Introduction
Microstrip patch antennas have been widely used in various types of communication systems due to their low profile, light weight, and ease of integration. However, low gain radiation makes them less attractive to the modern systems, in which long-distance communication is required. Besides, using circularly polarized (CP) antenna has more benefits than using linearly polarized (LP) antenna since it can reduce polarization mismatch and multipath interference as well.
Traditional microstrip patch antennas with CP radiation suffer from a critical drawback of low gain radiation [1–3], which is less than 8 dBi. Various approaches have been reported in the open literature to improve the gain of patch antenna. A typical scheme is increasing the number of radiating elements [4, 5]. However, the structures’ dimensions and complexity will also increase. Another approach is introduced by loading special structures, such as frequency selective surface (FSS) or dielectric superstrate [6–8]. Nonetheless, they will undoubtedly increase the antenna’s profile to at least quarter-wavelength at the operating frequency. Similar drawbacks can be observed by the techniques of using stacked radiating elements as reported in [9–11]. One of the potential solutions for gain enhancement while retaining the low-profile structure is a combination between the metasurface (MS) and microstrip patch radiator [12–15]. Overall, such above-mentioned methods have similar problems of high profile and complicated structures.
Currently, using high-order mode is an effective solution for gain enhancement due to the increase of electrical size. This method does not require any additional structure. In [16, 17], multiple shorting pins are inserted within the patch to achieve a high gain of about 10.8 dBi. Alternatively, the use of high-order mode of TM30 patch antenna is also the way to realize high gain property [18–20]. Although a high gain of about 12.0 dBi can be achieved, they suffer from disadvantages of large size and/or complicated structure.
In this paper, a single-feed CP patch antenna with high gain radiation, compact size, and simple structure based on the high-order TM30/TM03 mode is proposed. Four open slots are inserted into the square-shape patch to not only reduce the grating lobe but also reduce the antenna dimensions. Next, a substrate integrated waveguide (SIW) cavity is used to improve the front-to-back ratio by reducing the back radiation. In comparison with the related works, the proposed design possesses several advantages of compact size, simple structure, as well as high gain property.
High-order mode CP patch antenna
The geometrical configuration of the high-order mode CP patch antenna is presented in Fig 1. The antenna structure is simply comprised of a square patch and a ground plane. The patch and the ground are printed on top and bottom layers of a Taconic TLY-5 substrate with a dielectric constant of 2.2 and loss tangent of 0.0009. The patch is diagonally fed, and an unequal crossed slot is loaded at the patch’s center. The antenna is modelled and characterized using the commercial full-wave simulation software, High Frequency Structure Simulator (HFSS). The optimal design parameters are as follows: Ws = 100, h = 1.52, Wp = 51.4, ls1 = 14.6, ls2 = 12, ws = 0.8 (unit: mm).
[Figure omitted. See PDF.]
The radiating patch with overall dimensions of Wp Wp is designed to operate at high-order mode of TM03. At the desired frequency (fr), the resonant length can be estimated based on the following equation [21]:
(1)
where the light velocity is c, and and are dielectric constant and effective dielectric constant, respectively. Thickness of the substrate is h, and is the wavelength in substrate. For the high-order mode patch, the patch’s size is much greater than the substrate’s thickness; therefore, can be approximately equal to .
Fig 2 shows the simulated results in terms of reflection coefficient (|S11|), axial ratio (AR), and gain radiation pattern of the proposed antenna. It can be seen obviously that the antenna shows good operation at the desired frequency of 5.45 GHz, in which |S11| and AR are respectively less than –10 dB and 3 dB. For the gain radiation response, although the antenna radiates strong power in the broadside direction, the grating lobe is quite high. This is caused by the out-of-phase current flowing on the radiating patch. For a better demonstration, Fig 3 shows the simulated current distribution on the patch at different phases of and . Overall, the main vector currents in both cases are orthogonal and when the phase changes, the vector current rotates in clockwise direction. This demonstrates the left-hand CP radiation. However, the middle current (dot-black circle) is out-of-phase with the other currents, leading to a high grating lobe level.
