# Bandwidth Improvement of EBG Resonator Antennas Using Double-Layer FSS

Authors: Lina Moustafa; Bernard Jecko
Journal: International Journal of Antennas and Propagation
 (2008)

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## Abstract

A double-layer frequency selective surface (FSS) is proposed as a means to enhance the bandwidth of an electromagnetic band gap (EBG) resonator antenna. Due to its inverted reflection phase variation and its wide selectivity bandwidth, the structure used in the radiating wall of the resonator allows increasing the radiating bandwidth of the last one. The resonator is fed by a patch feeding source placed inside the cavity at the proximity of its metallic ground. The antenna bandwidth is significantly improved by virtue of employing the double-layer FSS. Modelled results of an antenna working at 5 GHz are shown.


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## Body

## 1. Introduction

In the past few years, new solutions that combine directivity and simple feeding mechanism
have been proposed to design compact antennas. Dielectric or metallic arrays
have been placed over a perfect electric ground. EBG resonator antennas have
been formed [1–4]. While
important gain values have been realised, the antenna profile has been kept
compact (close to the half wavelength). One drawback of this system is its
narrow bandwidth; only one frequency and a limited range around this central
frequency satisfy the resonant model. Recent works presented by Feresidis and Vardaxoglou [5] have
demonstrated a bandwidth enhancement of a resonator
antenna, in which the antenna thickness was equal to the operating wavelength.
They used combined FSS to create the
cavity radiating wall. In this work, we propose improving the bandwidth of a
λ/2 EBG resonator antenna using double-layer FSS as the cavity radiating wall.
The design of used frequency selective surfaces is first discussed. Second, the
optimised resonant structure that allows improving bandwidth of printed
microwave antennas is described.


## 2. Ebg Resonator Principle

EBG resonator antennas are good candidates to answer compactness and high-directivity
requirements of many applications. These antennas are easy to be fabricated
since they use dielectric or metallic slabs periodically arranged over a
grounded feeding source. Their compactness can be even more improved if the
cavity walls design includes frequency selective surfaces [6]. Whether the
radiating wall material is dielectric or metallic, a simple optical ray model
can be used to depict the cavity modes in the normal direction. If we consider
multiple reflections of the wave emitted by the feed, a resonance is achieved
when rays projected through the radiating aperture have equal phases. The
equation determining the resonance condition for a maximum of directivity in
the normal direction is(1)φup+φlow−2kh=2nπ,n=0,1,2,….φup  is the reflection phase of the resonant cavity upper wall. φlow is the reflection phase of the resonator lower wall. In general, EBG resonator
design has metallic ground as the lower wall, and φlow
is then equal to π. h is the resonant height of the cavity; k is the
propagation constant. This equation underlines the presence of a resonance in
the z-direction.If the wavelength is fixed, the height is determined in function ofφup. Usually, the phase decreases linearly with frequency, while 2kh increases
and in consequence (1) is satisfied for only one frequency and a narrow band
around this frequency.If (1) is verified for a wide frequency band, the general behaviour of the structure
should be also wideband. To answer the wideband requirement, the phase of the
resonator upper wall should be the following φup=2kh (n=0).For a given
value ofh, the operating bandwidth can be enlarged by minimising φup(f)−2kh, this can be realised by
reducing the φup(f)
curve slope in a frequency range as wide as possible and by inverting the phase
variation versus frequency. The linear increase of φup(f)
is more advantageous in terms of resonator bandwidth. While 2kh increases with frequency, φup(f)
increases too, and (1) can be satisfied in a very wide frequency band.


## 3. Cavity Walls Choice

Based on the above
analysis, the lower wall of the resonator is left unchanged while its upper
wall is replaced by a double-layer FSS. It has been shown that combining FSS
offers original reflection properties and particularly allows inverting the
phase slope [5].


