University of Bologna University of Ferrara

An EMI Reduction Methodology Based on An EMI Reduction Methodology Based on Nonlinear DynamicsNonlinear Dynamics

Gianluca Setti

Dep. of Engineering (ENDIF) – University of Ferrara

Advanced Research Center on Electronic Systems for Information Engineering and Telecommunications (ARCES) – University of Bologna

gsetti@ing.unife.it

IWCSN 2006Vancouver, Canada

18th August 2006

2

Acknowledment

Collaborators and Students

• Michele Balestra, University of Ferrara, Post-Doc

• Sergio Callegari, University of Bologna, Assistant Professor

• Luca de Michele, University of Bologna, Ph.D. Student

• Marco Lazzarini, University of Ferrara, Research Fellow

• Fabio Pareschi, University of Bologna, Ph.D. Student

• Riccardo Rovatti, University of Bologna, Associate Professor

3

Outline

• EMI due to timing signals and “signal-processing” based reduction methods

• Clock signals

Sinusoidal FM

Cubic (patented) FM

Chaos Based FM

Analytical results (statistical approach)

• Numerical and experimental results

• PWM signals

Boost DC/DC converter prototype

• Fast FM and implementation of a low EMI clock generator

FM modulator based on a PLL

High Throughput RNG based on Chaotic Maps

SATA and SATA-II

• Conclusion

4

EMI due to timing signals

EMI Problem: coupling between source and victim

• Source: radio transmitter, power lines, electronic circuits,…• Victim: radio receiver, electronic circuits and devices,…• Coupling methods: conducted, inductively/capacitively coupled, radiated,…

Problems: Cost, No guarantees to solve EMI problem

Usual solution: reduce coupling by means of filters

ConducetedEmissions

RadiatedEmissions

and shields (cables, connectors)

5

An “a priori” solution

REMARKS• Clock signals produce EMI at frequencies corresponding to harmonics• Regulation standard set a limit on peak emissions (mask)

FFT

0f 03 f 05 f 07 f …

In several applications filters and shields cannot be employed:• µP and board clock signals• Mixed-mode analog/digital ICs

Basic Idea: introduce a suitable modulation toslightly perturb a normally narrowband signal

⇒ energy spread over a larger bandwidth: peak value reduction

An a-priori (design-time) solution (on the EMI source) is required

FFT

0f 03 f 05 f 07 f …

slightly means “without impairing the circuit functionality”

6

A first idea for the modulation

• Sinusoidal Frequency Modulation: consider and a modulatingsinusoidal signal with frequency ⇒ FM modulated signal with index

( )0( ) sin 2cs t A f tπ=mf / mm f f= ∆

FM 0 0( ) sin[2 sin(2 )] ( )cos[2 ( ) ]m k mk

s t A f t m f t A J m f k f tπ π π∞

=−∞

= + = +∑

• Clock signal: same effect for each harmonicbandwidth

• Successfully applied to get 10dB EMI reductionDC/DC converters (Lin, Chen Trans. PE, 1994)

2 ( 1/ ) (2 )f n m n f∆ + ≈ ∆

Problem: FM sinusoidal modulation is not optimal for spectrum spreading

• Spectral component at frequencies (Ex: f0=100KHz, fm=1Khz, m=20)

• Power of = power of and the bandwidth is ⇒reduction of the power spectrum peak

0 mf k f±

FM ( )s t

0 0[ (1 1/ ), (1 1/ )]f f m f f m− ∆ + + ∆ +( )cs t

FM 0 0( ) sin[2 sin(2 )] ( )cos[2 ( ) ]mk

k ms t A f t m f m f tt A J k fπ ππ∞

=−∞

= ++ = ∑

( )0( ) sin 2cs t A f tπ=

...