[Figure omitted. See PDF.]
[Figure omitted. See PDF.]
The AR optimization of this antenna strongly depends on the dimensions of the unequal crossed slot locating at the center of the patch. This crossed slot contributes to producing two orthogonal modes, TM30 and TM03. By tuning the slot’s length, the magnitudes and phases of these modes can be controlled so that they are equal in magnitude and phase difference. Figs 4 and 5 show the simulated |S11| and AR for different values of ls1 and ls2. In the |S11| profile, there are two resonances corresponding to the TM30 and TM03 modes. Tuning ls1 and ls2 will have a significant effect on the corresponding resonance, which shifts upwards or downwards depending on the length variation of the slot’s length. When the phase requirement is satisfied, the AR value under 3 dB can be obtained.
[Figure omitted. See PDF.]
[Figure omitted. See PDF.]
High-order mode CP patch antenna with four open slots
Despite having high gain operation, the design in the previous section suffers from a critical drawback of high grating lobe, which significantly deteriorates the system’s performance. To overcome this drawback, the reverse phase current in the medial portion of the patch should be eliminated. In this context, the patch radiation is like two in-phase TM10/TM01 modes. To achieve this, four open slots are inserted along x– and y–direction, as shown in Fig 6. Noted that the width of such slots should be narrow so that the radiation from the circumventing current could be almost canceled with each other. Thus, the radiation of such slots will not have significant effect on the radiation of the patch. The antenna is optimized to achieve the best performance around 5.45 GHz. The optimal design parameters are as follows: Ws = 70, h = 1.52, Wp = 46, ls1 = 14.6, ls2 = 9.6, ws = 0.8, s = 2.8, l = 9.6 (unit: mm).
[Figure omitted. See PDF.]
Further demonstration about the effect of four open slots is shown in Fig 7, which shows the simulated |S11|, AR, as well as gain radiation pattern of the high-order mode CP patch antenna with four open slots. The data indicates that the antenna well operates at 5.45 GHz with a broadside gain of 12.2 dBi. Meanwhile, the grating lobe is much lower than that of the design in the previous section, which is –7.4 dB compared to 3.4 dB. This is attributed to the elimination of the center reverse phase current on the radiating patch. Fig 8 shows the simulated current distribution on the patch at 5.45 GHz. As observed, the out-of-phase current is circumvented along the four open slots. Therefore, the grating lobe can be suppressed. It is also noted that due to the presence of these open slots, the electrical length of the antenna can be increased by increasing the slot’s length, resulting in the patch size reduction. The effect of the slot’s length (l) on |S11| and AR is shown in Fig 9. As seen, the operating frequency can be tuned by changing l. Increasing l leads to a longer electrical length; therefore, the operating frequency shifts towards the lower frequency range.
[Figure omitted. See PDF.]
[Figure omitted. See PDF.]
[Figure omitted. See PDF.]
High-order mode CP patch antenna with four open slots and SIW cavity
Although compact size can be achieved when four open slots are employed, the back radiation of the antenna in the above-mentioned section is quite high of about –7.3 dB. This is due to the high diffracted power at the edges of the substrate. To reduce this diffraction, a SIW cavity is one of the effective solutions. Fig 10 shows the configuration of the proposed high-order mode CP patch antenna with four open slots and SIW cavity. The optimal dimensions of this design are as follows: Ws = 70, h = 1.52, Wp = 46, ls1 = 14.6, ls2 = 10.2, ws = 0.8, s = 2.4, l = 9.6, g = 3.4, = 0.5, p = 1.4, (unit: mm).
[Figure omitted. See PDF.]
The simulated performance of the final antenna realization is illustrated in Fig 11 The antenna has good matching performance in the frequency range from 5.4 to 5.57 GHz. The AR values of less than 3 dB are from 5.43 to 5.48 GHz. Across this band, the broadside gain is about 12 dBi. In terms of gain radiation patterns at 5.45 GHz, the back lobe of the antenna with SIW cavity is about –11.2 dB, which is lower than that of the antenna without cavity. Meanwhile, the grating lobe is about –7.2 dB. The performance metrics of three different antennas are summarized in Table 1. The main lobe and operating BW shown in the comparison table are almost similar. In contrast, the grating lobe and back lobe of the final antenna are better than the others.
