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Article

Tri-Band Bidirectional Antenna for 2.4/5 GHz WLAN and Ku-Band Applications

by
Suthasinee Lamultree
1,
Wutthipong Thanamalapong
1,
Sitthichai Dentri
2,* and
Chuwong Phongcharoenpanich
3
1
Department of Electronics and Telecommunication Engineering, Faculty of Engineering, Rajamangala, University of Technology Isan Khonkaen Campus, Khonkaen 40000, Thailand
2
Department of Electronics Engineering Technology, College of Industrial Technology, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand
3
Department of Telecommunications Engineering, School of Engineering, King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, Thailand
*
Author to whom correspondence should be addressed.
Appl. Sci. 2022, 12(12), 5817; https://doi.org/10.3390/app12125817
Submission received: 10 May 2022 / Revised: 3 June 2022 / Accepted: 6 June 2022 / Published: 8 June 2022

Abstract

:
A compact tri-band, low profile, and lightweight antenna is proposed for 2.4/5 GHz WLAN and Ku-band applications. The antenna geometry was a radiating rectangular patch surrounded by a wide circular slot with an inverted-L strip connected to one side of the slot. It was mounted on a copper layer of a single side FR4 substrate with a dielectric constant of 4.3 and a height of 1.6 mm. It was fed by a 50-Ω coplanar waveguide. This design was very compact (40 × 40 × 1.6 mm3). Simulated and actual measurements of an antenna setup in the laboratory verified that the antenna’s bidirectional radiation pattern completely covered the three transmission bands: 2.4–2.485 GHz, 5.15–5.825 GHz and 13.4–17.7 GHz with less than 10-dB return loss and maximum gains of 2.35 dBi, 4.41 dBi and 4.71 dBi, respectively. Wireless communication for the self-navigated vehicle, for one example, is fully supported by this single antenna.

1. Introduction

Recently, compact, multi-functionality, multi-band antennas have been in rising demand due to rapidly expanding wireless communication applications [1,2,3,4,5,6,7,8]. This kind of antenna is more economical for today’s multi-band wireless applications. Some compact printed antennas have already been designed to realize multi-band operations [1,2,3,6,7,8,9,10,11,12,13,14,15,16,17,18,19]. Various effective approaches have been applied to obtain multi-band characteristics, such as metamaterial [6,7], multi-radiating components [7,14,16], cutting slots [1,2,3,9,11,12], employing parasitic coupling elements [11,13,15], modified fed line [13,15], defected ground structure, adding slot and meander line [10,11,17,18,19]. In [20], a modified fork-shaped strip was used in a multiband antenna and covered 2.4/5.2/5.8 GHz WLAN and 3.5 GHz WiMAX bands. Additionally, dual L-shaped parasitic planes were also inserted at the bottom of the FR4 substrate to provide 3.5 GHz WiMAX band coverage. For another technique in [21], the cavity antenna with artificial magnetic conductor metamaterial was used to obtain a dual-band with a 15.2/18.8-dBi high-gain and unidirectional pattern. In [22], a bandpass filter was developed using step-impedance resonator with a first four resonance electrical lengths and a strip line. In [23], a meander line and inverted-L were incorporated into a monopole antenna to generate a dual-band operation. In [24], the also author proposed to reduce the space of the convenient to integrate the antenna with other microstrip circuits printed, in which the tri-band was generated by adjusting the u-slot shaped and two bridge elements of the antenna. For using the technique in [25], the Cassegrain circularly polarized antenna is appropriately located along the horizontal axial in order to observe the high frequency microwave, which is then downconverted and channelized by a 35–40 GHz analog front end.
For wireless communication in some specific service areas such as on the street, highway, skywalk, corridor, tunnel, and sky train or subway stations, bidirectional radiation pattern is most desirable [18,19,26,27,28,29,30]. Many techniques have been proposed to achieve bidirectional propagation antenna. For an example, rings of various shapes are employed to induce more propagation in the forward and backward directions. For another example, two elements of unidirectional antennas can be combined. Other examples are modification of the ground plane of a double-sided printed circuit board, addition of coupling parasitic components, and construction of the fractal antenna with a configurable pattern.
This study was a design and development of a tri-band bi-directional antenna, combining a rectangular patch with a wide-circular slot (WCS) and an inverted-L strip antenna, covering three frequency ranges: 2.4–2.484 GHz for 2.4 GHz WLAN, 5.15–5.825 GHz for 5 GHz WLAN and 13.4–17.7 GHz for Ku-band communication. With its compact size, the operating covered three transition bands, which is its advantage. Therefore, the proposed antenna could be applied in the urban areas where the outdoor movement was required to receive signals from WLAN towers and satellites. Nonetheless, the proposed antenna could be a part of array elements, since a very high gain antenna was required for the satellite communications. The proposed antenna theoretical design parameters were initially calculated using the design equations presented in Section 2. Then, with the CST microwave studio [31], simulation was performed using those parameters to numerically determine the output parameters. Many values of possible design parameters were then considered and simulated, and the final set of design parameters was achieved.