7

…and a better one - I• instantaneous frequency

⇒ for “quasi-stationary” modulation power concentrates where is small

( )FMs t 0( ) cos(2 )mf t f f f tπ= + ∆( ) /mds t dt

• Sin: peak in the spectrum if min or max reduced amplitude correspondingto zero crossing (large derivative)

( )ms t

( )ms t

• Hardin et al (Lexmark; US patent # 5,488,627, 1996) proposes to use a parametric family of cubic polynomials

to construct the modulating waveform

3( ) 16(4 ) , [ 1/ 4,1/ 4]bc x p x px x= − + ∈ −

8

… and a better one - II

… but the frequency modulation law is always periodic

⇒ the modulated signal does not have a continuous spectrum

⇒ power is densely concentrated around specific frequencies

An non periodic modulating signal would be better!

• Optimal choice of the parameter p ⇒ almost flat spectrum

p = 4.12

f0=100KHz, fm=1Khz, m=20

9

Can chaos be even better for EMI reduction?

10 20 30 40 50 60

0.2

0.4

0.6

0.8

1

FFT

Bro

adband

nois

elik

e

0.2 0.4 0.6 0.8 1

0.2

0.4

0.6

0.8

1

1+kx

∆kx

M

k ∈N

• Chaotic map

with and

k ∈N)(1 kk xMx =+

[ ] [ ]: 1,1 1,1M X = − − [ ]0 1,1x ∈ −

FM

0f f∆

Which is the shape of the power spectrum?

FFT

?

10

Spectrum of perfectly random FM - I

• Consider a sinusoid (clock

fundamental) that is frequency

modulated by random PAM

0( ) cos 2 ( )t

mc t f t f dπ ξ ϑ ϑ−∞

⎡ ⎤⎛ ⎞= +∆⎢ ⎥⎜ ⎟

⎢ ⎥⎝ ⎠⎣ ⎦∫

[ ] *

0

( ) 1( ) ( ) ( )2

T

cccc f C c t c t dtT

τ τΦ⎡ ⎤

⎡ ⎤= = +⎢ ⎥⎣ ⎦⎣ ⎦

∫EF F

• Compute power density spectrum for equivalent low-pass signal

0( ) ( )cc cc f ff Φ −Φ

• Power density spectrum can be expressed as

• Modulating PAM signal where are

independent random variables drawn according to a density

( ) ( )m k mk

t x g t kTξ∞

=−∞

= −∑ kx

ρ

g(t) is the unit rectangular pulse defined in [0,Tm[

11

Spectrum of purely random FM - II

Main results

[ ] [ ][ ]

21

3

2

( , ) Re( ,

)1

(( , )

)

xcc x

x

K x ff

K x f

xf

KΦ

⎡ ⎤= ⎢ ⎥

−⎢ ⎥⎣ ⎦

EE

E+1.

21

1sinc, )

2(

m fx

f fK x f mπ

⎛ ⎞⎛ ⎞= −⎜ ⎟⎜ ⎟∆ ∆⎝ ⎠⎝ ⎠

(

1

2 )

1

2(

(,

))

fi m xfe

im f

K x fx f

f

π

π

− −∆ −=− ∆∆

2

3

( )

( , )fi m x

fK x f eπ− −∆=

General analytical expression for as a function of for any value of mρ( )cc fΦ

1lim

2( )cc

m

f

f ff ρ

→∞

⎛ ⎞= ⎜ ⎟∆ ∆⎝ ⎠

Φ2.

For large m (slow modulation) has the same shape as ρ( )cc fΦ

Low-pass operator applied to ρ

12

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

-1 -0.5 0 0.5 1

rho(

x)

x

Modulating sequence PDF

An interesting exampleLow pass operator effect

-110

-105

-100

-95

-90

-85

-80

-75

-70

-65

8e+ 07 9e+ 07 1e+ 08 1.1e+ 08 1.2e+ 08

pow

er d

ensi

ty (

dB)

frequency (Hz)

THEORYSimulated experiment

0 100 MHz,

8.5 MHz, 1

f

f m

=∆ = =

… and with chaotic samples?

Low pass effect

To “implement” random source with the chaotic one, we need to assure that to get the same results!

