On the Scattering Reduction of an Aircraft

Wing Profile Enclosing an Antenna

Alireza Motevasselian

Licentiate Thesis

Electromagnetic Engineering

Royal Institute of Technology (KTH)

School of Electrical Engineering

Stockholm, Sweden 2010

TRITA-EE 2010:024 ISSN 1653-5146 ISBN 978-91-7415-652-2 Akademisk avhandling som med tillstånd av Kungl Tekniska högskolan framlägges till offentlig granskning för avläggande av teknologie licentiat-examen tisdagen den 25 maj 2010 klockan 14.00 i sal H1, Kungl Tekniska högskolan, Teknikringen 33, Stockholm. © Alireza Motevasselian, 2010 Tryck: Universitetsservice US AB

KTH School of Electrical Engineering SE-100 44 Stockholm

SWEDEN

i

Abstract

In this thesis we study the radar cross section reduction and transparency of an antenna radome placed in the front part of an aircraft wing. The antenna, not studied here, is a linearly polarized antenna operating at 1 GHz with a bandwidth of 30%. The thesis is split into two parts: a radar cross section reduction part for 2-16 GHz and a low-pass filter design to make the radome transparent at the antenna operating frequency and polarization. In the first part we design and compare shape optimization with a radar absorber as two methods for radar cross section reduction. For an optimized Jaumann absorber design we achieved a 5 dB reduction of the two-dimensional mono-static radar cross section over 68% of the frequency band as compared with the original metallic wing and for the polarization of the electric field is parallel to the wing axis. It was observed during the design process that Jaumann absorber keeps its major feature when it is applied to circular and elliptical surfaces; however, a resonant frequency shift occurs for elliptical structure due to varying thickness of the elliptical Jaumann layers. It is shown that the Jaumann absorber has a better performance for radar cross section reduction than shape optimized screen for the above mentioned polarization. Furthermore, by using the Jaumann absorber design we leave more space for antenna inside the wing.

The second part of the thesis is concerned with the transparency of the radome. It is required that the antenna enclosed by the radome can radiate through it. We propose a design where the main blocking element in the Jaumann absorber, the metal back sheet, has been replaced with a frequency selective surface. The frequency selective surface should be almost totally transparent over the antenna frequency band and conversely, it must be almost totally reflective over the remaining frequency band for the Jaumann absorber to function efficiently. The proposed FSS is a triangular lattice Gangbuster joint with a polarizer. This design has a mirror symmetry which can be utilized for a cylindrical structure with periodic boundary conditions. An optimization is done for the FSS backed Jaumann absorber to achieve a desirable performance. The new FSS back Jaumann absorber design not only provides a partial transparency for the radome but it also shows an improvement in radar cross section compare with ordinary Jaumann absorber. However, the FSS back Jaumann absorber suffers from a high transmission loss. The design is modified using circuit analogue absorber to reduce the transmission loss.

iii

Acknowledgements

I would like to express my deep and sincere gratitude to my supervisor Lars Jonsson. His wide knowledge and his logical way of thinking have been of great value for me. His understanding, encouraging and personal guidance have provided an excellent basis for the present thesis. He always had time for me and helped me to improve my confidence in research and also personal life.

I am also grateful to my co-supervisor Martin Norgren for his valuable participation in part of the work as well as helpful comments and hints for the courses I have had with him. Martin with his great electromagnetic knowledge is always a worthy reference at the department.

This thesis arose in part out of years of research that has been done since I came to Electromagnetic Theory Group at KTH. By that time, I have worked with a great number of people whose kind contribution aided me in several aspects of research, courses and also in general life in Sweden. It is a pleasure to convey my gratitude to them all in my humble acknowledgment.

To mention a few, in the first place I would like to record my gratitude to Anders Ellgardt for his advices, guidance and great ideas at every stage of this research and my courses as well as providing me with a broad familiarization with the rules in KTH and Swedish systems. Furthermore, I thank all present and former colleagues at the department for contributing to the nice atmosphere in the department. I am also thankful to my best friend Kaveh to assist me in some graphical part of the thesis.

It is also a pleasure to thank SAAB Microwave Systems and the Swedish Research Council, VINNOVA, under the NFFP 4 project SIGANT for their support in this project. Furthermore, EC Ericson Fond for sponsoring me to participate in conferences is gratefully acknowledged.

Finally, I wish to thank my parents, my sister Mahtab and also my dear friend Azadeh for their great love to me and for aiding me a lot to accept and enjoy my new life conditions in Sweden.

vii

List of papers

The thesis consists of a General Introduction and the following scientific papers:

I. A. Motevasselain, B. L. G. Jonsson, “Radar Cross Section Reduction of Aircraft Wing Front End” International Conference on Electromagnetics in Advanced Applications, ICEAA, Turino, Italy, pp 237-240, Sep. 2009.

II. A. Motevasselain, B. L. G. Jonsson, “A Partially transparent Jaumann Absorber Applied to an Aircraft Wing Profile” IEEE International Symposium on Antennas and Propagation, Toronto, Ontario, Canada, July 2010

III. A. Motevasselain, B. L. G. Jonsson, “A Low RCS Antenna Radome for an Aircraft Wing-Front Profile” Submitted to a Journal, April 2010

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Table of Contents

Chapter 1 Introduction ..................................................................................... 1

1.1 Background ............................................................................................. 1

1.2 Measures of scattered field ...................................................................... 3

1.3 Radar Cross Section Reduction ............................................................... 7

1.4 Problem Specification ............................................................................. 8

Chapter 2 Shape Optimization for RCSR ......................................................... 9

2.1 Introduction ............................................................................................. 9

2.2 Parameterization of the Radome Shape Used in the Optimization ......... 10

2.3 Scattering Problem and a Cost Function for RCSR ............................... 12

Chapter 3 Electromagnetic Radar Absorbers ................................................. 14

3.1 Introduction ........................................................................................... 14

3.2 Planar Stratified Absorbers .................................................................... 14

3.3 Jaumann Absorber for a Circular Cross-Section Cylinder ..................... 17

Chapter 4 Frequency Selective Surfaces ......................................................... 21

4.1 Introduction ........................................................................................... 21

4.2 The Gangbuster-Polarizer FSS .............................................................. 21

Chapter 5 Numerical Models .......................................................................... 24

5.1 Introduction ........................................................................................... 24

5.2 Scattering Model and RCS .................................................................... 24

5.3 Floquet Ports for Periodic Structures ..................................................... 26

Chapter 6 Results ........................................................................................... 28

6.1 Results for Numerical Scattering Calculation ........................................ 28

6.2 Results for Transparency ....................................................................... 30

6.3 High loss of FSS-Backed Jaumann Absorber and possibilities .............. 31

Chapter 7 Conclusion ..................................................................................... 33

References ...................................................................................................... 35

1

Chapter 1

Introduction

1.1 Background

Radar is an object detection system that uses electromagnetic waves to identify the range, altitude, direction, and/or speed of objects such as aircraft, ships, motor vehicles, and terrain. The term RADAR is conceived as an acronym for RAdio Detection And Ranging, see e.g. [1]. A radar system has a transmitter antenna which emits electromagnetic waves with a specific wavelength, phase and polarization. These waves are scattered in all directions when they come into contact with objects. Part of this scattered wave reflects back to the radar. Although the received signal is very week, it can be amplified and then processed for detection.

