DYNAMIC AND CIRCUIT THEORY MODELS FOR THE ANALYSIS …
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[Compatibility Mode]DYNAMIC AND CIRCUIT THEORY DYNAMIC AND CIRCUIT
THEORY MODELS FOR THE ANALYSIS OF SUBMODELS FOR THE ANALYSIS OF
SUB--
WAVELENGTH TRANSMISSION WAVELENGTH TRANSMISSION THROUGH PATTERNED
SCREENSTHROUGH PATTERNED SCREENS
A B Yakovlev C S R Kaipa Y R Padooru A. B. Yakovlev, C. S. R.
Kaipa, Y. R. Padooru, F. Medina, and F. Mesa
Third International Congress on Advanced Third International
Congress on Advanced Electromagnetic Materials in Microwaves and
Optics
London, United Kingdom 30 August 4 September 200930 August – 4
September, 2009
Introduction Introduction Analytical modeling of
sub-wavelengthAnalytical modeling of sub-wavelength multilayered
FSS grids
Homogenization of grid impedance in terms of Homogenization of grid
impedance in terms of effective circuit parameters
Transfer matrix approach
Circuit theory model of sub-wavelength multilayered FSS grids
Transmission line network formalism in terms of grid and slab
admittance (impedance)
Even and odd excitations for multilayered symmetric grids
2
Analysis of Fabry-Perot type resonances in relation to
sub-wavelength complete transmission
H
Incident wave
Layer N+1
d Layer 1
TE Polarization TE Polarization
xjkz dγ l
MMMM dzxMdzMx
Transfer matrix across the plane of grid
5
1 01
.....Nl 2,1
TM Polarization TM Polarization
ll l
.....Nl Y
Q l
.....Nl 2,1
D
w
h
Grid impedance D = 2 mm, w = 0.2 mm, h = 1 mm
dielectric permittivity: 10.2
2 effk
effk D w D
Luukkonen et al., IEEE Trans. Antennas Propagat., 56, June
2008
Circuit Theory Model Circuit Theory Model S
Port 1 Port 20Y
n+1 = even m = (n+1)/2
mh 1h nh
Even Excitation: Open Circuit (Magnetic Wall)
cosθηη 00 θsinεηη r00 m
9Tretyakov, Artech House, 2003
Medina, Mesa, Marques, IEEE Trans. Microw. Theory Tech. 56, Dec.
2008
Even ExcitationEven Excitation Even Excitation: Open Circuit
(Magnetic Wall)Even Excitation: Open Circuit (Magnetic Wall)
PMCPort 1 0Y 1Y Y
1gY 2gY
1h 2
in TE/TM
g TE/TM
10 TE/TM
P TE/TM
1gY 2gY
transmission line
TE TM TE TM P
Y Y S
multilayered structure
Y YY Y
1gY 1ngY
ngY 2gY 2
Y Y
Y gTE/TM m
Odd Excitation: Short Circuit (Electric Wall)
TE/TM
of grid and PEC
zIncident wave
Reflected wave
0 0
|S21| - Analytical 0
|S21| - Analytical 30
|S21| - Analytical 60
8 9 10 11 12 13 14 15 16 1717 -30
-25
|S11| - HFSS 0
|S11| - HFSS 30
|S11| - HFSS 60
8 9 10 11 12 13 14 15 16 1717 -30
-25
14
0 0
|S21| - Analytical 0
|S21| - Analytical 30
|S21| - Analytical 60
8 9 10 11 12 13 14 15 16 1717 -30
-25
|S11| - HFSS 0
|S11| - HFSS 30
|S11| - HFSS 60
8 9 10 11 12 13 14 15 16 1717 -30
-25
15
Paired Screens of FishnetsPaired Screens of Fishnets H
H
z
0 0
|S11| - Analytical 0
|S11| - Analytical 30
|S11| - Analytical 60
10 11 12 13 14 15 16 17 18 19 2020 -30
-25
|S21| - HFSS 30
|S21| - HFSS 60
10 11 12 13 14 15 16 17 18 19 2020 -30
-25
17
Reflection and Transmission Magnitude Reflection and Transmission
Magnitude TM PolarizationTM Polarization
0 0
|S21| - Analytical 0
|S21| - Analytical 30
|S21| - Analytical 60
10 11 12 13 14 15 16 17 18 19 2020 -30
-25
|S11| - HFSS 0
|S11| - HFSS 30
|S11| - HFSS 60
10 11 12 13 14 15 16 17 18 19 2020 -30
-25
18
Multilayer SubMultilayer Sub--Wavelength Patch GridsWavelength
Patch Grids Transmission Magnitude, TE polarization
5
0
0.9
Transmission Magnitude, TE polarization 45-degree incidence
15
-10
-5
-25
0
0.1
0.
D
Period D = 2 mm Gap w = 0.2 mm
rε h Increasing the number of grids • creates pass bands and stop
bands • sharp transition between bands
19
• increases the pass band
0
-10
-5
dB
-25
-20
Period D = 2 mm 0 5 10 15 20 25 30
-30
Frequency(GHz)
Period D = 2 mm Gap w = 0.2 mm Thickness h = 2 mm Permittivity:
10.2
20
Y YY Port 2Port 1
h
h
2 tan 0g
Y Y C
1 0
Total Transmission Total Transmission
Excess length associated with edge capacitance
TE/TM r
θε Ccη
h 2
(GHz) E l h
10
15
h = 1 mm h = 2 mm h = 4 mm(mm) Calculated Excess length
1 17.2105 13.0606
5
( 1h)
h 4 mm h = 6 mm h = 8 mm h = 10 mm
4 7.279 7.1182 6 5.458 5.4616 8 4.392 4.4304 -10
-5
H (
22
-15
for two-sided fishnet structure
TE/TM r
(mm) Calculated Excess length
TT
0
5
10
1h)
h = 4 mm h = 6 mm h = 8 mm h = 10 mm
4 9.165 9.0589 6 6.566 6.5359 8 5.124 5.1121 -10
-5
H (
23
-15
Analytical and circuit theory models are developed for rapid and
efficient analysis of reflection/transmission properties ofy p p
multilayered sub-wavelength patterned screens
The observed resonances of total transmission at low frequencies in
multilayered sub-wavelength grids correspond to Fabry-Perot type
resonances of a dielectric slab loaded with effective grid
admittances
Analytical formulas for frequencies of total transmission are
obtained for two-sided patch arrays and wire grids in terms of an
excess length associated with effective edge capacitance andexcess
length associated with effective edge capacitance and
inductance
24