13

An alternative approach for studying chaos

• Chaotic map

with and k ∈N)(1 kk xMx =+

[ ] [ ]1,01,0: =XM [ ]1,00 ∈x

∆

kx 1+kxM

• Evolution of points- following single trajectories

is difficult

- sensitive dependence on initial conditions

),(),(, 12010 xMxxMxx ==

4''0

'0 1010/,10/ −+== ππ xx

10 20 30 40 50 60

0.2

0.4

0.6

0.8

1

• Evolution of densities

0 :[0,1]ρ +→R{ } dxxdxxxdxx )(2/2/ Pr 00 ρ=+≤≤−

x0

dx

1

0ρ

If x0 is drawn according to ρ0, which is the density of x1 =M(x0), x2 =M(x1),...?

14

{ }Pr 2 2

dy dyy y y− ≤ ≤ + =

Evolution of densities: Perron-Frobenius operator)(xMy=

x

kρ

1+kρ

2x1x

yProbability conservation constraint:

{ } { }1 1 2 21 1 1 2 2 2Pr Pr

2 2 2 2dx dx dx dx

x x x x x x− ≤ ≤ + + − ≤ ≤ +

dy

dxx

dy

dxxy kkk

22

111 )()()( ρρρ +=+ )('

)(

)('

)()(

2

2

1

11

xM

x

xM

xy kk

k

ρρρ +=+221 11 )()()( dxxdxxdyy kkk ρρρ +=+ ⇒ ⇒

1( )

( )( ) ( )

'( )k

Mk kM x y

xy y

M x

ρρ ρ+=

= = ∑PPerron-Frobenius operator PM of M for maps with “several branches”

Linear functional operator

15

A Global Linearization

∆kx

0 0( ) ( )

k-times

kkx M M M x M x= =

)(1 kk xMx =+

☺ Finite dimension (one)Highly NonlinearExtremely Complex

∆

kMk ρρ P=+1

kρ

MP

0 0k

k

k MMρ ρ ρ= =P P

☺ Linear☺ “Simple” (Regular) Behavior

Infinite Dimensions (not always…)

Can we say something on the behavior of the “linearized system”?

16

1ρ2ρ

3ρ

4ρ5ρ

6ρ

1ρ

2ρ3ρ

4ρ5ρ

An example

0ρ0ρ

50ρ 50ρ

The evolution of densities has alimit fixed point

depending only on the map

lim kk

ρ ρ→∞

=

17

Properties of the linearized system

Chaotic systems are deterministic!

kx

∆

M

1kx + 1kρ +

kρ

… but can be studied with statistical tools

0ρ0 x

dx

1

0x 0 ( )xρis distributed according to

1x 1( )xρis distributed according to

kx ( )k xρis distributed according to

......

lim kk

ρ ρ→∞

=For any we know that 0ρ

Two important points

How to compute ?ρ How fast ?kρ ρ→

kx

∆

1kx + 1kρ +

kρ

P ρ ρ=Pmix 0kk

k rCρ ρ →∞− ≤ ⎯⎯⎯→

Difficult to be computed in general…

18

Statistical approach for PWAM maps

M

1X 2X 3X 4X

1X

2X

3X

4X

( ) ( ( )) 0 ,or j k j kX M X X M X j kµ⊆ ∩ = ∀

• Markov partition: such that 1, , nX X

• Kneading matrix (Transition matrix)

( )( )

1( )j k

jk

j

X M X

X

µµ

−∩=K =

Probability (µ) that x movesXj → Xk given that it is in Xj

Fraction of Xj which is mappend in Xk

• The invariant density of PWAM maps is piece-wise constant

• For such maps K≈P• To compute one computes the left eigenvector of Kρ α

(3/4,3/4,1/4,1/4)Wα α α= = K

ρ

1X 2X 3X 4X

• Moreover { }mix max | |, (map slopes)Fr λ= mix1

2r =

2X 4X

1X

2X

3X

3X

1/4 1/4 1/4 1/4

1/2 1/2 0 0

1/2 0 0

1/4 1/4 1/4 1/4

1/2

⎛ ⎞⎜ ⎟⎜ ⎟=⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

K

1X

2X

3X

4X

19

Characterization of Processes Generated by PWAM

( )k ky Q x= ∈Ckx

1kx +

M=?

