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Reuven Shavit

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Radome Electromagnetic Theory and Design explores the theoretical tools and methods required to design radomes that are fully transparent to the electromagnetic energy transmitted or received by the enclosed antenna. A radome is a weatherproof and camouflaged enclosure that protects the enclosed radar or communication antenna, and are typically used on a fixed or moving platform such as an aircraft, ship or missile. The author -- a noted expert in the field -- examines the theoretical methods that apply to all type of radomes: planar, conformal, airborne and ground based. The text offers a description of the various measurement methods that characterise the electrical parameters of a radome, and discusses their merits in terms of accuracy. This groundbreaking book brings together in one volume all the necessary theoretical tools to design radomes

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Table of Contents

Title Page

Copyright

Preface

Acknowledgments

Dedication

Chapter 1: Introduction

1.1 History of Radome Development

1.2 Types of Radomes

1.3 Organization of the Book

References

Chapter 2: Sandwich Radomes

2.1 Transmission Line Analogy

2.2 Multilayer Analysis

2.3 Single Layer

2.4 A-Sandwich

2.5 B-Sandwich

2.6 C-Sandwich

References

Chapter 3: Frequency Selective Surfaces (FSS) Radomes

3.1 Scattering Analysis of Planar FSS

3.2 Scattering Analysis of Multilayer FSS Structures

3.3 Metamaterial Radomes

References

Chapter 4: Airborne Radomes

4.1 Plane Wave Spectrum Combined with Surface Integration Technique

4.2 Surface Integration Technique Based on Equivalence Principle

4.3 Volume Integration Formulation Methods

4.4 Differential Equation Formulation Methods

References

Chapter 5: Scattering from Infinite Cylinders

5.1 Heterogeneous Beams—Volume Integral Equation Formulation

5.2 Homogeneous Beams—Surface Integral Equation Formulation

5.3 Conductive Beams—Surface Integral Equation Formulation

5.4 Tuned Beams—Surface Integral Equation Formulation

5.5 Scattering from Infinite Cylinders—Differential Equation Formulation

References

Chapter 6: Ground-Based Radomes

6.1 Scattering from an Individual Beam

6.2 Scattering Analysis of the Beams Assembly

6.3 Geometry Optimization

6.4 Intermodulation Distortion in MSF Radomes

References

Chapter 7: Measurement Methods

7.1 Panel Measurements

7.2 Characterization of Forward-Scattering Parameters

References

Appendices A Vector AnalysisAppen

A.1 Coordinate Transformations

A.2 Vector Differential Operators

Appendices B Dielectric Constants and Loss Tangent for Some Radome Materials

Appendices C Basic Antenna Theory

C.1 Vector Potentials

C.2 Far-Field Approximation

C.3 Directivity and Gain

C.4 Antenna Noise Temperature

C.5 Basic Array Theory

References

Index

End User License Agreement

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Guide

Cover

Table of Contents

Begin Reading

List of Illustrations

Chapter 1: Introduction

figure 1.2 Norton radome B787 dreamliner picture.

figure 1.1 Tejas aircraft (India) radome picture.

figure 1.3 Typical radomes installed on ships.

figure 1.4 Solid laminate radome of L-3 Communications-ESSCO, Concord, Massachusetts.

figure 1.5 A typical inflatable radome.

figure 1.6 Multipanel sandwich radome of L-3 Communications-ESSCO, Concord, Massachusetts.

figure 1.7 Metal space frame radome of L-3 Communications-ESSCO, Concord, Massachusetts.

figure 1.8 Dielectric space frame radome of AFC, Ocala, Florida.

Chapter 2: Sandwich Radomes

figure 2.1 The geometry of the incident plane wave.

figure 2.2 The geometry of a multilayer sandwich radome.

figure 2.3 Equivalent transmission line circuit of the multilayer structure.

figure 2.4 The geometry of a periodic PEC wire structure illuminated with parallel polarization and its circuit model.

figure 2.5 The geometry of a periodic wire structure illuminated with perpendicular polarization and its circuit model.

figure 2.6 A dielectric slab with two grids of PEC strips embedded.

figure 2.7 Comparison of the transmission loss through a dielectric slab and the dielectric slab with two PEC grids as a function of frequency at different incident angles for parallel polarization to the PEC strips. All simulations performed with HFSS.