One of the most studied categories of radar detection targets is military aircrafts, see e.g. [2]-[6]. A well known case of this category is the so called Stealth aircraft. Calculation of the scattered field from a complex object like an aircraft is difficult. The geometry of a real aircraft, or parts of it, is often described as a large and rather static mesh-net. Corners, sharp edges and surface discontinuities like wing flaps produce a large amount of scattering and must be taken into account. Even a small feature can be critical for visibility from a radar point of view. Additional complication occurs due to the pilot canopy, the engine inlets and the materials that are usually used on the surface of the aircraft. Furthermore, the aircrafts typically carry one or several antennas used for communication and aircraft radar. The contributed scattering by such antennas on the aircraft is significant but their size as compared to the aircraft is very small. All of the above mentioned parameters must be included to assess at different flight angles over a wide frequency band. Moreover, the scattered field from an aircraft is caused by a range of different phenomena among them single reflection, multiple reflection, edge diffraction and creeping waves [7].

Therefore, to calculate the radar echo of an aircraft is computationally heavy. It is therefore interesting to reduce the complexity and focusing on simplified

2

problems and generic shapes to allow dynamic interactive improvement in shape and material for a particular part. One such approximation approaches is to divide complex bodies into different parts [8]. For example wings and body could be studied separately. Another approximation is the simplification of the separated parts into more generic shapes such as plates, dihedrals, cylinders and spheres. The simplifications and approximations of the aircraft enable us to study a subpart to shape it and make improvement on its radar visibility. Once such an interactive improvement has been made, the body part has to be incorporated back into the aircraft body in order to take into account secondary effects like multiple reflections. In this way the total radar visibility can be assessed.

The front-end of an aircraft wing is a convenient space to place a multifunctional antenna array. However, due to the aerodynamic restrictions the antenna should be placed inside the wing. Such an antenna requires protection against radar detection which is the subject of this thesis. The antennas are a major potential source of high radar visibility on stealth object [9]. The aircraft wing is usually made by composite materials, in particularly aluminum-lithium [10], that almost perfectly reflects electromagnetic waves, whereas the antennas absorb incoming waves. This difference in behavior give rises to a change of impedance, a discontinuity, from almost perfect reflection to absorption. Such a discontinuity will give a sharp omnidirectional radar echo which is undesired on a stealth object. The design process of the multifunctional antenna is quite complex and outside the scope of this thesis. Here we study the protecting radome for the antenna and its scattering properties. The purpose of this thesis is to conceal the antenna against incoming radar waves using a radome. This protection radome needs to be transparent for waves emitted from the wing integrated antenna at its operation frequency band. By using the above mentioned body part study, we concentrate on the main feature of the radome rather than on the wing by assuming that the aircraft wing is a uniform infinite cylinder. This enables us to study how detailed changes in the radome construction affect the visibility. Furthermore, the computational time of the problem allows repeated runs to improve its performance. This cylinder approximation transforms the scattering problem into a two-dimensional problem or rather a two-dimensional unit cell reduction. In addition it allows the use of the infinite array approximation for antenna array analysis and design [11].

3

In the upcoming chapters we describe in detail our analysis towards reduction of radar signature of an antenna radome over a wide frequency band with a transparent window at 1 GHz. In Chapter 1 we briefly introduce the scattering quantification and a brief review of general techniques for reducing radar signature of an object as well as specification of the problem considered in this thesis. Chapter 2 describes the shape optimization which is a method for radar signature reduction. In Chapter 3 an electromagnetic absorber is introduced and applied to planar and circular geometries. In Chapter 4 a frequency selective surface is designed to allow transmission window. This design is improved and utilized to provide the transparency for the radome. The numerical model, methods and software which we use to analyze the problem are described in Chapter 5. In Chapter 6, we present some of the results. The thesis ends with conclusions.

1.2 Measures of scattered field

Above we outlined in general terms how the radar signature reduction is one of the main issues in this thesis. In this section we will study how such a radar signature is defined and quantized.

To measure scattered fields is the key aspect when discussing radar visibility of an object. In the consideration of the scattering fields we can divide the scattering objects into three categories: bodies of bounded extent or three-dimensional objects like e.g. a sphere, two-dimensional objects (infinite in one dimension) like an infinite cylinder, and one-dimensional planar object like a doubly infinite plane. Depending on which category our object belongs to, a different measure of the scattered field is introduced. The scattering measure for each of these categories is defined bellow.

The Radar Cross Section (RCS) of an object is the ability of the object to be detected by radar. As a more precise definition the RCS of a target is the hypothetical area required to intercept the transmitted power density at the target position such that if the total intercepted power were re-radiated isotropically, the power density actually observed at the receiver is produced [12]. This engineering quantity is known as differential scattering cross-section in electromagnetic theory. The multiplication of the differential cross section by a factor 4π gives the RCS, see (1.7). The geometry of a general scattering problem is shown in Figure 1-1. An incident plane wave with wave vector k0

4

and fields (Ei, Bi) is scattered by an object with surface Ss and size of order d. It creates scattered fields (Es, Bs) that at large distances propagate as spherically diverging waves. The unit normal n´ is directed outward from the surface Ss. At the observation point P, far away from the scatterer with (r >> d), it is sufficient to approximate

r′ ′− − ⋅x x n x≃ (1.1)

where n is a unit vector in direction of x and r = |x|. Furthermore, the inverse distance can be replaced by r.