2. Structure of the Tri-Band Antenna

This section describes the structure of the developed antenna and the rationale behind using a single arm inverted L-shaped strip (ILSS) in the design. The structure of the proposed antenna is shown in Figure 1. It consisted of a rectangular monopole printed on an FR4 substrate and fed by a 50-Ω coplanar waveguide (CPW), resonating at 5.5 GHz. The thickness of the substrate was 1.6 mm. The basic configuration was an omnidirectional pattern and dual bands. To make it a bidirectional pattern, a wide circular slot (WCS) connecting to the ground plane was constructed to encircle the monopole. An unintended benefit of this WCS was that it also expanded the impedance bandwidth. That basic structure still did not provide a tri-band capability. To make the antenna tri-band, an inverted L-shaped strip was welded to the inner surface of WCS at the location shown in the figure. This strip induced the resonance at a center frequency of 2.45 GHz [18].
The design parameters of this antenna were based on the following mathematical equations of the radiating antenna [32].
w r = c 2 f 2 ε r + 1
where wr was the width of the rectangular patch; c was the speed of light in free space; f was a resonant frequency at 5.5 GHz; and ε r was the relative permittivity of the FR4 substrate (a value of 4.3).
l r = c 2 f ε r e f f 0.824 h [ ( ε r e f f + 0.3 ) ( w r + 0.264 h ) ( ε r e f f 0.258 ) ( w r + 0.8 h ) ]
where lr was the length of the rectangular patch; ε r e f f was the effective dielectric constant of the substrate; and h was the thickness of the substrate base.
ε r e f f = ε r + 1 2 + ε r 1 2 1 + 12 h w r
From these three equations, which already took into account the fringing effect, the initial wr and lr of 17 mm and 12 mm were obtained, respectively. To achieve 50-Ω impedance matching, the width wf and length lf of fed line were calculated by Equations (4) and (5) [26],
w f = 2 h π { B 1 ln ( 2 B 1 ) + ε r 1 2 ε r ( ln ( B 1 ) + 0.39 0.61 ε r ) }
where B = 60 π 2 Z o ε r , and Z o was the characteristic impedance of 50 Ω.
l f = λ 4 ε r e f f
Feeding strip widths, wf, of 3 mm and a feeding strip length, lf, of 8 mm were selected and used. A gap g of 0.4 mm between the feed line and the ground plane was selected to support 50-Ω impedance. For compactness, the width w and length l of the substrate material were chosen to be 40, i.e., w × l = 40 × 40 mm2. This rectangular patch was encircled by a WCS of radius r connected to the ground plane, designed according to Equation (6) to provide the dominant mode propagation of TE11 at 2.45 GHz, where fr is the resonance frequency [26]. Consequently, r = 17 mm was selected and used throughout the study. In addition, a single-arm ILSS of width l1, thickness l2 and length l3 was welded to the inner wall of the WCS at the position p in Figure 1 to induce resonance at 2.45 GHz. The total length (l1 + l3) of the ILSS was about a quarter wavelength of 2.45 GHz [1].
r = 18 , 412 f r 2 π μ 0 ε 0
where μ 0 was the permeability in free space, and ε 0 was the permittivity in free space.
The rationale for the single-arm ILSS design of the developed antenna in contrast to the double-arm design of one of our previous works [18] is described below.
The rectangular patch in combination with the WCS antenna offered only a bidirectional pattern, covering the same dual-band resonance of 3.7–6.9 GHz and 13.2–17.6 GHz as [18]. A way to modify this structure to accomplish tri-band capability was by using an ILSS [18]. The narrow bandwidth for 5 GHz WLAN of the proposed antennas is specific to the required operating frequency and eliminates the adjacent bands, which is more advantageous for wireless communication compared to their counterparts. Supplementing this combination with an ILSS at the left (or right) side of the inner ring wall (see Figure 1a) induced the antenna to be sensitive to frequencies in another, new bandwidth—2.4 GHz WLAN, making it tri-band. In terms of current flow, it can be observed in Figure 2 that the ILSS addition changed the pattern of the flow—the flow was