Design of the antenna prototype

The proposed antenna structure consists of a radiating patch, a partially grounded plane, and an MS is composed of a 4 × 4 array of unit cells. The design process begins with an in-depth analysis of a single unit cell, focusing on its key properties, such as permeability, permittivity, refractive index, and impedance. Notably, the results reveal a negative refractive index within the frequency range of 7–13.5 GHz. This frequency band is targeted for the antenna’s operational bandwidth because, within this range, the unit cell exhibits metamaterial-like behaviour. By strategically placing the metasurface behind the antenna, the back-radiated power is redirected forward, resulting in constructive interference that enhances radiation. This effect results in a significant gain improvement. The design of the unit cell and the microstrip antenna are discussed in the following subsections.

Design of unit cell

The top and bottom views of the unit cell structure are shown in Fig. 1(a) and (b), respectively. The unit cell has overall dimensions of 6 mm × 6 mm × 1.6 mm and is etched on an FR4 substrate with a permittivity of 4.4 and a loss tangent of 0.02. The design includes a slotted circular annular ring that encloses a concentric circular element. The scattering parameters for this configuration (|S ₁₁| and |S ₁₁|) are computed using HFSS software, which employs a Floquet port to excite the unit cell. These values are then substituted into equations (1)–(4) [Reference Smith, Vier, Koschny and Soukoulis11] to determine the critical parameters of the proposed structure, such as effective permittivity, permeability, impedance, and refractive index. The calculations are performed using a MATLAB code [Reference Numan and Sharawi12], and the results are shown in Figs. 2 and 3 for a single unit cell. Fig. 2 illustrates the real and imaginary parts of the effective permittivity and permeability. While Fig. 3 presents the real and imaginary parts of the effective impedance and refractive index. The real parts of the effective permittivity and permeability are negative over the frequency range of 7–13.5 GHz, identifying the unit cell as a double-negative (DNG) metamaterial. The negative permittivity and permeability also lead to a negative refractive index over this frequency band, making the structure suitable for metasurface applications. The electric field distribution of the unit cell structure is shown in Fig. 4(a). It is observed that the electric field reaches its maximum on the right and left sides of the unit cell, while it is minimal on the top side and within the inner circular element. As a result, the high electric field around the annular ring facilitates coupling between adjacent unit cells, as denoted by C_c [Reference Samantaray and Bhattacharyya13] and illustrated in Fig. 4(b). This coupling primarily arises from the time-varying electric field across the annular ring, which induces a time-varying magnetic field. This magnetic field excites the adjacent unit cell, resulting in a time-varying current. The capacitance between the annular ring and the circular element is minimal compared to the capacitance resulting from the slot cut in the annular ring. This is denoted by C_eq, while the inductance due to the current flow in the annular ring is represented as L_eq [Reference Baena, Bonache, Martin, Sillero, Falcone, Lopetegi, Laso, Garcia-Garcia, Gil, Portillo and Sorolla14]. In addition to this, the resistive component has been ignored in Fig. 4(c). Thus, the equivalent circuit diagram for the unit cell structure is formed by combining the inductance and capacitance components, as illustrated in Fig. 4(c). The resonant frequency of this structure is given by: f ₀= $\dfrac{1} {2\pi \sqrt{L_{eq} C_{eq}}}$. Furthermore, when the unit cell is used in an array configuration, as shown in Fig. 4(d), the equivalent circuit includes C_x and C_y, which represent the coupling capacitances between the unit cell and its adjacent unit cells along the x- and y-directions of the centred unit cell, respectively. The details of the antenna design and its corresponding parameters have been discussed in the following sections.

Figure 1.

Design of unit cell and its parameters. (a) Top view, (b) bottom view, (c) $|S_{11}|$ and $|S_{21}|$ of unit cell, and (d) simulation of unit cell applying Floquet Port by using HFSS. [R ₁ = 1.1 mm, R ₂ = 2.43 mm, R ₃ = 1.75 mm, L ₁ = 0.68 mm, L ₂ = 0.5 mm, L ₃ = 3 mm.]

Figure 2.