[Figure omitted. See PDF.]
[Figure omitted. See PDF.]
Measurement results
The proposed antenna is fabricated and measured to validate the design concept. The photographs of the antenna prototype are shown in Fig 12. The measurements are carried out using a Vector Network Analyzer and Anechoic Chamber. Overall, the simulation is fairly matched with the measurement.
[Figure omitted. See PDF.]
The simulated and measured performance with respect to |S11|, AR, and broadside gain results are shown in Fig 13. Meanwhile, the simulated and measured gain radiation patterns in two principal planes are illustrated in Fig 14. As observed in the frequency range from 5.435 to 5.475 GHz, the antenna achieves good matching performance and low AR values of less than 3 dB. The measured broadside gain demonstrates that the fabricated antenna exhibits a high gain of around 12 dBi within the operating bandwidth. Meanwhile, the radiation patterns at 5.45 GHz are quite symmetrical around the broadside direction. The measured grating lobe is about –6.8 dB and the measured back lobe is approximately –10.5 dB.
[Figure omitted. See PDF.]
[Figure omitted. See PDF.]
Table 2 shows a comparison between the proposed antenna and several remarkable high gain antennas in the literature. According to the compared data, it is obvious that the proposed antenna has the lowest profile structure, small lateral dimensions, as well as simple structure with no additional feeding network and only single-layer. Several designs have wide bandwidth due to the use of complicated structure with large size and multiple layers to excite multiple modes. In terms of gain, the proposed design has comparable gain with the others. The use of FSS or dielectric substrate results in a very high structure profile [6, 7]. Meanwhile, lower profile and high gain can be achieved with the aid of MS layer; however, large lateral dimensions are critical drawback of the antennas in [12, 13, 15]. Compared to the similar method of using high order mode, the proposed antenna has lower grating lobe level and smaller size than the design in [18] while achieving similar front-to-back ratio (FBR). Besides, higher gain and/or less complexity are the advantages of the proposed design compared to the results in [16] and [19]. Noted that the design in [19] has wide bandwidth due to the use of chip coupler, which complicates the design and the insertion loss will affect the antenna gain.
[Figure omitted. See PDF.]
Application of the proposed antenna for unmanned aerial vehicle
The proposed antenna possesses high gain radiation and CP radiation as well. It could be benefit for long-range communication systems. Besides, CP radiation also helps to increase the channel reliability by avoiding polarization mismatch. Nowadays, unmanned aerial vehicles (UAVs) have been widely used in various fields such as public safety, monitoring, security surveillance, and so on. In this context, air-to-ground communication is very important. By using the proposed antenna, an antenna array system consisting of five elements with titled angle of is proposed in Fig 15. This antenna system is designed for covering the area downward the UAV-body. It can switch the radiation pattern in different directions, which allows wide air-to-ground communication coverage.
[Figure omitted. See PDF.]
The simulated reflection and transmission coefficients, as well AR with Port-1 excitation of the antenna array are presented in Fig 16. It can be observed that the array system achieves a good reflection coefficient around 5.45 GHz. Meanwhile, the isolation is always better than 44 dB. The AR values are lower than 3 dB in the frequency range from 5.43 to 5.47 GHz, which demonstrates the CP radiation of the proposed design. The simulated gain radiation patterns are shown in Fig 17. Changing the excited port, the beam can be switched at in the y–z plane. The maximum gain is about 12 dBi and the gain at the overlapped patterns is approximately 9.0 dBi. Similar operation features can be achieved in the y–z plane due to the symmetrical array configuration.
[Figure omitted. See PDF.]
[Figure omitted. See PDF.]
Conclusion
A high gain CP patch antenna with side-lobe reduction and size miniaturization is presented and investigated in this paper. The design evolution step is also given to better demonstration the working principle and optimization process of the proposed antenna. The design is first characterized using simulation and then validated by measurement. By using four-sided slots and four-crossed slots, the side-lobe level and lateral dimensions of the proposed antenna can be optimized. The measured data demonstrate that high gain of 12 dBi across the operating bandwidth from 5.435 to 5.475 GHz can be achieved with compact overall antenna’s dimensions of 1.27 1.27 0.03 .