asymmetrical. Moreover, simulation of the current flow pattern in the proposed antenna, an antenna without an ILSS, and an antenna with two symmetrical ILSSs at 2.45 GHz, demonstrated a more asymmetrical flow in the proposed antenna. Compared to a tri-band antenna with two symmetrical ILSSs reported in [18], this proposed design provided 3.5/9.7% higher gain in the 2.4/5 GHz WLAN band, which was most likely because the current flow was more asymmetrical. In contrast with the highest band for Ku applications, the proposed antenna with a single-arm ILSS provided 6.7% lower gain, as shown in Figure 3b. Comparing the antenna gain of the proposed antenna with a single-arm ILSS for a three-transition band to the proposed antenna without ILSS for a dual-transition band, the gain of proposed antenna was worsened to 8.7/0.4% in the 5 GHz WLAN/Ku-band applications. With this new design, the proposed antenna offers a resonance frequency at 2.2 GHz, with |S11| of −17.8 dB, covering a 10-dB return loss frequency band of 2–2.56 GHz with 2.35 dBi gain, while a design with two symmetrical ILSSs offers a resonance frequency at 2.1 GHz with |S11| of −32 dB, covering the 10 dB return loss frequency band of 1.9–2.7 GHz, as shown in Figure 3. In detail, the proposed antenna provides three different resonance frequencies of 2.2 GHz, 5.3 GHz and 15.5 GHz, covering three bandwidths—2–2.56 GHz, 4.42–6.82 GHz and 13.26–17.70 GHz—over 2.4 GHz WLAN, 5 GHz WLAN and Ku-band, respectively. It has minimum/maximum gains of 1.74/2.35 dBi, 3.61/5.04 dBi and 3.93/4.79 dBi for 2.4 GHz WLAN, 5 GHz WLAN and Ku-band, respectively, as shown in Figure 4. Of note is that the gains of the proposed antenna in the middle band and the upper band were higher than its gain in the lower band. This difference in gain at the lower frequency band and the higher frequency bands can be due to the antenna structure consisting of the dielectric that affecting to the total efficiency of the antenna at the difference frequency—−1.35/−0.85/−1.37 dB at the center frequency for the 2.4/5 WLAN/Ku band—as well as it can be attributed to the difference in the components of the radiating part of the antenna, i.e., the radiating rectangular patch and an induced ILSS. Incidentally, the middle and upper bands were mostly influenced by the radiating rectangular patch, as depicted by the current flows in Figure 5b,c, while the lower band was mostly influenced by the ILSS attaching at the side wall of the ring, as shown in Figure 5a. In addition, the length l3 of ILSS affected the resonance frequency of the lower band strongly, as shown in Figure 6: the longer the length l3, the lower the achieved resonance frequency. Lastly, l3 of 13 mm was selected, as it was the length that provided the best coverage of 2.4 GHz band for WLAN applications. Note that the change of the width, l1, and thickness, l2, of the ILSS was very faintly influenced to |S11|, as depicted in Figure 7 and Figure 8. The width l1 of 2 mm and thickness l2 of 1 mm were chosen, as the best return loss was achieved at the 2.4 GHz band.
Moreover, it was found that changing the height, p, of the ILSS on the side wall affected the |S11| only slightly, as shown in Figure 9, because the flow rate of the surface current along that side wall was nearly the same regardless of the placement of ILSS. However, if ILSS was placed at the top center of the inner ring wall, the radiation characteristics were quite different from the intended ones. Lastly, on designing the parameter of the ILSS, the height, p, of 30 mm was selected, wherewith it offered the deepest |S11|.
Finally, in the design process, the best parameters based on the best outcomes of simulation runs with a finite-difference time domain solver in the CST microwave studio were selected. Moreover, the final design parameters were manually optimized to provide a 10 dB return loss bandwidth for each of the three bands. A good gain and a bidirectional pattern for each band were achieved. The final design parameters are listed in Table 1. Numerical and experimental results are shown and discussed in the next section.

