Unit-cell geometry

Figure 1(a) shows the layout of the proposed uniplanar EBG which consists of two metal layers separated by a dielectric substrate. The back metal layer acts as a complete perfect electric conductor (PEC) ground plane. The unit-cell geometry is printed on the front side of the substrate and has a 2D periodic configuration. The substrate material is Taconic TLC-32 (relative permittivity e_r = 3.2 and loss tangent tan δ = 0.003) having a thickness of 0.79 mm. The proposed unit cell consists of interdigital capacitors (IDC) along the outer edges and a four-arm spiral resonator at the center making it interconnected with corner square patches of length l_i. Fingers of the IDC are folded to adjust the overall capacitance of the structure. Each unit element is connected at the corners with adjacent unit cells. Hence in a full 2D array configuration, surface current in the spiral resonator flows from one unit cell to its adjacent ones and causes an increase in total inductance. The periodicity (P_c) of the proposed EBG is 4.2 mm or 0.13 λ ₀, where λ ₀ is free space wavelength at the center frequency of the bandgap. The final dimensions of the unit cell are l_f = 0. 98 mm, l_i = 1.12 mm, w = 0.15 mm, g = 0.15 mm.

Fig. 1.

(a) Geometry of the proposed uniplanar EBG – front and side views; (b) simulated dispersion diagram.

Dispersion characteristics

EBG is generally characterized by its dispersion diagram which is a graphical representation of phase constant (β) and the wavenumber (k). For EBG, non-linear variation of β (or k) relative to frequency exists due to its lossy nature. EBG assists the propagation of different surface wave modes, each of them having a unique field configuration. The lowest propagation mode is transverse magnetic (TM) with zero cut-off frequency. Periodic geometry of EBG allows the existence of frequency bandgap between two modes. Within the bandgap, EBG suppresses the surface wave propagation. The proposed EBG is simulated in Eigen mode solver of high-frequency structure simulator (HFSS) by imposing periodic boundary conditions. Eigen mode frequencies are determined only over the Brillouin zone triangle consisting of Γ-X-M due to 90° rotational symmetry in the proposed geometry. The dispersion diagram of the proposed EBG is depicted in Fig. 1(b) and the result shows a bandgap from 7.37 to 12.4 GHz (50.9%) between the first two modes. The bandgap covers the entire X-band of the microwave spectrum.

The aforementioned bandgap is further characterized by placing a seven-element 1D EBG array on both sides of a 50 Ω microstrip line as illustrated in Fig. 2(a). The spacing between the transmission line (TL) and the EBG array is 0.15 mm. Capacitive coupling between the proposed EBG and TL interacts with propagating transverse EM wave and opposes the propagation of the wave over specific frequency regions due to EBG's resonance nature. Figure 2(b) shows the transmission coefficient (S ₂₁) of the EBG-loaded TL which exhibits two narrow stopbands at the center at 6.75 and 13.15 GHz. An increase in capacitance between the EBG and TL causes a shift of the first stopband frequency at a lower frequency range [Reference Kurra, Abegaonkar, Basu and Koul9]. The BW of two stopbands with S ₂₁<−3 dB are over 6.21–6.97 GHz (11.53%) and from 12.76 to 14.1 GHz (9.98%).

Fig. 2.

(a) Schematic diagram of EBG coupled with microstrip line; (b) simulated transmission coefficients of EBG-unloaded and loaded transmission line. Design parameters are: w_m = 1.9 mm and g₁ = 0.15 mm.

EBG as frequency-selective surface

The reflection and transmission coefficients of the proposed EBG are determined for plane wave incidence. The back metal layer of the EBG is removed to allow transmission through the structure. Scattering parameters are obtained from full-wave numerical simulation under Floquet port excitation. The results are compared with the circuit simulation and the measured filter response is obtained using the waveguide measurement technique. Figure 3(a) exhibits the experimental setup for waveguide measurement with FSS placed inside the sample holder. EM wave impinges on the FSS from WR-90 waveguide with an operating range between 8.2 and 12.4 GHz. Two such waveguides act as the source and the receptor of the EM waves. The equivalent circuit of the proposed FSS is modeled as parallel resonant circuit L_p-C _p as shown in Fig. 3(b). The effect of the dielectric substrate is taken into consideration by representing it as a short TL of characteristics impedance $Z_s = Z_0/\sqrt {\varepsilon _r}$and the length h same as the substrate thickness. Here Z ₀ is the wave impedance of free space having a value of 120 π or 377 Ω. While the surface current through the spiral resonator at the center contributes to total inductance (L_p), the fringing field between the fingers of IDC attributes to the capacitance (C_p). Numerical and circuit simulations of the proposed FSS are shown in Fig. 3(c) over the frequency sweep of 5–15 GHz. Final values of L_p and C_p are obtained using the curve fitting method in a circuit simulator and the values are 1.56 nH and 0.17 pF. The proposed FSS shows a simulated passband center at 9.32 GHz. The 3 dB transmission BW (S ₂₁ > −3 dB) extends over 7.16–11.61 GHz (47.4%). Inside the X-band frequency range, measured scattering parameters are found consistent with the simulation results except for little discrepancies at the band edges. The discrepancy is caused by an increase in attenuation outside the operating range of the WR-90 waveguide.

