Design of the proposed PCM

Figure 1 shows a unit cell consisting of a pair of square patch antennas with cut corners and a metal sandwiched between them. The antenna was placed on a 6 mm × 6 mm substrate (ɛ _r = 4.4, tan δ = 0.02) of thickness d. Figure 1(d) shows a simulation model of the unit cell in High Frequency Structure Simulator (HFSS).

Fig. 1.

(a) 3-D sketch of the PCM, (b) top-view of the patch antenna with trimmed corners, (c) top view of the metal, and (d) HFSS model of the unit cell

According to FP antenna theory, the cavity resonance between the ground of the source antenna and the PCM is excited when the FP resonant condition in equation (1) is satisfied:

(1)$$\phi _{\,pcm} + \phi _{GND}-\displaystyle{{4\pi h_c} \over {\lambda _0}} = 2N{\rm \pi }, \;\matrix{ {} & {} \cr } N = 0, \;\;\pm 1, \;\;\pm 2\ldots {\rm , \;}$$

where ϕ _PCM and ϕ _GND are the reflection phases of the ground plane and PCM, respectively; λ ₀ is the free space wavelength at the operating frequency, and h_c is the height of the cavity. Thus, a maximum directivity at the broadside of the FP antenna occurs because waves exit the cavity in phase. A low profile was achieved by setting N to 0, operating the cavity at first resonance. We then adjust the PCM reflection phase ϕ _PCM to satisfy equation (1). We calculate the boresight directivity of the antenna using equation (2) for the emitted, in-phase waves assuming a finite size for the resonant cavity:

(2)$$D_r = 10\log \displaystyle{{1 + R} \over {1-R}}$$

In equation (2), R is the reflection magnitude of the PCM. From this formula, we know that the boresight directivity is higher when R increased for D_r is an increasing function of R. The directivity is optimal and maximum when R is about 0.9 [Reference Xie, Wang, Li, Liang and Gao18].

Other studies have designed a novel composite metasurface to reduce the cross-polarization of reflective waves traveling through the medium, leading to a large AR [Reference Guo, Cao, Gao, Yanag and Jidi19]. Therefore, we considered the reduction of cross-polarization to ensure high gain and wideband CP in the antenna while designing our PCM.

We complete our design with a few remaining steps. First, to achieve CP, we trim a pair of corners based on dual conventional rectangular patches, where an equal magnitude and a 90° phase difference can be generated by tuning the transmission coefficients T_xx and T_yx. Second, to reduce the cross-polarization component of the reflected waves, we adopt a metal ring sandwiched between layers to improve the gain and enhance the wideband CP. We then form an FP cavity with the source patch antenna being designed, performing an LP to CP transformation of transmitted waves from the cavity to improve the gain further. Finally, we arrange the checkered antenna array using sequential rotation to reduce the RCS of the proposed antenna.

To design our unit cell, we modify the one shown in Fig. 2 to arrive at the one in Fig. 1. Referring to the simulation results in Fig. 3, the initial unit cell did not circularly polarize the waves, as indicated by the transmissivity and reflectivity of cross-polarization (T_yx, T_yx) being nearly zero. This suggests that the original metasurface is incapable of converting polarization.

Fig. 2.

(a) Initial square patch antennas, (b) corner-cut square patch antennas (ele.b), and (c) metal sandwiched by corner-cut square patch antennas (proposed ele.)

Fig. 3.

Simulated S parameters of the initial square patch antennas: (a) reflection magnitude and (b) transmission magnitude

The metasurface requires low cross-polarization to maintain the gain and bandwidth improvements [Reference Guo, Cao, Gao, Yanag and Jidi19]. The metasurface also requires a high transmission magnitude. We require two countermeasures to increase the reflectivity of the metasurface.

Referring to Fig. 2(b), we cut the corners of the square patch antennas to make T_xx and T_xy equal and create a 90° phase difference. The simulation results in Fig. 4 show that trimming the corners significantly improves the cross-polarization of transmissivity (T_yx) compared to the uncut square patch antenna. This means that the co-polarized transmissivity (T_xy) and cross-polarized transmissivity (T_xx) are nearly equal.

Fig. 4.

(a) Transmission magnitudes versus frequency for ele.b and proposed ele. and (b) phase difference versus frequency for ele.b and proposed ele.

We achieve the 90° phase difference in T_xy and T_xx by adjusting the length of the corner cut c to 3 mm. This length led to a phase difference variance of 15° in different frequency bands as shown in Fig. 4(b). The 3 mm corner cut length c ensures T_xy and T_xx are nearly equal, with a variation of ±3 dB. T_xy and T_xx have a phase difference of 90° and demonstrate that linear-to-circularly polarized conversion results and that the corner cuts radiate circularly polarized waves (Table 1).

Table 1.

Optimal dimensions of the proposed FP patch antenna

As shown in Fig. 2(c), we sandwich a metal ring between the top and bottom substrate to reduce cross-polarization and increase gain in the antenna. Figure 4 shows the transmission magnitude, magnitude difference, and phase difference, with and without the embedded metal (element b and proposed element, abbreviated as ele.b and proposed ele. in the related figures). Figure 4 demonstrates that linear-to-circular polarization conversion occurs in the 6–12 GHz range of wideband frequencies with the corner-cut square patch antennas.