References
1. 1. Nkimbeng CHS, Wang H, Park I. Coplanar waveguide-fed bidirectional same-sense circularly polarized metasurface-based antenna. J Electromagn Eng Sci. 2021;21(3):210—7.
* View Article
* Google Scholar
2. 2. Chen W-J, Chen H-H, Lee C-H, Hsu CG. Differentially fed wideband circularly polarized slot antenna. IEEE Trans Antennas Propag. 2019;67(3):1941—5.
* View Article
* Google Scholar
3. 3. Bilotti F, Vegni C. Design of high-performing microstrip receiving GPS antennas with multiple feeds. IEEE Antennas Wireless Propag Lett. 2010;9:248—51.
* View Article
* Google Scholar
4. 4. Zou Y, Li H, Xue Y, Sun B. A high-gain compact circularly polarized microstrip array antenna with simplified feed networks. Int J RF Microw Comput-Aided Eng. 2019;29:e21964.
* View Article
* Google Scholar
5. 5. Yang W, Zhou J, Yu Z, Li L. Bandwidth- and gain-enhanced circularly polarized antenna array using sequential phase feed. IEEE Antennas Wireless Propag. Lett. 2014;13:1215—8.
* View Article
* Google Scholar
6. 6. Leszkowska L, Rzymowski M, Nyka K, Kulas L. High-gain compact circularly polarized X-band superstrate antenna for cubesat applications. IEEE Antennas Wireless Propag Lett. 2021;20(11):2090—4.
* View Article
* Google Scholar
7. 7. Ta SX, Nguyen TK. AR bandwidth and gain enhancements of patch antenna using single dielectric superstrate. Electron Lett. 2017;53(15):1015—7.
* View Article
* Google Scholar
8. 8. Zeb BA, Hashmi RM, Esselle KP. Wideband gain enhancement of slot antenna using one unprinted dielectric superstrate. Electron Lett. 2015;51(15):1146—8.
* View Article
* Google Scholar
9. 9. Cheng G, Huang B, Huang Z, Yang L. A high-gain circularly polarized filtering stacked patch antenna. IEEE Antennas Wireless Propag Lett. 2023;22(5):995–9.
* View Article
* Google Scholar
10. 10. Dao T, Kearns A, Reyes Paredes D, Hueber G. Wideband high-gain stacked patch antenna array on standard PCB for D-band 6G communications. IEEE Antennas Wireless Propag Lett. 2024;23(2):478–82.
* View Article
* Google Scholar
11. 11. Ramanujam P, Ponnusamy M. Design of dual circular polarized stacked patch antenna for BeiDou navigation satellite systems. J Electromagn Waves Appl. 2024;38(7):766—77.
* View Article
* Google Scholar
12. 12. Kedze KE, Wang H, Park I. A metasurface-based wide-bandwidth and high-gain circularly polarized patch antenna. IEEE Trans Antennas Propag. 2022;70(1):732—7. 10.1109/TAP.2021.3098574
* View Article
* Google Scholar
13. 13. Rajanna PKT, Rudramuni K, Kandasamy K. A high-gain circularly polarized antenna using zero-index metamaterial. IEEE Antennas Wireless Propag. Lett. 2019;18:1229—33.
* View Article
* Google Scholar
14. 14. Zhao C, Wang CF. Characteristic mode design of wide band circularly polarized patch antenna consisting of H-shaped unit cells. IEEE Access. 2018;6:25292—9.
* View Article
* Google Scholar
15. 15. Gu L, Yang W, Feng W, Xue Q, Meng Q, Che W. Low profile ultrawideband circularly polarized metasurface antenna array. IEEE Antennas Wireless Propag. Lett. 2020;19(10):1714—8.
* View Article
* Google Scholar
16. 16. Zhang X, Zhu L. High-gain circularly polarized microstrip patch antenna with loading of shorting pins. IEEE Trans Antennas Propag. 2016;64(6):2172—8.