### 3.1. Double-Layer Fss Design

The optimised resonator
upper wall is composed of two layers of FSS separated by a distance ofd. Low
layer FSS1 is a stop band FSS with square loop elements. The unit cell has
outer length Lo1=26 mm and inner length Li1=19 mm. They are
periodically arranged in x- and y-directions with a periodicity of P=28 mm. A
study of the FSS reflectivity has been done, and reflection coefficient
magnitude and phase are shown in Figures 2 and 3. As illustrated in Figure 2,
the reflection coefficient magnitude |R1| varies between a value of 0.85 and 1 in the operating frequency
band around 5 GHz (4.5–5.5 GHz), and the
reflection phase φ1 of FSS1 is
positive (150°~170°) and it
decreases with frequency (see Figure 3).High layer FSS2
is a pass band FSS made of a metallic grid fitted out with square loops. The
grid unit cells have outer lengthLo2=28 mm and inner length Li2=26 mm
(see Figure 1). Square loops inside the grid have Lo3=15 mm and Li3=13 mm.
Reflectivity of the FSS is studied; the reflection coefficient magnitude |R2|
varies between a value of 0 and 0.55 in the frequency band of interest
(4.5 GHz–5.5 GHz) (see Figure 2), and the reflection phase φ2 of the surface is negative (−125°~−90°) and it decreases with frequency (see Figure 3).Figure 1
FSS1 and FSS2 unit cells geometry.Figure 2
Reflection coefficient magnitude.Figure 3
Reflection coefficient phase.Association of
FSS1 and FSS2 can produce inverted reflection phase slope, if the reflection
magnitudes of FSS layers have opposite variation with frequency. In addition,
to provide this particular phase shape, FSS1 and FSS2 have to be separated by a
distance ofd calculated using (1) with (φlow=φ1, φup=φ2);
this behaviour is the result of a resonance installed between the FSS layers:(2)ϕ1+ϕ2−2kd=0.d is thus equal to 4 mm at
the operating frequency. φ1 and φ2 have to be almost equal and of opposite sign to achieve a value of d as small
as possible.Reflectivity
of the double-layer FSS has been analysed. The examination of the double-layer
FSS reflection coefficient is necessary to determine the appropriate height
between the last one and the metallic ground to form the resonator.As shown in Figures2 and 3, the behaviour in terms of reflection of the double-layer FSS is
remarkable; it has the minimum value of magnitude and an increasing phase in
the frequency band around 5 GHz. The reflection coefficient magnitude varies
between 0.55 and 1 in the analysis band; it is equal to 0.55 at 5 GHz and increases by moving away from
this frequency. The resonator formed between the studied material and the
ground plane is more selective and less wideband when the reflection
coefficient tends to 1. The reflection phase has a particular shape in the
frequency range 4.8–5.4 GHz. In this
band, the phase rises from 80° to 100° and it is equivalent to a phase excursion
of 20° in a band of 12%.Consequently,
to obtain increasing reflection phase, double frequency selective surface
layers are needed and they should be combined with appropriate separating
distance calculated in a manner to create a resonance between layers. The low
layer determines in part the reflectivity of the final structure (its
reflection coefficient magnitude) and a resonant layer with low reflectivity,
and a negative phase is needed to realise compact resonator upper wall. The
resonance of the high layer is chosen to be lower or higher than the operating
frequency but not at this frequency. The high layer can then be totally transparent.Geometry of
the upper wall unit cell is chosen in a manner to have reasonable antenna
directivity value (around 15 dBi) at 5 GHz. This value is the function of a double-layer
FSS reflection coefficient magnitude and thus of each layer reflection
magnitude. A directivity value of 15 dBi corresponds to a 0.55 total reflection
magnitude value.


### 3.2. Resonator Transfer Function

The material studied above
can be now used to realise an EBG resonator. The double-layer FSS is employed as
the resonator upper wall. The resonant height is calculated using (1) (see Figure 4) with φup
(the reflection phase of the double-layer FSS), φlow
(the reflection phase of the metallic ground), and h (the resonant
height). As we can notice, there is a frequency range for which h is
almost constant (h=27 mm). The resonant height is maintained constant in a
frequency range of about 20% around 5 GHz. Equation (1) is satisfied in a wide
band of frequencies.Figure 4
Height of the EBG resonator.Once the
height is determined, it is possible to predict the operating bandwidth of the
antenna. An approximate value can be found by solving (3). It can be calculated
at −3 dB of maximum value of selectivity.The functionS(f) characterises the frequency response of the EBG structure. Its calculation
allows the estimation of the resonator intrinsic operating bandwidth without
taking into consideration the quality of the feeding source. S(f) can be
calculated by considering the sum of the contributions outgoing from the upper
wall while exciting the resonator by a plane wave source. This takes in
consideration the multiple paths of the electromagnetic waves between the EBG
material and the metallic plane. By using Trentini model, for fixed polarisation and normal
incidence, we get (3)S(f)=T(f)exp(−jk0h)1+R(f)exp(−j2k0h).T(f) and R(f) are,
respectively, the transmission and reflection coefficients of the double-layer
FSS, k0 is the wave vector, h is resonator height.As we can see
in Figure5, the formed resonator has a pass- band filtering function in a wide
range of frequencies limited by flow=4.6 GHz and fup=5.7 GHz
and equivalent to 22% of band. It is the resonator bandwidth that can likely be
obtained using the studied double-layer FSS. The shape of the resonator antenna
directivity is not the same as for its selectivity because the source
contribution is not determined in (3).Figure 5
Selectivity of the
resonator for normal incidence and various resonant height values.