The scattered electric field takes it’s asymptotic form in far field region [13], using the exp (-jωt) time dependence

( ) ( ) ( )0

exp j, ,s

kr

r→E x k F k k (1.2)

where F(k,k0) is vectorial scattering amplitude and k is the wave vector in the direction of observation. Using the Kirchhoff integral relation for the scattered field [13],[14] and considering the transversality of F, that is k · F = 0, an integral expression for the scattering amplitude F(k,k0) can be written as

( ) ( ) ( )0

1, exp

4s

ss

S

cda

kπ′

′ ′ ′= − ⋅ −

∫k × n ×B

F k k k × k x n × Ε j (1.3)

where c is the speed of light in vacuum. The terms in the bracket can be interpreted as electric and magnetic current sources for the scattered field.

The differential scattering cross-section, a quantity with dimension of area per unit solid angle, is defined as

( )

( )02 ,s

i

k tdr r

d t

⋅Σ = → ∞Ω ⋅ 0

W n

W k (1.4)

where W(t) is the poynting vector and it’s time average defined as

1

Re2

= *W E× H (1.5)

Therefore the differential scattering cross-section is represented as

( ) ( )( )

2

00 2

0i

d

d

Σ =Ω

F k,kk,k

E k (1.6)

5

Figure 1-1 Scattering geometry

In the engineering literature the term radar cross section is mostly used. The radar cross section σ and differential scattering cross-section are related as

4d

dσ π Σ = Ω

(1.7)

The RCS of a target is called mono-static RCS when the transmitter and receiver radar are at the same location (k = -k0) and it is referred to as bistatic RCS when they are at different locations. In this thesis, after this introduction, the term RCS refers to the mono-static RCS. In more general cases than the ones considered here one has to take into account the polarization vector [13]. However, for the normally illuminated cylindrical object we will not have polarization impurity, caused by cross polarization, in the scattered field.

The RCS is defined generally for three-dimensional objects. Essentially all targets in practice are three dimensional. However, sometimes for theoretical consideration we need a measure of scattering from two-dimensional objects. In this case the scattering parameter is usually referred to as scattering width [15] also called two-dimensional RCS, σ2-D. The definition of the two-dimensional RCS is

( )( )

2

02 2

0

lim 2 lim 2 ss

i i

W

Wρ ρσ πρ πρ− →∞ →∞

= =

E k ,k

E kD (1.8)

6

here σ2-D is two-dimensional RCS and ρ is the distance from target to observation point.

It is often useful to compare the three-dimensional RCS of a slice of an infinite cylindrical object with its scattering width (two dimensional RCS) or vice versa. The RCS is a far field parameter (kr → ∞); thus, the major difference between the scattered field by an infinite cylindrical object and a finite slice of extent l of it, for normal illumination, comes from the exponential term integrand in (1.3). For the two-dimensional field we can (see e.g. [14]) estimate

( )2 2exp j exp j4

k d kπρ ζ ζ ρλ ρ

+∞

−∞

+ +

∫ ≃ (1.9)

where ζ is the parameter along the cylinder and ρ is the radial component in cylindrical coordinate system and λ is the wavelength. The integral is evaluated by using the saddle point method [16].

In the three-dimensional case we have a finite integration over the phase term

( ) ( )2 2

0

exp j exp jl

k d l kρ ζ ζ ρ+∫ ≃ (1.10)

which is estimated by using the Taylor series expansion method [16].

Using (1.6), (1.8), (1.9) and (1.10) the two- and three- dimensional RCS of a cylinder with normal incident are related by [15]

2

2

2lσ σλ−≃ D (1.11)

where λ is the wavelength of incident wave.

For one-dimensional objects (infinite planar structure) the scattering parameter is the power reflection coefficient |Г|2 defined as

( ) ( )( )

22 0

0 2

0

,, s

i

Γ =E k k

k kE k

(1.12)

where Ei and Es are the electric fields of the incident and reflected plane waves respectively.

Looking over the three above mentioned quantities, it can be seen that the all have the power reflection ratio term. Furthermore, for each case there is a factor of distance raised to power of a unit less than the dimension of the

7

object; thus in some sense we expect that some features of the scatterer will persist across the dimensions. This feature will be utilized in the design of the radome.

1.3 Radar Cross Section Reduction

Reducing the radar visibility is a factor of survivability for military targets. In consequence, stealth or invisibility to the radar is of widespread attention by researchers [17],[18]. Shaping and radar absorbing structures are two fundamental means for radar cross section reduction (RCSR). The Shaping is a broad concept. For example for an aircraft, avoiding right angles, internally carrying of weapons, keeping the engine away from radar wave bombardment and concealing the antennas behind radomes, all are some senses of shaping. However, in this text the term shaping implies changing the geometrical profile of the object. The purpose of shaping is re-directing the scattered electromagnetic fields away from the backscattering direction. This reduces the mono static RCS on the expense of the total scattered wave.

Another method for RCSR is to use radar absorbing materials. As it is implied from the name, the radar absorbing materials reduce the reflected power back to the radar receiver antenna by means of absorption of the electromagnetic energy. This absorption can be produced through several loss mechanisms [19]. The loss mechanism in this case is essentially the conversion of electromagnetic energy of incident radar wave into heat. This transformation does not create a detectable temperature increase on the object due to the small amount of incident electromagnetic energy.

There are other methods for RCSR as well. The passive and active cancelations are two of them. The passive cancelation could be considered as a kind of shaping. It is based on designing the target surface such that the reflected radar signal from a part of the target cancels the reflected radar signal from another part of the target. For the active cancelation, the RCS of a target is reduced by emitting radiation that will partially cancel the reflected radar energy [20].

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1.4 Problem Specification

In this thesis we aim for RCSR for an idealized aircraft wing. To simplify the problem we consider the wing as an infinitely long cylinder. The cross section of the wing is shown in Figure 1-2. The outer profile of the wing is unchanged throughout this project due to the aerodynamic requirements of the flying object. However, the front part of the wing shell could theoretically be made with a low permittivity dielectric material.

An array of antenna elements is supposed to be placed inside the first 15% of the length at the front part space as well as the RCSR means. The existence of the antenna increases the complexities of the design problem and it also restricts the problem: The RCSR means which are used should leave enough space for antennas placement as well as providing a low loss transparent path for antenna radiation at its operation frequency and polarization. The radiating elements are usually the most detectable parts of the target by radar. Therefore, as it is already mentioned, particular care should be considered to protect them against radar waves.

In this thesis we study and compare two methods of RCSR applied to the first 15% of an aircraft wing front end profile. The RCSR is done for both the TMz and the TEz polarization (see Figure 1-2) and over the frequency band 2-16 GHz while the antenna transmit/receive TEz polarized wave at operation frequency of 1 GHz with 30% bandwidth. The RCSR requirements are for ±20º cone in the forward direction.