figure 2.8 Comparison of the transmission loss through a dielectric slab and the dielectric slab with two PEC grids as a function of frequency and different incident angles for perpendicular polarization to the PEC strips. All simulations performed with HFSS.

figure 2.9 The geometry of a single layer illuminated by an oblique plane wave.

figure 2.10 The geometry of a single layer slab illuminated by an oblique linear polarized plane wave.

figure 2.11 Transmission coefficient through dielectric slab (ϵ

r

= 3.8, tan

δ

= 0.015) (a) perpendicular polarization, (b) parallel polarization.

figure 2.12 Phase delay through dielectric slab (ϵ

r

= 3.8, tan

δ

= 0.015): (a) perpendicular polarization, (b) parallel polarization.

figure 2.13 A sandwich panel geometry.

figure 2.14 Transmission coefficient through A sandwich with skins dielectric constant (ϵ

r

= 3.8, tan

δ

= 0.015) and thickness/wavelength (free space) ratio 0.03 and with core dielectric constant (ϵ

r

= 1.07, tan

δ

= 0.002) (a) perpendicular polarization, (b) parallel polarization.

figure 2.15 Insertion phase delay as a function of the core thickness of A sandwich with skins dielectric constant (ϵ

r

= 3.8, tan

δ

= 0.015) and thickness/wavelength ratio 0.03 and with core dielectric constant (ϵ

r

= 1.07, tan

δ

= 0.002) (a) perpendicular polarization, (b) parallel polarization.

figure 2.16 B-sandwich panel geometry.

figure 2.17 Transmission coefficient for (a) perpendicular and (b) parallel polarizations through B-sandwich with skins thickness 0.18

λ

0

and electrical parameters (ϵ

r

= 1.95, tan

δ

= 0.002) and core parameters (ϵ

r

= 3.8, tan

δ

= 0.015) for angle of incidence (0°, 40°, 60°, and 80°).

figure 2.18 Insertion phase delay for (a) perpendicular and (b) parallel polarizations through B-sandwich with skins thickness 0.18

λ

0

and electrical parameters (ϵ

r

= 1.95, tan

δ

= 0.002) and core parameters (ϵ

r

= 3.8, tan

δ

= 0.015) for angle of incidence (0°, 40°, 60°, and 80°).

figure 2.19 C sandwich panel geometry.

figure 2.20 Transmission coefficients through a C sandwich with skins dielectric constant (ϵ

r

= 3.8, tan

δ

= 0.015), thickness/wavelength ratio = 0.03 outer, 0.06 center, and with core dielectric constant (ϵ

r

= 1.07, tan

δ

= 0.002) at various angles of incidence: (a) perpendicular polarization, (b) parallel polarization.

figure 2.21 Insertion phase delay as a function of core thickness through a C sandwich with skins dielectric constant (ϵ

r

= 3.8, tan

δ

= 0.015), thickness/wavelength ratio = 0.03 outer, 0.06 center, and with core dielectric constant (ϵ

r

= 1.07, tan

δ

= 0.002) at various angles of incidence: (a) perpendicular polarization), (b) parallel polarization.

Chapter 3: Frequency Selective Surfaces (FSS) Radomes

figure 3.1 The concept of using FSS to reduce antenna RCS out of band.

figure 3.2 Geometry of FSS structure.

figure 3.3 Some FSS unit cell geometries: (a) Square patch; (b) Dipole; (c) Circular patch; (d) Cross dipole; (e) Jerusalem cross; (f) Square loop; (g) Circular loop; (h) Square aperture.

figure 3.4 The FSS embedded between a superstrate and substrate dielectric media.

figure 3.5 Equivalent circuit model of the FSS embedded between a superstrate and substrate dielectric media: (a) TM case; (b) TE case.

figure 3.6 The coordinate system transformation.

figure 3.7 Rooftop basis functions.

figure 3.8 Normal incidence: (a) reflection [dB]; and (b) transmission [dB] vs. frequency for an array of square patches printed on dielectric slabs with various thicknesses,

h

;

a = b

= 20 mm, patch dimensions

L

x

=

L

y

= 10 mm,

ϵ

r

= 3.8, tan

δ

= 0.015; all simulations performed with HFSS.

