end +>, [Kiriaki '971 Master S/H

0 Problem: S/H must operate at the full sampling rate

AnalOg A- Fdem Slide 70 of 100 Pmf. T. Chan Carusone. UnWW of T m t o

~

IEEE International Symposium on Circuit and System 2003 Tu101ial Guide

Discrete Time Filters Other discrete time structures possible Example: lattice filters have desirable properties for

IIR, but stability can be guaranteed by ensuring lkil Same analog building blocks

0 Have not been common in practice

adaptive filters 1

Slide 71 of 100

/ Continuous Time Filters

Active filters preferred for integrated circuits Continuous time filter building blocks:

Integrator Multiplier or Programmable Gain Summation: usually use current summation for high-speed, as before

Adaptive Fillers hf. T. Chan Caruuule. Utuvemly of T o m b

Slide 72 of 100

fEEE Intemationd Symposium on Circuit and System 2003 Tutorial Guide

Continuous Time Filters

in

Integrators: two main types In both cases, input voltage is converted into a current, then integrated on a capacitor

RC or MOSFET-C Gm-C

"log Ada* fitm Prof. T. Cham Carusone, University d T C "

Slide 73 of f DO

Continuous Time Filters f

Multiplier I Programmable Gain 1. Can use a Gilbert cell as before 2. Can use a programmable gain stage

P may even combine with the integrator P Example: Gm-C integrator with

programmable gain

Slide 74 of 100

IEEE International Symposium on Circuit and system 2003 I ulonill uuiac

Continuous Time Filters F a Many options for filter structures e Example: Laguerre Filter Structure

Special case of ALC (guaranteed stable, easy LMS adaptation, fixed zero locations, etc.. .)

Adcg A@apbLe Fi!lers Prof. T. Chan Carusare, Unrfersity of Toronto

Slide 75 of 100

Continolous Time Filters Essentially a continuous time tapped delay lir [Sands, '961, [Parsi, ,961

e Instead of first-order allpass delay elements as in Laguerre structure), one can also use B essell allpass delay stages

e

An&g Adaptin HRws Slide 76 of 100 Prof. 1. Chan Carusam, Unrversity OlTmlO

IEEE Intemational S lmposim on Circuit mnd System 200; Tutorial Guide

Continuous Time Filters e Could also use a biquad with adaptive wo & Q (e.g.

[Shoval ‘951): cl$ + a,s + a,

S - + 4 + W o Z

H ( s ) = 7 w

J Easy to build Q -Y Easy to adapt while maintaining stability (usually using

“alternate” non-LMS algorithms) Y Limited to Znd order transfer functions

P Cascade adaptive biquads to get higher order transfer

x May have problems with dynamic range scaling functions

Slide 77 of 100 Analog Adaptive Frliem Prof, T. Chan Carusme. University olTomnto

/ Continuous Time Filters

Orthonormal ladder filter structure /Arbitrary rational transfer function /Good dynamic range scaling x Difficult to obtain gradient signals

An&g Adaptmt Filters Pro?. T. Chan Camsone. Univewty d T m t 0 Slide 78 of 100

Outline I. 2. 3. 4. 5.

Motivation Adaptive Filter Introduction Adaptation algorithms Filter structures & implementations Applications a) Co-axial cable b) Magnetic storage .

c) High-speed ethernet d) Chip-to-chip communications e) Optical Fibre

Analog Adaplws Allem Prof T. Chan Carusone. University of Tomnio

Slide 79 of 700

/--

Go-axial Cable

Application: high-speed point-to-point links Channel transfer function: H ( s ) = e IS1 can be cancelled using inverse of channel response: H-' (s) = 1 / H ( S )

Approximate, H-' (s) = e where Y(s) is fixed with + I O to +I2 dBldecade slope

-OL&

aL& = 1 + b - Y(s)

Slide 80 of 100 nnarog Auaplwe finers Pro!. T. Chan Carusone. Unwersityalioronto

IEEE International Symposium on Circuit and System 2003 I utonal CIuide

Co-axial Cable

FW"e;C"

B Equalizer examples: [Hartman '991, [Shakrba '991 b is adapted via a LMS or other algorithm

a An adaptive linear combiner Must be careful to avoid boosting noise too much

3 Practical implementations have a limited bandwidth

AMlWAdaplivs FvHers Slide 81 of 100 Pmf. T Chan Carusone, Unrvenity of Toronto

Magnetic Storage

Input

Media

Read Waveform

Output

0 1 0 0 t

+I -1 0 +I

k Partial Response Signal!

lEEE International Symposium on Circuit and System 2U03 d m

-F

I Magnetic Storage

6b or 7* order 5-9tap continuous time SIH 3 discrete time anti-alias filter adaptive filter

~

Input 0 1 0 0 I

-F

Media

6b or 7* order 5-9tap continuous time SIH 3 discrete time anti-alias filter adaptive filter

Increased Density

> Intersymbol Interference!