Q

∆

M

1X 2X 3X 4X

1X

2X

3X

4X

PWAM withfinite partition

• Probability density (i.e. how often a certain value appears in the process history)

• Rate of mixing (i.e. how fast the probability describing the distribution of the state converges to the invariant

one)

•Exact finite time crosscorrelation profile (i.e. how each realization of the process is related to other realizations of the same process)

• Exact finite time autocorrelation (i.e. the short-time power spectral density of the process)

• Asymptotic trend of autocorrelation (i.e. power spectral density at low frequencies: exponential trend, polynomial trend, combinations)

• Higher order moments/correlation (i.e. how multiple samples from the process relate to each other)

What can we analize/design?

20

Spectrum of chaotic FM - I • Chaotic map generates the samples { }kx

Main results (Proc IEEE 2002, TCAS-I, 2003)

[ ] [ ][ ]1

3

2

2

mix 0Re

1( ,

( , ))

( ))(

,lim x

x

c xcr K x

K x fKf

fx f

→

⎡ ⎤=Φ ⎢ ⎥

−⎢ ⎥⎣ ⎦

EE

E+1.

If rmix low chaotic samples approximate purely random variables

1lim such that) (

2k

mcc

f f ff M

f f ff k

fρ

→∞

⎛ ⎞ ⎛ ⎞= ∀ ∃ =⎜ ⎟ ⎜ ⎟∆ ∆ ∆ ∆⎝ ⎠ ⎝ ⎠

Φ2.

For slow modulation has the same shape asfor all frequencies not corresponding to fixed points of (iterate of) map

ρ( )cc fΦ

21

improvement of ≈ 16dB

Spectrum of chaotic FM - IIM

1X 2X 3X 4X

1X

2X

3X

4X

f0=100KHz, fm=1Khz, m=1,5,10

1m =

5m =

10m =

An easy optimal solution

• For slow modulation

Maximum spreading (peak reduction)

Uniform density⇓

)(xMy =

x

f0=100KHz, fm=1Khz, m=10, resolution 4Hz

mix 1=2

( 2

) 1rxρ =

22

• Reduction of ≈ 13dB with respect to the sinusoidal FM

Spectrum of chaotic FM : experimental results - I

• Tent map implementation with of-the-shelf components

• f0=100KHz, fm=150Hz, m=15, with a HP35670A –

digital SA with RBW=4Hz

23

CB-reduction of timing signal generated EMI

• f0=10KHz, fm=50Hz, m=40, with a HP35670A – digital SA with RBW=8Hz

9dB peak reduction with respect to the best known and patented method

PowerPC 450GP

IXP42X Network processor

CY25823

24

Problems - I • Methods for reducing EMI due to periodic timing signals

Sinusoidal FMCubic FM (Lexmark patent)Chaos-based FM

• Measured peak reduction of 9dB with respect to previously patented methods

• Analytical tools for computing power spectrum density of chaotic FM signals

Example of a Boost Current Controlled DC/DC Converter

Spectrum of the timing control signal only in case of clocks:• Does this work also for PWM signals?• Is the reduction present also for all voltages and currents? • Does it work with a feedback?

25

Implementation of a Low EMI Current Feedback Boost DC/DC Converter - I

Chaotically Chaotically

Jittered ClockJittered Clock

TMS320C6711 DSP board

Vin = 6 V

f0 = 50 kHz

IRF540 power MOSFET (switch)

NBR1540 power diode

R = 100 ΩC = 100 μF

L=1.5 mH

26

Implementation of a Low EMI Current Feedback Boost DC/DC Converter - II

• Feedback is present. How does the converter work?

• Assume “standard behavior”, i.e. that c(t) is periodic (Tk ) ⇒ when c(t) → 1, i.e. at h

Tk, the switch closes and iL (t) ↑ until it reaches Iref when the comparator

changes its status, the switch opens and iL(t) ↓. The behavior of iL(t) is periodic

and

( 1 1 2

1 2

) k

ref

h T

kL

m mi I Tm m

+ → − +

⇒ we can expect peaks in the PDS!!!