figure 3.9 (a) reflection and (b) transmission vs. incident angle

θ

i

for an array of circular patches; unit cell dimensions

a

=

b

= 20 mm, patch radius

R

= 6.25 mm, printed on a dielectric slab with thickness

h

= 2 mm and dielectric constant ϵ

r

= 3.8, tan

δ

= 0.015 at

f

= 10.4 GHz. All simulations performed with HFSS.

figure 3.10 FSS made of a crossed dipole on a thin dielectric substrate: (a) side and front view of the unit cell; (b) equivalent circuit of the FSS; and (c) reflection performance for normal incidence and different dielectric constants of the substrate based on HFSS simulations.

figure 3.11 FSS made of a Jerusalem cross slot: (a) front view of the unit cell with parameters

L

x

= 9.75 mm,

L

y

= 12.28 mm,

W

x

= 3.9 mm,

W

y

= 5.11 mm,

d

x

= 1.95 mm,

d

y

= 1.02 mm,

t

x

= 0.975 mm,

t

y

= 2.04 mm,

p

x

= 16.57 mm,

p

y

= 14.33 mm; (b) equivalent circuit of the FSS; and (c) transmission/reflection performance as a function of frequency for TM and TE polarizations and normal incidence based on HFSS simulations.

figure 3.12 FSS made of two square loops on a thin dielectric substrate with ϵ

r

= 3.5: (a) side and front view of the unit cell; and (b) transmission performance at normal incidence for different dimensions

d

of the inner loop based on HFSS simulations.

figure 3.13 Transmission vs. frequency for TM polarization (solid lines) and TE polarization (dashed lines): (a) a dielectric λ

g

/2 radome panel; (b) a slotted FSS surface made of copper with conductivity

σ

= 5.8 × 10

7

S/m; (c) a combination of the FSS on top of the dielectric

λ

g

/2 radome panel; (d) the FSS is positioned in the center of the dielectric

λ

g

/2 radome panel. All results are based on HFSS simulations.

figure 3.14 The general multilayer periodic geometry.

figure 3.15 A terminal plane defining the normalized incident and reflected voltage waves.

figure 3.16 Cascade connection of scattering matrices

S

I

and

S

II

.

figure 3.17 A multilayer periodic medium and its equivalent transmission matrices.

figure 3.18 Geometry of an FSS unit cell composed of two identical dipoles cascaded (all dimensions in mm) [15].

figure 3.19 The first eight transmitted harmonics at 16 GHz (normalized to the incident field): (a) amplitudes; (b) the decay with distance of the first eight harmonics [15].

figure 3.20 The first eight reflected harmonics at 16 GHz (normalized to the incident field): (a) amplitudes; (b) the decay with distance of the first eight harmonics [15].

figure 3.21 The reflection coefficients of two identical dipole FSS for normal incidence TE

z

case with

d

= 7 mm [15].

figure 3.22 Geometry of the transmitter/absorber radome [3].

figure 3.23 Transmission line equivalent circuit of the transmissive/absorbing radome [3].

figure 3.24 Geometries for the metallic FSS: (a) slotted cross; (b) slotted Jerusalem cross; (c) slotted interdigitated Jerusalem cross.

figure 3.25 Normal incidence reflection/transmission of FSS with slotted cross, slotted Jerusalem cross, and interdigitated slotted Jerusalem cross elements [3].

figure 3.26 Transmission coefficient of three different square loop shaped metallic FSSs. The periodicity of the FSS is 11 mm in all cases [3].

figure 3.27 Reflection coefficient of the absorbing structure with metallic ground and loops with surface resistance 15 [Ω/sq]. The thickness of the structure is 5 mm and the unit cell size is 11 mm [3].

figure 3.28 The radome in transmission mode: (a) the geometrical configuration in transmit mode; (b) the transmission/reflection performance in transmit mode [3].

figure 3.29 The radome in the receiving mode: (a) geometry in the receiving mode; (b) transmission/reflection in receiving mode; (c) absorption in the receiving mode [3].

figure 3.30 Transmission coefficient of the radome for 0, 30, and 45 deg incident angles and for TE and TM polarizations in receive mode [3].