Slide 83 of 100

f f -

Magnetic Storage Equalization #I: Analog discrete time

o Examples: [Xu '961, [Kiriaki '971, [Wang '981

I I - ' 9

e Switched capacitor transversal filters with rotating tap weights or rotating switch matrix SS-LMS (digital) adaptation

J Robust and simple adaptation

Slide 64 of 100 L

nna~cg Adaprive Fiiters Pmf. T. Chan Canrwfle. UnNersrly Or Tomnio

IEEE Intcmational Symposium on Circuit and System 2003 Tutorial Guide

f 6th or 7th order

\ f Magnetic Storage

Timing recovery

EquaIiration #2: Analog continuous time 0 Examples: [Pai '961, [Brown '991

-+

. . I

continuous time * S/H --+ ADC - -

Data I

adaptive filter

/ recovery

Continuous time ladder structures with adapted zeros SS-LMS (digital) adaptation

./ Generally lower power & smaller area at high speeds

An* Adaplw f i l twrs Slide 85 of 700 Pmf. T. Chan Carusone, Unrverslty offomnto

Magnetic Storage

Equalization #3: Digital

I I

continuous time

1 f Timing U 5-9tap

digital

Robust and simple adaptation 4 Scales well

Slide 86 of 100 Anal%' Adeutwa FMws Pml. T Chan Carusom. Unlverslty ofTomnio

lEEE International Symposium on Circuit and System 2003 Tutonal Ciuide

( Gigabit Ethernet over Copper I

250 Mbis

250 Mbis - - 250 Mbis

250 Mbis a

250 Mbls

250 Mbis

250 Mbls

250 Mbis

-L

=

250 Mb/s

250 Mb/s

250 Mbls

250 Mbfs

250 Mbis

250 Mb/s

250 Mbis

250 Mb/s

e

= J

Received Signal = Echo + Crosstalk 3- Desired

Slide 87 of 100 analq Adaptive Fillers Pmf. T. Chan Carusone, Unrvenityof Toronto

I

Gigabit Ethernet over Copper I I

Challenges:

I Elimination of ISI, echo, crosstalk Integration of entire transceiver with reasonable power & cost

Xtalk Cancellers

I

Slide 88 of 100 Analog Adapfrve Ftners Prof T Chan Carusom. Univemty of Toronto

,,. 1-3 U L

IEEE lnternatianal Symposium on Circuit and System 2003 Tutorial Guide

r

Analog vs, Digital Adaptive Filters

9 bit AID

ACC + Anti-aliasing r

filter ,

DSP based: [He '011, [Roo '011 From other transmitters

r

* Cancellers

9 bit AID

ACC + Anti-aliasing r

filter ,

9-bit AID design is challenging

Slide 89 of 100 Amkg A m F&m Prcd. T. Qlan Carusone. University o f T m t n

Analog vs, Digital Adaptive Filters

From other transmitters Mixed signal architecture: [Lee '01 ]

Digital transma data I ,

L

Coarse Echo Canceller

Analog 4-7 bit e Equalizer AID

/

Coarse Echo Fine Echo

S/H based transversal equalizer with rotating tap weights Digital SS-LMS adaptation using DACs for the tap weights Echo canceller accepts digital inputs from transmit path

\ A "rover" tap in the echo canceller eliminates distant echoes ,' A n e l o g A m F i k prof. T. Ch8n Camsone. UnwarsnV d T m ! n Slide 90 of 100

IEEE Inlernational Symposium on Circuit and System 2003 Tutorial Guide

Chip-to-chip communication

e Usually consists of sending information from one IC to another over PCB traces and (possibly) connectors

>Attenuation (conductor

>lntersymbof interference (limited bandwidth)

b Reflectionslechoes

losses)

(mismatches at connectors and termination)

z0osstalk (from neighbouring channels)

Slide 91 of 100

/- \ Chip-to-chip communication

e Most popular approach is adaptive pre- emphasis at trans mitt er

Example:

'3 Minimal additional a0 + U l Z I + a,z2

hardware With preemphasis

Slide 92 of 100 L

Anatcg h d a p k FiUecS Pmf. T. man C a r u m , Unrversily of T m t o

lEEE International Symposium on Circuit and System 2003 Tutorial Guide

Chip-to-chip communication Crosstalk cancellation is similarly possible at the transmitter; e.g. [Zerbe ’011 Challenge is performing adaptation, which requires information from the receiver [Stonick ’031 Current research 8 development is directed at receive-side equalization

I I

I I

I I

Slide 93 of 100 Amleg Adapciva Fihn Pmt T. Chan Canrswul. U w d T o m n t o

I/ Optical Fiber

Different colors (wavelengths) of light propagate along fiber at different velocities 3 “Chromatic dispersion”

Intersymbol Interference Causes pulses to spread out

Slide 94 of 100

IEEE International Symposium on Circuit and System 2003 Tutorial Guide

/---

Optical Fiber

a Imperfections in the fiber cause light with different polarizations to propagate with d iff e re n t s peed s : “ B i ref r i n g e n ce” o r “ Po I a r iza t i o n mod e d is pe rs i o n ”

DGD = Differential y(f)a Group Delay 1 I-

Slide 95 of I00

Optical Fiber I

Multimode fiber supports multiple modes of light propagation, each with a different velocity resulting in many received pulses of light with different amplitudes Bandwidth limitations of the receiver front-end smear together pulses into one Gaussian electrical Dulse

~aaptns finen Slide 96 of 100 Pml T thsn Camsone. Umvemty afTOronl0

i-3m

IEEE lntemational Symposium on Circuit and System 2003 Tutorial Guide

f Optical Fiber e Can be cancelled using equalization

(a. k.a. "Dispersion compensation") [Azadet '021

Continuous time taped delay line 8 Delay elements are passive LC networks

Andog Ad- Filters Pml. T. Chan Carusone. Universrty or Tomla

Slide 97 of 100

References Adaptation Maorithms and Filter Structures . . . 0 . .

.

J. Everitt. 5. F. Parker, P. Hurst. D. Naclc, and K. R. Konda, 'A CMOS Transceiver for IO-Mb/s and fOO-Mbls Ethemet.' IEEEJ. Sdldslele CircUts. vol. 33, pp. 2169-2t77. Dec. 1998. A: S e a l , W. M. Snelgrwe, and D. A. Johns. 'A IOOMbk BiMOS Adaptive Puk.sShaphg Filter. /f€€J. Select Areas Commun.. vol. 13, pp. 1692-1702. Dec. 1995. Techni ue for adaptive equalization of digital wmmunications systems,' Bell Syst, Tech. J., pp. 255-268. Feb. 1966. 4. Chan Carusone and D. A. Johns, "Analog Filter Ada tation Using a Dithered Linear Search Algorithm," IEEE Inf. Symp. Circuiis and Syst, May 2012. R. Gomez M. Rofou aran and A A Abidi 'A Discrete-Time Analog Signal Processor for Disk Read Chahnels," /&E /nt.'Sdid-itate Cifchs Conf. Dig. Tech. Papers. pp. 212-213, Feb. 1993. Y. A. Ha ue and M. A. Copeland, 'Design and Characterization of a Real-Time Correlator." /E€€ J. Solid-& Circuifs, vol. SC-12, pp. 642-649. Dec. 1977. B. K Ahu'a, M A Copeland. and C. H. Chan, 'A Sam led Analog MOS LSI Adaptive Filter." ffEE J. Sol,d-dtale Ci&s, vol. SC-14. pp. 148-154, Feb.?979. J. Synta , 0 As"', P. Aziz, H. Burger! V. Comino, M. Heimann, T, Karanink, J. Khoury. G. Madine, d! Nagaraj. G. Offord, R. P e m . J. Play, N. Rao. N. Sayiner, P. Setty, and K. Threadgill, "A Hi h S ed, Low Power PRML Read Channel Device," E€€ Trans. Magnetics. vol 31, pp, 1166-1185, 1995. N. P. Sands. M. W. Hause. G. Lian , G Gmnewold, S. Lam, C.H. Lin. J. Kuklewiu, L. Fang, and R. Dakshinamufthy, -A 20OMbkAnal OFE Read Channel," I€&€/nf. So/id-Slate Circuds Conf; Dia Tech. Papers, pp. 72-73, Feb. 896. N. Parsi;N. Rao. R:Bums;A. Chaiken. M. Chambers, R. Cheung. 8. Fomi. D. Harmishfeger. C. Jam, S. Ka tor, M. Penneil. J. Perez. M. Rohrbabau h. M Ross. G. Stuhlmiller. and N. Weiner. 'A 20OMbls PhML Reamrite Channel IC." I€E€/n! Solid-state Cimufts Coot Dig, Tech. Papers, pp. 66-67, Feb. 2996.