Unit cell’s real and imaginary part of (a) effective permittivity and (b) effective permeability.

Figure 3.

Unit cell’s real and imaginary part of (a) effective impedance and (b) effective refractive index.

Figure 4.

Unit cell’s (a) electric field distribution, (b) coupling between adjacent unit cells, (c) equivalent circuit model, (d) MS and (e) equivalent circuit of MS [2].

(1)\begin{align} z&= \sqrt{\dfrac{(1+S_{11})^{2} -{S_{21}}^{2}} {(1-S_{11})^{2} -{S_{21} }^{2}} } \end{align}

(2)\begin{align} n &= \frac{1}{kd} {\cos^{-1} \left(\frac{1}{2 S_{21}}\right) \left(1-{S_{11}}^{2}+{S_{21}}^{2}\right)} \end{align}

(3)\begin{align} \mu_{eff} &= n\times z \end{align}

(4)\begin{align} \epsilon_{eff} &= \frac{n}{z} \end{align}

Where, ϵ_eff = effective permittivity, µ_eff = effective permeability, $z =$ effective impedance, and $n =$ effective refractive index of unit cell.

(5)\begin{align} Z_{1}&= j\omega L_{1}+ \frac{1}{j\omega C_{1}} \end{align}

(6)\begin{align} Z_{2}&= \frac{1}{R_{1}}+j{\omega}C_{2}+\frac{1}{j\omega L_{2}}\nonumber\\ &= \frac{j\omega L_{2} + j\omega C_{2}(j\omega L_{2} R_{1})+ R_{1}} {j\omega R_{1} L_{2}} \end{align}

(7)\begin{align} Z_{3}&= \frac{1}{j\omega C_{3}} \end{align}

(8)\begin{align} Z_{4}&= \frac{1}{R_{2}}+j\omega C_{4} +\frac{1}{j\omega L_{3}}\nonumber\\ &= \frac{j\omega L_{3} +j\omega C_{4}(j \omega L_{3} R_{2})+ R_{2}} {j \omega R_{2}L_{3}} \end{align}

(9)\begin{align} {Z_{5}}&= \frac{1}{j\omega C_{3}} \end{align}

(10)\begin{align} Z_{in}&= Z_{1} +Z_{2} + Z_{3} + Z_{4} + Z_{5} \end{align}

Design of the radiating patch with MS

Fig. 5 illustrates the step-by-step design process of the proposed antenna. In Fig. 5(a)–(i), a circular patch is connected to a microstrip feed line, with a partial ground plane placed on the bottom side of the antenna. In Fig. 5(a)(ii), the ground plane remains the same as in Fig. 5(a) – (i), but a stub is added just above the feed point on the top side. In Fig. 5(a)(iii), the top side remains unchanged from the previous structure, but the ground plane is loaded with MS. The S ₁₁ responses of structures used in Fig. 5(a) are shown in Fig. 5(b) by the green, blue, and red traces, respectively. Although the variation in bandwidth between Fig. 5(b)(i) and Fig. 5(b)(ii) is not significant, the depth of the S ₁₁ response in Fig. 5(b)(iii) is noticeably improved compared to the structure in Fig. 5(b)(ii). Therefore, the final structure chosen is Fig. 5(iii).

Figure 5.

(a) Step by step design of proposed antenna (i) without stub on the front side and MS on bottom side, (ii) with stub on front side and without MS on the bottom side, and (iii) With stub on front side and MS on bottom side and (b) S₁₁ parameters for (a).

