Optimization of single element of antenna
The performance of the proposed single patch element is significantly enhanced by the introduction of a pair of bow-tie slots. These slots modify the antenna’s geometry and electromagnetic behavior, disrupting the uniform surface of the patch and creating additional resonant features that broaden the frequency response. In other words, the bow-tie slots induce a complex current distribution, allowing energy to be radiated from multiple regions of the antenna rather than just the edges, effectively increasing the effective radiating area and thus enhancing bandwidth and gain. Additionally, the bow-tie slots mitigate surface wave effects by interrupting conductive paths, preventing destructive interference and further improving radiation efficiency. They also influence the impedance characteristics of the antenna, resulting in better matching between the antenna and the feed line, maximizing power transfer while minimizing reflection losses.
As illustrated in Fig. 2a, the incorporation of two bow-tie slots etched near the central radiating patch (Antenna without pins) significantly improves the antenna’s performance. This modification enhances reflection characteristics (\(S_{11}\)), expands the input impedance bandwidth from 28 to 29.3 GHz, and achieves a substantial gain enhancement of up to 8 dBi. Furthermore, Parametric investigations presented in Fig. 3a explore the influence of change in radius of triangular slots creating change in bow-tie slot dimensions on the radiating patch, improving impedance matching. Variations in slot dimensions are believed to alter the resonance characteristics due to changes in the overall resonating length. The optimal slot dimensions, identified with \({r_{b}}\)=0.5 mm. Moreover, the variation in the positioning of these bow-tie slots is illustrated in the Fig. 3b. It is evident that increasing the distance between the diagonally placed bowtie slots leads to changes in the reflection coefficient. Specifically, as the separation distance (denoted as \({dr_{b}}\)) increases, the reflection coefficient varies accordingly, indicating how the positioning of the slots influences the antenna’s impedance matching characteristics. Notably, at a distance of \({dr_{b}}\) = 0.35 mm, we achieve optimum performance, corresponding to the best impedance matching and minimal reflection losses. This optimal positioning enhances the antenna’s overall efficiency and effectiveness, underscoring the importance of precise slot placement in achieving the desired performance metrics. Furthermore, The gain of the presented antenna is increased by utilizing the two prominent techniques.
(a) \(S_{11}\) comparison of all the design steps. (b) Comparison of gain of all the design steps.
(a) Effects of dimensions(radius) of bowtie slots on s-parameters (b) Effects of spacing between bow-tie slots s-parameters.All the dimensions are in millimeters(mm).
(a) Effects of position of shorting pins. (b) Effects of size of shorting pins. All the dimensions are in millimeters (mm).
Gain enhancement with loading of shorting pins
The proposed antenna features a small rectangular patch with bow-tie slots and shorting pins near the upper and lower edges, respectively. Figure 10a shows the physical measurements of the shorting pins based antenna. Figure 2a,b illustrate reflection coefficients and gain curves for each design step, from the initial to the final version of the shorting pin-based patch antenna. First, the physical measurements of the antenna operating at the desired 28 GHz frequency band are calculated using the equations mentioned in34. Impedance matching is achieved through a quarter-wave transformer feed to minimize energy reflection in the initial stage of a simple antenna. Then after incorporating two bow-tie slots etched near the central radiating patch (Antenna without pins), the antenna with improved reflection characteristics (\(S_{11}\)) achieved a significant improvement in both input impedance bandwidth ranges from 28–29.3 GHz and gain enhancement antenna upto 8 dBi. In final design step, the diagonal placement of two shorting pins into the slotted patch structure brings an operating frequency band from 27.1–29.5 GHz closer to the desired 50 \(\Omega\) impedance and improves the gain by up to 10 dBi. This improvement in the peak gain is accomplished without broadening the antenna footprint. Figure 4a,b present a parametric analysis of the reflection coefficient, examining the impact of shorting pin positions while maintaining a constant distance (\(D_P\)) and varying the pin radius (\(P_r\)). The results demonstrate that optimizing pin placement and size significantly enhances impedance matching between the antenna and feed line, leading to increased power transfer and higher gain. Strategically positioning shorting pins on an antenna patch can significantly improve gain by influencing surface current distribution and introducing inductive and capacitive effects. By concentrating current in specific areas and effectively shortening the radiating structure, shorting pins enhance radiation efficiency and enable resonance at the desired frequency. A precise adjustment of the initial shorting pin position (P1) to a distance of \(D_P = 2.5\) mm from the center feedline edge allows for a fine-tuned fundamental resonance frequency of approximately 28 GHz. The optimal pin radius is determined to be \(P_r = 0.1\) mm. Increasing the radius beyond this value leads to a shift in frequency towards higher values and affects impedance matching.