An+ A d a p l k Fi#m Pmf T. Chan Carumne. Un- of Toronto

Slide SE of 100

IEEE I n t e m z Symposium on Circuit and System 2003 Tutonal Guide

/------- 7 ' References ~- . - . - - . . . .

CO-axial cable 4 G. P. Hartman. K. W. Martin, and A. McLaren. 'Continuous-time adaptive-analog

coaxial cable equalizer in 0.5 um CMOS," l€€€/nt. Symp. Circuits Syst.. pp. 97-200, May 1999. M. H. Shakiba. "A 2.5 Gbls adaptive cable equalizer," /€€E lnt. Solid-state Circuits Cod. Dig. Tech. Papers, pp. 396397, Feb. 1999.

+

Magnetic Storage P. K. D. Pai, A. D. Brewster, and A. Abidi, "A 160-MHz Analog Front-End IC for EPR- IV PRML Ma netic Storage Read Channels," I€€€./. Solid-state Circuits, pp. 1803- 1816, Nov. 1j96. J. E. C. Brown, P. J. Hurst. B. C. Rothenberg, and S. H. Lewis, "A CMOS Adaptive Continuous-Time Forward Equalizer. LPF, and RAM-DFE for Magnetic Recording," /€€E J. Solid-state Circuits, pp. 162-1 69, Fe b. 1999. D. Xu, Y. Song, and G. T. Uehara, 'A 200 MHz 9-Tap Analog Equalizer for Magnetic Disk Read Channels in 0.6" CMOS," lEE€ lnt. SolidState Circuits Con[ Dig. Tech. Papers, pp. 74-75, Feb. 1996. S. Kiriaki, T. L. Viswanathan, G. Feygin, B. StaFewski, R. Pierson, B. Krenik, M. de Wit, and K. Na araj, "A 160-MHz Analog Equalizer for Magnetic Disk Read Channels," lE&J. Solid-state Circuits, pp. 1839-1850, Nov. 1997. X. Wan and R R Spencer, "A Low-Power 170-MHz Discrete-Time Analog FIR Filter," I%€€ J. Sojid-State Circuits, pp. 41 7426, March 1998.

Slide 99 of 100 AwogAWlrve FitIers Prof T. Chan Carusone. Unwemly ofTomnl0

References Ethemet

T.-C. Lee and B. Razavi, "A 125-MHz CMOS mixed-signal equalizer for gi abit ethernei on capper wire,- EEE Custom /ntegmtd circuits cont. pp. 131-134, June 401. T.k . Lee and B. Razavi, "A 12SMHz mixed-signal echo canceller for gigabit ethemet on copper wire," lEEE J. Soldstate Cikcuits. pp. 366-373, March 2001.

0 R. He, N. Nazari. and S. Sutard-a, 'A DSP based receiver for 100DBase-T PHY," I€€€ Inf. Solid- Slate Circuits Conf Dig. Tech. hpers, pp. 308-309, Feb. 2001. P. Roo, S. Sutardga. S. Wei, F. Aram. and Y. Chen -A CMOS transceiver analog frontend for ,pabit ethemet over CAT-5 cables," /E€€ Int. So/i&tote Circuits COOL Dig. Ted. Papers, pp.

0-31 1, Feb. 2001

Chiptochip communication J. L. Zerbe et al. *A 2 Gblslpin 4-PAM parallel bus interface with transmit crosstalk cancetlation, equalization, and integrating receivers,- I€€€ Int. Solid Stale Circuits Coof , pp. 66-67. Feb. 2001. J. T. Stonick, G.-Y. Wei. J. C. Sonnta , and 0. K. Weinlader. *An adaptive PAM4 5 Gb/s backplane transceiver in 0.25 um CdOS," l€E€J. Solid-state Circuits, pp. 436443, March 2003.

Optical Fibre K. Aradet et al, 'E ualization and FEC techniques for optical transceivers; I€€€ J. Solid-Slate Circuits, pp. 317-327. March 2002. H. Wu. J. Tiemo, P. Pepeljugoski. J. Schaub. S. Go@a. 3. Kash, A. Ha'imiri, 'Differential 4-tap and 7-tap transverse filters in SiGe for 10 Gb/5 multimode fiber optic lid equalization," /€€E In(. Solidsfate Circuits Cod, pp. 180-181. Feb. 2003.

Slide 100 of 100 Analog Adaptha Finen prol. T. Char, Carusone. UniveIsity ol Toronto

I