Design and analysis of unit cell

Unit cell design

The geometry of the proposed unit cell is illustrated in Fig. 1. The unit cell consists of two semi-circular rings coupled through a narrow horizontal slot. The radius of the concentric rings in the unit cell follows an iterative logic to achieve the necessary phase swing. The outermost ring is given by the factor ${C_0} = {C_{in}} + \,(4\,\; \times \;{w_0})$, while the middle ring is expressed as ${C_m} = {C_{in}} + {\text{ }}(2\,\; \times \;{w_0})$. The gap and width of the rings are fixed as ${g_{o\,}} = \,{g_m}$ = 0.3 mm. To these rings, phase-compensating PDLs are attached to the outer periphery, as described in Fig. 1. The length of the PDLs is adjusted to meet the necessary phase compensation requirements during the design of the RA. The unit element with a grid periodicity of 0.52${\lambda _0}$ is developed on RT Duroid 5870 substrate with height h ₁ = 0.254 mm and relative permittivity ${\varepsilon _r}$ value as 2.33 with tan δ as 0.0012. The proposed unit cell has a full conductive ground, as shown in Fig. 1(b), supported by FR4 substrate thickness of h ₂ = 0.8 mm. For smoother and more dynamic reflection phase response and mechanical stability, 2 mm polyurethane is loaded between the substrate and the ground. The proposed element design is characterized using Floquet ports with periodic boundary conditions using CST Studio Suite.

Note: cyan denotes metal; pink denotes RT Duroid substrate; and brown denotes FR4 substrate.

Figure 1. Layout of the reflectarray proposed unit cell: (a) front view and (b) side view.

Evolution

In this research, phase range enhancement is achieved with concentric ring elements, as described by Veluchamy et al. [Reference Veluchamy, Selvan, Jyoti and Sravan Kumar22]. Unlike [Reference Veluchamy, Selvan, Jyoti and Sravan Kumar22], the evolution of the proposed reflectarray element starts with coupled half-circular rings, as shown in the inset of Fig. 2 (referred to as Cell 1). The spacing between the half-circular rings is carefully adjusted to induce coupling between the top and bottom circular rings. Two arc-shaped PDLs are represented as $({\theta _s}),$ systematically connected to the outermost half-circular ring to achieve the desired phase compensation. The phase characterization using the Floquet boundary condition indicates that the coupled half-circular rings provide a reflection phase range of 380° corresponding to a reflection bandwidth of 29%. To further enhance the phase variations, a vertical slit of width ${g_m}$ is introduced in the middle ring as evident in Cell 2 of Fig. 2. The resultant configuration has an improved phase span of 450° along with a reflection bandwidth of 32%.

Figure 2. Reflection phase characteristics during the evolution stages.

However, the Cell 2 phase response is limited by the fact that the element produces a steep phase variation. The current distribution plot of the proposed antenna, as shown in Fig. 3(a–b), reveals that the propagating current in the reflectarray element is highly localized to the outermost ring. Hence, distributing the current throughout the aperture of the element would significantly improve the phase characteristics of the reflectarray element. Thus, to control the phase slope, the outer and the middle rings are connected using short stubs as in Cell 3. The localized surface currents on the outer ring of the reflectarray element find an additional current path (Fig. 3(c)), leading to a gradual phase variation of 539°, as shown in Fig. 2. Further improvement in current propagation characteristics is achieved by interconnecting the middle and the innermost rings, as described in Fig. 3(d). The final geometry has a convoluted structure with a phase range improvement of 636°. The corresponding reflection bandwidth is estimated to be 65.6%. Figure 4 illustrates the proposed unit cell reflection phase characteristics varying as a function of arc length (${\theta _s}$) with a reflection magnitude less than −0.48 dB. Thus, from the study of the unit cell characteristics, it is inferred that the proposed reflectarray element combines three resonant modes to achieve a wider reflection bandwidth. The optimized dimensions of the unit cell are given in Table 1.

Figure 3. Evolution of the proposed element through surface current distribution. (a) Unit cell 1; (b) Unit cell 2; (c) Unit cell 3; and (d) Proposed.

Figure 4. Reflection phase characteristics as a function of varying arc angle (${\theta _s}$).