The shorting pins create shunt inductive shortcuts, reducing the effective length of the antenna, enabling resonance at a smaller physical size, and enhancing its directivity. Additionally, they introduce capacitance and inductance, modify the current distribution, and improve impedance matching. Although, the pin primarily introduces inductive reactance, as expected from its structure. However, in our specific design, the proximity of the pin to the adjacent conductive surfaces can also introduce a small parasitic capacitance due to interaction between ground plane and patch. When the pin is near other conductive elements, it can create a parasitic capacitance due to the electric field between the pin and the nearby surfaces. However, the inductance of an individual pin can be calculated using the formula35, where \(\mu _0\) represents the vacuum permeability, and h denotes the height of the pins.
$$\begin{aligned} L_{pin} = \frac{\mu _0}{2\pi } \left[ h_{pin} \ln \left( \frac{h_{pin}+\sqrt{{h_{pin}}^2+{R_{pin}}^2}}{R_{pin}}\right) – \sqrt{{h_{pin}}^2+{R_{pin}}^2} + \frac{h_{pin}}{4} + R_{pin} \right] \end{aligned}$$
(1)
Assuming that the interaction between the pins is negligible, the equivalent inductance \(L_p\) can be calculated as \(L_{pin}\) / N, where N is the total number of pins, and \(L_{pin}\) denotes the inductance of each pin. The calculation of \(L_p\) considers the radius \(R_{pin}\), height \(h_{pin}\), and the total number of pins \(N_{p}\).
Surface current distribution at 28 GHz. (a) Without shorting pins (b) with shorting pins.
The surface current patterns for antennas equipped with and without shorting pins are depicted in Fig. 5. In the absence of shorting pins, the current distribution is uniform across the patch, indicating a balanced excitation of the antenna. However, upon the introduction of shorting pins, the current distribution becomes significantly perturbed. The current density is notably enhanced in the upper and central regions of the radiator, where it concentrates along the path from the feed point toward the shorting pins. This shift in current flow indicates that the pins are effectively influencing the electromagnetic behavior of the antenna. Furthermore, pronounced current concentrations are observed along the edges of the bowtie-shaped slots and within the central area of the patch. These variations in current density highlight the impact of shorting pins on the antenna’s performance, as they alter the current paths and enhance the overall radiating capability of the antenna. The enhanced concentration of current in specific areas underscores the role of shorting pins in optimizing the antenna’s radiation characteristics and improving its efficiency.
Gain enhancement with loading of metasurface superstrate configuration above pin-loaded antenna
(a) Unit cell dimensions with simulation setup. (b) Reflection and transmission coefficients. (c) Reflection phase characteristics. (d) Effective permittivity and permeability plots.
Furthermore, a metasurface approach is presented to further improve the gain of the antenna. This involves creating an array of regularly spaced unit cells using the same substrate as that used in Rogers 5880. CST Microwave Studio simulates the unit cell using the time-domain finite-difference approach (FDTD) method. Figure 6a depicts the layout of the presented unit cell, which incorporates circular and hexagonal conductive rings featuring diagonally etched slits at their terminations. In the proposed unit cell, SRR naturally presents a negative real part of permittivity. Whereas, hexagonal shapes are chosen for their geometric advantage in providing uniform field distribution and efficient packing within metasurface designs. The inner hexagonal plane and rings serve as resonators, designed to store and exchange electromagnetic energy between electric and magnetic fields, which is essential for metamaterial behavior. The combination of plane and rings adjusts the structure’s effective capacitance and inductance-where capacitance is influenced by gaps between elements and inductance by conductive paths-allowing precise tuning of the resonance frequency by modifying the size and spacing of the hexagonal elements as seen in the S-parameters (Fig. 6b), where a strong resonance is achieved with minimal reflection (low \({S_{11}}\)) and maximum transmission (high \({S_{21}}\)) near the targeted frequency. This behavior proves that the design efficiently channels electromagnetic energy, leading to improved performance in terms of gain and radiation efficiency when integrated with the antenna.