## 3.1. Double-Layer Fss Design

The optimised resonator
upper wall is composed of two layers of FSS separated by a distance ofd. Low
layer FSS1 is a stop band FSS with square loop elements. The unit cell has
outer length Lo1=26 mm and inner length Li1=19 mm. They are
periodically arranged in x- and y-directions with a periodicity of P=28 mm. A
study of the FSS reflectivity has been done, and reflection coefficient
magnitude and phase are shown in Figures 2 and 3. As illustrated in Figure 2,
the reflection coefficient magnitude |R1| varies between a value of 0.85 and 1 in the operating frequency
band around 5 GHz (4.5–5.5 GHz), and the
reflection phase φ1 of FSS1 is
positive (150°~170°) and it
decreases with frequency (see Figure 3).High layer FSS2
is a pass band FSS made of a metallic grid fitted out with square loops. The
grid unit cells have outer lengthLo2=28 mm and inner length Li2=26 mm
(see Figure 1). Square loops inside the grid have Lo3=15 mm and Li3=13 mm.
Reflectivity of the FSS is studied; the reflection coefficient magnitude |R2|
varies between a value of 0 and 0.55 in the frequency band of interest
(4.5 GHz–5.5 GHz) (see Figure 2), and the reflection phase φ2 of the surface is negative (−125°~−90°) and it decreases with frequency (see Figure 3).Figure 1
FSS1 and FSS2 unit cells geometry.Figure 2
Reflection coefficient magnitude.Figure 3
Reflection coefficient phase.Association of
FSS1 and FSS2 can produce inverted reflection phase slope, if the reflection
magnitudes of FSS layers have opposite variation with frequency. In addition,
to provide this particular phase shape, FSS1 and FSS2 have to be separated by a
distance ofd calculated using (1) with (φlow=φ1, φup=φ2);
this behaviour is the result of a resonance installed between the FSS layers:(2)ϕ1+ϕ2−2kd=0.d is thus equal to 4 mm at
the operating frequency. φ1 and φ2 have to be almost equal and of opposite sign to achieve a value of d as small
as possible.Reflectivity
of the double-layer FSS has been analysed. The examination of the double-layer
FSS reflection coefficient is necessary to determine the appropriate height
between the last one and the metallic ground to form the resonator.As shown in Figures2 and 3, the behaviour in terms of reflection of the double-layer FSS is
remarkable; it has the minimum value of magnitude and an increasing phase in
the frequency band around 5 GHz. The reflection coefficient magnitude varies
between 0.55 and 1 in the analysis band; it is equal to 0.55 at 5 GHz and increases by moving away from
this frequency. The resonator formed between the studied material and the
ground plane is more selective and less wideband when the reflection
coefficient tends to 1. The reflection phase has a particular shape in the
frequency range 4.8–5.4 GHz. In this
band, the phase rises from 80° to 100° and it is equivalent to a phase excursion
of 20° in a band of 12%.Consequently,
to obtain increasing reflection phase, double frequency selective surface
layers are needed and they should be combined with appropriate separating
distance calculated in a manner to create a resonance between layers. The low
layer determines in part the reflectivity of the final structure (its
reflection coefficient magnitude) and a resonant layer with low reflectivity,
and a negative phase is needed to realise compact resonator upper wall. The
resonance of the high layer is chosen to be lower or higher than the operating
frequency but not at this frequency. The high layer can then be totally transparent.Geometry of
the upper wall unit cell is chosen in a manner to have reasonable antenna
directivity value (around 15 dBi) at 5 GHz. This value is the function of a double-layer
FSS reflection coefficient magnitude and thus of each layer reflection
magnitude. A directivity value of 15 dBi corresponds to a 0.55 total reflection
magnitude value.