Chapter 4: Airborne Radomes

figure 4.1 The cross section of an airborne radome based on super-spheroids geometry profile.

figure 4.2 Antenna and conical radome geometry.

figure 4.3 Transmitted field on outer radome surface using PWS and single plane wave approximation [3].

figure 4.4 Boresight errors for constant wall thickness ogive radome 6.6

λ

in diameter and 14.4

λ

in length made of material with dielectric constant, ϵ

r

= 5.7 and operating in the

X

frequency band with

F

L

and

F

H

constituting 2.5% band [10].

figure 4.5 Comparison between the radiation patterns of a reflector antenna with diameter

D

= 7.5

λ

0

and

f/D

= 0.28 inclined

Ω

= 20 deg from the

z

-axis (solid line) and that of the reflector covered with a conical radome base diameter

d

c

= 11.3

λ

0

in, length

L

= 15.5

λ

0

and

θ

a

= 20 deg. The radome thickness is 0.15

λ

0

with ϵ

r

= 5.7. All simulations are performed with HFSS.

figure 4.6 Radiation pattern of the antenna in the conical radome with the flash lobe positions for various pointing angles within the radome [11].

figure 4.7 Aperture radiation geometry and its domain decomposition.

figure 4.8 Cubic interpolation between grids of levels

L

and

L

– 1 in the range and near range boundary. Two additional points beyond range of interest are used. The central cubic interpolation weights are shown.

figure 4.9 The geometry of an arbitrary shaped radome excited by an embedded antenna and an external receiving antenna.

figure 4.10 The equivalence regions for the radome analysis: (a) equivalence for the external problem; (b) equivalence for the region bounded by

S

0

and

S

1

; (c) equivalence for the internal problem.

figure 4.11 (a) coordinates of common edge associated with two triangles; (b) geometry for normal component of basis function at common edge.

figure 4.12 Local coordinates and edges for source triangle

T

q

with observation point in triangle

T

p

.

figure 4.13 Comparison of radiation patterns of MoM solution, hybrid PO-MoM, and antenna without the ogive radome for an antenna aperture tilted 10 deg. The radome's length is 10

λ

and its diameter is 5

λ

. The antenna is circular with 4

λ

in diameter. The radome thickness is 0.2

λ

and its dielectric constant ϵ

r

= 4 [23].

figure 4.14 The tetrahedron mesh of an ogive-shaped radome.

figure 4.15 Cells in dielectrics (shaded) and auxiliary cells (unshaded). The auxiliary cells are introduced to terminate the mesh (the dimension

h

is arbitrary and is taken to be zero in the numerical implementation).

figure 4.16 Comparison of the normalized radiation of a reflector antenna (6

λ

0

in diameter) in the presence of three types of radome shapes: hemisphere shape (dot line), ogive shape (long dash line), conical shape (dash line), and radiation of the reflector in free space (solid line). All simulations performed with HFSS.

figure 4.17 Finite element mesh for analysis of axisymmetric radome.

figure 4.18 Radiation pattern in

x-z

plane of a reflector antenna enclosed in a conical radome: (a) the conical radome geometry with θ

a

= 20 deg, Ω = 30 deg, (b) the radiation pattern of the reflector antenna with (dash line) and without the radome (solid line). All simulations performed with HFSS.

Chapter 5: Scattering from Infinite Cylinders

figure 5.1 -Beam geometry.

figure 5.2 Linear pyramid basis function.

figure 5.3 The geometry of the oblique incident beam.

figure 5.4 Bistatic scattering of a rectangular beam 1.38 × 6.2 in.

2

with ϵ

r

= 4.6, tan

δ

= 0.014 normal incidence illumination by a plane wave on its narrow side at 5 GHz for TE

z

polarization (solid line) and TM

z

polarization (dash line) simulated with HFSS.

figure 5.5

IFR

as function of frequency for a dielectric beam with dimensions 1.38 × 6.2 in.