The simulated environment utilizes suitable electric and magnetic field distribution along both axis of x and y, respectively. Two waveguide ports placed along the Z-axis allow electromagnetic waves to propagate. The transmission and reflection planes are separated into two discrete areas where the electric fields of the associated waves are combined.36.
$$\begin{aligned} E_{a}=e^{\left( -\gamma _C h_1\right) }+BC_1 e^{\gamma _C h_1} \end{aligned}$$
(2)
$$\begin{aligned} E_{b}=BC_2 e^{\left( -\gamma _{c}\left( h+h_2\right) \right) } \end{aligned}$$
(3)
where
$$\begin{aligned} \gamma _{c}= j\left[ \left( \frac{\omega _{o}\mu _{r} \varepsilon _{r}}{c_{o}}\right) ^2 – \left( \frac{2 \pi }{\lambda _{o}}\right) ^2\right] ^{1/2}. \end{aligned}$$
(4)
Here, the symbol \(c_{o}\) denotes the speed with which the light travels, while \(\omega _{o}\) represents the angular frequency. The cut-off wavelength is given by \(\lambda _{o} = 2l\), where l corresponds to the waveguide width. The boundary states of electric and magnetic fields can be exploited to find \(BC_1\) and \(BC_2\). The entire height of the waveguide structure is determined as \(h_{\text {sum}} = h_1 + h + h_2\). In this expression, \(h_1\) and \(h_2\) refer to the heights of the receptive ports, and h represents the substrate height of the unit cell model. Thus, for these two ports, the scattering parameters37 are computed as:
$$\begin{aligned} S_{11}=P_a^2\left[ \frac{\Gamma _s\left( 1-T_s^2\right) }{1-\Gamma _s^2 T_s^2}\right] \end{aligned}$$
(5)
$$\begin{aligned} S_{22}=P_b^2\left[ \frac{\Gamma _s\left( 1-T_s^2\right) }{1-\Gamma _s^2 T_s^2}\right] \end{aligned}$$
(6)
$$\begin{aligned} S_{12}=S_{21}={P_{a}}{P_{b}}\left[ \frac{\Gamma _s\left( 1-T_s^2\right) }{1-\Gamma _s^2 T_s^2}\right] \end{aligned}$$
(7)
where \(P_a\) and \(P_b\) represent the two-port reference plane modification. \(\Gamma _s\) and \(T_s\) are the reflection and transmission coefficients for the suggested 3D-metamaterial unit cell. Figure 6b depicted simulated reflection and transmission properties of a unit cell. At 28 GHz, the periodically arranged unit cells exhibit a reflection phase of 0\(^\circ\), as depicted in Fig. 6c: The reflection phase varies by \(\pm {180}^{\circ }\) over the operating frequency range. By using the method described in38, Fig. 6d illustrates that both permittivity (\({\varepsilon _ {r}}\)) and permeability (\({\mu _ {r}}\)) are negative at approximately 28 GHz, indicating negative refractive indices.39,40. In addition, as shown in Fig. 11b, The planar 2D lattice is created by arranging the unit cells in a periodic pattern along the x and y axes. This lattice served as a superstrate positioned above the proposed antenna. The resulting three-dimensional (3D) structure, incorporating a metasurface superstrate, is depicted in Fig. 12c. This configuration forms a Fabry-Perot cavity (FPC)18. The cavity is intended to modify and improve the antenna’s radiation capabilities by harnessing multiple reflections within its confines. Waves undergo repeated reflections within the cavity before partially escaping through the metasurface superstrate. A conductive ground plane suppresses backward radiation, creating a parallel plate configuration with the reflective metasurface. This arrangement facilitates multiple internal reflections. Positioned at a distance \(b_h\) above the radiating substrate, the electrically thin metasurface contributes to the cavity resonance. This resonance occurs when emitted and reflected waves align in phase after completing a full round trip within the cavity. To optimize performance, the Fabry-Perot (FP) resonator antenna’s cavity height was adjusted to satisfy resonance conditions. A 2 \(\times\) 2 lattice of small cells was utilized as a superstrate over the modified patch antenna, with a separation distance of \(b_h\) between