estimation of the electromagnetic field radiated by...
TRANSCRIPT
Estimation of the Electromagnetic Field Radiated by a Microwave Circuit
Encapsulated in a Rectangular Cavity
M. KADI, S. KHEMIRI, Z. RIAHIRSEEM/ESIGELEC
AGENDA
� Introduction
� Cavity Resonance frequencies
� Influence of the cavity on the electromagnetic field
distribution
� Estimation of the EM fields in a closed cavity from an
open cavity EM cartographies
• Proposed approach
• Radiated Emission Model
• Results
� Conclusion and prospects
2
The designers of the Rx/Tx modules attach particular importance to the electromagnetic compatibility problems of their products.
Introduction (1/2)
RF Power modules
Radiated Emission
Radiated Immunity
Electromagnetic Environment?
Failure Mechanism
Evalution of the cavity effect on the circuit performances
sdqsdsqdDC supply Control
board
Transmitter module
3
Introduction (2/2)
� HPA (High Power Amplifier) :
� Simplified circuits:
Microstrip lineSimple amplifier
4
Cavity Resonance Frequencies (1/2)
� Electromagnetic Field in Metallic Cavity
� Expression of the electric field
� Expression of the magnetic field
y
z
x
a
b
c
= zc
py
b
nx
a
mAEx .
.sin..
.sin..
.cos.1
πππ
Ey = A2.cosn.πb
.y
.sin
p.πc
.z
.sin
m.πa
.x
Ez = A3.cosp.πc
.z
.sin
n.πb
.y
.sin
m.πa
.x
H x = B1.sinm.πa
.x
.cos
n.πb
.y
.cos
p.πc
.z
H y = B2.sinn.πb
.y
.cos
p.πc
.z
.cos
m.πa
.x
H z = B3.sinp.πc
.z
.cos
m.πa
.x
.cos
n.πb
.y
5
� Studied Case : a simpleMicrostip line
Cavity Resonance Frequencies (2/2)
S21 parameter decreases at two frequenciesbecause a portion of the electromagneticenergy ends up being stored in the cavity.
These frequencies are two eigenmodes of thecavity which correspond to the mode (1,1,0)and (2,1,0).
Microstrip line
Rogers Duroid substrate
z
x b=30 mm
c=10 mma=60mm
y
6
EM Field with and without cavity(1/2)
Ex (A/m)
0 0.050
0.01
0.02
0.03
0
100
200
300
400
Ey (A/m)
0 0.050
0.01
0.02
0.03
0
100
200
300
400
Ez (A/m)
0 0.050
0.01
0.02
0.03
0
100
200
300
400
Ex (A/m)
0 0.050
0.01
0.02
0.03
0
100
200
300
400
Ey (A/m)
0 0.050
0.01
0.02
0.03
0
100
200
300
400
Ez (A/m)
0 0.050
0.01
0.02
0.03
0
100
200
300
400
Coveropen
Coverclosed
Hx (V/m)
0 0.050
0.01
0.02
0.03
0
0.5
1
1.5
2
2.5
Hy (V/m)
0 0.050
0.01
0.02
0.03
0
2
4
6
Hz (V/m)
0 0.050
0.01
0.02
0.03
0
1
2
3
4
Hx (V/m)
0 0.050
0.01
0.02
0.03
0
0.5
1
1.5
2
2.5
Hy (V/m)
0 0.050
0.01
0.02
0.03
0
2
4
6
Hz (V/m)
0 0.050
0.01
0.02
0.03
0
1
2
3
4
Coverclosed
Coveropened
� Field cartographie at f= 3 GHz)
No impact on the profiles except in the vicinity of the metal walls:
• EM fields shows only slight reduction along the line.• Significant decrease next to the metal walls of the cavity (about 5
V/m for the Ey component and 10 V/m for the Hz component).