Table 1. Geometrical parameters of the proposed unit cell

Effect of the air gap and dielectric constant

To verify the unit cell characteristics, parametric analysis is performed for varying thicknesses and different dielectric constants of the microwave laminate. The variation in the air gap “h” produces a drastic impact on phase range. For h = 2 mm, 636° even phase variation with reduced phase slope is achieved. With h = 3 mm, the phase range decreases by 100° along with a larger phase slope. When the substrate thickness is increased to 4 mm, a 400° phase span with a steep slope is observed. Hence, the 2 mm air gap is fixed as a compromise between the gradual phase slope and large reflection phase response, as shown in Fig. 5(a). The next investigation was attempted on the impact of the dielectric material parameters on the phase response. The unit cell with a thick substrate offers a low-phase range and a wider bandwidth. The substrate with low permittivity (${\varepsilon _r}$= 2.2) is chosen as it offers a smaller phase slope of 72°/mm and an improved phase range, as shown in Fig. 5(b).

Figure 5. Reflection phase vs. varying arc angle (${\theta _s}$) (a) for varied air gap (h), (b) for varied dielectric permittivity (${\varepsilon _r}$), (c) for different frequencies in Ka-band, and (d) for different angle of incidence in Transverse Electric (TE) and Transverse Magnetic (TM) modes.

Parallel phase slopes and incident angle effect

To analyze the performance of the proposed element concerning bandwidth, the phase span is observed for various frequencies from 26.2 to 37.1 GHz by varying the values of ${\theta _s}$, as shown in Fig. 5(c). It is observed that the designed unit cell offers minimal space parallel phase span for the frequency range from 26.5 to 36 GHz, making it suitable for wideband performance in comparison with [Reference Xia, Wu, Wang, Yu and Hong17, Reference Sharifi, Basiri and Zareian-Jahromi23]. The angular and polarization stability of the unit cell is investigated for different angles in steps of 15° and 25° for θ and ϕ planes, respectively. The unit cell remained insensitive to both TE and TM modes of operation within the acceptable phase deviation up to 20°, as shown in Fig. 5(d). The simulated reflected phase of the proposed element for varying arc lengths from 10° to 120° in the frequency range between 23 and 40 GHz is illustrated in Fig. 6. From the figure, it is inferred that the reflected phase curve of the proposed unit cell is a linear parallel phase range concerning frequency, thus justifying the bandwidth improvement. Therefore, parametric analysis and parallel phase slope designate this RA to be suitable for large-sized and offset-fed reflectarray applications.

Figure 6. Reflection phase vs. varying arc angle (${\theta _s}$) at different frequencies.

Reflectarray design and analysis

Based on optimized unit cell elements, a wideband RA (13.46${\lambda _0}$ × 13.46${\lambda _0}$) with 513 elements is built to operate at the center frequency of 30 GHz. The reflectarray is first constructed using a rectangular aperture with 625 elements. Equation (1) is used to calculate the phase compensation required for each element in the reflectarray configuration [Reference Liu, Cheng, Lei and Kou15].

(1)\begin{equation}{\Phi_{mn\left( r \right)}} = {k_0}({d_i} - ({x_i}{\textrm{cos}}\Phi{_{\textrm{0}}} + {y_i}{\textrm{sin}}\Phi{_{\textrm{0}}}){\textrm{ }} \times {\textrm{sin}}{\theta _0})\end{equation}

where ${k_0}$ is the propagation constant in free space, ${d_i}$ is the separation between the midpoint of ith element (${x_i}$, ${y_i}$) of the developed RA to the midpoint of the antenna source, and (${\theta _0},{\phi _0}$) is the primary beam direction. The calculated phase distribution of the reflectarray construction is given in Fig. 7(a).

Figure 7. (a) Phase distribution of the proposed array. (b) Measured radiation pattern of K/Ka-band feed horn.

The RA uses 18–40 GHz pyramidal horn with a flare length of 20.5 mm as a feed source with an average gain of 15 dB in both the principal planes. The measured radiation pattern of the K/Ka-band standard pyramidal horn is shown in Fig. 7(b). The 1 dB bandwidth achieved from 26.5 to 35 GHz was obtained utilizing 513 elements. At higher frequencies between 33.1 and 37.1 GHz, a steep slope is observed. To mitigate this steep slope, a constant reference phase $\left( {\Delta\Phi {_1}} \right)$ = 25° is added to the 33.1 GHz phase curve elements. By using this procedure, the overall performance of the reflectarray is changed. This 25° constant phase change was fixed with a parametric analysis procedure [Reference Mao, Xu, Yang and Elsherbeni24], as shown in Fig. 8. For different reference phase values of 15°, the gain of the higher frequency range increased, whereas in the case of 35°, the gain drastically reduced, where 1 dB bandwidth was not achieved compared with 25°. The addition of the reference phase to the existing phase values is given by Equation (2). Hence, by applying 25°, the phase slope tends to be gradual, which contributes to the parallel phase slope.