The radiating patch of the antenna consists of a circular element with a radius of 6.5 mm, coupled to a microstrip feed line measuring 11.18 mm × 3 mm. The opposite side of the radiating element features an array of unit cells and a partially grounded plane of dimensions 27 mm × 1 mm. A horizontal stub, with dimensions of 2.5 mm × 10 mm, is placed 2.5 mm above the bottom part of the antenna. The complete antenna structure has sizes of 27 mm × 27 mm × 1.6 mm, and its dimensions are illustrated in Fig. 6, which utilizes FR4 dielectric material. As the unit cell array expands from 1 × 1 to 4 × 4, the antenna gain increases. This is because, when we gradually increase the number of unit cells from a 1 × 1 to 4 × 4 array on the MS, the convergence of the incident electromagnetic (EM) wave in a particular direction also increases. Therefore, we select the MS with a 4 × 4 array of unit cells. However, a 5 × 5 array cannot be used due to space constraints. Fig. 7 depicts the variation of the gap between the ground plane and the lower row of MS (W ₅). As W ₅ increases from 2.03 mm to 3.57 mm, the depth of the resonance frequency increases and shifts from right to left. The bandwidth also increases with W ₅, reaching its maximum at W ₅=3.57 mm. Beyond this value, the bandwidth decreases drastically from W ₅ = 3.57 mm to W ₅=4.17 mm. Therefore, the optimal value of W ₅ is chosen as 3.57 mm, as it provides the maximum bandwidth and resonance depth. In the next section, we discuss the simulated and measured parameters of the proposed prototype.

Figure 6.

Designed antenna prototype with proper dimensions (a) top view, (b) bottom view, (c) fabricated top view, and (d) fabricated bottom view. [R = 6.5 mm, W ₁ = 27 mm, W ₂ =11.18 mm, W ₃ = 2.5 mm, W ₄ = 6 mm, W ₅ = 3.57 mm, L ₁ = 10 mm, L ₂ = 27 mm, L ₃ = 2.1 mm, L ₄ = 6 mm, width of ground plane = 1 mm.]

Figure 7.

Response of S ₁₁ of proposed antenna when varying W ₅.

Discussion of results

The MS-inspired antenna has been fabricated using the photo etching method, and its parameters have been tested in an anechoic chamber with the KEYSIGHT N5224B PNA Microwave Network Analyzer. Fig. 8 depicts the image of the Network Analyzer while measuring the S₁₁ parameter of the proposed antenna. The designed prototype operates in two frequency bands: one from 7 to 7.6 GHz and another from 9.7 to 13 GHz. The first band is not shown in any figures in this paper because, in this region, the prototype exhibits low gain, and our primary objective is to enhance gain in the X-band frequency range. The simulation of the antenna prototype has been performed using High Frequency Structure Simulator (HFSS) software, whereas the equivalent circuit diagram of the designed prototype, modelled using Advanced Design System (ADS) software through an iterative method, is shown in Fig. 9. Modelling an antenna prototype using an equivalent circuit provides a simplified yet effective way to analyze and optimize its performance. This approach translates the complex electromagnetic behavior of an antenna into familiar circuit elements such as resistors, inductors, and capacitors. The circuit model helps engineers understand the impedance characteristics of the antenna without requiring full-wave electromagnetic simulations. It offers an intuitive way to analyze key antenna parameters, including resonance, bandwidth, and impedance matching. Full-wave electromagnetic simulations (e.g., using HFSS or CST) can be computationally expensive and time-consuming. In contrast, circuit models provide a faster alternative for preliminary analysis, significantly reducing computational costs in the early design stages. The feed line with stub structures is represented as a series combination of L ₁ and C ₁. The equivalent circuit for the patch includes the first tank circuit, comprising L ₂, C ₂ and R ₁, followed by C ₃, which represents the capacitance between the patch and the MS. The second tank circuit represents the MS, where C ₄ accounts for C_x, C_y, and C_eq. Finally, the gap W ₅ between the partial ground plane and the lower array of the MS introduces C ₅, as shown in Fig. 9.

Figure 8.

Measured S ₁₁ parameter of proposed antenna.

Figure 9.

Equivalent circuit of proposed antenna. [L ₁ = 599.74pH, L ₂ = 382.94pH, L ₃ = 100.03pH, C ₁ = 2.47pF, C ₂ = 614.20fF, C ₃ = 36.4 pF, C ₄ = 2.63 pF, C ₅ = 9.21 pF, R ₁ = 40 Ohm, R ₂ = 59.99 Ohm.]