7
EM Field with and without cavity(2/2)
� Field cartographie at f= 6,75 GHz)
Ex (A/m)
0 0.050
0.01
0.02
0.03
100
200
300
400
500
600
Ey (A/m)
0 0.050
0.01
0.02
0.03
200
400
600
Ez (A/m)
0 0.050
0.01
0.02
0.03
0
0.5
1
1.5
2
x 104
Ex (A/m)
0 0.050
0.01
0.02
0.03
100
200
300
Ey (A/m)
0 0.050
0.01
0.02
0.03
100
200
300
400
Ez (A/m)
0 0.050
0.01
0.02
0.03
0
200
400
600
800
Coveropen
Coverclosed
Hx (V/m)
0 0.050
0.01
0.02
0.03
0
10
20
30
40
Hy (V/m)
0 0.050
0.01
0.02
0.03
0
10
20
30
40
Hz (V/m)
0 0.050
0.01
0.02
0.03
1
2
3
4
Hx (V/m)
0 0.050
0.01
0.02
0.03
0.5
1
1.5
2
2.5
3
Hy (V/m)
0 0.050
0.01
0.02
0.03
1
2
3
4
Hz (V/m)
0 0.050
0.01
0.02
0.03
1
2
3
4
Coverclosed
Coveropen
• Total change of the electromagnetic field distribution.• A difference of 50 dBA/m is observed on the normal component of
the electric field (Ez).• Presence of a stationary wave which represents the cavity mode
with an index (2,1,0).
8
Estimation of the EM fields in a closed cavity from an open cavity EM cartographies
Inserting the model in HFSS
Encapsulate the model in a cavity
Modeling by electric dipole
EM field mapping with Cover Open
Mapping of the EM field in closed cover
� Proposed approach
9
Estimation of the EM fields in a closed cavity from an open cavity EM cartographies
� Radiated Emission Model
dℓ = Dipole length
θ1
θ2
I1
θ3 θp
I2
IpI3
Electric Dipole
Array
DUT
y
x
1- Model topography
Each dipole is represented by:• its position,• its orientation with respect to the
x-axis (θ),• its length (dℓ),• the current flowing through it (I).
In our model, we are pre-fixed:• The length,• Position.
And we extract :• the orientation of each dipole,• The current,• the effective relative dielectric constant (εreff) of
the DUT.
A. Ramanujan et al, “On the radiated emission modeling of on-chip microwave components ”, IEEE Int. Sym. EMC, USA, Jul. 2010.
10
Estimation of the EM fields in a closed cavity from an open cavity EM cartographies
� Radiated Emission Model
[ ] [ ][ ][ ][ ]( )[ ] [ ] [ ][ ][ ]( )[ ] [ ][ ][ ][ ][ ][ ]( ),frε,k,θ,I,P,PfE
,frk,θ,IαfH
,frk,θ,I,αfH
doEzz
yHyy
xHxx
===
,
• fr is the modeling frequency,• [αx] and [αy] are constants based on the dipole positions, their lengths and
the observation point,• [ε] is the medium’s permittivity given by [ε0εreff], ε0 = 8.85418e-12 F/m,• [k] is the wave number given by [k] = (2π/λ) x [εreff]
0.5
• [Pd] is the dipole position vector,• [Po] is the position vector of the observation point,• fHx, fHy, and fEz are non-linear mathematical functions associating all the
other parameters and variables.
1- Model topography
11
Estimation of the EM fields in a closed cavity from an open cavity EM cartographies
� Radiated Emission Model2-Parametric Extraction
oThe extraction is a two steps technique:
�the initial parameter vector is first calculated
�they are then passed through a two-level non-linear optimizationprocedure based on the Levenberg-Marquardt technique.
oThe model is extracted based on the following imposed conditions:
�Physically 1 < εreff < εr (of the substrate present in the DUT).