3. Simulation and Measurement Results

To validate the simulation results, a prototype antenna was fabricated on a copper layer of 0.003 mm thickness, glazed on the FR4 substrate with an ε r of 4.3 and a height of 1.6 mm, as depicted in Figure 1b. Later, an experiment was set up to determine the impedance and radiation characteristics of the antenna with an E5071C network analyzer. The numerical and experimental values of |S11| are shown in Figure 10. It can be observed that both types of values follow a common trend, and the most corresponding numerical and experimental values do not deviate much from each other. The deviation was likely to be from a minor difference in the numerical and experimental setup: a 50-Ω SMA connector in the experimental setup was not taken into account in the simulation [21]. The reason was that we wanted to focus only on the simulated properties of the antenna itself, not any other external components, as well as to reduce simulation time. The second resonant frequency was increased with the inclusion of SMA, whereas the first resonant frequency variation was less due to the smaller reflection at the low frequency. The simulated |S11| results were better than −10 dB over the frequency ranges of 2–2.56 GHz/4.42–6.82 GHz/13.26–17.70 GHz, and the measured |S11| results were better than −10 dB over the frequency ranges of 2.10–2.70 GHz/4.82–6.10 GHz/12.73–18 GHz. In addition, the proposed antenna with the two-arm ILSS also provided the common trend of both simulated and measured |S11| < −10 dB over the frequency ranges of 1.92–2.69 GHz/4.67–6.54 GHz/13.51–17.72 GHz and 2.02–2.62 GHz/5.08–6.27 GHz/11.97–18 GHz covering the 2.4/5 GHz WLAN/Ku-band applications, respectively [18].
Besides the impedance characteristics, the 2D radiation patterns in xz- and yz-planes of the proposed antenna were also measured and plotted in Figure 11, Figure 12 and Figure 13. Evidently, this proposed antenna furnished a bidirectional pattern with a different main beam shape for each band. At the operating frequency of 2.45 GHz, the main beam propagated in forward- and backward-directions, while at the operating frequency of 5.5 GHz, the main beam elevated up about 25°. At the operating frequency of 15.5 GHz, this antenna provided a bidirectional pattern with a beam peak directed at about 180° in both numerical and experimental results. The application of an antenna was in an outdoor WLAN system, where the pattern in the yz-plane elevated up from a 0° to receive the signal from the WLAN transmission tower as well as around a high angle for the application of Ku band. The added reflector could be helpful to increase the antenna gain at the expense of size enlargement. Nonetheless, the arrangement of a number of antenna elements in an array was an alternative means to enhance the antenna gain. Furthermore, an appropriate design for a metal ground structure of vehicular surface could also achieve the additive reflection to improve the radiation pattern and antenna gain. Overall, this antenna provided linear polarization with less than −15 dB cross-polarization for all intended frequency ranges. It provided simulated/measured gains of 2.34/2.63 dBi, 4.21/4.6 dBi and 4.35/4.14 dBi, at 2.45 GHz, 5.5 GHz and 15.5 GHz, respectively. The simulated radiation efficiency values were at least 73%, 82% and 73% for the lower-, middle- and upper-band, respectively.
Furthermore, the performance of the proposed multi-band antenna was compared with existing omnidirectional and bidirectional antennas, as listed in Table 2. In [18], the bidirectional pattern with the slightly lower gain was achieved at the lower and middle bands, contrasting with the higher frequency band that more gain was yielded. In [5,9], the antenna achieved higher gain but lower frequency and large size. In [1,6,14], the antennas were smaller than the proposed antenna but achieved lower antenna gain. In [2], the antenna had narrower bandwidth and lower antenna gain. In [13], the antennas achieved wide bandwidth but suffered from bulkiness. For antennas operable in the three-frequency band, the proposed single-fed bidirectional antenna efficiently achieves high bidirectional antenna gain with compact size.