2

with

ϵ

r

= 4.6, tan

δ

= 0.014 and illuminated by a normal plane wave on its narrow side: (a)

IFR

-amplitude; (b)

IFR

-phase.

figure 5.6 The homogeneous geometry and its external and internal equivalent problems.

figure 5.7 Flat-strip model of the surface of a homogeneous dielectric cylinder.

figure 5.8 The back scattering RCS from a circular dielectric cylinder with radius

a

= 24 mm, for normal incidence TM polarized as a function of frequency. The cylinder is a lossy dielectric with ϵ

r

= 4 and conductivity σ = 0 (solid line), 0.017 S/m (dot line), 0.05 S/m (dash-dot line). All simulations are performed with HFSS.

figure 5.9 RCS of lossless elliptic cylinder (

ϵ

r

= 2) with a = 38 mm and b = 19 mm illuminated by normal incidence TM polarized wave at angle

φ

inc

= 60 deg with respect to

x

-axis: (a) scattering pattern at 5GHz; (b) forward (

φ

= 60 deg, solid line) and backward (

φ

= 240 deg, dot line) RCS as a function of frequency. All simulations are performed with HFSS.

figure 5.10 Comparison of bistatic RCS between SIE and exact solutions for three penetrable circular cylinders with normal incidence TE excitations [14].

figure 5.11 Comparison of the EFIE, CFIE, and exact solutions for the TM current density on a circular PEC cylinder of radius 0.82

λ

0

. The numerical result was obtained using 40 equal sized cells: (a) EFIE and exact current distribution results; (b) CFIE and exact current distribution results [5].

figure 5.12 Comparison of the EFIE, CFIE, and exact solutions for the TM bistatic radar cross section scattering patterns from a circular PEC cylinder of radius a = 0.82

λ

0

[5].

figure 5.13 Comparison of the EFIE, CFIE, and physical optics solutions for the TM current density on a pie-shaped PEC cylinder: (a) EFIE and physical optics distribution results; (b) CFIE and physical optics distribution results [5].

figure 5.14 Tuned-beam geometry with a periodic vertical and horizontal wire loading.

figure 5.15 Rectangular dielectric cylinder, loaded periodically with two horizontally and two vertically oriented PEC strips: (a) cross section: (b) front view; (c) perspective view.

figure 5.16 RCS (0 deg) of the unloaded and loaded cylinder as a function of frequency, for

s

v

= 0.6,

s

h

= 0.8, and

p

= 0.75: (a) TE polarization; (b) TM polarization. All simulations are performed with HFSS.

figure 5.17 IFR as a function of frequency for a tuned/untuned dielectric beam 2 × 0.4 in.

2

for vertical polarization and normal incidence.

figure 5.18 Field distribution in an untuned and tuned dielectric beam at the tuning frequency (5.6 GHz) at normal incidence: (a) untuned; (b) tuned.

figure 5.19 Scattering pattern for tuned and untuned beam at 5.6 GHz.

figure 5.20 Measured and calculated blockage widths

w

eq

of cylinder realized as parallel-plate waveguide and outer walls of the cylinder coated with strip-loaded dielectric material to obtain the hard boundary condition for both TE and TM cases: (a) geometry; (b) absolute value of

w

eq

for TE and TM cases [19].

figure 5.21 Cross section of the cylinder geometry showing the imbedded PEC region whose surface is denoted .

figure 5.22 Comparison of the

E

z

field produced on the surface of a circular dielectric cylinder with and

ϵ

r

= 50 – j20 by a TE wave incident at an oblique angle of 30 deg computed analytically, numerically with volume integral equation (VIE) and with partial differential equation (PDE) or FEM [20].

Chapter 6: Ground-Based Radomes

figure 6.1 Geometry of a typical space frame radome.

figure 6.2 The

IFR

of a PEC cylinder as a function of its diameter in wavelengths [4].

figure 6.3 The

IFR

of a dielectric cylinder with

ϵ

r

= 5 as a function of its diameter in wavelengths [2]: (a) parallel polarization, (b) perpendicular polarization.

figure 6.4 Basic geometry of a dielectric beam with tuning grid.

figure 6.5 The geometry of the radome and the scattering mechanism.

figure 6.6 Computed azimuth radiation patterns (perturbed and unperturbed) and the scattering pattern due to the beams with (dashed) and without (solid) the divergence effect @ 1.09 GHz.

figure 6.7 Sky temperature for clear air for 7.5 g/m

3

of water vapor concentration [20].

figure 6.8 Comparison of the radome-scattering patterns between (a) quasi-random and (b) parallel geometries.

figure 6.9 Comparison between the scattering patterns of a quasi-randomized geometry with (a) untuned and (b) tuned beams.

figure 6.10 Beams blockage dependence on aspect angle for a “bad” and a “good” (uniform density) radome geometry.

figure 6.11 Third IMP signals power levels for a standard MSF radome and a special treated MSF radome [22].