⇒ we need to introduce a jittered clock

27

Implementation of a Low EMI Current Feedback Boost DC/DC Converter -III

EstimationEstimation of the of the inductorinductor currentcurrent PDSPDS

ComparingComparing thesethese expressionsexpressions withwith the the previousprevious, , wewe havehave thatthat the the inductorinductor currentcurrent PDS can PDS can bebe estimate via estimate via separatedseparated FM of FM of eacheachharmonicharmonic formingforming the the spectrumspectrum of the of the currentcurrent in a in a converterconverter working in working in a a periodicperiodic regime at regime at frequencyfrequency ff00

[ ]

2

1

( )

3

2( )1

mix 0Re(

( ,,

)

( ,( )

1)

)lim h

x

x

hx

hr

K x fK x

K xf

ff

∞

=→

⎧ ⎫⎡ ⎤⎡ ⎤⎪ ⎪⎣ ⎦⎡ ⎤ ⎢ ⎥= ⎨ ⎬⎣ ⎦ −⎢ ⎥⎪ ⎪Φ

⎣ ⎦⎩ ⎭∑

EE

E+

0(1

x)

2

h

1A si c

2( n, )h f hfm

mf

Kf

x hxf π⎛ ⎞⎛ ⎞+= −⎜ ⎟⎜ ⎟∆ ∆⎝ ⎠⎝ ⎠

2

3

( )

( , )fi m x

fK x f eπ− −∆=

( )( )

2 0) x

h( A sinc ( [ ), ]( )

fh i m x

fK x m me f h f x ff f

fπ

π− −∆= − + ∆∆ ∆

28

313

43.53

mV

dBm

== −

R

High-EMC Chaos-

ip

based Clock

ple

Peak

Measurement Results

313

21.2

mV

dBm

== −

Ripple

Periodic C

Peak

lock

22dB EMI reduction with respect to the conventional case

Ripple performances are not affected by modulation

29

ρ

1X 2X 3X 4X

Idea: generate samples with a density “inverse” of the shape of Φ

ρ

1X 2X 3X 4X

Ultimate limit of this idea: perfectly random binary modulation

Problems -II • Methods for reducing EMI due to periodic timing signals• Measured peak reduction of 9dB with respect to previously patented methods

• Analytical tools for computing power spectrum density of chaotic FM signals

• Methods is applicable for EMI reduction in switching power converters

• Bernoulli shift f0=1MHz, ∆f=100KHz, m=0.425

Slow modulation is a good trick to pass the tests, but real failure is proportional to the

energy delivered to the victim!

⇒ A fast modulation (low m) would be much better!

)(xMy=

x

30

Fast binary FM - I

FM

f∆

( )c t

0f

( )tξRANDOM

BIT GENERATOR

Among different spread-spectrum techniques, we choose

, output signal

Random {xk} random variable which assumes the values {0,1} with the same probability p=0.5

Fast Binary Random frequency modulation

Binary driving signal is a PAM signal with only two values

Fast Tm short with respect to 1 / ∆f

Any change in the shape of the power

spectrum?

FFT ?

( ) ( )( )0sgn cos 2t

c t f t f dπ ξ τ τ−∞

⎛ ⎞⎡ ⎤= + ∆⎜ ⎟⎢ ⎥⎣ ⎦⎝ ⎠∫

31

Fast binary FM - II

The shape of the spectrum depends on the modulation index

0.10

. 8

6

0 31m

m

==

-100

-90

-80

-70

-60

-50

0 200000 400000 600000 800000 1e+06 1.2e+06 1.4e+06

m is set properly to flatten the power spectrum in the desired interval

The first harmonic has thehighest power content

usually m = 0.318

It is a fast modulation, i.e. the output frequency is maintained unaltered for a very short period of time

It achieves the best peak reduction on the first harmonic with respect to all other known modulations

Why do we use this modulation if it still features peaks on the spectrum?