* View Article
* Google Scholar
17. 17. Zhang X, Zhu L. Gain-enhanced patch antennas with loading of shorting pins. IEEE Trans Antennas Propag. 2016;64(8):3310—8.
* View Article
* Google Scholar
18. 18. Zhang Y, Liu A, Pan T, Wu Y, Li P, Liang X, et al. High-gain circularly polarized array antenna with low grating lobe property based on TM30/TM03 mode. IEEE Antennas Wireless Propag Lett. 2021;20(3):401—5.
* View Article
* Google Scholar
19. 19. Kang E, Lim TH, Cho H. Design of a circularly polarized high-gain patch antenna using a higher-order mode with a heterogeneous substrate layer for GPS applications. IEEE Access. 2023;11:79224—31.
* View Article
* Google Scholar
20. 20. Kang E, Choo H. Circularly polarized high-gain patch antenna using higher-order mode for GPS applications. In: 2022 IEEE International Symposium on Radio-Frequency Integration Technology (RFIT), Busan, Korea, Republic of, 2022, pp. 95–97. https://doi.org/10.1109/RFIT54256.2022.9882420
21. 21. Balanis CA. Antenna theory: analysis, design, 4th edn. New York, NY and USA: Wiley; 2005.
Citation: Nguyen-Huy H, Tran-Viet D-N, Kim-Thi P, Tran-Huy H (2025) Compact high-gain circularly polarized patch antenna based on TM30/TM03 mode. PLoS One 20(5): e0321091. https://doi.org/10.1371/journal.pone.0321091
About the Authors:
Hoang Nguyen-Huy
Roles: Investigation, Writing – original draft
Affiliation: Faculty of Electrical and Electronic Engineering, PHENIKAA University, Yen Nghia, Ha Dong, Hanoi 12116, Vietnam
Duc-Nguyen Tran-Viet
Roles: Investigation, Validation
Affiliation: Faculty of Radio-Electronic Engineering, Le Quy Don Technical University, Hanoi 11917, Vietnam
ORICD: https://orcid.org/0000-0003-4647-9371
Phuong Kim-Thi
Roles: Supervision, Writing – review & editing
Affiliation: Faculty of Electrical and Electronic Engineering, Thuyloi University, Hanoi, Vietnam
Hung Tran-Huy
Roles: Methodology, Supervision, Writing – review & editing
E-mail: [email protected]
Affiliation: Faculty of Electrical and Electronic Engineering, PHENIKAA University, Yen Nghia, Ha Dong, Hanoi 12116, Vietnam
ORICD: https://orcid.org/0000-0003-0652-2232
[/RAW_REF_TEXT]
[/RAW_REF_TEXT]
1. Nkimbeng CHS, Wang H, Park I. Coplanar waveguide-fed bidirectional same-sense circularly polarized metasurface-based antenna. J Electromagn Eng Sci. 2021;21(3):210—7.
2. Chen W-J, Chen H-H, Lee C-H, Hsu CG. Differentially fed wideband circularly polarized slot antenna. IEEE Trans Antennas Propag. 2019;67(3):1941—5.
3. Bilotti F, Vegni C. Design of high-performing microstrip receiving GPS antennas with multiple feeds. IEEE Antennas Wireless Propag Lett. 2010;9:248—51.
4. Zou Y, Li H, Xue Y, Sun B. A high-gain compact circularly polarized microstrip array antenna with simplified feed networks. Int J RF Microw Comput-Aided Eng. 2019;29:e21964.
5. Yang W, Zhou J, Yu Z, Li L. Bandwidth- and gain-enhanced circularly polarized antenna array using sequential phase feed. IEEE Antennas Wireless Propag. Lett. 2014;13:1215—8.
6. Leszkowska L, Rzymowski M, Nyka K, Kulas L. High-gain compact circularly polarized X-band superstrate antenna for cubesat applications. IEEE Antennas Wireless Propag Lett. 2021;20(11):2090—4.