Chapter 7: Measurement Methods

figure 7.1 Panel measurement setup.

figure 7.2 The geometry of the proposed far-field probing measurement setup: (a) side view; (b) top view.

figure 7.3 Comparison of

IFR

e,h

as a function of

w/λ

computed and processed through measurements using the far-field probing technique: (a)

IFR

e

for circular and square PEC cylinder; (b)

IFR

h

for circular PEC cylinder; (c)

IFR

h

for square PEC cylinder [1].

figure 7.4 The measurement setup for panel/seam test.

figure 7.5 Measured

TL

and

IPD

for tuned (- - - -) and untuned () seam: (a) vertical polarization; (b) horizontal polarization.

figure 7.6 Schematic configuration of the near-field measurement setup.

figure 7.7 Recorded signal throughout the 0.75” diameter metal cylinder motion () VP, () HP: (a) amplitude; (b) phase.

figure 7.8 Scattering pattern of a metal cylinder with diameter 0.75” ( ) based on near-field data, () analytical solution eq. (7.21), (-) approximate form eq. (7.18).

figure 7.9 Schematic configuration of the focused beam system.

figure 7.10 Focused beam system of L-3 Communications-ESSCO, Concord, Massachusetts.

figure 7.11 Computed and measured amplitude and phase distribution (co-polarized and cross-polarized) in the focal plane for vertical polarization.

figure 7.12 Recorded signal (amplitude and phase) for co-polarized and cross-polarized with the dielectric cylinder inclined 30 deg (

θ

0

= 60 deg) in the focal plane, illuminated on its broadside at 12 GHz with vertical polarization.

figure 7.13 Comparison among computed (FEM) and reconstructed scattering radiation patterns (co-polarized + cross-polarized) of the dielectric cylinder inclined 30 deg (

θ

0

= 60 deg) in the focal plane, illuminated on its broadside at 12 GHz with vertical polarization.

List of Tables

Chapter 7: Measurement Methods

Table 7.1 Comparison of

IFR

values for metallic and plastic beams

Table 7.2 Comparison between measured and computed IFR values

Radome Electromagnetic Theory and Design

 

Reuven Shavit

Department of Electrical and Computer Engineering Ben-Gurion University of the Negev, Israel

This edition first published 2018

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Library of Congress Cataloging-in-Publication Data:

Names: Shavit, Reuven, 1949- author.

Title: Radome electromagnetic theory and design / by Reuven Shavit.

Description: Hoboken, NJ : John Wiley & Sons, 2018. | Includes

bibliographical references and index. |

Identifiers: LCCN 2017057991 (print) | LCCN 2018006051 (ebook) | ISBN

9781119410829 (pdf) | ISBN 9781119410843 (epub) | ISBN 9781119410799

(cloth)

Subjects: LCSH: Radomes.

Classification: LCC TK6590.R3 (ebook) | LCC TK6590.R3 S43 2018 (print) | DDC

621.3848/3--dc23

LC record available at https://lccn.loc.gov/2017057991

Cover Design: Wiley

Cover Image: © ra-photos/Getty Images;

Background: © rionm/Getty Images

Preface

Thirty years ago, I started working for ESSCO company in the United States while being on leave of absence from my job in Israel, and for the first time I was exposed to the subject of large radomes and their design. I found this subject very interesting and enlightening, especially because it includes almost all disciplines of analytics and numerical analysis in electromagnetics (EM), such as scattering, array theory, numerical analysis of integral equations and differential equations, circuit analysis modeling, and measurements (near and far field). It is quite amazing that such a niche topic in applied EM involves so many disciplines in electromagnetics. At ESSCO, I was lucky to meet Al Cohen, the CEO and founder, who tried successfully to couple his enthusiasm to the subject with his engineers and with me in particular, and Professor R. Mittra from University of Illinois at Champaign–Urbana, from which I learned a lot on computational electromagnetics. He served at that time as the company's advisor, and with his students developed many of the numerical codes used at ESSCO. I also would like to mention my colleagues at ESSCO, A. Smolski, C. Cook, E. Ngai, T. Wells, J. Sangiolo, T. Monk, A. Mantz, M. Naor, and Y. Hozev, from which I have learned a lot and have been enriched on the subject throughout numerous interactions.