�The effect of εreff is negligible on the near-magnetic field very closeto the DUT
oThe dipole orientations and currents are first extracted and subsequently theeffective relative permittivity is determined
12
Estimation of the EM fields in a closed cavity from an open cavity EM cartographies
� Radiated Emission Model3 - Obtaining initial vector of model parameters
The initial vector of the dipole orientations [θinit] is estimated through the inverse methodas shown:
H x[ ]mx1
= αx[ ]mxp
× I init ⋅ sin( θ init )[ ]px1
⇒ Ai = αx[ ]mxp
−1 × H x[ ]mx1
= I init ⋅ sin(θ init )[ ]px1
H y[ ]mx1
= αy[ ]mxp
× I init ⋅ cos(θ init )[ ]px1
⇒ Bi = αy[ ]mxp
−1 × H y[ ]mx1
= I init ⋅ cos(θ init )[ ]px1
∴ θ init[ ] = tan−1 Ai Bi( )∈ R, for i =1,2,...,p
Where, m is the number of measurement points, and p is the number of dipoles used formodeling.. The initial current vector [Iinit] is calculated by back-substituting the values of [θinit].The initial [εreff] vector is a unity vector [εreff_init] = 1.
13
Estimation of the EM fields in a closed cavity from an open cavity EM cartographies
� Radiated Emission Model
A two-level optimization technique based on the Levenberg-Marquardt non-linear least-squares method is deployed in order to extract the modelparameters. The system is separated into real and imaginary parts andoptimized simultaneously so that the error functions are minimum.
f1 =real Hx,y
meas − Hx,ymodel( )
imag Hx,ymeas − Hx,y
model( )
With
H xmodel = fHx αx[ ], I init[ ], θ init[ ], k[ ], fr( )
H ymodel = fHy αy[ ], I init[ ], θ init[ ], k[ ], fr( )
{ modelmeas2 zz EEf −= With Ez
model = fEz Po[ ], Pd[ ], I sol[ ], θ sol[ ], kinit[ ], εinit[ ], fr( )
4 - Optimization of parameters
14
Estimation of the EM fields in a closed cavity from an open cavity EM cartographies
� Radiated Emission Model
5 – Insertion of the model in HFSS
Electric dipoles
� Possibility to adapt the boundary condition to define a metallic cavity (PEC on the top of the box)
15
Estimation of the EM fields in a closed cavity from an open cavity EM cartographies
� Results
1– At a frequency of 3 GHz
Excellent agreement is found between both the results, with slight differences in certain field components
0 0.050
0.01
0.02
0.03
0
100
200
300
400
Ey (V/m)
0 0.050
0.01
0.02
0.03
0
100
200
300
400
Ez (V/m)
0 0.050
0.01
0.02
0.03
0
100
200
300
400
Ex (V/m)
0 0.050
0.01
0.02
0.03
0
100
200
300
400
Ey (V/m)
0 0.050
0.01
0.02
0.03
0
100
200
300
400
Ez (V/m)
0 0.050
0.01
0.02
0.03
0
100
200
300
400
Ex (V/m)
Line-cavity
Model
Hx (V/m)
0 0.050
0.01
0.02
0.03
0
0.5
1
1.5
2
2.5
Hy (V/m)
0 0.050
0.01
0.02
0.03
0
2
4
6
Hz (V/m)
0 0.050
0.01
0.02
0.03
0
1
2
3
4
Hx (V/m)
0 0.050
0.01
0.02
0.03
0
0.5
1
1.5
2
2.5
Hy (V/m)
0 0.050
0.01
0.02
0.03
0
2
4
6
Hz (V/m)
0 0.050
0.01
0.02
0.03
0
1
2
3
4
Line-cavity
Model
Open cavity
16
Estimation of the EM fields in a closed cavity from an open cavity EM cartographies
� Results