Fig. 10 compares the simulated, measured, and equivalent circuit responses of the S ₁₁ parameter for the designed prototype. The measured bandwidth is 3.3 GHz (from 9.7 to 13 GHz), while the simulated bandwidth is 2.75 GHz (from 10 to 12.75 GHz), and the bandwidth from circuit analysis is 3 GHz (from 10 to 13 GHz). Additionally, the maximum S ₁₁ dips for the measured, simulated, and circuit analysis results are −18, −29, and −29 dB, occurring at 11.5, 10.5, and 10.85 GHz, respectively. Comparing the S ₁₁ parameter of the proposed antenna with that of the antenna without MS reveals that the bandwidth of the antenna without MS is narrower by 0.35 GHz ((10–12.75 GHz)–(10–12.4 GHz)) compared to the antenna with MS. Furthermore, the depth of S ₁₁ is also smaller for the antenna without MS. All the relevant results of the proposed antenna are shown in Table 1. The proposed antenna has been designed using the FR4 dielectric material. The difference between the simulated and measured results may occur due to fabrication tolerances. This could be attributed to soldering between the microstrip feed line and the SMA connector or copper loss in the metallic portion of the designed antenna prototype above and below the FR4 dielectric material during polishing. Additionally, the shift may be caused by the insertion loss of the SMA connector, leading to discrepancies between the frequency responses in the simulated and measured results as shown in Fig. 10.

Figure 10.

Simulated and measured S-parameters and circuit responses of the designed antenna.

Table 1.

Some important parameters of the proposed antenna

Fig. 11(a) shows the measured and simulated gains of the prototype antenna, compared with those of a conventional antenna (an antenna without MS). The maximum measured gain of the designed prototype is 12.8 dBic at 10.3 GHz, while the simulated gain reaches 14.4 dBic at the same frequency. In contrast, the maximum gain of the conventional antenna is 6.6 dBic at 10.1 GHz. The measured gain increases significantly from 10 to 11 GHz, after which it drops to 2.2 dBic at 13 GHz. Similarly, the simulated and measured axial ratio bandwidths of the prototype antenna with MS are 9.45–12.52 and 9.3–12.47 GHz, respectively, whereas the simulated result for the prototype antenna without MS is found to be 9.4–12.7 GHz, as illustrated in Fig. 11(b). Notably, the simulated and measured 3 dB axial ratio bandwidths are nearly identical. The circular polarization of the proposed antenna is solely due to the circular patch, not the MS. Fig. 12 depicts the surface current distribution on the radiating element and MS at various frequencies, including 10, 11, 12, and 13 GHz. At 13 GHz, the maximum current density (CD) is observed at the top-left section of the circular patch and on the ground plane. In contrast, at 12 GHz, the highest CD occurs on either side of the lower part of the microstrip feed line. The current density on the MS structure decreases sequentially at frequencies of 13, 10, 12, and 11 GHz. Fig. 13 shows the laboratory set-up used for measuring the antenna’s radiation pattern and scattering parameters. The Antenna Under Test (AUT) is positioned in front of a calibrated reference horn antenna with known gain, at a minimum distance of $d = \frac{2D^2}{\lambda}$ inside an anechoic chamber. Here, D denotes the largest dimension of the AUT, d is the separation between the AUT and the reference antenna, and λ is the operating wavelength. To measure the YZ-plane radiation pattern, the AUT is fixed at $\phi = 0^\circ$ and rotated from $\theta = 0^\circ$ to 180^∘ (vertical scan), as shown in the upper left and lower right parts of Fig. 13. For the XY-plane radiation pattern, the AUT is fixed at $\theta = 90^\circ$ (horizontal scan) and rotated from $\phi = 0^\circ$ to 360^∘, as depicted in the upper right and lower left sections of Fig. 13.

Figure 11.

(a) Gain of the designed antenna and (b) axial ratio of proposed antenna.

Figure 12.

Surface current density of proposed prototype at (a) 10 GHz, (b) 11 GHz, (c) 12 GHz, and (d) 13 GHz.

Figure 13.

Pictures of the set-up while measuring the parameters of a designed antenna in the lab.