Figure 1-2 Cross section of the aircraft wing

9

Chapter 2

Shape Optimization for RCSR

2.1 Introduction

The dimensions of typical radar targets like ships, airplane, etc are much greater than the radar wavelength. Due to this fact, the scattered field from the objects has a quasi-optical character and strongly depends on the shape of the objects [17]. The objective of shaping is to deflect the incoming radar waves into directions other than the backscattering direction of the field and thus reducing the amount of energy that returns to the radar. Nevertheless, the RCSR achieved by shaping cannot be done for all illumination angles because on a closed surface there will always be observation angles at which the surface is normal to the incident direction.

In this chapter we intend to reduce the RCS of the new radome covered the antenna inside the wing as compared to the metallic surface of the aircraft wing front profile introduced in Chapter 1 by the body shaping approach. It should be emphasized again that for flying structures the body shape is specified by aerodynamic requirements and can therefore not be changed substantially. Even the small changes considered here in conducting body shape must be covered by a low permittivity dielectric outer skin conforming to the aerodynamic shape of the wing. Furthermore, we should leave as much space as possible for the antenna array element placed inside the wing. Although the outer skin affected the scattering characteristics of the object, for simplicity, it is not considered in shape optimization process. The restrictions on the body shape optimization in this work are detailed in the next section.

In the process of designing a radome, covering the wing integrated antenna, we first decided to compare the RCSR properties of the shaped PEC screen with the original wing. This study is done for the frequency band (2-16 GHz). The second step, to make the radome transparent at antenna operation frequency (1 GHz), is only made for the better of the considered cases with RCSR means. We return to such an evaluation in Chapter 5.

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2.2 Parameterization of the Radome Shape Used in the

Optimization

In this section we describe how shape optimization can be used to reduce the RCS for the wing front profile. A completed RCSR approach based on an inner shape optimized conducting surface should also consist of an outer dielectric skin and absorbing layers. To simplify the problem of shape optimization, it is here done independent of the outer skin. Such an outer skin would allow multiple reflections between the surface of optimized shape and the skin and it would require a careful impedance matching and absorption in order to further lower RCS.

As it is already mentioned in Chapter 1, a cylindrical structure is considered for the wing. Thus, the shape of the wing can be defined by its cross section in two dimensions i.e. in the x-y plane. Furthermore, by means of curve fitting we found that the first 15% front end of the wing profiled can be well expressed by the elliptical curve

( )2 2

12 2

1x x y

a b

−+ = (2.1)

where a = 400 mm, b = 49.4 mm, x1 = 250 mm, and x ≥ 0.

The idea here is to consider the front part of the wing essentially as if it was a low reflective substance (for simplicity we use air) and then to vary an inner surface to redirect the electromagnetic incident waves into a direction other than the incident direction. The optimized shape function representing the front profile is chosen to be a smooth curve to allow as much of the volume behind it to be used for the antenna. The curve connecting the point A (x = 0) on the elliptical curve (2.1) to an intersection point p on x-axis in the interval p є (0,15) cm. The point p on the x-axis is chosen at x = 138 mm (and not at x = 150 mm) to leave space for dielectric outer skin and possible absorbing material. The optimized curve should have the same height and derivative as the ellipse has at the point A in order to avoid any discontinuity in the wing to radome transition region. These geometrical conditions can be easily satisfied by choosing a family of splines.

The group of chosen profiles is characterized by two parts. The first part is two third order splines with matched height and continuous first and second derivative

11

( ) 3 21 1 1 1 1 0 intf x a x b x c x d x x= + + + ≤ ≤ (2.1)

( ) 3 22 2 2 2 2 138 mmintf x a x b x c x d x x= + + + ≤ ≤ (2.2)

where xint is the intersection point of two functions f1 and f2 .(see Figure 2-1). The second part is a small radius half circle on the front part. It is introduced to avoid sharp edge at the joining point of spline f2 and the x- axis

( ) ( )223 0f x R x x= ± − − (2.3)

The resulting curve is shown in Figure 2-1.

The unknown coefficients a1, b1, c1, d1 and a2, b2, c2, d2 are determined from the geometrical requirements. First, the height and tangent of f1 at x = 0 is known from the information we have from the original wing shape

( )1 0 38.6 mmf = (2.4)

( )1 0 0.1f

x

∂ = −∂

(2.5)

Figure 2-1 Optimized shape for the wing front part represented by the three functions, f1, f2, f3.

3.86 cm

12

The next geometrical condition is the continuity of the curve as well as of its first and second order derivatives of the functions f1 and f2 at the intersection point xint

( ) ( )1 2int intf x f x= (2.6)

1 2

int intx x x x

f f

x x= =

∂ ∂=∂ ∂

(2.7)

2

12

0intx x

f

x =

∂ =∂

(2.8)

2

22

0intx x

f

x =

∂ =∂

(2.9)

Finally, the value and tangent of f2 at the endpoint is zero

( )2 138 mm 0f = (2.10)

2

13.8

0x

f

x =

∂ =∂

(2.11)

Thus, there are eight unknowns for eight equations and the unknowns can be determined for each value of the free parameter xint. For each realization of the spline the shape can be completed by fitting a small radius arc in the front end of the splines. This is done by moving the circle of radius R from x0 = 0 toward the point p, to find the first position where the spline and the circle touch.

Hence we have two unknowns in this optimization problem. The intersection point xint and the radius of the front circle R. Ideally we should let xint є [30, 90] mm and R є [2, 4] mm. The lower limit of xint is set in order to allow space for the antenna. However, to evaluate the RCS for both polarizations and the frequency range 2-16 GHz and a number of incident directions takes a large amount of computational time for each value of (xint, R). To speed up the procedure we consider a limited function space of the parameters as xint є 30, 50, 70, 90 mm and R є 2, 3, 4 mm.

2.3 Scattering Problem and a Cost Function for RCSR

The wing with the above described shape is illuminated by a plane wave Ei, of the form

13

( ) ( )0, exp cos sini i ix y jk x yϕ ϕ= + 0E E (2.12)

where φi is the incident direction and E0 is either

0ˆ

zE=0E a (2.13)

or

( )0 ˆ ˆsin cosx i y iE ϕ ϕ= − +0E a a (2.14)

corresponding to TMz and TEz wave polarization respectively, see Figure 2-1. The scattered field Es is generated at the illuminated object. The RCS of the object can be determined using (1.6).

