parametric identification of stochastic emi sources based
TRANSCRIPT
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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
Characterization of stochastic EM radiated emission
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
Characterization of stochastic EM radiated emission
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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
Characterization of stochastic EM radiated emission
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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
Characterization of stochastic EM radiated emission
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• Periodic mean value
• Periodic mean power
where
Order of cyclo WSS process
11
11 ,)}({
MN
kkTtCtxE
Characterization of stochastic EM radiated emission
22
12
2 ,)}({MN
kkTtCtxE
102,1 2cos,
nnn t
TnAATtC
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Characterization of stochastic EM radiated emission
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
Characterization of stochastic EM radiated emission
Num
ber o
f rea
lizat
ion
Leve
l [dB
]
Frequency
Frequency
EMI 2nd order CWSS
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Characterization of stochastic EM radiated emission
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
Non-parametric estimation of stochastic EMI sources
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Non-parametric estimation of stochastic EMI sources
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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Non-parametric estimation of stochastic EMI sources
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
Non-parametric estimation of stochastic EMI sources
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
Non-parametric estimation of stochastic EMI sources
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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Non-parametric estimation of stochastic EMI sources
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 of stochastic EMI sources
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
Parametric identification of stochastic EMI sources
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Parametric identification of stochastic EMI sources
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
Parametric identification of stochastic EMI sources
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
Parametric identification of stochastic EMI sources
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Parametric identification of stochastic EMI sources
||
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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Experimental Results
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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Experimental Results
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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Experimental Results
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
Experimental Results
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.