Frequency selective surfaces integrated with phased array antennas

269 Pages·2005·12.06 MB·English

Frequency Selective Surfaces
Integrated with Phased Array Antennas
Analysis and Design using Multimode Equivalent Networks

Frequency Selective Surfaces
Integrated with Phased Array Antennas
Analysis and Design using Multimode Equivalent Networks
PROEFSCHRIFT
ter verkrijging van de graad van doctor aan de
Technische Universiteit Eindhoven, op gezag van de
Rector Magni(cid:12)cus, prof.dr.ir. C. J. van Duijn, voor een
commissie aangewezen door het College voor
Promoties in het openbaar te verdedigen
op maandag 27 juni 2005 om 16.00 uur
door
Stefania Monni
geboren te Cagliari, Itali(cid:127)e
Dit proefschrift is goedgekeurd door de promotor:
prof.dr. A.G. Tijhuis
Copromotor:
dr. G. Gerini
CIP-DATA LIBRARY TECHNISCHE UNIVERSITEIT EINDHOVEN
Monni, Stefania
Frequency selective surfaces integrated with phased array antennas :
analysis and design using multimode equivalent networks
/ by Stefania Monni. - Eindhoven : Technische Universiteit Eindhoven, 2005.
Proefschrift. - ISBN 90-386-1713-5
NUR 959
Trefw.: frequentie(cid:12)lters / fasegestuurde antennestelsels /
microgolfantenne / golfgeleiders / elektromagnetisme ; numerieke methoden.
Subject headings: frequency selective surfaces / antenna phased arrays /
microwave antenna arrays / waveguides / computational electromagnetics.
Copyright c 2005 by S. Monni, TNO, The Hague, The Netherlands
(cid:13)
Cover design: S. Monni, implemented by P. Verspaget (Gra(cid:12)sche Vormgeving)
Press: Universiteitsdrukkerij, TUE
The work presented in this thesis has been performed at TNO and (cid:12)nanced by TNO with
support of the Dutch Ministry of Defense.
To my parents
To Michel

i
Abbreviations
BCMM Boundary Contour Mode Matching
EBG Electronic Band Gap
EFIE Electric Field Integral Equation
EMC Electromagnetic Compatibility
EMI Electromagnetic Interference
FSS Frequency Selective Surface
FT Fourier Transform
GAM Generalized Admittance Matrix
GF Green’s Function
GIM Generalized Impedance Matrix
GSM Generalized Scattering Matrix
GTM Generalized Transmission Matrix
HPB Half Power Beamwidth
IE Integral Equation
IEMENIntegral Equation’s method for the derivation of Multimode Equivalent Networks
IPD Insertion Phase Delay
ITD Integrated Topside Design
MAC Microwave Anechoic Chamber
MEN Multimode Equivalent Network
MFIE Magnetic Field Integral Equation
MFR Multi-Frequency Radar
MoM Method of Moment
PEC Perfect Electric Conductor
PSWW Phase Shift Wall Waveguide
PWL Piece Wise Linear
PWS Piece Wise Sinusoidal
RAM Radar Absorbing Material
ii Abbreviations
RCS Radar Cross Section
RNLN Royal Netherlands Navy
RX Receiving Antenna
TE Transverse Electric
TEM Transverse ElectroMagnetic
TFW Truncated Floquet Waves
TL Transmission Line
TM Transverse Magnetic
TX Transmitting Antenna
WAIM Wide Angle Impedance Matching
iii
Contents
Abbreviations i
1 Introduction 1
1.1 Frequency Selective Surfaces: historical context . . . . . . . . . . . . . . . 3
1.1.1 Applications of frequency selective surfaces . . . . . . . . . . . . . . 5
1.2 Analysis techniques for FSS’s . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.3 Design techniques for FSS’s . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.4 Outline of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2 Multimode Equivalent Networks: the IEMEN method 17
2.1 Multimode equivalent networks for waveguides . . . . . . . . . . . . . . . . 19
2.1.1 The microwave network formalism . . . . . . . . . . . . . . . . . . . 20
2.1.2 MEN of a waveguide junction . . . . . . . . . . . . . . . . . . . . . 26
2.1.3 MEN of a rectangular waveguide section . . . . . . . . . . . . . . . 36
2.1.4 MEN of a cascade of uniform waveguides . . . . . . . . . . . . . . . 37
2.2 Multimode equivalent network formulation for in(cid:12)nite periodic arrays . . . 40
2.2.1 MEN of the junction waveguide-PSWW . . . . . . . . . . . . . . . 41
2.2.2 Numerical results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.3 Thick FSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
2.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3 IEMEN approach for aperture- and patch-based FSS’s 57
3.1 Theoretical basis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.2 Patch-based FSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.2.1 Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.2.2 Multimode Equivalent Network . . . . . . . . . . . . . . . . . . . . 63
3.3 Aperture-based FSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.3.1 Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
iv Contents
3.3.2 Multimode Equivalent Network . . . . . . . . . . . . . . . . . . . . 68
3.4 Thin layer problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.5 Solution of the integral equation . . . . . . . . . . . . . . . . . . . . . . . . 72
3.6 Numerical results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
3.6.1 Free-standing FSS . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
3.6.2 Multi-layer FSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
3.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4 FSS design 83
4.1 Description of the design problem . . . . . . . . . . . . . . . . . . . . . . . 83
4.1.1 Single-mode design . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
4.1.2 Full-wave re(cid:12)nement . . . . . . . . . . . . . . . . . . . . . . . . . . 94
4.1.3 Discussion of the results . . . . . . . . . . . . . . . . . . . . . . . . 96
4.2 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
5 Experimental validation 101
5.1 Manufacturing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
5.1.1 Modi(cid:12)ed design: thin layer problem . . . . . . . . . . . . . . . . . . 105
5.2 Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
5.2.1 Far (cid:12)eld of the TX and far (cid:12)eld of the FSS measurement setup . . . 108
5.2.2 Far (cid:12)eld of the TX and the near (cid:12)eld of the FSS measurement setup 112
5.2.3 Quasi far (cid:12)eld of the TX and near (cid:12)eld of the FSS measurement setup116
5.2.4 Discussion of the results . . . . . . . . . . . . . . . . . . . . . . . . 118
5.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
6 Reduced kernel integral equation 123
6.1 Two-dimensional TM problem . . . . . . . . . . . . . . . . . . . . . . . . . 124
6.1.1 Geometry and IE formulation . . . . . . . . . . . . . . . . . . . . . 124
6.1.2 Non-accessible Green’s function . . . . . . . . . . . . . . . . . . . . 126
6.1.3 Ill conditioning of the sub-domain expansion . . . . . . . . . . . . . 129
6.1.4 Eigenvalues and eigenfunctions . . . . . . . . . . . . . . . . . . . . 131
6.2 Truncated Floquet waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
6.2.1 Convergence study . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
6.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141