32

The SSCG architecture

• produces sequences with very low correlation (performances depends on sequence statistics)

• achieves a very high throughput(we want a fast modulation)

chaos-basedtrue-randombit generator

( )tξ FM

0f f∆

• Sets the main frequency with high precision (quartz) external clock

• Could perform a frequency multiplier

• Only few modifications are required in order to achieve a binary modulator from a standard PLL

PLL-basedclock generator

0f f∆

33

PLL-based frequency modulator – I

A conventional PLL

OSCPFD CP

÷N

VCOLPFout inf N f= ⋅

Frequency/PhaseDetector

Charge Pump andLow Pass Filter

Voltage ControlledOscillator

Inputstage

RingOscillator

Wave-shapingBuffer

FrequencyDivider by N

IBIAS

34

PLL-based frequency modulator – II

A conventional PLL

OSCPFD CP

÷N

VCOLPF+

( )tξ

has been modified with the interposition of an analog adder at the VCO input

• The driving signal is added to the VCO control voltage, and “modulate" directly the output clock

• If the driving signal is high frequency with respect to the LPF bandwidth, it cannot pass through the feedback loop.

With respect to high frequency driving signals, this circuit behaves as a frequency modulator!

out inf N f= ⋅ ( )out inf Nf f tξ= + ∆

35

70

80

90

100

110

120

130

1.6 1.7 1.8 1.9 2 2.1

The PLL-based frequency modulator – III

• Since the driving signal is a digital signal a full analog adder is not required!!

VCO

“0” modulated “1” modulated

non modulated

the digital driving signal drives two pass-transistors, changing the biasing of the VCO and shifting its f/v characteristic

IBIAS

I0I0

( )tξ

( )tξ

+VCO frequency/voltage [MHz/v] characteristic

36

The true-random bit generator – I

Random Bit Generator can be obtained by the following Markov chain:

• Chaotic map

with and

k ∈N)(1 kk xMx =+

[ ] [ ]: 1,1 1,1M I = − − [ ]0 1,1x ∈ −

T

kx 1+kxM

0X1X

1

2

1

2

1

2

1

2

• We based our random bit generator on a simple, chaotic map…

…and obtain a random bit from a quantization of the map state xk.

Not all chaotic map are suitable for a real implementation!

0 1

0X1X

1+1−

37

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

How to deal with map robustness?

a possible true-implementedBernoulli map

true-implemented systems could reach stability

MAP ROBUSTNESS is a fundamental issue!!!

-1

-0.5

0

0.5

1

1.5

2

0 10 20 30 40 50 60 70

Is there a particularly interesting solution?

Parasitic stableequilibrium points!

• To prevent parasitic equilibria one introduces suitably defined behavior outside the invariant set: hooks, tails,…

-1.5

-1

-0.5

0

0.5

1

1.5

-1.5 -1 -0.5 0 0.5 1 1.5

-1.5

-1

-0.5

0

0.5

1

1.5

0 10 20 30 40 50 60

38

0X1X

2X 3X

1

2

1

2

1

2

1

2

1

2

1

2

1

2

1

2

The true-random bit generator – II

The implemented map is the following variation of the Bernoulli map

– It is a robust map, i.e. it still maintains the desired behavior even with little implementation error (analog implementation is necessary)

x

M x

0X1X 2X 3X

0 3X X+ 1 2X X+

1

21

2

1

21

2

– It is a Markov Map, i.e. it can be studied through a Markov chain

– A circuit implementing this map is used in pipeline 1.5 bit/stage ADCs!

39

Comparisons

NIST 800-22, 140.2 and DieHard in implementation

UnknownNIST 800-22 in implementation

RNG Conformance for cryptograpicapplications

>20 Mb/s

(>100 times faster)Up to 1 Mb/s per

source (5 per chip)70 Kbit/secRandom bit Rate

14 MHzUp to 1 MHz90 MHzSystem Speed

PWAM (ADC)PWAM (reconfig)Microcosmic (PLL)

Randomness source

ADC Based True RNG

FPAA Chaotic True RNG

FPGA True RNG

Patent Pending

40

Circuit prototypeA prototype has been implemented in AMSCMOS 0.35µm technology

Features:

BIAS

true-randombit generator

PLL

10 MHzMaximum TRBG

working frequency

20 MHzMaximum frequency

deviation

100 MHzTypical working

frequency

6.2 mW (PLL)20.5 mW (whole

circuit)Power consumption

3.3 VPower supply

voltage

1380 µm x 1180 µmArea

41

Circuit post-layout simulations

• Comparison between theoretical and simulated (from extracted netlist) power spectrum