the superstrate and ground plane (Fig. 13b). Our main focus is to design a metasurface , covering only the radiating patch of the antenna that led to the selection of a four-unit cell metasurface superstrate.This choice minimizes complexity and cost while achieving the desired electromagnetic properties. Increasing the number of unit cells would introduce fabrication challenges and necessitate more intensive simulations for optimization. Fig. 7a,b explains the effect of number of increasing unit cells on bandwidth and gain of antenna. To assess the influence of these uniquely designed unit cell number on gain and bandwidth, a comparative study is conducted using different number of unit cells \({N_{cell}}\)=2,4,6,8 configurations, aiming to optimize the number of unit cells to cover the radiating patch of the antenna. The main focus is on enhancing capacitive coupling between cells and the interaction between the metasurface and the conventional antenna, which are crucial for mitigating the inductive effect of the slot. The results showed that the unique configuration of four \({N_{cell}}\) = 4 unit cells in the metasurface array configuration to cover the radiating patch of antenna efficiently and yielded the best performance in terms of both gain and bandwidth. Furthermore, For the presented superstrate based metasurface antenna, the resonant conditions are represented in equations (8) and (9), where \(b_h\) represents the cavity height, \(\Phi _{sup1}\) depicted the phase of reflection for superstrate and \(\Phi _{grnd1}\) denotes the phase of reflection of the ground plane, respectively, and \(\lambda _{0}\) is the operating wavelength within the substrate.
(a) Effects of number of unit cells on bandwidth. (b) Effects of number of unit cells on gain.
$$\begin{aligned} \Phi _{sup1} + \Phi _{grnd1} – \frac{4\pi b_{h}}{\lambda _{0}} = 2N_{1}\pi , \quad N=0,\pm 1,\pm 2,\ldots \end{aligned}$$
(8)
$$\begin{aligned} \Phi _{sup1} = \frac{c}{4\pi b_{h}} (\Phi _{sup1} + \Phi _{grnd1} – 2N_{1}\pi ) \end{aligned}$$
(9)
The FPC cavity is excited by a patch antenna at one aperture and is open to free space at the opposite end. Careful management of higher-order mode propagation within the cavity is essential to achieving enhanced gain performance. The specific modes excited are influenced by the patch antenna’s position and the cavity’s geometric configuration. Upon fulfillment of condition (8), The FP antenna’s overall gain (dB) can be written as41:
$$\begin{aligned} G_{\text {total}} = G_{\text {ant1}} + G_{\text {sup1}} \end{aligned}$$
(10)
where \(G_{\text {sup1}}\) represents the improved gain brought on by the metasurface and \(G_{\text {ant1}}\) represents the gain of the source antenna. The value of \(G_{\text {sup1}}\) is contingent upon the metasurface’s reflection magnitude, \(|\Gamma _{\text {sup1}}|\), given as follows:
$$\begin{aligned} {G_{\text {sup1}}} = 10 \log _{10} \left( \frac{1 + |\Gamma _{\text {sup1}}|}{1 – |\Gamma _{\text {sup1}}|} \right) \end{aligned}$$
(11)
Equation (10) demonstrates a direct correlation between the magnitude of the metasurface superstrate’s reflection coefficient, \(|\Gamma _{sup1}|\), and the overall gain, \(G_{total}\). Optimizing the metasurface for maximum reflection coefficient is crucial for achieving high antenna gain.
Moreover, according to the classical theory of FP antenna42, the distance between the superstrate and ground layers, considered as a cavity length \({b_{h}}\) is chosen as the value of 0.5 \(\lambda _{0}\), where \(\lambda _{0}\) represents the millimeter wavelength at the 28 GHz resonance frequency. After some parametric analysis on \({b_{h}}\), The impedance bandwidth reaches its optimal value at \({b_{h}}\) = 5.22 mm or 0.5\(\lambda _{0}\) for the final suggested configuration yielded a maximum gain enhancement up to 13 dBi, respectively.