It took me a long time to come to the conclusion that such a book is necessary. Over the years some books on the subject have been published, but most of them are practical books for radome design engineers. The book compiles in a unified manner the major theoretical and numerical tools needed for radomes design, which are currently dispersed over many scientific papers. The book is intended for graduate students and electromagnetic engineers working in the field who are interested in the theoretical and numerical aspects of the subject beyond running simulations with commercial EM software such as CST and HFSS. Enough detail is given such that readers can write their own computer programs to test new numerical algorithms or designs.

Reuven Shavit

September 2017

Acknowledgments

I would like to thank Al Cohen from ESSCO (now a subsidiary of L3 Communications) for introducing me to the subject through my association with ESSCO, Joe Sangello my direct supervisor who gave me full support and encouragement in my stay at ESSCO, and Professor R. Mittra, advisor to ESSCO, from whom I learned a lot on computational electromagnetics.

To my wife, Liora, and my daughters: Sarit, Liat, Shirley, and Libby, without whose constant support this book would not have become a reality.

Chapter 1Introduction

The word radome, is an acronym of two words “radar” and “dome” and is a structural, weatherproof enclosure that protects the enclosed radar or communication antenna. The main objective of the radome is to be fully transparent to the electromagnetic energy transmitted/received by the enclosed antenna, and in this sense its objective is similar to that of a glass window for light in the optics spectrum. Radomes protect the antenna surfaces from weather and, in contrast to a glass window, can also conceal the antenna electronic equipment from the outside radome observer. Another benefit for using a radome is that it enables use of a low-power antenna rotating systems and weaker antenna mechanical design, followed by a significant price reduction, since the enclosed antenna is not exposed to the harsh outside weather. Radomes can be constructed in several shapes (spherical, geodesic, planar, etc.), depending on the particular application using various construction materials (e.g., fiberglass, quartz, polytetrafluoroethylene (PTFE)-coated fabric, closed cell foam (rohacell), honeycomb). The radomes are assembled on aircrafts, ships, cars, and in fixed ground-based installations. In case of high-speed moving platforms like aircrafts, another important consideration is related to the streamline shape of the radome to reduce its drag force.

The materials used to construct radomes are often used to prevent ice and freezing rain (sleet) from accumulating directly on its external surface to avoid extra losses of the communication link. In case of a spinning radar dish antenna, the radome also protects the antenna from debris and rotational problems due to wind. For stationary antennas, excessive ice accumulation on the radome surface can de-tune the antenna, causing extra losses and internal reflections, which may go back to the transmitter and cause overheating. A good designed radome prevents that from happening by covering the exposed parts with a sturdy' weatherproof material like PTFE, which keeps debris or ice away from the antenna. One of the main driving forces behind the development of fiberglass as a structural material was the need for radomes during World War II. Sometimes radomes may be internally heated to melt the accumulated ice on their exterior surface. The most common shape of ground-based radomes is spherical because of the rotational symmetry such a radome offers. Large ground-based radomes are made of sandwich panels interconnected by seams or beams, which may affect the enclosed antenna radiation pattern as described in Chapter 6. Small or medium-sized radomes are usually made of one molded piece. In this case, only the transmission loss and boresight error caused by the radome need to be considered in the design as explained in Chapter 4.

figure 1.1 Tejas aircraft (India) radome picture.

Static electricity caused by air friction on the radome surface can present a serious shock hazard. Thin antistatic coatings are used to neutralize static charge by providing a conducting path to attached structures. Lightning strikes to aircraft are common, so metallic lightning-diverter strips are used to minimize structural damage to the radome. Diverters cause some increase in sidelobe levels; this effect can be estimated using the computational tools described in Chapter 5.