4. Conclusions

In this work, a compact rectangular patch antenna, surrounded by WCS with an inverted-L strip connected to one side of the slot, and fed by 50-Ω CPW, was developed for triple band operations—2.4 GHz and 5 GHz WLAN, and 15.5 GHz Ku-band—with less than −10 dB |S11|. Both the simulated results at the design stage and the measured results from experiments indicated satisfactory average gains—2.34, 4.22 and 4.32 dBi—for the lower, middle and upper band, respectively. All of these results demonstrate that the proposed antenna fulfills the design goal completely and can be readily used in practical applications of these three frequency bands.

Author Contributions

Conceptualization, S.L. and S.D.; methodology, S.L., W.T. and S.D.; validation, S.L.; design and analysis, S.L. and W.T.; investigation, S.L. and W.T.; data and graph, W.T.; writing—original draft preparation, S.L.; writing—review and editing, S.L., S.D. and C.P.; supervision, C.P.; funding acquisition, S.L. and S.D. All authors have read and agreed to the published version of the manuscript.

Funding

This research was supported by Rajamangala University of Technology Isan with Contract no. Eng16/65. This work was financially supported by Office of the Permanent Secretary, Ministry of Higher Education, Science, Research and Innovation under Grant No. RGNS 63-091.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Acknowledgments

This research project was supported by Rajamangala University of Technology Isan.

Conflicts of Interest

The authors declare no conflict of interest.