Furthermore, Fig. 8 depicts a circuit model of the patch antenna loaded with loading of pins and then combined with a metasurface. This circuit is created with the simulation program of Keysight Advanced Design System (ADS). The dielectric substrate is represented by a transmission line model, with its thickness denoted by \(h_s\). The substrate’s intrinsic impedance, \(Z_{is}\), is calculated as the impedance of free space (\(Z_{os} = 377 \Omega\)) divided by the square root of the substrate’s relative permittivity (\(\epsilon _r\)). The suggested patch antenna is defined as an RLC circuit with parallel connections comprising resistance (\(R_{a}\)), inductance (\(L_{a}\)), and capacitance (\(C_{a}\)) components. The effects of the shorting pins are divided into two components: the interaction with the patch, modeled by \(R_{p_i}\), \(L_{p_1}\), and \(C_{p_1}\), and the interaction between pins, represented by \(L_{p_2}\) and \(C_{p_2}\). This approach enhances antenna gain through the introduction of shorting pins, requiring precise optimization of pin position and radius for optimal resonance. The resonant frequency of shorting pin loaded patch antenna can be determined using the following equation7:
(a) Circuit representation of the proposed antenna configuration with lumped circuit parameters as: \({R_{i}}\) = 21\({\Omega }\), \({C_{s}}\) = 0.078 pF, \({L_{a}}\) = 1.14 nH, \({C_{a}}\) = 0.12 pF, \({R_{a}}\) = 51 \({\Omega }\), \({L_{f}}\) = 0.89 nH, \({C_{f}}\) = 0.13 pF, \({C_{p1}}\)= 1.28 pF, \({C_{p2}}\) = 1.56 pF, \({L_{p1}}\) = 1.45 nH, \({L_{p2}}\) = 1.16 nH , \({R_{pi}}\) = 55\({\Omega }\), \({R_{p}}\)= 44 \({\Omega }\), \({C_{p}}\) = 0.061 pF, \({C_{ms}}\) = 0.33 pF, \({L_{ms}}\) = 0.28 nH, \({R_{ms}}\) = 50.5 \({\Omega }\),\({C_{ms1}}\)= 0.26 pF, \({C_{ms2}}\) = 0.15 pF and \(Z_{o}\) = 50 \({\Omega }\). (b) \(S_{11}\) comparison between CST simulation and ADS simulation characteristics.
28 GHz surface current patterns (a) aerial view of antenna (b) aerial view of the metasurface.
(a) Gain comparison of all the design steps. (b) Comparison of efficiencies of all the design steps.
$$\begin{aligned} f_{ra }=1 / 2 \pi \sqrt{\left( L_a \Vert 0.5 L_{p_1}\right) \left( C_a+2 C_{p_1}\right) } \end{aligned}$$
(12)
Moreover, the equivalent circuit analysis for the metasurface-based pin-loaded antenna considers mutual coupling and circuit element uncertainties. The model integrates electric field interactions, surface current distribution, and metasurface losses. The metasurface is represented by an LC-resonant circuit with \({L_{m}}\), \({C_{m}}\), and \({R_{m}}\). Coupling capacitors are calculated using C=\({\epsilon _{r}}\) \({\epsilon _{o}}\)A/\({b_{h}}\), and multi-layer structures contribute to capacitance \({C_{a}}\). Lumped circuit parameters are determined through Keysight ADS simulation analysis as displayed in Fig. 8a. Figure 8b showcases the \({S_{11}}\) responses acquired from the simulations using both the circuit model and the numbers. These results demonstrate agreement between numerical and circuit simulations.
Whereas, Fig. 9 illustrates the distribution of surface currents across the antenna operating at a 28 GHz frequency, revealing a notable amplification in the intensity of surface currents around the antenna aperture and the metasurface at the 28 GHz operating frequency. The presence of multiple unit cell slots contributes to an expanded route of current distribution on the upper surface. Furthermore, Fig. 10a,b represent a comparative analysis of broadside gain and efficiency conducted across different design iterations, starting from a single antenna to the final metasurface inspired pin-loaded configuration. The results indicate a substantial enhancement in both parameters, with peak gain increasing from 7.9 to 13.4 dBi and efficiency rising from 85 to 94% upon metasurface integration.