The US Air Force Aerospace Defense Command operated and maintained dozens of air defense radar stations in the United States, including Alaska, during the Cold War. Most of the radars used at these ground stations were protected by rigid or inflatable radomes. The radomes were typically at least 15 m (50 ft) in diameter, and the radomes were attached to standardized radar tower buildings that housed the radar transmitter, receiver, and antenna. Some of these radomes were very large. The CW-620 was a rigid space frame radome with a maximum diameter of 46 m (150 ft), and a height of 26 m (84 ft). This radome consisted of 590 panels and was designed for winds of up to 240 km/h (150 mph). The total radome weight was 92,700 kg (204,400 lb) with a surface area of 3680 m2 (39,600 ft2). The CW-620 radome was designed and constructed by Sperry-Rand Corp. for the Columbus Division of the North American Aviation. This radome was originally used for the FPS-35 search radar at Baker Air Force Station in Oregon. Two typical airborne radomes are shown in Fig. 1.2 and Fig. 1.1. Both of them are ogive type, but with different contours.

figure 1.2 Norton radome B787 dreamliner picture.

For maritime satellite communication service, radomes are widely used to protect dish antennas, which are continually tracking fixed satellites while the ship experiences pitch, roll, and yaw movements. Large cruise ships and oil tankers may have radomes over 3 m in diameter covering antennas for broadband transmissions for television, voice, data, and the internet, while recent developments allow similar services from smaller installations, such as the 85 cm motorized dish used in the ASTRA2 Connect Maritime Broadband system. Small private yachts may use radomes as small as 26 cm in diameter for voice and low-speed data transmission/reception.

1.1 History of Radome Development

The first radomes appeared in United States in 1940 with the introduction of the radar during the World War II when radars were installed on aircrafts and aerodynamics considerations were imposed to cover the radar antennas to reduce the drag forces on a high speed aircraft. The first reported aircraft radomes used simple, thin-wall designs. In 1941, the first in-flight radome was a hemispherical nose radome fabricated from plexiglass [1, 2]. It protected an experimental S-band, Western Electric radar flown in a B-18A aircraft. Beginning 1943, production airborne radars used plywood radomes [1].

In this period, plywood radomes also appeared on Navy PT boats and blimps, as well as in ground installations. Because plywood has moisture absorption problems and does not easily bend into doubly curved shapes, new radome construction techniques and materials were introduced. In 1944, the MIT Radiation Laboratory developed the three-layer A-sandwich, which used dense skins and a low-density core material. The skins were fabricated from fiberglass and the core from polystyrene. Since World War II, radome materials have developed in the following areas: ceramics for high-speed missile radomes, quartz, fiberglass, honeycomb, and foam for sandwich composites radomes. Today, the majority of aircraft radomes use sandwich-wall designs. Fig. 1.3 shows some typical radomes installed on ships.

figure 1.3 Typical radomes installed on ships.

Various authors have contributed to the literature describing the evolution, design, and manufacture of radomes. Cady [3] describes the electrical design of normal and streamlined radomes and their installation, together with the theory of reflection and transmission of electromagnetic waves through dielectric materials. The focus is on airborne radomes. Hansen [4] describes large ground radomes, their environmental, structural and design problems. Walton [5] describes advanced airborne radomes. Skolnik [6] and Volakis [7] gave theoretical electrical characteristics for sandwich panels and typical requirements for airborne and ground radomes. Chapters describing the radome theory and design rules can also be found in [8] and [9] and in books like [10].

The major electrical parameters that determine the radome performance are:

Insertion loss (IL) due to the presence of the radome.

Increased antenna sidelobe levels of the radiation pattern.

Depolarization radiation pattern increase.

Boresight error (BSE) and boresight error slope (BSES).

Insertion loss is a reduction in the signal strength as the electromagnetic wave propagates through the radome wall. Part of the loss is due to the reflection from the air/dielectric interface. Additional losses are due to internal and external diffraction, refraction effects, and polarization shift. The remainder is due to the dissipation within the dielectric layers. The computation of these parameters in multilayer radomes, including analysis in frequency selective surfaces (FSS), are described in Chapters 2 and 3.

The reflection and scattering from the radome also causes changes of the main beam-shape and increases the radiation pattern sidelobes. The scattering mechanism from a single beam in a space structure radome is described in