Small-Size Wide-Band Low-Profile “Pixel Antenna”: Comparison of Theoretical and Experimental Results in L Band

This paper presents a small (≈λ/2 × λ/2) low-profile (λ/10) planar antenna built to work on a very large frequency band (≥40%) for applications in Telecom, Radar, IoT, etc. This antenna is called a “Pixel Antenna” because it was first used as a pixel in an agile beam radiating surface. In this paper, the pixel antenna is used alone to design multiband or wide-band antennas keeping the same radiation pattern and polarization throughout the band. The working principle used to design the Pixel Antenna is deduced from the well-known EBG (electromagnetic band gap) antenna in its low-profile version which already has a bandwidth close to ≈20%. The aim of this present work is to double this bandwidth by simultaneously feeding two modes of the original EBG material. The theoretical and experimental results are compared for an L band application, exhibiting bandwidth from 1 GHz to 1.52 GHz (41%). In addition, good radiation patterns of pixel antenna stay constant over the entire useful band without any degradation of the antenna performance. This proposed antenna design can be used to obtain wide bandwidth for any chosen frequency band (S band, X band, C band, etc.) using frequency scaling.


Introduction
In the electromagnetic domain today, applications like telecommunications, radar, IoT, and so on need antennas working on a very large frequency band able to include both Tx and Rx links, to perform frequency hopping, frequency sweeping techniques, pulse generation, and so on.
In the state-of-art wide-bandwidth applications, traveling wave antennas are able to reach 100% bandwidth, but with large dimensions in comparison to the operating wavelength. On the other hand, resonant antennas like patch antennas are usually limited to around 20% bandwidth.
Extensive research has been carried out in the past two to three decades in an attempt to increase the bandwidth of planar antennas. ese bandwidth enhancement techniques include use of frequency selective surface (FSS) [1,2], use of low dielectric substrate, use of multiple resonators, use of thicker substrate [3], employing stacked configuration [4], and use of slot antenna geometry [5,6]. Lolit Kumar Singh et al. [7] proposed a T-slot rectangular patch antenna with an impedance bandwidth of 25.23%. Aneesh et al. [8] demonstrated that an S-shaped Microstrip patch antenna can achieve a bandwidth of 21.62%. Mulgi et al. [9] proposed a wideband gap-coupled slot rectangular microstrip array antenna with an impedance bandwidth of 26.72%. Khanna and Srivastava [10] designed a square patch antenna with modified edges and square fractal slots with a bandwidth of 30%.
To further improve the bandwidth of the antenna, i.e., to attain a bandwidth higher than 30%, while respecting the small size, the EBG antenna is the best candidate to increase the bandwidth. A generic EBG antenna consists of a cavity created by a frequency selective surface (FSS) at the top and a metallic ground plane at the bottom. e energy is coupled to the cavity using a feeding antenna such as a dipole, slot, or patch [11,12].
e EBG antenna has aroused a growing interest among researchers in the last few years due to its capacity to enhance the directivity of a single source, its potentiality in beam forming, its dual-band frequency, bandwidth enhancement, and its polarization diversity [13][14][15][16]. e low-profile pixel antenna, developed from the EBG antenna [17], has a bandwidth limitation of 20%, since it was fed using only one EBG mode. e novelty of this research work lies in the fact that the dimensions of the pixel antenna are very small compared to those of the EBG antenna and similar to the dimension of the patch antenna: (λ/2)x(λ/2) with a λ/10 height (approximately), but the performances in terms of bandwidth are quite different. is is because EBG modes inside the cavity are quasi TEM modes with no variations of such modes in the radial direction.
is paper presents a new technique to increase the frequency band by designing a low profile "Pixel Antenna." e Pixel Antenna is characterized computationally by the commercially available electromagnetic simulation CST Microwave studio software.

The "Pixel Antenna" Concept
e high-gain EBG antenna [17], from which the pixel is deduced, is a simple one; a semireflective material (usually FSS) located above a ground plane. e working mode of this structure [17] shows a resonance (f 0 ) in z direction ( Figure 1) like in a Fabry-Perot resonator characterized by: where R sup , R inf , ϕ sup , and R inf are the magnitudes and phases of the reflection coefficients of the upper wall (FSS structure) and of the lower wall (ground plane), respectively. So, normally this height is around λ 0 /2 [17] because the reflection phase of the FSS material usually is near +π in the entire frequency band and the reflection phase of the ground plane is equal to π. For frequencies higher than "f 0 ," leaky Wave modes and other modes propagate in the structure and the axial directivity evolution as a function of the frequency [17] decreases strongly for f ≥ f 0 . e frequency band of interest to obtain a directive antenna is characterized by f ≤ f 0 . In this frequency range, the axial directivity of any EBG antenna decreases slowly with the decrease in frequency due to the vanishing behavior of the EM field in the "r" direction inside the structure [17].
If a low-profile EBG antenna [18], characterized by a negative phase of the upper partially reflecting surface [1], is used to design the pixel, the bandwidth highly increases because the quality factor (2) of the resonator strongly decreases [18]. is approach gives a frequency band up to 20% with a suitable feeding technique.
e "pixel antenna" [19] is built from the previous EBG large-size low-profile antenna (Figure 2(a)) by introducing walls (Figure 2(b)) around the feeding probe (usually a patch) [17]. Figure 3(a) shows the pixel structure with the metallic walls fed by the square patch inside the cavity ( Figure 3(b)). Due to the radially vanishing mode, the surface EM field is almost constant on the top of the "pixel antenna" (Figure 3(c)), thus generating a directive radiation pattern [19].
In the following example, the upper semireflective surface is a dielectric slab with FSS pattern. R sup (f ) and ϕ sup (f ) are given in the

Ultra Wide Band Solution
e fundamental objective of this paper is to at least double the previous results (≈20%) by considering a "Pixel Antenna" working on two or more EBG modes.
As mentioned earlier in Section 2, the "pixel antenna" (and also the original EBG antenna [17]) is designed from an EBG material slab built with 2 parallel FSS [17]; a CCE plane has been introduced in the symmetrical plane and the structure is transversally limited by walls.