7. Ta SX, Nguyen TK. AR bandwidth and gain enhancements of patch antenna using single dielectric superstrate. Electron Lett. 2017;53(15):1015—7.
8. Zeb BA, Hashmi RM, Esselle KP. Wideband gain enhancement of slot antenna using one unprinted dielectric superstrate. Electron Lett. 2015;51(15):1146—8.
9. Cheng G, Huang B, Huang Z, Yang L. A high-gain circularly polarized filtering stacked patch antenna. IEEE Antennas Wireless Propag Lett. 2023;22(5):995–9.
10. Dao T, Kearns A, Reyes Paredes D, Hueber G. Wideband high-gain stacked patch antenna array on standard PCB for D-band 6G communications. IEEE Antennas Wireless Propag Lett. 2024;23(2):478–82.
11. Ramanujam P, Ponnusamy M. Design of dual circular polarized stacked patch antenna for BeiDou navigation satellite systems. J Electromagn Waves Appl. 2024;38(7):766—77.
12. Kedze KE, Wang H, Park I. A metasurface-based wide-bandwidth and high-gain circularly polarized patch antenna. IEEE Trans Antennas Propag. 2022;70(1):732—7. 10.1109/TAP.2021.3098574
13. Rajanna PKT, Rudramuni K, Kandasamy K. A high-gain circularly polarized antenna using zero-index metamaterial. IEEE Antennas Wireless Propag. Lett. 2019;18:1229—33.
14. Zhao C, Wang CF. Characteristic mode design of wide band circularly polarized patch antenna consisting of H-shaped unit cells. IEEE Access. 2018;6:25292—9.
15. Gu L, Yang W, Feng W, Xue Q, Meng Q, Che W. Low profile ultrawideband circularly polarized metasurface antenna array. IEEE Antennas Wireless Propag. Lett. 2020;19(10):1714—8.
16. Zhang X, Zhu L. High-gain circularly polarized microstrip patch antenna with loading of shorting pins. IEEE Trans Antennas Propag. 2016;64(6):2172—8.
17. Zhang X, Zhu L. Gain-enhanced patch antennas with loading of shorting pins. IEEE Trans Antennas Propag. 2016;64(8):3310—8.
18. Zhang Y, Liu A, Pan T, Wu Y, Li P, Liang X, et al. High-gain circularly polarized array antenna with low grating lobe property based on TM30/TM03 mode. IEEE Antennas Wireless Propag Lett. 2021;20(3):401—5.
19. Kang E, Lim TH, Cho H. Design of a circularly polarized high-gain patch antenna using a higher-order mode with a heterogeneous substrate layer for GPS applications. IEEE Access. 2023;11:79224—31.
20. Kang E, Choo H. Circularly polarized high-gain patch antenna using higher-order mode for GPS applications. In: 2022 IEEE International Symposium on Radio-Frequency Integration Technology (RFIT), Busan, Korea, Republic of, 2022, pp. 95–97. https://doi.org/10.1109/RFIT54256.2022.9882420
21. Balanis CA. Antenna theory: analysis, design, 4th edn. New York, NY and USA: Wiley; 2005.
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Abstract
This paper presents a circularly polarized (CP) microstrip patch antenna with high gain and compact size characteristics. For high gain radiation, the principle is to employ high-order mode patch. By using diagonal feed and unequal center crossed slot, two orthogonal modes including TM03 and TM30 modes are generated with equal magnitude and phase difference. Thus, the high-order mode patch antenna can radiate CP waves with high gain. To achieve small lateral dimensions with low back radiation, the patch is surrounded by a substrate integrated waveguide (SIW) cavity. For validation, measurement is implemented on an antenna prototype. The final design has overall dimensions of 1.27 1.27 0.03 at the center operating frequency. The measured operating bandwidth, in which reflection coefficient and axial ratio are respectively less than –10 dB and 3 dB, is from 5.435 to 5.475 GHz. Within this band, the antenna exhibits high gain radiation of about 12 dBi. Besides, compared to the antenna without SIW cavity, the back radiation of the proposed design can be decreased by two times.
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Details
; Kim-Thi, Phuong; Tran-Huy, Hung