Fig. 3.

(a) Waveguide measurement setup for the proposed EBG acting as FSS for plane wave incidence; (b) equivalent circuit model of the FSS; (c) simulated and measured reflection and transmission coefficients.

To illustrate the angular stability of the proposed FSS, the reflection and transmission coefficients of the FSS are simulated at different incidence angles. The simulated result in Fig. 4 exhibits a stable passband filter response of the FSS up to a high oblique incidence of 60° for both transverse electric (TE) and TM polarizations. The shifts in resonance frequency are <0.86% for TE mode and <4.5% for TM mode. The performance of the proposed EBG is compared with earlier reported unit cells in Table 1. Compared to unit cells in [Reference Venkata and Kumari4, Reference Yang, Fan, Chen, She and Feng6–Reference Abedin, Azad and Ali11], the proposed geometry achieves a higher bandgap with comparable unit-cell periodicity and thickness. Moreover relative to mushroom-type EBGs in [Reference Venkata and Kumari4, Reference Yang, Fan, Chen, She and Feng6–Reference Bhavarthe, Rathod and Reddy8], the proposed uniplanar configuration has an added advantage of less fabrication complexity due to the absence of metallic via.

Fig. 4.

Simulated reflection and transmission coefficients of the EBG acting as FSS for different incidence angles: (a) TE mode; (b) TM mode.

Table 1.

State-of-the-art performance comparison of the proposed uniplanar EBG with previously reported unit cells

RIS-backed broadband antenna

RIS exhibits in-phase reflection near its resonance for a plane wave incidence [Reference Meng, Liu and Sharma18]. Away from the resonance, the inductive reactance of RIS compensates for the capacitance associated with the electric energy stored in the antenna near-field region. This results in broadband impedance matching and miniaturization of radiating patch dimensions. In the present work, RIS consists of periodic square patches of array size 8 × 8 on a ground-backed TLC-32 substrate with a height of 0.79 mm. RIS unit cell has periodicity (D_x) 3.27 mm with a square patch length (a) of 2.87 mm. The copper with a thickness (t) of 0.035 mm is used as conducting material. The grounded dielectric substrate is modeled as short-circuited TL, which provides an equivalent inductance according to TL theory. The spacing between the adjacent square patches contributes to capacitance in parallel. The simulated reflection phase of the proposed RIS unit cell and its simulation setup for plane wave incidence are depicted in Fig. 5. The wave is incident along the Z-axis with the perfect magnetic conductor and PEC boundaries are assigned in the YZ and XZ planes, respectively. Figure 5(b) shows that the reflection phase varies from +180° to −180° and it decreases with the increase in frequency. The zero-crossing of the phase occurs at 11.8 GHz. The operating BW of the RIS is 10.36–12.92 GHz (22%) over which the reflection phase varies between +90° and −90°.

Fig. 5.

(a) RIS unit cell with simulation setup for plane wave incidence; (b) simulated reflection phase.

Figure 6(a) represents the layout of the rectangular patch antenna with the RIS-backed ground plane. Radiating patch has length (L_p) 5.8 mm, width (W_p) 7.6 mm, and it is printed on Taconic TLC-32 substrate with a height of 0.79 mm. The probe feeding is used to excite the antenna with the probe being located at a distance P_x from the center along the x-axis. Simulation of the proposed patch antenna is performed in HFSS and the results are shown in Figs 7(a) and Figs 7(b). Antenna resonates at 11.1 GHz with a simulated impedance BW of S ₁₁ < −10 dB from 10.31 to 12.76 GHz (21.24%) and having peak realized gain of 6.02 dBi.

Fig. 6.

(a) Schematic of the proposed broadband antenna on RIS; (b) side view of the proposed FP-CRA with EBG as PRS.

Fig. 7.

Simulated (a) reflection coefficient and (b) gain characteristics of the proposed broadband reference antenna and the EBG superstrate-loaded FP-CRA.

Antenna with EBG superstrate

Low directivity of the proposed RIS-backed patch antenna is enhanced by placing an EBG superstrate over the radiator at a distance d from the patch surface as depicted in Fig. 6(b). The ground plane of the antenna and the superstrate layer form the two reflecting surfaces of the Fabry–Perot cavity inside which the radiating patch is placed as a primary feed. The EBG superstrate has the characteristic of PRS at the operating frequency of the antenna at which the magnitude of reflection coefficient is >0.55 and the reflection phase decreases linearly with frequency (see Fig. 8). Directivity of the primary antenna is enhanced due to multiple reflections of the radiating wave between the superstrate and the ground plane [Reference Foroozesh and Shafai13]. From the cavity, the wave is leaking out partially without any reflection while part of the wave is being transmitted after suffering reflection between the cavity walls. According to the principle of ray theory, two transmitted rays interfere constructively when the phase difference (Δϕ) between them is even multiple of 360° as obtained using (1) [Reference Foroozesh and Shafai13]

(1)$$\Delta \phi = \phi _{PRS}-\pi -\displaystyle{{4\pi {h}^{\prime}} \over \lambda } = 2N\pi , \;$$

where N = 0, 1, 2, … (1)

Fig. 8.