The goal of the optimization is to find a shape with low RCS for both wave polarizations and for incident waves in the sector of φi є [-20˚,20˚] and over the frequency band 2 – 16 GHz. A cost function which can represent all these constraints with an acceptable number of calculation points can be defined as

( ) ( )2 2 2, ,D D Dn m n m

n m

f fξ σ ϕ σ ϕ⊥= +∑∑ (2.15)

Here σ#2D is the two dimensional RCS which is defined in (1.8). The subscripts

and represent vertical (TMz) and horizontal (TEz) polarization respectively. fn are frequency points and φm are angle points. The frequency and angle steps are chosen as

0 0, 2,3,...,16 and 1 GHznf nf n f= = = (2.16)

o0 0, 0,1,2 and 10m m mϕ ϕ ϕ= = = (2.17)

An approximation to the optimum shape is found by sweeping the cost function over 12 pairs of (xint, R) in the optimization domain and finding the best value of (xint, R), among all evaluated pairs, which minimizes the cost function. The optimal values found for the parameters are (xint, R) = (70 mm, 3 mm). Figure 2-1 shows the realization of the optimized shape. The resulting RCS response is shown in Chapter 6 together with a discussion and comparison to alternative RCSR means.

14

Chapter 3

Electromagnetic Radar Absorbers

3.1 Introduction

Another method to reduce the radar signature of an object is to use the electromagnetic radar absorbers, which was briefly discussed in Section 1.3. In order to gain an understanding of the absorber characteristics we first study absorber designs for the planar structures. Planar scattering is well studied and computationally fast as compared with designs on curved surfaces. To examine if the main features of the planar design carries over to curved surfaces, we applied the resulting design to a circular cylinder of the same diameter as the wing front thickness. The comparison of the scattering parameter for planar and circular cylinder absorber indicates to which extent the design is consistent when it applies to different shapes and more precisely the wing front profile.

3.2 Planar Stratified Absorbers

It is common to divide absorbers into two classes: magnetic absorbers and electric absorbers. In both cases a lossy electric or magnetic sheet is placed at the location of maximum electric or magnetic field respectively. In the case of reducing the reflection from a perfect electric conductor (PEC) surface the maximum electric field occurs at a quarter of a wavelength away from the PEC surface while the magnetic field has its maximum on the PEC surface. Therefore, for an electric absorber a screen having a matched resistivity is positioned a quarter of a wavelength apart in front of the metallic plate. These designs are often referred to as Salisbury screens [21]. A magnetic lossy sheet can be placed directly onto the PEC surface. A consequence of the absorber lossy sheet position is that a Salisbury absorber is thicker than a magnetic absorber. Furthermore, the Salisbury absorbers are efficient only for a narrow frequency band because of their resonant nature. However, the magnetic absorbers are often heavy and fragile [22], making them inappropriate for flying structures. Furthermore, it is difficult to find materials that meet

15

particular desired conditions and they often have a strong frequency variation [19]. Another complication is that the magnetic lossy sheet must have enough low intrinsic impedance to let the incident radiation penetrate so that the conductor will be effective to establish a boundary condition that position the maximum magnetic field within the lossy sheet. However, there are ongoing research efforts to overcome problems with magnetic absorbers, see e.g. [22], [23], [24].

The bandwidth of a Salisbury screen can be improved by adding extra resistive sheets and dielectric spacers to form a Jaumann absorber [19], [21]. The reason of this improvement is to create an extra resonance in the screen structure which increases the bandwidth of efficient absorption. A two layer Jaumann absorber is shown in Figure 3-1. It is well known that reflection and transmission of a plane wave against a planar stratified media can be modeled with a transmission line, see e.g. [25],[26]. The transmission line equivalent of the Jaumann screen of Figure 3-1 is shown in Figure 3-2.

Figure 3-1 Planar Jaumann absorber

()

11

,ε

µ

()

22

,ε

µ

16

Figure 3-2 Transmission line equivalent model for the Jaumann absorber shown in Figure 3-1

Using transmission line theory and an initial design of [21] together with a trial and error optimization procedure [28], we design a Jaumann absorber with 100% bandwidth of -10 dB reflection coefficient at central frequency of 10 GHz. This trial design for Jaumann absorber is achieved with parameters values of : εr1 = 3.78, εr2 = 1.5, d1 = λ10GHz /4√εr1, d2 = λ10GHz /4√εr2, R1 = 188.5 Ω /, and R2 = 754 Ω /. Here it is assumed that the dielectric spacers in the Jaumann design are lossless, non – magnetic (µr = 1) and non – dispersive. The symbol Ω / means ohm per square and is a measure for description of resistance or impedance of a thin lossy sheets [19]. To recall the reason for the definition of Ω / consider the resistance R between two sides of the resistive block as shown in Figure 3-3. The resistance is given by [29]

l l

RS WT

ρ ρ= = (3.1)

where ρ is resistivity of material of dimension Ωm, l is the length of the block between the two sides and width, W, and thickness, T, both measured in meters. Here, S, denotes the cross-section area of the block.

For the case of a square we have l = W, the length and width cancel each other in (3.1) and the resistance become R = ρ / T. Thus, if we measure the resistance across any square piece of the material, as shown in Figure 3-3, regardless of size of the square, the result would be the same. It is the definition for Ohm per square.

The reflection coefficient of the above mentioned design is shown in Figure 3-4.

11

1cZ

µε

= 0Z

Γ

1R

22

2cZ

µε

=

2R

17

Figure 3-3 Block of resistive material

Figure 3-4 Reflection coefficient of a trial design of planar Jaumann absorber with: εr1 = 3.78, εr2 = 1.5, d1 = λ10GHz /4√ εr1, d2 = λ10GHz /4√ εr2, R1 = 188.5 Ω /,

and R2 = 754 Ω /

3.3 Jaumann Absorber for a Circular Cross-Section

Cylinder

The Jaumann absorber is a conformal structure. Hence, it can be applied to cylindrical objects. For a circular cross section cylinder a Jaumann structure can be made by coating an inner PEC core cylinder by co-central cylinders of dielectric layers and resistive sheets as shown in Figure 3-5.

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-5-5-5-5

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Frequency (GHz)

Ref

lect

ion

(dB

)

18

Figure 3-5 The cross section of a circular cylindrical Jaumann absorber

Figure 3-6 Two dimensional RCS of a PEC cylinder oriented on z-axis with and without Jaumann absorber coating for TMz polarized wave illumination

The propagator approach joint with modal matching technique in cylindrical coordinate system is used to analyze this structure [27]. The two dimensional RCS (scattering width) of a PEC circular cylinder of radius 40 mm and an identical cylinder coated by a Jaumann absorber are shown in Figure 3-6 and Figure 3-7 for TMz and TEz incident wave polarization respectively.