Fig. 14 presents the normalized 2D field patterns of the intended prototype at frequencies of 10.4 and 12 GHz. The red and blue colour traces represent the left-handed circular polarization (LHCP) and right-handed circular polarization (RHCP) radiation patterns, respectively. In both the XZ- and YZ-planes, LHCP dominates, except at angles θ = 60^∘, and 210^∘ in the XY-plane at 10.4 GHz, and at θ = 60^∘ and 270^∘ in the same plane at 12 GHz.

Figure 14.

Two-dimensional radiation parameters of designed antenna at (a) 10.4 GHz and (b) 12 GHz.

Fig. 15 shows the vector current density (VCD) at a frequency of 11.4 GHz at t = 0, T/4, 2T/4, and 3T/4. The resultant VCD at t=0 is almost horizontal toward the right-hand side, as shown in Fig. 15(a). Similarly, for t = T/4, 2T/4, and 3T/4, the resultant VCD points vertically downward, toward the left-hand side, and vertically upward, respectively, as shown in Fig. 15(b)–(d). Thus, the resultant VCD rotates according to the left-hand rule. This type of rotation in the VCD confirms that the polarization is Left-Handed Circular Polarization (LHCP). Two main types of parameters are presented: simulated and measured in the lab. Notably, some tolerable differences exist between the simulated and measured values of the antenna parameters, largely due to ambient effects, faulty soldering, and other fabrication-related imperfections. Fig. 16 shows the radiation efficiency of the proposed antenna. From same figure, we observe that the maximum simulated efficiency is 94.2%, whereas the maximum measured efficiency is 92.8%, recorded at 12.3 and 12.2 GHz, respectively.

Figure 15.

Vector current density (VCD) at a frequency of 11.4 GHz for different times.

Figure 16.

Simulated and measured radiation efficiency values of the proposed antenna.

Table 2 compares the present work with several recent studies from the literature, spanning references [Reference Baena, Bonache, Martin, Sillero, Falcone, Lopetegi, Laso, Garcia-Garcia, Gil, Portillo and Sorolla14–Reference Wu, Ji, Li, Liu, Zhang, Zhang and Kong20]. As noted in references [Reference Baena, Bonache, Martin, Sillero, Falcone, Lopetegi, Laso, Garcia-Garcia, Gil, Portillo and Sorolla14–Reference Baba, Hashmi, Esselle, Marin and Jan17], all the high-gain antennas discussed are linearly polarized (LP). Among these, the antenna with the smallest profile size (1.16λ ₀) achieves a moderate gain of 9.3 dBi [Reference Baena, Bonache, Martin, Sillero, Falcone, Lopetegi, Laso, Garcia-Garcia, Gil, Portillo and Sorolla14], while the antenna with the highest gain (18.8 dBi) has the largest profile size, measuring 3.1λ ₀ [Reference Sharma, Gangwar, Kanaujia, Dwari and Kumar16]. Among the circularly polarized (CP) antennas [Reference Ameen and Chaudhary18–Reference Wu, Ji, Li, Liu, Zhang, Zhang and Kong20], the antenna in [Reference Ameen and Chaudhary18] has the smallest size (0.27λ ₀) and the lowest gain of 4.74 dBic, while [Reference Wu, Ji, Li, Liu, Zhang, Zhang and Kong20] reports the maximum gain of 13 dBic, with the largest profile size measuring 1.4λ ₀. In comparison, the proposed high-gain LHCP antenna achieves a maximum gain of 12.8 dBic and has a moderate size of 0.88λ ₀. Among all the papers mentioned in Table 2, apart from our design, the antenna described in [Reference Wu, Ji, Li, Liu, Zhang, Zhang and Kong20] stands out as the best because, offering CP, a high gain of up to 13 dBic, and a moderate size of 1.4λ. However, when comparing our designed antenna with [Reference Wu, Ji, Li, Liu, Zhang, Zhang and Kong20], it is observed that the gain is slightly lower by 0.2 dBic, while the dimensions are significantly smaller (37% less) than those in [Reference Wu, Ji, Li, Liu, Zhang, Zhang and Kong20]. Therefore, it is concluded that our proposed antenna is superior to all the antennas listed in Table 2.

Table 2.

Comparative study of the proposed antenna with some other high-gain antennas