Comparative Study of Surface Waves on High-Impedance Surfaces With and Without Vias

35 Pages·2012·5.77 MB·English

Comparative Study of Surface
Waves on High-Impedance
Surfaces With and Without Vias

O. Luukkonen, A. B. Yakovlev, C. R. Simovski,
and S. A. Tretyakov
AP-S International Symposium
URSI National Radio Science Meeting
San Diego, California
5 – 11 July, 2008
Outline

Introduction and Motivation


Surface Waves on HIS Structures

Without Vias
 Dynamic Models
 Patch and Jerusalem Cross Arrays

EBG Properties of HIS Structures With

Vias
 Wire Media Slab and Mushroom Array
 Mushroom-like Jerusalem Cross Array

Conclusion

2
Introduction
Analytical modeling of dense FSS grids
and HIS structures with and without vias

 Homogenization of impedance surface
in terms of effective circuit parameters

Dynamic model obtained from full-wave
scattering problem via the averaged
impedance boundary condition

 Homogenization of wire media slab and
mushroom-like HIS structures – ENG
approximation

3
Surface Waves on HIS Structures
Without Vias
Dynamic Models
4
Model 1 – Impedance Surface
Transmission Line Model
Z Z
g d
η Z Z Z
o g d
s
Z Z
g d
Z
s
Impedance Surface Model
TEz TMz
H E
y y
E H
x x
H E Z
z z
s
h
z
No fields beyond the impedance surface
5
S. A. Tretyakov, Analytical Modeling in Applied Electromagnetics, Boston, MA: Artech House, 2003
Model 1 – Impedance Surface
Impedance Surface Model Impedance Boundary Condition
at y=0:
TEz TMz
H E
y y
E Z yˆ H
E H
x H x E Z s
z z
s
z
No fields beyond the impedance surface
TEz TMz
E ZTEH E E e jkzTEz kTyEy E ZTM H H H e jkzTMz kTyM y
x s z x 0 z s x x 0
2 2
j ZTM
kTE 0 kTE k 1 0 kTM j ZTM kTM k 1 s
y ZTE z 0 ZTE y 0 s z 0
s s 0
6
S. A. Tretyakov, Analytical Modeling in Applied Electromagnetics, Boston, MA: Artech House, 2003
Grounded Dielectric Slab with Grid
Model 2 -
Impedance on Air-Dielectric Interface
TEz y
H
y
E
x
H air

z
1 1 grid
Z
TMz g
E h slab
y
2 2
H
x
E
z
z
PEC
Two-sided impedance boundary condition at y=h
E E Z yˆ H H
1 2 g 1 2
7
Dispersion Equations
Two-sided impedance boundary condition at y = h
TEz-odd TMz-even
TE TM
E E Z H H E E Z H H
x1 x2 g z1 z2 z1 z2 g x1 x2
Dispersion equations
j j k
2 k k coth(k h) 2 k tanh(k h) ZTM 2 y1
y1 y2 y2 ZTE y2 y2 g j ZTM k
1 g 1 g y1
8
Complex Wavenumber Plane
Branch points in the complex k -plane at k k
z z 1
Re{k } 0
- proper modes on the top Riemann sheet
y
1
Re{k } 0 - improper modes on the bottom Riemann sheet
y
1
Re{k } 0 - branch cuts condition
y
1 Im{k }Re{k }
Im{k } 1 1
Hyperbolic k -plane branch cuts: z Re{k }
z z
Re{k } Re{k }
z 1
Im{k / k }
z 1
k k2 k2
y z i
i
2
-1 1
Re{k / k }
k2 n2
z 1
i i
c
1/2
c 9
0 0
Transmission-Line Network Analysis
k
θ
η Z Z
o g d
Z
s
HIS
Reflection coefficient
Z Z
g d
Z
Z cos
s
Z Z
TE , s 0
g d
Z cos
s 0
Parallel resonance
Z cos
X X 0
TM , s 0
g d
Z cos
s 0
10
S. A. Tretyakov, Analytical Modeling in Applied Electromagnetics, Boston, MA: Artech House, 2003