0 2 4 6 8 10 12 14 16

x 109

-30

-25

-20

-15

-10

-5

19

The radius of the cylinder is chosen close to the wing front y-dimension (d0 ≈ 9 cm). The Jaumann absorber parameters, layers thickness and permittivity, and resistivity of the lossy sheets are the same as the planar design in Section 3.2. That is d1 = 3.85 mm, d2 = 6.12 mm, R1 = 188.5 Ω /, and R2 = 754 Ω / and the relative permittivity of inner (red) and outer (green) cylindrical layers are 3.78 and 1.5 respectively. It is observed from Figure 3-4, Figure 3-6 and Figure 3-7 that apart from some amplitude rapid oscillation in TEz polarization the resonance characteristics of the Jaumann absorber is very similar for both planar and cylindrical structures. For example in both planar and cylindrical case a 10 dB reflection coefficient and RCS reduction is achieved over the same frequency band and with almost the same frequency behavior. This behavior persists for cylinders of the above mentioned diameter size range or larger in this frequency band.

The similarity of the frequency response of the scattered field in both the cylindrical and the planar case indicates that the main features can survive when it is applied to an elliptic wing front-end. It facilitates us with means to utilize and develop results in the planar case. However, the absorber cannot be applied to the entire wing but only to the first 15%, to reduce reflection from a possible discontinuity where the radome ends and for the rest of the wing we let the layers conform to a sequence of translated ellipses making the layers

Figure 3-7 Two dimensional RCS of a PEC cylinder oriented on z-axis with and without Jaumann absorber coating for TEz polarized wave illumination

0 2 4 6 8 10 12 14 16-30

-25

-20

-15

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-5

20

thinner as they approach the end of the radome. The precise details of this design is described in papers I and II. The resulting scattering width of this semi-elliptical Jaumann structure will be presented and discussed in Chapter 6.

21

Chapter 4

Frequency Selective Surfaces

4.1 Introduction

A periodic structure is basically an assembly of identical elements arranged into a one-, two- or three dimensional infinite arrays. Periodic structures have a variety of applications in electromagnetic and antenna engineering. Photonic crystals [30], electromagnetic band-gaps [31], antenna arrays [32] and Frequency Selective Surfaces (FSSs) [21] are some examples of periodic structures.

Frequency selective surfaces (FSSs) are two-dimensional periodic structures that consist of metallic patch elements printed on a thin dielectric layer or aperture elements within a metallic screen. FSSs basically are filters that transmit or reflect electromagnetic waves at chosen frequency bands. Metallic-patch FSSs exhibit total reflection at the element resonant frequency. Aperture-element FSSs on the other hand produce total transmission at the element resonant frequency. There is a diversity of patch or aperture element geometries reported in literature, see e.g. [33]. Gangbuster dipole [21], multi pole, ring, polygon loops, and cross are some examples for FSS element geometry. The size and geometry of the element are chosen to fit the desired overall frequency response of the structure. Planar and curved FSS have been used for a variety of applications including antenna radome design [9], [36], dichroic surfaces for reflectors and sub-reflectors of large aperture antennas [21] or even radar absorbers [37], [38].

4.2 The Gangbuster-Polarizer FSS

In this thesis we are interested in the filtering behavior of FSSs for incoming electromagnetic waves. The desired structure should ideally totally reflect one linearly polarized wave while having a low-pass behavior for the polarization

22

Figure 4-1 A type 2 (n = 2) Gangbuster FSS (black) superposed by orthogonal infinite strips (yellow) embedded in a dielectric substrate with εr = 2.2 and its

reflection coefficient, L = 13.5 mm, W= 0.7 mm, Dx = Dy = 7.35 mm.

orthogonal to the first one. Furthermore, we are interested in a structure which is rather robust in function when it is bent over the curve surface of the wing. The band-stop feature can be implemented by a Gangbuster FSS with dipoles parallel to the electric field of the incident wave. Without any significant effect on the Gangbuster behavior, one can superimpose it with a periodic array of infinitely long strips as shown in Figure 4-1. These infinite strips provide a nearly perfect reflection for linearly polarized waves where the electric field is parallel to them. The Gangbuster unit cell is shown in Figure 4-1. It is a type 2 Gangbuster [21] and its dipoles are aligned in a direction having an angle of 26.6º with respect to the x-axis, while the infinite strips are arranged as being perpendicular to them. The infinite strips thickness and periodicity are chosen the same as the Gangbuster dipoles.

The FSS structure is illuminated by a plane wave Ei, of the form

( ) ( )0, expi x y jk z= 0E E (4.1)

where

0 5 10 15 20-18

-16

-14

-12

-10

-8

-6

-4

-2

0

Ref

lect

ion

(dB

)

Dx

rε

W

23

( )ˆ ˆcos sinx yϕ ϕ= +0E a a (4.2)

The reflection coefficient of the above mentioned structure is shown in Figure 4-1. It is observed that for the polarization in which the electric field is parallel to the infinite strips we have an almost perfect reflection up to 15 GHz; while for the polarization perpendicular to the infinite strips (parallel to the Gangbuster dipoles) it exhibits a band stop behavior. Thus, the above described design provides the desired reflection characteristics for two orthogonal polarizations. This design will be modified to have mirror symmetry and then applied to the wing surface. The procedure is described in paper III.

24

Chapter 5

Numerical Models

5.1 Introduction

There are several numerical methods to solve electromagnetic problems; see e.g. [34], [39]. These numerical methods can be generally divided into two major categories: integral equation (IE) methods and differential equation (DE) methods. Each category consists of different computational methods. The Method of Moment (MOM) or Boundary Element Method (BEM) is a technique which belongs to IE group. The Finite Difference (FD) and the Finite Element Method (FEM) are two methods belong to DE category. The finite difference is usually in time domain and is known as Finite Difference Time Domain (FDTD). FEM method is the most common frequency domain numerical DE method [40].

Based on these methods, numerous commercial software tools have been developed. Ansoft HFSS is a well known software within electromagnetic research and engineering. It is an industry-standard simulation tool for three dimensional (3-D) full-wave electromagnetic simulations [41]. HFSS utilizes 3-D full-wave frequency domain FEM to calculate the electromagnetic behavior of a model. We found HFSS an accurate tool to solve both scattering and periodic structure problems when comparing against known cases. In the next two sections two applications implemented in this software which were used in this thesis will be detailed.