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Figure 1. Structure of the proposed antenna: (a) schematic model (b) prototype.
Figure 1. Structure of the proposed antenna: (a) schematic model (b) prototype.
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Figure 2. Surface current of the proposed antenna at the operating frequency of 2.45 GHz: (a) without ILSS, (b) with single-arm ILSS and (c) two-arm ILSS.
Figure 2. Surface current of the proposed antenna at the operating frequency of 2.45 GHz: (a) without ILSS, (b) with single-arm ILSS and (c) two-arm ILSS.
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Figure 3. Simulated |S11| and gain of the proposed antenna with and without ILSS: (a) |S11| and (b) Gain.
Figure 3. Simulated |S11| and gain of the proposed antenna with and without ILSS: (a) |S11| and (b) Gain.
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Figure 4. Simulated |S11| and gain of the proposed antenna.
Figure 4. Simulated |S11| and gain of the proposed antenna.
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Figure 5. Surface current of the proposed antenna with single-arm ILSS at the operating frequencies of: (a) 2.45 GHz, (b) 5.5 GHz and (c) 15.5 GHz.
Figure 5. Surface current of the proposed antenna with single-arm ILSS at the operating frequencies of: (a) 2.45 GHz, (b) 5.5 GHz and (c) 15.5 GHz.
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Figure 6. Simulated |S11| of the proposed antenna for various l3.
Figure 6. Simulated |S11| of the proposed antenna for various l3.
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Figure 7. Simulated |S11| of the proposed antenna for various l1.
Figure 7. Simulated |S11| of the proposed antenna for various l1.
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Figure 8. Simulated |S11| of the proposed antenna for various l2.
Figure 8. Simulated |S11| of the proposed antenna for various l2.
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Figure 9. Simulated |S11| of the proposed antenna for various p.
Figure 9. Simulated |S11| of the proposed antenna for various p.
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Figure 10. Simulated and measured |S11| of the proposed antenna with a single-arm and two-arm ILSSs.
Figure 10. Simulated and measured |S11| of the proposed antenna with a single-arm and two-arm ILSSs.
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Figure 11. Simulated and measured radiation pattern at 2.45 GHz: (a) xz-plane and (b) yz-plane.
Figure 11. Simulated and measured radiation pattern at 2.45 GHz: (a) xz-plane and (b) yz-plane.
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Figure 12. Simulated and measured radiation pattern at 5.5 GHz: (a) xz-plane and (b) yz-plane.
Figure 12. Simulated and measured radiation pattern at 5.5 GHz: (a) xz-plane and (b) yz-plane.
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Figure 13. Simulated and measured radiation pattern at 15.5 GHz: (a) xz-plane and (b) yz-plane.
Figure 13. Simulated and measured radiation pattern at 15.5 GHz: (a) xz-plane and (b) yz-plane.
Applsci 12 05817 g013
Table 1. Selected are the best values for parameters of the proposed antenna.
Table 1. Selected are the best values for parameters of the proposed antenna.
SymbolParameterPhysical Size (mm)
wWidth of the substrate40
lLength of the substrate40
wrWidth of the rectangular patch19
lrLength of the rectangular patch10
lfLength of feeding strip8
wfWidth of feeding strip3
lgLength of ground plane7
gGap between feed line and ground plane0.4
rRadius of wide circular slot17
l1Width of a single-arm ILSS2
l2Thickness of a single-arm ILSS1
l3Length of a single-arm ILSS13
pPosition of a single-arm ILSS30
sSpacing between the bottom of rectangular Patch and ground plane1
hThickness of the substrate1.6
tThickness of the copper layer0.003
Table 2. Comparison between previous studies and this current research.
Table 2. Comparison between previous studies and this current research.
ReferencesFractional Bandwidth of |S11|PatternPeak Gain (dBi)ApplicationOverall Antenna Dimension (mm)Structure
[1]2.34–2.82 GHz,
3.16–4.06 GHz,
and 4.69–5.37 GHz
Omnidirectional3.06/3.13/3.10WLAN
and WiMAX
32 × 28 × 1FR-4
[2]1.67–2.07 GHz,
2.35–4.23 GHz,
and 4.65–5.43 GHz
Bi-directional3/3.5/1DCS, WiMAX, WLAN, and IMT48 × 50 × 0.8FR-4
[5]790–1061 MHz,
1650–2775 MHz,
and 3132–6382 MHz
Omnidirectional3/4/5GSM/UMTS/LTE and WLAN/WiMAX115 × 60 × 0.5TLY-5
[6]2.5–2.78 GHz,
3.24–4 GHz,
and 5.18–5.88 GHz
Omnidirectional1.65/2.59/3.94WLAN
and WiMAX
22 × 14 × 0.5F4B
[9]2.26–2.68 GHz,
3.28–4.09 GHz
and 4.75–6.04 GHz
Omnidirectional1.67/2.75/5.5WLAN
and WiMAX
33 × 33 × 1.6FR-4
[13]685–1012 MHz,
1596–2837 MHz,
and 3288–3613 MHz
Omnidirectional1.4–2.54G/5G/WLAN60 × 120 × 1.5FR-4
[14]2.24–2.85 GHz,
3.29–4.12 GHz,
5.13–6.24 GHz,
and 6.58–8.57 GHz
Omnidirectional2.87/3.48/1.82/3.34WLAN/WiMAX/X-Band18 × 22 × 1FR-4
[18]2.02–2.62 GHz,
5.08–6.27 GHz,
and 11.97–18 GHz
Bidirectional2.27/4.02/5.052.4/5 GHz WLAN and Ku-band40 × 40 × 1.6FR-4
[20]2.35–2.49 GHz,
3.27–3.8 GHz,
and 4.65–5.89 GHz
Omnidirectional2.24/2.88/4.29WLAN and WiMAX34.5 × 18 × 1FR-4
[23]2342–2548 MHz
and 4877–5987 MHz
Omnidirectional-WLAN and HIPERLAN40 × 45 × 0.8FR-4
Proposed2.10–2.70 GHz,
4.82–6.10 GHz,
and 12.73–18 GHz
Bidirectional2.35/4.41/4.712.4/5 GHz WLAN and Ku-band40 × 40 × 1.6FR-4
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Lamultree, S.; Thanamalapong, W.; Dentri, S.; Phongcharoenpanich, C. Tri-Band Bidirectional Antenna for 2.4/5 GHz WLAN and Ku-Band Applications. Appl. Sci. 2022, 12, 5817. https://doi.org/10.3390/app12125817

AMA Style

Lamultree S, Thanamalapong W, Dentri S, Phongcharoenpanich C. Tri-Band Bidirectional Antenna for 2.4/5 GHz WLAN and Ku-Band Applications. Applied Sciences. 2022; 12(12):5817. https://doi.org/10.3390/app12125817

Chicago/Turabian Style

Lamultree, Suthasinee, Wutthipong Thanamalapong, Sitthichai Dentri, and Chuwong Phongcharoenpanich. 2022. "Tri-Band Bidirectional Antenna for 2.4/5 GHz WLAN and Ku-Band Applications" Applied Sciences 12, no. 12: 5817. https://doi.org/10.3390/app12125817

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