Figure 5(b) shows a plot of the transmission and reflective magnitudes versus frequency for different metal widths w_a. The reflective magnitude of cross-polarization was nearly zero at 8.5 GHz with w_a of 0.4 mm, ensuring high gain and CP in the proposed antenna, as shown in Fig. 5(a). Figure 5(b) also shows that the highest gain occurs at 8.5 GHz.

Fig. 5.

(a) Reflection magnitude of cross-polarization and (b) effects of metal width w_a on the S parameters

Figure 6 shows a plot of transmission coefficients versus the incident angle at 8.5 GHz in the xoz plane. The properties of the proposed PCM change slightly when an oblique incident wave passes through. The properties of the proposed PCM rapidly deteriorate once the incident angle exceeds 60°. Thus, we hold the incident angle stable to maintain the performance of the PCM.

Fig. 6.

(a) Transmission magnitude versus incident angle at 8.5 GHz, and (b) phase difference versus incident angle at 8.5 GHz

We adopt an off-center microstrip patch antenna (MPA) as the radiation source for the antenna. The MPA feeder is composed of an FR4 substrate (ɛ_r = 4.4, tan δ = 0.02) with a thickness of 3 mm, as described in Figs 7(c)–7(d). We print the ground plane and radiation patch at the bottom and top of the substrate, respectively.

Fig. 7.

Proposed PCM with MPA: (a) schematic, (b) top view, (c) bottom view, and (d) side view

We simulate the FP antenna with and without the proposed PCM, and with no metal-ring PCM, as shown in Fig. 8. It can be seen obviously that bandwidth enhancement and gain improvement of patch antenna would be achieved by the proposed PCM adopted, though a nearly zero AR point occurred when no metal-ring PCM was utilized in this design, which is quite narrow. Resonance achieves the gain enhancement in right-hand circular polarization (RHCP) antennas with PCM, with a maximum improvement of 2.5 dBic. According to other design guidelines, the resonance in the cavity of the FP antenna should satisfy the requirements for y- and x-polarizations [Reference Qin, Gao, Wei, Luo, Mao, Gu, Xu and Li8]. The reflection coefficients of the PCM should also satisfy the requirements for y- and x-polarizations [Reference Sun, Chen, Zhang, Chen and See9]. The height of the resonance cavity (H) is given by equation (3):

(3)$$H = \displaystyle{c \over f}\left({\displaystyle{{\Phi_{1x} + \Phi_{2y} + 2n\pi } \over {4\pi }}} \right){\rm , \;}$$

where n is an integer (n = 0, 1, 2 …), H is the height of the resonance cavity, and c is the speed of light in a vacuum. Φ_1x and Φ_2y are the phases of the reflection coefficient in the y and x directions of the ground, respectively.

Fig. 8.

(a) |S11| with and without PCM superstrate and (b) AR and gain with and without PCM superstrate

It is important that the sum of the phases of the reflection coefficients be equal in both directions to satisfy the resonance requirements of the y- and x-polarizations, as expressed in equation (4):

(4)$$\Phi _{1x} + \Phi _{1y} = \Phi _{2x} + \Phi _{2y}{\rm , \;}$$

where Φ_2x and Φ_1y are the phases of the PCM. We assume that both polarizations use the same value of n. The phases of the reflection coefficient in the ground of the antenna are equal to π, i.e. Φ_1x = Φ_1y = π. This is required to obtain an FP antenna with high gain and circular polarization. As explained elsewhere, the symmetrical structure of the proposed PCM with respect to the 45° diagonal, the reflection magnitudes and phases have a similar curve in the x and y directions and the reflection phases, proving that PCM can be used to construct resonance cavities [Reference Li, Liu, Jia and Guo16]. PCM plays a role in transmission, which explains the backscattering in the antenna. We employ a perfect electrical conductor (PEC) ground to simulate the PCM unit cell since both the ground and radiation patches of the source antenna are PECs. The distance between the unit cell and PEC was optimized to 6.15 mm. Through adopting simulated model in HFSS as depicted in Fig. 9(a), Fig. 9(b) shows the cross- and co-polarization reflections in the PCM unit cell with PEC ground. The reflection coefficients of cross-polarization are consistent, while those of co-polarization were lost at 15 GHz. We etch the PCM into the substrate with a checkered pattern to reduce RCS and wideband operation [Reference Li, Liu, Jia and Guo16]. The extent of the RCS reduction depends on the reflective properties of the PCM. Referring to Fig. 8(b), RHCP radiation is present when the PCM is etched into the square patch antenna. Left-hand circular polarization (LHCP) radiation can be gathered by replacing a PCM with a mirror.

Fig. 9.