5.2 Scattering Model and RCS

In DE numerical modeling of wave propagation and scattering in an unbounded media, the problem must be truncated into a bounded domain, in contrast to IE numerical methods e.g. MOM which can handle unbounded domains. In HFSS, an air box surrounding the target is usually defined which is considered as the whole computational domain. The air box must be at least a quarter of a wavelength (λ/4) away from the target at the lowest frequency. Furthermore, truncation of an unbounded domain requires appropriate boundary condition on

25

the surfaces of the truncated computational domain. Theoretically this boundary condition should be a transparent condition and hence not producing any reflection at the truncation boundary. Thus all incoming field needs to be absorbed at the boundary of computation area (air box). One such boundary condition can be provided by the perfectly matched layers (PMLs) [42] which in HFSS is constructed by artificial materials that absorb the electromagnetic waves coming across them. These materials have complex anisotropic permittivity. The thickness of the PML is critical for the solution accuracy of problem and must be adjusted to the thickness close to λ/4 at the lowest frequency [43]. The ‘radiation only’ option should be selected for PML radiation boundary.

For the excitation source of the model, an incident plane wave is assigned. There are three options for solution type in HFSS: ‘driven modal’, ‘driven terminal’ and ‘eigenmode’. For a scattering problem which is excited by a plane wave a ‘driven modal’ solution type should be used. The adapted frequency should be assigned as the highest frequency of the desired solution sweep band.

As was mentioned in Chapter 1, we use an infinite cylindrical shape to approximate the wing profile. This cylindrical assumption enables us to consider only a finite slice of the cylinder with a periodic (Master/slave)

Figure 5-1 Simulated structure in HFSS solver

26

boundary condition on the top / bottom face of the cylinder. The scattering width of the infinite cylinder is then evaluated by (1.11). Even after this cylindrical simplification the problem is still computationally heavy. The wing length in x – direction is almost 50λ at the highest frequency.

In order to reduce the calculation size of the problem, another size reduction is assumed for the model; such that only the first 15 cm of the wing front is considered in the computational domain. For such a model we need to truncate the structure. The truncation should produce as little scattered field as possible from the terminated part. The best way we found was obtained by letting the wing penetrated into the PML. To minimize the scattered field at the point which PML and metallic target touch, the tangent of the target should be perpendicular to the PML surface. The objective is to avoid a first derivative discontinuity which could enhance the scattering. It is done by using an intermediate slice between the 15% front-end part and the PML penetrating block with outer boundary represented by f (x) in Figure 5-1. This part is used to transform the tangent of the wing at 15% front end to zero when it touches the PML. The length of the intermediate part in x – direction is 4 cm. The prolongation of the model is then penetrating into the PML as shown in Figure 5-1.

Simulation of this two-dimensional structure is certainly possible in several other software, e.g. 2-D type software as well, but due to the FSS that essentially should be added to the structure, breaking the 2-dimensional symmetry, it was better to use software that can handle three-dimensional models as well.

5.3 Floquet Ports for Periodic Structures

The Floquet port in HFSS is used exclusively to analyze two-dimensional periodic structures like planar phased arrays and frequency selective surfaces. Using the Floquet port the analysis of the infinite structures is achieved by analyzing a unit cell. Master/Slave boundary is used to provide the periodic condition of the structure. The scan angle of the Master/Slave boundaries together with Floquet ports lattice phase information assign the angle of illumination [43]. The vectors a and b which defines the unit cell area are used to define a Floquet port on the top and bottom of the unit cell box as shown in

27

Figure 5-2. Only one port (on the top) and one Master/Slave boundary are shown in Figure 5-2 to illustrate the concept. The Floquet ports are used in FSS analysis and design of the planar FSS strycture in this thesis.

Figure 5-2 (a) A two dimensional periodic structure and (b) its model schematic in HFSS, the other Floquet port at the bottom and the second Master

/ Slave boundaries are hidden for clarity of the picture.

28

Chapter 6

Results

6.1 Results for Numerical Scattering Calculation

When we started the project it was not known which of the two RCSR methods described earlier would be the better one, while leaving as much space as possible for an antenna elements. It should be mentioned that several studies with larger freedom had suggested the shape optimization, see e.g. [18], [44], [45] where there are no limitation on antenna placements and aerodynamic requirements.

In this thesis, the evaluation of the complex problem of both RCSR and transparency (at 1 GHz) was split into first considering the RCSR and then the transparency for the better of the two studied models.

The 2-D RCS (scattering width) of three different cases of targets for three different angles of illumination and for both TMz and TEz polarization is shown in Figure 6-1. The first target is the reduced model of the original PEC wing with its outer surface expressed analytically by the elliptical equation (2.1); the second case is the model of the optimized PEC shape described in Chapter 2, and third is the model of the wing with Jaumann absorber as described in Chapter 3.

In Figure 6-1 we can compare the RCSR reduction for the Jaumann absorber and the shape optimized one. For the TMz polarization it is clear that the Jaumann absorber is the better one, whereas for the TEz polarization it is more unclear. To quantify these differences we count how large part of the curve is below -5db RCSR. For the TMz polarization and all three incident angles Jaumann absorber accomplishes a 5dB 2D-RCSR over 68% of the frequency band or more at the sampled points. The achieved 5dB 2D-RCSR for the TEz polarization is at least 43% of the overall frequency band. The RCSR for the TMz polarization, achieved by shape optimization, is generally smaller than the RCSR of the Jaumann absorber; whereas for the TEz polarization the RCSR obtained by two methods are comparable. Notice that there is a shift in resonant frequencies as compared with the planar and circular cylinder case. The reason

29

Figure 6-1 Comparison of 2D-RCS of the reduced model of the original wing, optimized shape and wing with Jaumann absorber, (a) TMz polarization (φi=0˚), (b) TEz polarization (φi=0˚), (c) TMz polarization (φi=10˚), (d) TEz polarization

(φi=10˚), (e) TMz polarization (φi=20˚) and (f) TEz polarization (φi=20˚)

0 2 4 6 8 10 12 14 16-35

-30

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30

of this frequency shift is the varying thickness of the Jaumann layers over the semi-elliptical surface of the wing front.

Once it was observed that the Jaumann absorber have better or comparable RCSR and in addition leave more space for the antenna, we decided to continue the studies on Jaumann absorber only to implement transparency around 1GHz.