Simulated reflection coefficient magnitude and phase variation of the proposed EBG superstrate.

Here ϕ_PRS is the reflection phase of the proposed EBG superstrate and “π” corresponds to change in phase after reflection from the PEC ground. Note that h′ is the total height of the superstrate from the ground plane and this can be rearranged according to (2)

(2)$${h}^{\prime} = d + 2h\sqrt {\varepsilon _r} = \left({\displaystyle{{\phi_{PRS}} \over \pi }-1} \right)\displaystyle{\lambda \over 4} + N\displaystyle{\lambda \over 2}.$$

For the lowest order mode inside the cavity, N is equal to “0” and the height of the superstrate will be approximately λ/2 when the reflection phase of the superstrate is close to −180°. The gain and reflection coefficient of the proposed FP-CRA are illustrated in Fig. 7 along with the reference microstrip antenna. The performance of the proposed EBG as PRS is also compared with the dielectric superstrate-loaded RIS back antenna. Figure 7(b) shows the simulated peak realized gain of the combined antenna–superstrate structure reaches 12.35 dBi at 10.8 GHz with a gain improvement of 6.59 dB as compared with the reference antenna. Simulated impedance BW of the FPCA is 23.79% from 10.07 to 12.79 GHz and 3 dB gain BW is from 10.13 to 12.34 GHz (19.67%). The simulation result shows that composite antenna resonates at two frequencies center at 10.5 and 11.75 GHz. These two resonances correspond to radiating patch and the cavity resonance between the ground and PRS. EBG as PRS allows better impedance matching of the antenna over a wideband and a significant gain improvement as compared to dielectric superstrate. Sensitivities of the return loss and gain characteristics of the proposed FP-CRA are also observed by varying the superstrate height. Figures 9(a) and 9(b) present simulated S ₁₁ and the gain of the proposed antenna for different air spacer heights (d). Impedance matching and gain of this FP-CRA significantly depend on the height of the PRS. Finally, the optimum height is determined to be 14.5 mm through parametric variation in HFSS.

Fig. 9.

Simulated (a) reflection coefficient and (b) gain variation of the proposed CRA at different air spacer heights.

The improvement in gain due to superstrate loading can be explained by the electric field distribution over the radiating aperture of the FP-CRA. The unit cells of the EBG-superstrate behave as radiating elements due to partial reflecting characteristics and in effect increase the radiating aperture of the antenna. Figure 10 shows the magnitudes of the tangential electric field on a plane at a distance of 2 mm away from the radiating patch for the unloaded reference antenna and that on a plane at 2 mm away from the EBG superstrate for the proposed FP-CRA. For the reference antenna, a significant variation of electric field magnitude exists over the radiating aperture, which causes the low gain of the primary feed antenna. When the patch antenna is loaded with the superstrate, a uniform field distribution is achieved over a large area which increases the radiating aperture of the antenna. The enhancement in the effective radiating aperture of the antenna causes a higher gain of the CRA. The field magnitude on the radiating aperture of the cavity antenna follows a Gaussian distribution. For superstrate with the infinite lateral size, the directivity enhancement of the CRA is related to the reflection magnitude (ρ) of the PRS using (3) [Reference Wang, Liu, Wu, Talbi, Zeng and Xu28]

(3)$$D_r = 10\log \displaystyle{{1 + \rho } \over {1-\rho }}.$$

Fig. 10.

Magnitude of tangential electric field distribution on a plane for (a) unloaded reference patch; (b) EBG superstrate-loaded cavity resonator antenna at frequency 11 GHz.

Figure 8 shows that at the resonance frequency of the primary feed antenna, the designed PRS has ρ = 0.59 which gives the calculated value of D_r = 5.9 dB. Thereby total directivity of CRA is obtained as D = D_feed + D_r. The directivity (D_feed) of the reference patch antenna is 7.7 dBi at the resonance and results in total directivity of the CRA as D = 13.6 dBi. Assuming 80% efficiency of the antenna, the aperture area (A) of the superstrate is determined using (4) [Reference Wang, Liu, Wu, Talbi, Zeng and Xu28]

(4)$$A = \displaystyle{{{10}^{D/10}\lambda ^2} \over {0.8\pi ^2}}.$$

Here λ is the wavelength at the operating frequency. The lateral size of the CRA is found as 1.7 × 1.7 λ ² for the required directivity of 13.6 dBi. The calculated radiating aperture size of the antenna closely matches with the actual aperture dimension of 45 × 45 mm² consisting of 49 FSS unit cells.