## 3.2. Resonator Transfer Function

The material studied above
can be now used to realise an EBG resonator. The double-layer FSS is employed as
the resonator upper wall. The resonant height is calculated using (1) (see Figure 4) with φup
(the reflection phase of the double-layer FSS), φlow
(the reflection phase of the metallic ground), and h (the resonant
height). As we can notice, there is a frequency range for which h is
almost constant (h=27 mm). The resonant height is maintained constant in a
frequency range of about 20% around 5 GHz. Equation (1) is satisfied in a wide
band of frequencies.Figure 4
Height of the EBG resonator.Once the
height is determined, it is possible to predict the operating bandwidth of the
antenna. An approximate value can be found by solving (3). It can be calculated
at −3 dB of maximum value of selectivity.The functionS(f) characterises the frequency response of the EBG structure. Its calculation
allows the estimation of the resonator intrinsic operating bandwidth without
taking into consideration the quality of the feeding source. S(f) can be
calculated by considering the sum of the contributions outgoing from the upper
wall while exciting the resonator by a plane wave source. This takes in
consideration the multiple paths of the electromagnetic waves between the EBG
material and the metallic plane. By using Trentini model, for fixed polarisation and normal
incidence, we get (3)S(f)=T(f)exp(−jk0h)1+R(f)exp(−j2k0h).T(f) and R(f) are,
respectively, the transmission and reflection coefficients of the double-layer
FSS, k0 is the wave vector, h is resonator height.As we can see
in Figure5, the formed resonator has a pass- band filtering function in a wide
range of frequencies limited by flow=4.6 GHz and fup=5.7 GHz
and equivalent to 22% of band. It is the resonator bandwidth that can likely be
obtained using the studied double-layer FSS. The shape of the resonator antenna
directivity is not the same as for its selectivity because the source
contribution is not determined in (3).Figure 5
Selectivity of the
resonator for normal incidence and various resonant height values.


## 4. Antenna Performance

The optimised FSSs separated by a distance ofd=4 mm are used to design the
antenna upper wall. They are placed at a distance of h=27 mm from a
perfect mirror. Formed resonator is fed by a single patch source (see Figure 6).
Lateral size of the antenna is 21*21 cm2 (about 3.5λ*3.5λ at 5 GHz).Figure 6
Schematic design of the FSS layers and the resonator antenna formed
between the double-layer FSS and the ground.Simulations of
the whole antenna have been carried out using the FDTD method. The directivity
of the prototype is shown in Figure7. A maximum directivity value of about 15 dBi
has been obtained at 5.5 GHz, the directivity bandwidth at −3 dB of maximum
directivity is equal to 1.3 GHz (about 25% from 4.2 GHz to 5.5 GHz). The
directivity rises quickly from 12 dB at 4.2 GHz to attend 15 dB at the cut
frequency 5.5 GHz, frequency after which the axial directivity decreases and the
radiation patterns deflect. A bandwidth enhancement of about 12% in comparison
to classical EBG antenna designs, with same value of directivity, has been
obtained.Figure 7
Directivity versus frequency.Radiation
patterns in the E- and H-plane are shown at the centre- and near-edges
frequencies of the operating bandwidth (see Figures8, 9, and 10). Side lobe levels
are below −20 dB in both planes, they only rise to −15 dB at the upper end
frequencies of the band and particularly in the H-plane.Figure 8
Radiation patterns at the lower end frequency (4.5 GHz) of
the operating bandwidth in the E- and H-plane.Figure 9
Radiation patterns at the
central frequency (5 GHz) of the operating bandwidth in the E- and H-plane.Figure 10
Radiation patterns at the
upper end frequency (5.5 GHz) of the operating bandwidth in the E- and H-plane.We can underline that the
directivity bandwidth is in accordance with the bandwidth determined using the
resonator selectivity function (22%) even the shape is not exactly the same.
The directivity takes into account the effect of the source. It explains the
difference with the frequential selectivity that only predicts the frequential
response of the resonator


## 5. Conclusion

An optimised design of a
broadband EBG resonator antenna using double-layer FSS has been presented. The double-layer FSS has replaced the classical
upper wall of the resonator design. Combining FSS with particular separating
distance has allowed inverting the reflection phase variation with frequency,
thus enlarging the selectivity of built resonator. Formed EBG resonator antenna
has wider bandwidth than classical EBG resonator antenna design. A 12% of
bandwidth enhancement has been realised.



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*Source: 315052-2008-12-30.xml*