(a) Proposed model in HFSS, and (b) cross-polarization and co-polarization reflections

Analysis and design of the proposed FP antenna

As shown in Fig. 10, we obtain a 2 × 2 FP antenna array arrangement using sequential rotation. Referring to Fig. 10, there are four sequential rotation orders, labeled parts I, II, III, and IV. As indicated in Fig. 10(b), we design a Wilkinson feeding network with four ports and a 90° phase difference for the proposed FP antenna array.

Fig. 10.

(a) Schematic of FP antenna with checkered PCM, and (b) Wilkinson feeding network

LHCP and RHCP radiations reduce gain and produce four grating lobes in the direction of the boresight if two kinds of PCMs are excited at similar points [Reference Liu, Liu, Jens, Zhao and Kong20]. To mitigate this kind of interference, we select an RHCP antenna array with circularly polarized radiation and a sequentially rotated feeding network as the source antenna. The feeding network excites four orthogonal RHCPs and is printed at the bottom of the 0.5 mm substrate. The ambient RHCPs are excited using a 90° phase difference. RHCP waves are produced when LP waves pass through the PCM or mirror. Gain degradation does not occur in the direction of the boresight. The selected source antenna ensures scattering without reducing radiation. RHCP radiation can be produced without PCM; however, the antenna with PCM possesses a broader AR bandwidth because higher polarization occurs by replacing the four LP elements with four circularly polarized elements. RHCP gain could be improved further through operational frequency. Wideband operation and low RCS are enabled by the checkered PCM. There are several similarities between the x- and y-polarized incident waves and RCS reduction.

Simulated and measured results

To evaluate our design, we simulated, fabricated, and tested our proposed FP antenna design. Figure 11 shows the sample fabricated prototype. As Fig. 11 shows, the substrates of the fabricated prototype were extended by 6 mm compared to the simulation model and fastened with a 3.5 mm subminiature version A connector. The fabricated array had dimensions of 66 mm × 66 mm × 12.65 mm.

Fig. 11.

Fabricated sample of the proposed FP antenna

As shown in Figs 12(a) and 12(b), our antenna had a 10 dB bandwidth at 3.4 GHz (5.6–9 GHz) and a 3 dB AR bandwidth at 3.3 GHz (6.2–9.5 GHz), where the bandwidth enhancement and gain improvement were obtained, compared to the PCM-based antenna element. It can be explained by the application of sequential rotation technical on the 2 × 2 antenna array, which can improve radiation of antenna array significantly.

Fig. 12.

(a) Simulated and measured |S11| and (b) simulated and measured broadside gain and AR

Figure 13(a) shows a plot of RCS reduction versus frequency. The proposed antenna achieved wideband operation and low RCS between 5 and 14 GHz, representing 94.7% of the bandwidth. RCS reduction reached −18 dBsm. We classified the insert that provided the reflective energy into four lobes, reducing RCS significantly. The distribution of scattering is shown in Fig. 13(b). Parts I, II, III, and IV had different resonances, which led to the efficient phase difference between them.

Fig. 13.

(a) RCS reduction versus frequency with and without PCM and (b) distribution of scattering at 7.5 GHz

Figure 14 shows plots of radiation patterns at 8.5 GHz in the yoz and xoz planes. The proposed FP antenna achieved good radiation patterns, with cross-polarizations lower than −32 dB and side-lobes lower than −13 dB. These results were validated by real-world measurements with reasonable margins for errors.

Fig. 14.

Simulated and measured radiation patterns at 8.5 GHz on (a) the xoz plane and (b) the yoz plane

Figure 15 plots reflection coefficients versus frequency with different cavity height h_p. Compared with resonate modes without a CPCM superstrate (circled in black), an additional resonance mode (circled in red) was created between 6.5 GHz and 7 GHz when cavity height h_p increased to 3.15 mm. Therefore, we conclude that this additional resonance mode was produced by the FP cavity. As depicted in Fig. 15(b), it resonated better at 8.5 GHz by increasing h_p from 6.15 mm to 10.15 mm. In conclusion, another resonance mode was also created by the FP cavity at 8.6 GHz. When h_p was set to 6.15 mm, both additional resonant modes existed simultaneously. Moreover, the two resonance modes produced by the source antenna shifted to lower frequency bands when CPCM was applied in this design, as seen in Fig. 15(a).

Fig. 15.

Simulated and measured results for |S11| with different cavity height, h_p, (a) different values under 6.15 mm, and (b) different values above 6.15 mm

Figure 16 shows a plot of the simulated AR versus the incident angle at 7, 8.5, and 9 GHz. The AR curves were all below 3 dB in the scope of ±15°, and the width of the 3-dB beam was consistent with that of the antenna boresight beam at different frequencies.

Fig. 16.

Simulated AR versus incident angle at 7, 8.5, and 9 GHz

Table 2 compares the proposed FP antenna to other kinds of FP antennas. Our proposed FP antenna produced circularly-polarized radiation using the checkered PCM and off-center linearly-polarized MPA. Additionally, the proposed FP antenna possessed high gain, wideband operation, circular polarization, and low RCS, giving it a low profile.

Table 2.

Performance of the proposed FP antenna and other kinds of FP antennas

“–” represents null.