Application Article | Open Access

Lina Moustafa, Bernard Jecko, "Bandwidth Improvement of EBG Resonator Antennas Using Double-Layer FSS", *International Journal of Antennas and Propagation*, vol. 2008, Article ID 315052, 5 pages, 2008. https://doi.org/10.1155/2008/315052

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

**Academic Editor:**Lance Griffiths

#### 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.

#### 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 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 is the reflection phase of the resonant cavity upper wall. is the reflection phase of the resonator lower wall. In general, EBG resonator
design has metallic ground as the lower wall, and
is then equal to . 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 of . Usually, the phase decreases linearly with frequency, while 2*kh* 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 ().

For a given
value of , the operating bandwidth can be enlarged by minimising , this can be realised by
reducing the
curve slope in a frequency range as wide as possible and by inverting the phase
variation versus frequency. The linear increase of
is more advantageous in terms of resonator bandwidth. While 2*kh* increases with frequency,
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 of *d*. Low
layer FSS1 is a stop band FSS with square loop elements. The unit cell has
outer length mm and inner length mm. They are
periodically arranged in *x*- and *y*-directions with a periodicity of 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 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 of FSS1 is
positive () 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 length mm and inner length mm (see Figure 1). Square loops inside the grid have mm and mm. Reflectivity of the FSS is studied; the reflection coefficient magnitude 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 of the surface is negative () and it decreases with frequency (see Figure 3).

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 of *d* calculated using (1) with (, );
this behaviour is the result of a resonance installed between the FSS layers:*d* is thus equal to 4 mm at
the operating frequency. and 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 Figures
2 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
(the reflection phase of the double-layer FSS),
(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 ( 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.

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 function 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. 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 and are,
respectively, the transmission and reflection coefficients of the double-layer
FSS, is the wave vector, *h* is resonator height.

As we can see in Figure 5, the formed resonator has a pass- band filtering function in a wide range of frequencies limited by GHz and 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).

#### 4. Antenna Performance

The optimised FSSs separated by a distance of mm are used to design the antenna upper wall. They are placed at a distance of mm from a perfect mirror. Formed resonator is fed by a single patch source (see Figure 6). Lateral size of the antenna is c (about at 5 GHz).

Simulations of the whole antenna have been carried out using the FDTD method. The directivity of the prototype is shown in Figure 7. 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.

Radiation patterns in the E- and H-plane are shown at the centre- and near-edges frequencies of the operating bandwidth (see Figures 8, 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.

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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#### Copyright

Copyright © 2008 Lina Moustafa and Bernard Jecko. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.