-120

-110

-100

-90

-80

-70

-60

100e6 200e6 300e6 400e6 500e6 600e6

0 100

3.18

0.318

f MHz

f MHz

m

=∆ =

=

-95

-90

-85

-80

-75

-70

-65

-60

100e6Very good matching

42

-120

-110

-100

-90

-80

-70

-60

-50

100e6 200e6 300e6 400e6 500e6 600e6

Circuit post-layout simulations

Comparison between non-modulated (standard clock) and modulated (spread-spectrum clock) power spectrum

0 100

3.18

0.318

f MHz

f MHz

m

=∆ =

=

Peak reduction = 13dB(on the fundamental tone)

13 dB

120RBW kHz=(as indicated by

CISPR regulation)

43

Integrated spread-spectrum clock prototypeComparison between non-modulated (standard clock) and modulated (spread-spectrum clock) power spectrum

Peak reduction = 17dB(on the fundamental tone)

0 100

3.18

0.318

f MHz

f MHz

m

=∆ =

=

44

• New prototype of clock generator designed to work at in a tunable range between 2 and 2.5 GHz (UMC L180, 0.18µm, 1P6M)

Does it work at hiher frequencies?

45

Conclusion -I

• Novel chaos-based methodology for EMI reduction in switching power converters and digital circuits and boards…

• … shields need is reduced so that cost and volume occupation are reduced senza introdurre schermi e quindi

• Low-EMI clock generator: 9dB EMI reduction with respect to the best known and previously patented methods (used by IBM, Intel, Cypress). IC prototype working at 100MHz has been implemented and fully tested. Working frequencies can be increased.

• Current Feedback DC-DC converter: 22dB EMI reductionwith respect to the unperturbed case. Prototype realized with off-the-shelve components. Integrated version is a future step.

• Can be applied with all switching converters (also to drive motors)

• Future works: Application to SATA2 drivers (1.5GHz to 3GHz)

46

Conclusion -II• Chaos-based generation of stochastic process with prescribed statistical

features has been proved to give key advantages in:

True Random Number Generation for Cryptographic Applications (Patent

Pending)

– Implementation based on standard pipeline ADC structure ⇒ extreme design reuse

– Analytical proof that ideal system generates perfectly random bits (i.i.d.)

– Implementation in 0.35 AMS CMOS technology (3.3V supply, A=1480 um x 1620 um, fB = 40Mb/s (8-stages)) ⇒ >100 times faster than state of the art True-RNG

– Implementation satisfy NIST test suites (800-22, 140.2) and DieHard

47

Statistical Approach to Chaos1. A. Lasota and M. C. Mackey, “Chaos, Fractals, and Noise” New York: Springer-Verlag, 1994.

2. G. Setti, G. Mazzini, R. Rovatti, S. Callegari, “Statistical Modeling and Design of Discrete Time Chaotic Processes: Basic Finite-Dimensional Tools and Applications,” Proceedings of the IEEE, vol. 90, pp. 662-690, May 2002.

3. G. Keller, “On the rate of convergence to equilibrium in one-dimensional systems,” Commun. Math. Phys., vol. 96, pp. 181–193, 1984.

4. F. Hofbauer, G. Keller, “Ergodic properties of invariant measures for piecewise monotonic transformations,” Math. Zeitschrift, vol. 180, pp. 119–140, 1982.

5. V. Baladi, L.-S. Young, “On the spectra of randomly perturbed expanding maps,” Commun. Math. Phys., vol. 156, pp. 355–385, 1993.

6. N. Friedman and A. Boyarsky, “Irreducibility and primitivity using Markov maps,” Linear Algebra Appl., vol. 37, pp. 103–117, 1981.