Feeding Procedure.
e working frequency band for the pixel antenna, deduced from the original EBG antenna, is limited by the "f 0 " frequency defined previously in Section 2.
en, for wide bandwidth applications, the central frequency f c of the expected band is chosen away from this value to have a wide bandwidth not limited by the presence of leaky waves. All the geometrical characteristics of the antenna can be written as a function of the wavelength λ c corresponding to this frequency ( Figure 5) and to obtain a 40% bandwidth, the antenna S 11 parameter must be less than − 10 dB between the two frequencies 0.8λ c and 1.2λ c .
A patch antenna probe used to feed the 2 modes simultaneously is introduced in the structure as shown in patch antenna. For example, for such optimizations, consider the S 11 parameter and impedance evolutions (Figure 6(a)) as a function of the frequency for different patch lengths. When the patch length is varying, the 2 EBG modes are more or less excited. A good compromise is obtained when the length of patch is 0.29λ c .
It can be observed in another optimization of the resonance frequency versus the height of the cavity, as shown in Figure 6(b), that the second and third resonance frequencies are very sensitive to the variation in the heights of cavity, and it is also seen that we can shift both the second and third resonances towards the first resonance frequency.   It is important to verify that the pixel antenna behaviour remains the same for all the frequencies of the band by showing the electric field cartography on radiating surface (Figure 7) for some frequencies. A uniform radiation surface is obtained on the roof of the pixel antenna generating axial gaussian beams on wide frequency band, approximately 40%.

Radiation Patterns.
As for EBG antennas [17,18], the directivity of the antenna and the intrinsic IEEE gain are nearly the same. e difference between the directivity and the IEEE gain is due to the small losses in the dielectric substrate and their frequency evolution (Figure 8) smoothly decreases due to the vanishing effect in the radial direction.
is behaviour introduces very wide radiating bandwidth which is limited for high frequencies by the "f 0 " given in (1) corresponding to the emergence of the leaky wave. e antenna is fed by a 50 Ω coaxial cable. As mentioned before, a probe (patch antenna equivalent to a magnetic dipole) is introduced on the ground plane in the middle of the structure (Figure 3), where the impedance of the EM field is near 50 Ω for both the EBG modes. e realized gain vs frequency band (Figure 8, blue curve) is then limited only by the magnetic dipole emission for low frequencies and by the leaky waves for high frequencies. Consequently, the realized gain exhibits a very large bandwidth (nearly ≈40%).

Theoretical and Experimental Results Comparison
To compare the theoretical results with the experimental ones, a frequency band between 1 GHz and 1.5 GHz was chosen.  Figure 6: (a) S11 parameter evolution vs frequency (theoretical patch resonances when the patch is alone are positioned on the frequency axis when the patch is alone), (b) S11 parameter evolution vs frequency for the height of cavity using patch length (Lpatch) excitation � 0.295λ c .

Manufactured Structure.
Following the geometrical specifications given in Section 3.1, a pixel antenna was designed and manufactured to work between 1 GHz and 1.5 GHz (Figure 9). Because of the wide thickness of the dielectric slab supports, two bulks of PolyEther-Ether-Ketone "PEEK" substrates were used. e metallic patch and the metallic FSS patterns were inserted in these substrates.

S-Parameters Comparison.
e theoretical and experimental S 11 parameter evolution as a function of the frequency is shown in Figure 10. Both theoretical and experimental results exhibit a wide bandwidth larger than 40%.

Realized and Experimental Gains Comparison.
e theoretical and experimental maximum realized gains vs frequency are compared in Figure 11. e results are in good agreement.
eoretical and experimental patterns are also very similar for all the frequencies of the band; Figure 12, obtained for the central frequency f c , illustrates this behaviour. Figure 13 shows the measured normalized E-plane radiation pattern of the proposed antenna at different     frequencies. ere is good agreement between the simulated and measured radiation patterns at different frequencies.

Conclusion
A new kind of antenna called "Pixel Antenna" is introduced in this paper. is antenna is characterized by a very wide frequency bandwidth up to 40%. It has a stable radiation pattern and polarization across the entire band in both linear and circular polarizations [20][21][22]. Besides the square-shaped surface, the antenna surface can also assume regular shapes like rectangular, circular, trapezoidal, and so on [23].
is antenna can either be used alone or connected to other pixel antennas to build a large radiating surface with a high gain [24], in which case it is called "ARMA" (agile radiating matrix antenna) antennas [19].

Data Availability
Previously reported data were used to support this study, and these prior studies are cited at relevant places within the text as references. International Journal of Antennas and Propagation 7