parametric identification of stochastic emi sources based

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Parametric Identification of Stochastic EMI Sources Based on

Near-Field Measurements Yury Kuznetsov

Theoretical Radio Engineering Department Moscow Aviation Institute (National Research University)

Moscow, Russia [email protected]

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• Motivation • Characterization of stochastic EM radiated emission • Non-parametric estimation of stochastic EMI sources • Parametric identification of stochastic EMI sources • Simulation examples • Experimental results • Conclusion

Outline

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Motivation

A2 A1

A3

l1 l2

l3

I/O2

I/O1

I/O3

IC

ts1

ts3

ts2

t T3 0

t T2 0

t T1 0

PCB as multi-input / multi-output DUT

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Motivation

Probe 2 Probe 1

Port 2

0 1 2 3 4 5 6 7 8 9 10 -0.05

0

0.05

0[ s]

[ V ]

0 1 2 3 4 5

50 100

[GHz]

[dB V]

0

• Digital oscilloscope • Vector network analyzer

1 2

• 2-point scanning system of EMI sources

Position

Port 1

DUT

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Motivation

We will concentrate on the localization of traces on the surface of the PCB. The reason is that such type of source can be used as a model of the information bearing signal transmitting between spatially separated blocks of the electronic device through transmission lines along the surface of PCB or some bus interface. The accurate localization and parameter estimation of such source could significantly improve the validity of the F-F spatial distribution of the information bearing EMI pattern.

Frequency

E-fie

ld

Time

Volta

ge

Axis x

Axi

s y

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For the computation of the F-F EM radiation and for the recovering of the input electric current densities on the surface of the DUT it is sufficient to measure H -fields at the knots of the periodic array in the observation plane.

x, cm y,

cm

• Map of dipoles

-5 0 5

-5

0

5

• H -field

y, c

m

x, cm

Motivation

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Characterization of stochastic EM radiated emission

7

Volta

ge

Leve

l [dB

]

Volta

ge

Leve

l [dB

]

Time

Time

Frequency

Frequency

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• PAM signal

• PPM signal

• Impulse response

• Additive noise


Near-field received signal twtgTtstgTtstwtxty

M

jjj

N

iii

11,,

nini TntTts δ,

nnii TntTts δ,

NMpa

pbKpALtg N

nn

n

Mm

mm ,

0

01

wNtw ,0

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Impulse response g( t ) n

nn nTtδ

• LTI system • Generalized

information signal • EMI

nnn nTtg

The discrete-time WSS process converted into the continuous-time random signal by its transition through the LTI dynamic system characterizing by the impulse response g(t) which duration in general could be more then interval T of the initial WSS process.

5/30/2015

Cyclo WSS process


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The binary information signal consists of two possible outcomes “1” and “0”. A discrete Bernoulli distribution can represent it by assuming of two corresponding probabilities:

qpPpP 1}0{;}1{

Another important feature of the information signal is the synchronization by a clock generator with a repetition rate 1/T.

• Clock signal

t T 0


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To transmit information between separate devices it must be converted into a continuous signal, which can be measured in the observation plane due to the radiation of its common mode. This stochastic signal exhibits the properties of the cyclo WSS process.

Equivalent LTI system

t

0 0 T T 2T T …

t

T

• Received signal • Information signal • Impulse response


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• Periodic mean value

• Periodic mean power

where

Order of cyclo WSS process

11

11 ,)}({

MN

kkTtCtxE


22

12

2 ,)}({MN

kkTtCtxE

102,1 2cos,

nnn t

TnAATtC

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0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

x 108

10

20

30

40

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

x 108

-100

-80

-60

-40

-20

Num

ber o

f rea

lizat

ion

Leve

l [dB

]

Frequency

Frequency

EMI 1st order CWSS

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0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

x 108

10

20

30

40

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

x 108

-100

-80

-60

-40

-20


Num

ber o

f rea

lizat

ion

Leve

l [dB

]

Frequency

Frequency

EMI 2nd order CWSS

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Output signal

0 0.2 0.4 0.6 0.8 1 1.2

x 10-8

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Output signal

0 0.2 0.4 0.6 0.8 1 1.2

x 10-8

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Time Time

Volta

ge

Volta

ge

EMI 1st order CWSS

EMI 2nd order CWSS

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Non-parametric estimation of stochastic EMI sources

Direct Reconstruction

RadiatedStructure

Near-Field Region

Observation

Plane

rH

rE

Angular limitations

yx DD yx LL

rH

rE

Near-Field RegionO

bjectPlane

Observation

Plane

RadiatedStructure

Model-Based Approach

The adequate model is need

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Sampling interval:

Object plane: Mx My grid

Observation plane: Nx Ny grid

Distance between planes: d

x y

Planar sources: p( x, y, z = 0 )

Field distribution: H( x, y, z = d )

Scanning step:

z


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yx

j

jjMM

jx

jj

fkrj

y lr

jkr

edIrH1

2

2 14

)(

yx

j

jjMM

jy

jj

fkrj

x lr

jkr

edIrH1

2

2 14

)(

fjlI

p yxyx 2

,,

Nonparametric estimation of stochastic EMI sources produces the dipole moment parameters for all knots of the mesh in the object plane of the electronic device. The main topic of our research was to reconstruct the geometry of transmission lines designated for transferring the information signal between separated blocks of the electronic device.

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The relations between the measured complex amplitudes of the tangential harmonic magnetic fields in the observation plane and the complex amplitude of the current are defined in accordance with the electric dipole model

xpGHpGH yyyxx ][][

The complex amplitudes of the cross correlation spectra could be expressed by the following matrix expression

xyyyyxyxxx pAHWpApGHW ][][][ *0

*0

*0 yxx HHH

Obtained parameters of dipole moments in the object plane

yyxxxy WApWAp ][][

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• Complex amplitude of scanning probe

• Complex amplitude of reference probe

• Time samples

• Weighting coefficients of time window

• Frequencies

• Cross-correlation coefficients

• Complex coefficients


yx

N

n

tfjn

kin

ki NNitHw

NH nm ,...,2,1,e)(1 1

0

2

Cross-correlation Estimation

yxijij

jkr

mji MMjdr

jkr

efjGij

,...,2,1,14

2,

K

k

kkii HH

KW

1

*0

1

,...2,1,0,mTmfm

nw

1,...,1,0, Nntnt sn

1

0

200 e)(1 N

n

tfjn

kn

k nmtHwN

H

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• Singular value decomposition

• Tikhonov regularization

where

• L-curve Method


WUΣVpWpApb

HH ][]][[}])||(||)||][||[(minarg{ 22

222

ii

iH 1diag][ 22

2

Σ

22 log,][logcurvmax: pWpA

Reconstruction of Dipole Moments

][][diag][][ VUA i

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1

2][log WpA

2log p

1.0

310

210

410

510

• Typical L-curve for an ill-posed problem

measure for the mismatch

mea

sure

for t

he il

l-con

ditio

ning

210

10

1

110

210 310 210 110

more constrained

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The distributed multi-dipole model of the EMI source consists of the linked together electric dipoles characterized by dipole moments for some predefined frequency of the harmonic current flowing through the transmission line.

Parametric identification of stochastic EMI sources

• Model Parameters

• s-th dipole orientation vector

• current delay in s-th dipole s

ss

lΘ

Orders ,...2,1 )( yx MMOrder

y

x

P(x,y,z)zrj

Object Plane

dL

Mx

1

My

ReferenceDipole, I

δ

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• Space frequency-domain

model of planar sources

where


Parametric identification procedure allows significantly reduce the number of the effective dipoles and linking them to form the geometry of the distributed stochastic EMI source.

1,...1,01,...1,0

ee,

,,e)0,,(,

11

22

1

2

y

x

Order

syxs

Order

s

Dyj

Dxj

s

MM

j

Dy

Dx

j

jj

MM

zzF

NFzyxpG

ssy

s

x

s

yxy

j

x

j

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• Data Matrix

where

2,

][][][

][][][][][][

][

11

121

10

x

MLL

LM

LM

NM

ML

x

x

x

DD

DDD

DDDDDD

D

2,

]1,[],[]1,[

]1,[]2,[]1,[],[]1,[]0,[

][ y

y

y

y

MJ

MGJGJG

JMGGGJMGGG

D


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The appropriate number of sources can be chosen using the information criteria such as Akaike information criterion (AIC) or Minimum Description Length (MDL) criterion. The general formof any information criteria looks as follows:

]},~,ln2arg{min[ kNfkrLOrder k ΘD

Model Order Selection

1 2 3 4 5 6 7 8 9 10 11 120

0.2

0.6

Number

0

0

Sing

ular

Val

ues

noise

1 2 3 4 5 6 7 8 9 10 11 12-800

-400

0

Info

rmat

ion

Cri

teri

on

min (IC)

Model Order

• Singular Value Decomposition • Information Criterion

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• Effective Source

Coordinates Estimation:

2arg][diag

][][][][][

][]][[][][

][][][][][

][][

][

211

121

12

2

2

1

1

xxxx

ssx

xss

ss

s

Ls

Ls

ss

D zxZz

QUUQZ

QZQUU

UUMUU

UU

U

• x-coordinates • y-coordinates

2arg

][diag

][][][][][

][]][[][][

][][][

][][

][][

][][][

211

121

12

2

2

1

1

yyyy

PPy

yPP

PPP

P

JP

JP

PssP

Dz

yZz

QUUQZ

QZQUU

UUMU

UUU

UPU


Hnnn

Hsss

H ][][][][][][]][][[][ VUVUVUD

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• Minimum least squares algorithm

where

• Complex amplitudes of dipole moments estimation:

RL

Order

ZGZ2

1

diag

y

OrderOrderOrder

y

y

x

Order

xx

Order

Order

Myyy

Myyy

Myyy

R

Mx

Mx

Mx

xxx

xxx

L

zzz

zzzzzz

zzz

zzzzzz

2

2

2

222222

111

21

21

21

ZZ


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||

2||2

}2arg{

2

},{},{ I

fl

fpfj

lpfjI

msyxsyx

m

sms

m

Finally the geometric parameters of dipoles such as delays and orientation in the object plane could be calculated from the estimated dipole moments. It allows predicting of the far field distribution for any information bearing stochastic signal flowing through the identified distributed EMI source.

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Experimental Results Measurement setup

• Field Probes

• Object Plane

• Observation Plane

• Digital oscilloscope

• Laptop • Scanning • Reference

• Magnetic Field Probe

• Measured tangential component of vector H

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Experimental Results

0 100 200 300 400 500 600 700 800 900 1000-110

-100

-90

-80

-70

-60

-50

-40

X: 125Y: -67.87

Frequency, MHz

Lev

el, d

B

X: 250Y: -69.89

X: 375Y: -84.68

LAN onLAN off

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0 100 200 300 400 500 600 700 800 900 1000-1

-0.5

0

0.5

1

Time, ns

Nor

mal

ized

Mag

nitu

de

0 100 200 300 400 500-1

-0.5

0

0.5

1

Time, ns

Nor

mal

ized

Mag

nitu

de

300 320 340 360 380 400-0.012

-0.008

-0.004

0

0.004

0.008

0.012

0.016

0.02

Time, ns

Nor

mal

ized

Mag

nitu

de

• Autocorrelation function • Impulse response

• Autocorrelation function region after this filtering

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Experimental Results Comparison of cross-correlation spectra for

mutually spaced WCSC sources

• Non-parametric ensemble averaging • Parametric identification procedure

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DUT: Monitor mainboard

Measurement parameters

• Cross-correlation in the observation plane

Frequency, f = 240 MHz Distance between observation plane and object plane, d = 3 cm

Scanning step, = 1 cm Resolution in the object plane, = 1 cm

Number of scanning points, 15 16

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Experimental Results Localization Result f = 240 MHz

Order = 17

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Experimental Results Localization Result f = 214.8 MHz

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32,5 MHz 228,6 MHz 601,5 MHz

DUT: Notebook • Autocorrelation spectrum of the H-field

Measurement parameters Frequency range, f = 1…1000 MHz

Distance between observation plane and object plane, d = 3.5 cm Scanning step, = 2 cm

Resolution in the object plane, = 2 cm Number of scanning points, 28 17

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f = 601,5 MHz


f = 32,5 MHz f = 228,6 MHz

Far-Field Pattern Distance, r = 2 m

Polarization, Horizontal

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Conclusion • The N-F measurements of the stochastic fields radiating

by PCB can be used for the prediction of the F-F distribution of the EMI containing the information bearing signal and for the localization of the stochastic CWSS EMI sources on the surface of the PCB or electronic device under test.

• The improvement of the localization accuracy could be archived by specific signal processing in addition to the conventional averaging technique for stochastic EM field.

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Conclusion • The proposed algorithm of Tikhonov regularization in conjunction

with L-curve method allows the finding of the stable inverse reconstruction of the multi-dipole model distribution in the object plane • Additional parametric identification procedure based on the model

order selection in accordance with AIC and also on the 2 D Matrix Pencil Algorithm with subsequent fitting by MLS technique gives the geometrical configuration of the information bearing CWSS stochastic sources of the electronic device under test. • Implemented simulations and measurement experiments verified

the choice of the proposed signal processing algorithms for the purpose of the EM sources localization and the prediction of the far-field unintentional emissions pattern.

parametric identification of stochastic emi sources based

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