1– At a frequency of 3 GHz
Excellent agreement is found between both the results, with slight differences in certain field components
Closed cavity
Ex (A/m)
0 0.050
0.01
0.02
0.03
0
100
200
300
400
Ey (A/m)
0 0.050
0.01
0.02
0.03
0
100
200
300
400
Ez(A/m)
0 0.050
0.01
0.02
0.03
100
200
300
400
Ex (A/m)
0 0.050
0.01
0.02
0.03
0
100
200
300
400
Ey (A/m)
0 0.050
0.01
0.02
0.03
0
100
200
300
400
Ey (A/m)
0 0.050
0.01
0.02
0.03
0
100
200
300
400
Line-cavity
Model
Hx (V/m)
0 0.050
0.01
0.02
0.03
0
1
2
Hy (V/m)
0 0.050
0.01
0.02
0.03
0
2
4
6
Hz (V/m)
0 0.050
0.01
0.02
0.03
0
1
2
3
4
Hx (V/m)
0 0.050
0.01
0.02
0.03
0
1
2
Hy (V/m)
0 0.050
0.01
0.02
0.03
0
2
4
6
Hz (V/m)
0 0.050
0.01
0.02
0.03
0
1
2
3
4
Line-cavity
Model
17
Estimation of the EM fields in a closed cavity from an open cavity EM cartographies
� Results
1– At a frequency of 6,75 GHz
Closed cavityE
x (V/m)
0 0.050
0.01
0.02
0.03
100
200
300
400
500
600
Ey (V/m)
0 0.050
0.01
0.02
0.03
200
400
600
Ey (V/m)
0 0.050
0.01
0.02
0.03
0
0.5
1
1.5
2
x 104
Ex (V/m)
0 0.050
0.01
0.02
0.03
0
500
1000
1500
Ey (V/m)
0 0.050
0.01
0.02
0.03
100
200
300
400
500
600
Ez (V/m)
0 0.050
0.01
0.02
0.03
0
500
1000
Line-cavity
Model
Cavity’s modes are excited and it imposes itselectromagnetic fields and therefore the model is notcapable to reproduce this phenomenon.
18
Conclusions
� The developed approach gives a good estimation ofelectromagnetic field in the closed cavity atfrequencies when the resonance modes are notexcited,
� When the resonance modes are excited, theapproach is not capable to estimate the closedcavity electromagnetic field :• Because the developed approach is based on a 2D emission
model
• The εreff is different in the two cases (open and closedcavity)
19
Prospects
� Using the same approch with à 3D emission model(PhD of H. Shall – IRSEEM/E-CEM ANR project)
-200
20
-20
0
20
-10
-5
0
5
10
x (m)
|Ex| simulé (dBV/m)
y (m)
z (m
)
-100
-90
-80
-70
-60
-50
-40
-30
-200
20
-20
0
20
-10
-5
0
5
10
x (mm)
|Ey| simulé (dBV/m)
y (mm)
z (m
m)
-90
-80
-70
-60
-50
-40
-30
-20
-200
20
-20
0
20
-10
-5
0
5
10
x (mm)
|Ez| simulé (dBV/m)
y (mm)
z (m
m)
-90
-80
-70
-60
-50
-40
-30
-20
-200
20
-20
0
20
-10
-5
0
5
10
x (mm)
|Ex| modélisé (dBV/m)
y (mm)
z (m
m)
-100
-90
-80
-70
-60
-50
-40
-30
-200
20
-20
0
20
-10
-5
0
5
10
x (mm)
|Ey| modélisé (dBV/m)
y (mm)
z (m
m)
-90
-80
-70
-60
-50
-40
-30
-20
-200
20
-20
0
20
-10
-5
0
5
10
x (mm)
|Ez| modélisé (dBV/m)
y (mm)
z (m
m)
-90
-80
-70
-60
-50
-40
-30
-20
20
References
Estimation of the electromagnetic field radiated by a microwave circuit encapsulated in a rectangular cavity
Khemiri, S.; Ramanujan, A.; Kadi, M.; Riah, Z.; Louis, A.
2011 IEEE International Symposium on Electromagnetic Compatibility (EMC)
Digital Object Identifier: 10.1109/ISEMC.2011.6038309 Publication Year: 2011 , Page(s): 196 - 201 IEEE Conference Publications
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