(2)\begin{equation}{\Phi_{mn\left( r \right)}}\left( {\Delta\Phi {_1}} \right) = {\Phi_{mn\left( r \right)}} + \Delta\Phi {_2}\end{equation}

Figure 8. Simulated gain performance by adding a constant reference phase.

where ${\Phi_{mn\left( r \right)}}\left( {\Delta\Phi {_1}} \right)$ is given by the required phase range with the addition of a constant reference phase and ${\Phi_{mn\left( r \right)}}$ is the required phase range.

Furthermore, the phase error function is calculated as the difference between the achievable reflection phase and the required phase range [Reference Dahri, Jamaluddin, Seman, Inam, Sallehuddin, Ashyap and Kamarudin25] and is given by Equation (3).

(3)\begin{equation}{\textrm{ }}P{E_{mn}} = {\textrm{ }}\left| {{\Phi_{mn\left( a \right)}} - {\Phi_{mn\left( r \right)}}\left( {\Delta\Phi {_1}} \right)} \right|{\textrm{ }}\end{equation}

where $P{E_{mn}}$ is the phase error function and ${\Phi_{mn\left( a \right)}}$ is the achieved phase range.

By using the addition of a constant phase reference technique, this phase error function is to be minimized, thereby leading to a 1 dB wider bandwidth. To attain maximum aperture efficiency, the footprint of its feed should not be extended more or less than the aperture area. A circular-shaped reflector is preferred for the proposed center-fed reflectarray to achieve high aperture efficiency. To reduce cross-polarization, a special arrangement is adopted in which the reflector is divided into four quadrants, and each quadrant is mirror-symmetrical to one along the x and y directions. Because the surface currents are oppositely directed for the neighboring elements, the transverse currents are canceled in the far field, thereby reducing cross-polarization [Reference Li and Yang26], as shown in Fig. 11(a). The photograph of the fabricated prototype in the test setup is shown in Fig. 11(b). The distance between the source K/Ka-band pyramidal horn and the reflector is maintained at 140 mm, considering the focal distance to diameter (f/D) ratio as 1. The fabricated RA is measured in the 7 × 3 × 3-m anechoic chamber using an N9917A microwave analyzer for observing the radiation and gain plot characteristics.

After reflectarray construction, the square aperture geometry consists of 625 elements. The outer edge elements contribute to increased sidelobe level for radiation pattern formation. Hence, a circular aperture is designed in which the 28 corner elements in each quadrant with the total number of elements as 112 from 625 elements are omitted and gain is improved up to 0.5 dB compared to square aperture reflectarray, as shown in Fig. 9. Thus, by using the optimization procedure, the gain of the reflectarray is improved to 28.2 dBi. Typically, a circular footprint is projected onto the antenna aperture surface for the center feed. The area illuminated by a feed within its intended 3 dB beamwidth coverage on the surface of a reflectarray is referred to as the feed’s footprint. To maximize efficiency for a reflectarray, the footprint must be identical as shown in the study by Dahri et al. [Reference Dahri, Jamaluddin, Seman, Inam, Sallehuddin, Ashyap and Kamarudin25]. The circular shaped aperture is chosen to achieve maximum aperture efficiency combined with selecting an acceptable feed distance where f/D = 1, as illustrated in Fig. 12(e) based on this center feed footprint behavior. To improve the cross-polarization performance, PDLs attached to the unit cell are reoriented, as described in Fig. 10. The fourfold symmetrical reflectarray aperture is converted into mirror-symmetrical to enhance the cross-polarization performance, as described in Fig. 10. The vector current distribution of the proposed RA is shown in Fig. 11. From the figure, it can be inferred that the current cancellation occurs between the mirror-symmetrically oriented PDLs in the proposed reflectarray geometry. The currents in the PDL get canceled in each quadrant, thereby reducing the cross-polarization.

Figure 9. Optimization procedure of conversion from square aperture geometry to circular aperture geometry.

Figure 10. Mirror-symmetry arrangement to reduce cross-polarization effect.

Figure 11. (a) Surface current distribution of the reflectarray structure. (b) Proposed reflectarray in the measurement setup.

