Unit cell characterization and dispersion diagram

Figure 1 displays the configurations of CTBG-CSRR unit cell. Figure 1(a) shows a customary CSRR unit cell and Fig. 1(b) exhibits the proposed unit cell. Upon placement of two cross-shaped CSRRs in all four corners of every unit conventional CSRR cell, two other frequency bands were added to it; only one-quarter of them are visible in the unit cell, which eventually causes our final model to operate as triple band. To show CTBG-CSRR stop-band characterization, the dispersion diagram of the unit cell is simulated with the eigen-mode solver using the CST Microwave Studio, where the corresponding Brillouin diagram for each unit cell is plotted along the Γ–X axis of the periodic structure. Figures 2(a) and 2(b) display the dispersion diagram of conventional and presented unit cells, respectively. As can be observed in Fig. 2(b), band-gaps which are around 3.65, 4.9, and 5.8 GHz are practical in WLAN bands.

Fig. 1.

(a) Conventional CSRR unit cell. Unit cell parameters: W _c = 4 mm, L _c = 4 mm, S ₁ = 1 mm, S ₂ = 1 mm, P = 0.5 mm. (b) Proposed CSRR unit cell. Unit cell parameters: W _p = 4 mm, L _p = 4 mm, W ₂ = 4 mm, L ₂ = 4 mm, Q ₁ = 2 mm, Q ₂ = 2 mm, Q ₃ = 2 mm, Q ₄ = 2 mm, Q ₅ = 2 mm, G ₁ = 2 mm, G ₂ = 2 mm, G ₃ = 2 mm, G ₄ = 2 mm, G ₅ = 2 mm.

Fig. 2.

Dispersion diagrams for (a) conventional and (b) proposed unit cells.

Examining unit cells in parallel plate waveguide setup

To increase the simulation speed and also ensure the correct operation of the presented unit cell, parallel plate waveguide setup is used; previously, other models of transmission lines were used in [Reference Tan, Wang, Wu, Liu and Kishk15, Reference Jiao, Jiang and Li19]. As illustrated in Fig. 3, 4 × 4 unit cells are used in the X and Y directions, and two wave ports are located in the direction of the X-axis, where the transmission coefficient between the two ports is less than 20 dB within 3.55–4.1 GHz and 4.76–5.02 GHz and 5.84–6.16 GHz. Differences in the basics of both methods (dispersion diagram and parallel plate setup) such as the limited number of unit cells used in the parallel plate setup and the lack of support for calculating losses in the eigen-mode solver method are the most important reasons for the slight difference in the operation band, especially at higher frequencies.

Fig. 3.

Simulated S ₂₁ with the parallel plate waveguide method in the x-direction.

Microstrip-fed Vivaldi antenna array design with CTBG-CSRR loaded

A Vivaldi antenna is part of a group called traveling-wave antenna which has a wide impedance bandwidth with an end-fire radiation pattern. A microstrip-fed Vivaldi antenna is manufactured with a dielectric substrate which lies on a metal side with an exponentially tapered slot connected to a circular slot-line cavity. On the other side of the substrate there is a microstrip line ending in a broadband radial quarter-wave stub. In this work, two microstrip-fed Vivaldi antenna arrays have designed to operate at 3.65 and 4.9 and 5.8 GHz printed on an FR4 substrate (ɛ _r = 4.4, loss tangent = 0.025); it is referred to as the reference antenna whose details are shown in Fig. 4. In the proposed antenna array, 4 × 14 unit cells are loaded between two antennas, which in Fig. 5, the surface current distribution is shown in two states suggesting that the suppression of surface waves has been done at three operation band wells. The simulated S-parameters for the reference and proposed antenna arrays are depicted in Fig. 6. The antennas resonate at 3.65, 4.9, and 5.8 GHz. From the transmission coefficient S ₂₁, we see a high reduction in mutual coupling when CTBG-CSRR is located between the radiating elements. The mutual-coupling reduction is 8.5, 10.5, and 18 dB at 3.65, 4.9, and 5.8 GHz, respectively.

Fig. 4.

Configuration of reference antenna: (a) top view and (b) bottom view: W = 103.3 mm, L ₁ = 60.8 mm, L ₂ = 45.6 mm, S ₁ = 2.9 mm, S ₂ = 0.96 mm, S ₃ = 11.7 mm, G = 0.87 mm, R ₁ = 3 mm, R ₂ = 0.92 mm, D ₁ = 31.6 mm, D ₂ = 32 mm, D ₃ = 10.1 mm, D ₄ = 130 mm, θ = 73°, H = 1.6 mm.

Fig. 5.

(a) Proposed Vivaldi array antenna (loaded unit cell) and (b) surface current distribution at 3.65, 4.9, and 5.8 GHz in the top view of reference and proposed antennas.

Fig. 6.

Simulated transmission and reflection coefficients of the reference and proposed antenna array.

Antenna fabrication and measurement

Figure 7 demonstrates a photograph of the fabricated antenna and its measured S-parameters. The measured results show excellent agreement with the simulated results. Figure 8 displays the simulated and measurement radiation patterns of the reference and proposed antenna, at 3.65, 4.9, and 5.8 GHz in the YOX-plane and the ZOX-plane. As can be seen, both radiation antenna parameters are better in three bandgaps which are mentioned in the previous section. Removal of annoying surface waves by CTBG-CSRRs helps improve the antenna radiation performance of maximum gain and front-to-back ratio. Also, in order to have a better image of radiation pattern, the 3D-view of the radiation pattern is presented in Fig. 9. Figure 10 shows the measured and simulated realized gains of the proposed antenna array. The simulated and measurement gain of the traditional antenna array is also included for comparison. The performance of the array for MIMO systems could be checked by the envelope correlation coefficient (ECC). The rich diversity performance with a low correlation coefficient could be achieved. For a two-element antenna system, ECC can be calculated using equation (1) where S ₁₁ and S ₂₂ are return losses at two ports, and S ₂₁ and S ₁₂ are the isolation parameters [Reference Chouhan, Panda, Gupta and Singhal23]:

(1)$$\rho _{12} = \displaystyle{{{\vert {S_{11}^\ast S_{12} + S_{21}^\ast S_{22}} \vert }^2} \over {\lpar {1-{\vert {S_{11}} \vert }^2-{\vert {S_{21}} \vert }^2} \rpar \lpar {1-{\vert {S_{22}} \vert }^2-{\vert {S_{12}} \vert }^2} \rpar }}$$

Fig. 7.

Proposed Vivaldi array antenna (loaded unit cell). (a) Photograph of the fabricated antenna. (b) Measured and simulated reflection coefficient compared with the reference antenna. (c) Measured and simulated transmission coefficient compared with the reference antenna. (d) The 3D view of two antennas with CSRR.

Fig. 8.

Measured and simulated radiation patterns (YOX-plane and ZOX-plane) of reference and proposed antenna array at (a) 3.65 GHz, (b) 4.9 GHz, and (c) 5.8 GHz.

Fig. 9.

3D radiation pattern at (a) 3.65 GHz, (b) 4.9 GHz, and (c) 5.8 GHz.

Fig. 10.

Comparison of simulated and measured results for the realized gain.

The ECC has been calculated and compared in Table 1. By reducing the ECC, the higher diversity gain can be ensured.

Table 1.

Performance of the proposed decoupling structures and previous studies

N.M., not mentioned.

In Table 1, the performances of the proposed decoupling structures and previous studies are compared from different perspectives such as edge to edge distance, number of operating frequencies, ECC, etc.