7. G. Froyland “Extracting dynamical behaviour via Markov models” In Alistair Mees, editor, Nonlinear Dynamics and Statistics: Proceedings, Newton Institute, Cambridge, 1998, pages 283-324, Birkhauser, 2000

8. M.l Dellnitz, G. Froyland, S. Sertl, “On the isolated spectrum of the Perron-Frobenius operator,” Nonlinearity, 13(4):1171-1188, 2000

9. M Goetz, W. Schwarz, “Statistical analysis of chaotic Markov systems with quantised output” Proceedings. ISCAS 2000 Geneva, 2000, pp. 229 -232 vol.5

10. T.Kohda, A.Tsuneda, “Statistics of Chaotic Binary Sequences”, IEEE Trans. Inf. Theory, vol. 43, pp. 104-112, 1997

11. T.Kohda, A.Tsuneda, “Explicit Evaluations of Correlation Functions of Chebyshev Binary and Bit Sequences Based on Perron-Frobenius Operator”, IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, vol. E77-A, pp. 1794-1800, 1994

Some bibliography - I

48

EMI Reduction12. G. Setti, M. Balestra, R. Rovatti, “Experimental verification of enhanced electromagnetic compatibility in chaotic FM clock signals,”

Proceedings. ISCAS 2000 Geneva, 2000, pp. 229 – 232, vol.3

13. M. Balestra, A. Bellini, S. Callegari, R. Rovatti, G. Setti, “Chaos-Based Generation of PWM-Like Signal for Low-EMI Induction Motor Drives: Analysis and Experimental Results,” IEICE Transactions on Electronics, pp. 66-75, vol. 87-C, n. 1, January 2004

14. S. Santi, R. Rovatti, G. Setti, “Zero Crossing Statistics of Chaos-based FM Clock Signals,” IEICE Transactions on Fundamentals, pp. 2229-2240, vol. 88-A, n. 9, September 2003

15. S. Callegari, R. Rovatti, G. Setti, “Chaos-Based FM Signals: Application and Implementation Issues,” IEEE Transactions on Circuits and Systems- Part I, vol. 50, pp. 1141-1147, August 2003.

16. S. Callegari, R. Rovatti, G. Setti, “Generation of Constant-Envelope Spread-Spectrum Signals via Chaos-Based FM: Theory and Simulation Results,” IEEE Transactions on Circuits and Systems- Part I, vol. 50, pp. 3-15, 2003 (Recipient of the IEEE CAS Society Darlington Award)

17. R. Rovatti, G. Setti, S. Callegari, “Limit Properties of Folded Sums of Chaotic Trajectories,” IEEE Transactions on Circuits and Systems- Part I, vol. 49, pp. 1736-1744, December 2002.

18. S. Callegari, R. Rovatti, G. Setti, “Chaotic Modulations Can Outperform Random Ones in EMI Reduction Tasks,” IEE ElectronicsLetters, vol. 38, n. 12, pp. 543-544, June 2002.

19. F. Pareschi, L. De Michele, R. Rovatti, G. Setti, “A chaos-driven PLL based spread spectrum clock generator”, EMC Zurich 2005, (Recipient of the Best Student Paper Award)

Random Numbers Generation20. S. Callegari, R. Rovatti, G. Setti, “ADC-based Design of Chaotic Truly Random Sources'', Proceedings of IEEE NDES200, pp. 5-9--5-

12, Izmir, Turkey, June 2002

21. S. Callegari, R. Rovatti, G. Setti, “Efficient Chaos-based Secret Key Generation Method for Secure Communications,” Proceedings of NOLTA2002, X'ian, Cina, October 2002

22. S. Poli, S. Callegari, R. Rovatti, G. Setti, “Post-Processing of Data Generated by a Chaotic Pipelined ADC for the Robust Generation of Perfectly Random Bitstreams,'' Proceedins of ISCAS2004, pp. IV-585--IV-588, Vancouver, May 2004

23. S. Callegari, R. Rovatti, G. Setti, “First Direct Implementation of a True Random Source on Programmable Hardware,” International Journal of Circuit Theory and Applications, vol. 29, Jan 2005

24. S. Callegari, R. Rovatti, G. Setti, “Embeddable ADC-Based True Random Number Generator Exploiting Chaotic Dynamics,” IEEE Transactions on Signal Processing, Feb 2005

Some bibliography - II

49

Measurements Results