6.2 Results for Transparency

The second part of the project was to provide transparency for the antenna protected by a Jaumann absorber radome. The antenna should operate at 1 GHz with TEz polarization (see Figure 1-2). The ordinary Jaumann structure has a metallic back surface. The radiated waves from an antenna placed beyond of this metallic surface cannot pass this metallic surface. Therefore, the metallic surface should be replaced by a surface which is partially transparent at 1 GHz for TEz polarization. However, this surface should keep as metallic behavior as possible over the frequency band 2 – 16 GHz for the TMz and TEz polarization for Jaumann absorber to be an efficient absorber. One of the solutions which would approach these conditions is a Gangbuster FSS [21] composed with a periodic infinitely long strips polarizer [21].

Figure 6-2 Two-dimensional RCS of the reduced model of the original wing, wing with Jaumann absorber and FSS wing with Jaumann absorber, (a) TMz

polarization, (b) TEz polarization

0000 2222 4444 6666 8888 10101010 12121212 14141414 16161616-35-35-35-35

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2D M

ono-

stat

ic R

CS

(dB

)

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2D M

ono-

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ic R

CS

(dB

)

31

The design of an absorber with a FSS is detailed in paper III. Here we focus on the results. It should however be noted that an ordinary Gangbuster FSS cannot be easily simulated when it is bended over a finite slice of an infinite cylinder (the wing profile) with periodic boundary condition. It is due to the lack of mirror symmetry in the ordinary Gangbuster FSS structure. To overcome this problem of periodicity we replace the ordinary Gangbuster FSS with a triangular lattice design. The triangular lattice is easy to construct both in simulation and practice, while it has almost the same characteristics as the ordinary lattice (see paper III).

The resulting design is bended to replace with the metallic surface of the wing. In Figure 6-2, the 2-D RCS of the reduced model of the original wing, the wing with Jaumann absorber and the wing with FSS backed Jaumann absorber for both polarization are shown for normal incident wave. The Jaumann absorber parameters in this case are optimized for a compromise between low reflection at 1 GHz and absorption over the remaining frequency band (see paper III). The parameters values are then: εr1 = 2.2, εr2 = 1.4, d1 = λ16.7GHz /4√ εr1, d2 = λ11.2GHz /4√ εr2, R1 = 414.3 Ω /, and R2 = 1257 Ω /. For the TEz polarization and for FSS wing with Jaumann we get a 9 dB difference in RCS at 1 GHz which is related to the low-pass characteristic of FSS and material absorption. The RCSR over the frequency band 2 – 16 GHz is slightly improved for the FSS backed Jaumann absorber with respect to the regular Jaumann absorber case. It is expected that this 9 dB reflection reduction provides transparency around 1 GHz.

6.3 High loss of FSS-Backed Jaumann Absorber and

possibilities

It was observed in the previous section that we got a low reflection at antenna operation frequency (1 GHz). However, a low reflection coefficient does not necessarily provide a high transmission in a lossy structure. For the optimized values of the FSS-backed Jaumann structure that were described in Section 5.2, we get 43% loss at 1 GHz. This amount of loss is not appropriate for good antenna performance. Furthermore, for a high power intensity antenna, this amount of loss can cause physical damages on the radome like melting in the

32

dielectric radome layers. This loss at 1 GHz cannot be decreased while keeping the specific absorption bandwidth with the above described FSS Jaumann.

The cause of the absorption is the lossy resistive sheets. One solution which could reduce the losses is to make the sheets as a low-pass FSS using the Circuit Analog (CA) absorbers [21]. The CA absorbers are made of sheets that provide not only resistivity but also reactive characteristics. It is shown in [46] and [47] that a pure capacitive sheet absorber improves the absorption bandwidth and also reduces the thickness of absorber with respect to an ordinary Jaumann absorber. Moreover, it is simple to synthesis and fabricate a capacitive sheet by periodic patch of resistive sheets [47], [48]. Such capacitive parameters are usually used for absorbing bandwidth extension or thickness reduction of the absorber [47]; however, they can also be used to achieve lower loss at the antenna operation frequency in our structure.

The equivalent circuit model of a two layers capacitive Jaumann absorber is shown in Figure 6-3. An optimization on R and C values while keeping the same values for permittivity and thickness of layers as earlier Jaumann case provide a significant reduction of the losses. Losses to less than 10% as well as improvement of absorption bandwidth for normal incidence have been achieved. One of the disadvantages of the CA absorbers is the difficulty of fabrication. Another as of yet unexamined problem is the behavior of the CA absorbers on curved surfaces. It is expected that the performance will reduce somewhat due to the presence of different inter-element coupling. This part of the work is still going on.

Figure 6-3 Circuit model for general two layers capacitive Jaumann absorber

33

Chapter 7

Conclusion

The thesis presented two methods for RCSR over the frequency band 2-16 GHz, Shaping and Jaumann absorber, applied to an aircraft wing front profile enclosing an antenna array. It was shown that the Jaumann absorber has a better RCSR performance than the one parameter shape optimization solution. Furthermore, using the Jaumann absorber as RCSR means more space is allowed for antenna placement inside the wing. The Jaumann absorber was designed first for a planar case. It was observed that applying such a planar design of Jaumann absorber to a circular cylindrical shape, the main absorption characteristic features remain unchanged. Based on this preservation of the Jaumann absorber characteristics under this geometrical change we applied the design to the semi-elliptical surface of the wing. A resonant frequency shift was then observed in the semi-elliptical Jaumann absorber as compared to the planar and circular cases, which is due to variations in thickness of the Jaumann layers over the semi-elliptical surface.

The next part of the thesis was concerned with transparency of the above designed radome. It is required that the antenna enclosed by the radome can radiate through it. The main blocking element, the PEC sheet, in the Jaumann absorber was replaced with a frequency selective surface which is partially transparent at the antenna operation frequency (1 GHz). However, it must be nearly totally reflective over the remaining frequency band to maintain the Jaumann absorber efficient. The proposed FSS is a triangular lattice Gangbuster together with a polarizer. This design is a mirror symmetric which is an advantage when it is applied to a cylindrical structure using periodic boundary condition. An optimization was done for the planar FSS backed Jaumann absorber to achieve a desirable performance. The achieved design was then applied to the wing front profile. The new FSS back Jaumann absorber design not only provides a partial transparency for the radome but also shows an improvement in radar cross section compare with ordinary Jaumann absorber on the wing front profile. However, the FSS back Jaumann absorber suffers from a high transmission loss. For the planar case a 43% loss was observed. The design can be modified using circuit analogue absorber to reduce the transmission loss. Using a capacitive circuit absorber the transmission loss

34

is reduced to less than 10%. The implementation and integration of such absorbing layers will be considered in future work.

35

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