Results and discussion

The simulated and measured E and H plane radiation patterns and cross-polarization depict consistency in the radiation pattern at almost all frequencies ranging from 26.5 to 36 GHz, as shown in Fig. 12(a–d). The experimental 1 dB and 3 dB gain bandwidths of 31.3% and 41.6% along with a peak gain of 28.2 dBi are shown in Fig. 12(e). The variations between the measured and simulated results are attributed to the cable loss factor. The aperture efficiency is given by Equation (4), and the peak aperture efficiency of the proposed reflectarray is 31.4% at 30 GHz.

(4)\begin{equation}{A_{eff}} = \frac{{G{\lambda ^2}}}{{4\pi }}\end{equation}

Figure 12. Normalized E and H plane radiation patterns at different frequencies: (a) 26.5 GHz, (b) 30 GHz, and (c) 36 GHz. (d) Cross-polarization characteristics. (e) Gain and aperture efficiency characteristics.

The optimal trade-off between aperture efficiency, spillover, and feed blockage is obtained by choosing the right f/D ratio. The small f/D value results in spillover loss, while high aperture efficiency is achievable for f/D ratio in the range of 0.7–1 [Reference Dahri, Jamaluddin, Seman, Inam, Sallehuddin, Ashyap and Kamarudin25, Reference Jamaluddin, Gillard, Sauleau, Koleck, Castel, Benzerga and Le Coq27, Reference Narayanasamy, Mohammed, Savarimuthu, Sivasamy and Kanagasabai28]. For f/D = 0.8, the 1 dB gain bandwidth is 26.6%, and an aperture efficiency of 39.23% is achieved. Similarly, for f/D = 1, 1 dB gain bandwidth and peak aperture efficiency are reported as 31.3% and 31.4%, respectively, as shown in Fig. 12(e). Since the bandwidth and aperture efficiency for f/D = 1 are high comparably, the focal distance between the array and horn is maintained as 140 mm. Table 2 provides 1 dB gain bandwidth and aperture efficiency values for different f/D ratios. Table 2 imparts the proposed reflectarray performance comparison with earlier research works.

Table 2. Performance comparison with similar works

NR = Not reported.

^a 1 dB gain bandwidth (BW), SLL: Side Lobe Level.

The following are some of the advantages of the present research over the previous works:

1. 1. In comparison with the unit cell structures presented in [Reference Zhang8, Reference Zhao, li, Zhou, Wang, Tianming, Biao and Zou9, Reference Zhao, Fu, Li, Li and Hu12, and Reference Suresh, Mohammed and Narayanasamy16], the proposed unit cell configuration offers an increased phase span of 636° covering the frequency range of 26.5–36 GHz.

2. 2. The novel RA structure affords a better 1 dB gain bandwidth of 31.3%, covering the bandwidth from 26.5 to 36 GHz, compared to other structures reported in [Reference Veluchamy, Mohammed, Krishnasamy and Jyoti4–Reference Suresh, Mohammed and Narayanasamy16].

3. 3. Using the mirror-symmetry technique, the cross-polarization is reduced to <−50 dB in comparison with other literature reported in [Reference Suresh6, Reference Zhang8, Reference Zhao, li, Zhou, Wang, Tianming, Biao and Zou9, and Reference Zhao, Fu, Li, Li and Hu12].

4. 4. The fabricated RA offers 28.2 dBi peak gain in comparison with the research reported in [Reference Veluchamy, Mohammed, Krishnasamy and Jyoti4, Reference Zhao, li, Zhou, Wang, Tianming, Biao and Zou9, Reference Yu, Zhang, He, Gao, Chen and Zhu11, and Reference Sharifi, Basiri and Zareian-Jahromi23] and 31.4% aperture efficiency when compared to [Reference Veluchamy, Mohammed, Krishnasamy and Jyoti4] and [Reference Yu, Zhang, He, Gao, Chen and Zhu11] using only 513 elements.

5. 5. In comparison with work by Zhao et al. [Reference Zhao, li, Zhou, Wang, Tianming, Biao and Zou9], the current work is better in terms of phase span ranging over 636°, gain of 28.2 dB, 1 dB gain bandwidth of 31.3%, and cross-polarization less than 50 dB.

Therefore, the developed RA structure operates at 5G communication satellite frequencies by inheriting characteristics like narrower beamwidth, enhanced bandwidth performance, and a reduction in cross-polarization levels.