Analysis of High Gain Wideband 2 × 2 Printed Slot Array With AMC Surface by Presenting Equivalent Transmission Line Model for C and X-Band Applications

A low-profile broadband $2\times 2$ printed slot array with V-shaped slots by loading broadband artificial magnetic conductor (AMC) is demonstrated. A proposed wideband printed array with tapered V-shaped slots with the feeding of coplanar-waveguide (CPW) is measured in 8.24-11.13 GHz. Also, the proposed wideband planar AMC surface is embedded into the printed array to attain enhanced radiation properties. The printed slot array with the $7\times 7$ AMC surface covers -10 dB measured bandwidth from 4.47 to 13.32 GHz (100%). The design loaded by AMC compared to the design without AMC introduces a reduced size of 109.4%, a bandwidth improvement of 70%, and good impedance matching. Moreover, by adding an AMC surface into the printed array, an enhanced gain of 12.3 dBi with uni-directional radiation patterns is attained. The measured gain over the wide bandwidth shows acceptable stability with an average gain of almost 11 dBi. The proposed AMC unit cell is proposed to resonate at 10.10 GHz with a bandwidth of 7.85-12.24 GHz (43.7%) for X-band applications. In addition, the proposed equivalent transmission line model of the antenna with AMC is presented with acceptable output results. This model forecasts the input impedance of the printed array with AMC at the frequency band of 4.50-13.30 GHz as well.


I. INTRODUCTION
Most modern wireless networks have utilized electromagnetic band gap (EBG) structures for broadband networks due to their significant and unique characteristics. These structures conclude the conditions of high-impedance surfaces and, consequently, abolish surface waves [1]. The artificial magnetic conductor (AMC) structures show the same performance as a perfect magnetic conductor. In this regard, the image elements for PMCs are in-phase with the primary element that allocates applying those as reflectors in antennas. Also, it concludes placing the radiating elements very nearby to the PMC, which leads to low-profile antennas. In the recent decade, many low-profile antennas The associate editor coordinating the review of this manuscript and approving it for publication was Bilal Khawaja .
Nowadays, by extending the wireless networks and communications, microstrip patch antennas have been taken into account in several research works. It is due to important features of a simple fulfillment, low-profile antenna, and light weight. In reported works many approaches have been carried out to enlarge the bandwidth of microstrip antennas [11]. Wireless systems have an excellent data rate transmission, and coating multipath circumstance, and hence, low-profile wideband microstrip antennas are paid attention for related applications [12], [13], [14], [15]. Various EBG surfaces for WLAN systems have been used with their attractive features [14]. In this regard, several compact antennas are used AMC surfaces to promote the radiation properties [16], [17], [18], [19], [20], [21], [22], [23].
This study reports a wideband printed slot array with the AMC surface. A wideband AMC unit cell is presented to resonate at 10.10 GHz (7.85-12.24 GHz), firstly. By loading the 7 × 7 AMC periodic surface, the low-profile wideband printed array is realized. The 2 × 2 printed array includes four tapered V-shaped slots and a CPW feeding system to expand the bandwidth for X-band. Consequently, a broadband AMC reflector is located beneath the antenna to measure the −10 dB bandwidth in 4.47-13.32 GHz (100%) and an increased gain of 12.3 dBi. Eventually, the equivalent transmission line model is prepared to anticipate the input impedance of the printed array with AMC surface.     coefficients with a periodic boundary condition as shown in Fig. 1 The bandwidth improvement of the AMC is concluded from the physical and electrical characteristics. The effective couplings of slots and arms result in the physical specification of the wide bandwidth. The optimal AMC bandwidth is obtained by selecting the given electrical characteristic of h and ε r . Eventually, various scan angles of reflection waves are investigated with proper stability for a wideband operation. Indeed, different parts and inserted slots into the AMC surface lead to a wider bandwidth.
The mushroom-type EBG structure is composed by a via-loaded patch with an equivalent parallel LC model of f r = 1/(2π √ LC) [18]. The L and C parameters, and impedance bandwidth are determined by the bellow equations [18]: where, ε 0 , and µ 0 are the permittivity and permeability of free space, respectively.  The proposed AMC design evolution is provided in Fig. 2. It shows four steps to achieve the final design of the proposed 59166 VOLUME 11, 2023 Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply.

B. PROPOSED PRINTED SLOT ARRAY
The geometry of the 2 × 2 printed slot array by applying the AMC structure is demonstrated in Fig. 3. Four tapered V-shaped slots are embedded on an FR4 substrate with 1.6 mm thickness. Beneath the printed antenna the 7×7 AMC surface is located. It is constructed of a substrate thickness (FR4) of h 1 to move the power to the printed array on the top layer. The dimensions of the width and length of tapered slots are 24 mm. These printed slots are placed on the substrate with dimensions of 79.1 × 80 mm 2 . The 50-CPW feeding system is applied from the side of the printed antenna with an SMA connector (see Fig. 6). The parameters of FR4 substrates select as thicknesses of h 1 = 2.1 mm, h 2 = 1.6 mm, ε r = 4.4, and tanδ = 0.02. The 50-CPW feed is considered with the width of the slot 0.3 mm and the width of the strip 3 mm to achieve the optimized design. The optimum length of L cpw = 30.4 mm for the length of CPW is selected.
To optimize the final sizes and slots' lengths, parametric operations are performed in HFSS. Table 1 lists the sizes of the suggested design. The proposed printed slot array is realized based on tapered V-shaped slots for expanding the bandwidth with different resonances. The insertion of four tapered V-shaped slots into the printed antenna results in two resonances and consequently, the operating bandwidth can be widened. Meanwhile, according to Fig. 6, the proposed design is assembled by etching the AMC layer to the printed slot antenna and it is fed by 50-Ohm CPW from the center of the structure. It is noted that there is no gap layer between the AMC and the antenna.
The basic process of the design of the microstrip patch with the width (W) and length (L) is exhibited by the equations in [3]. In terms of the provided formulas in [3] at the X-frequency band, the basic width and length of the printed antenna are selected. In this design, dielectric constant substrate, ε r = 4.4 is considered and for the simple patch at 9.7 GHz, the fundamental width and the length are regarded for height h 2 = 1.6 mm. Finally, the optimum sizes and lengths with the parametric studies are achieved. The proposed design evolution is provided in Fig. 4. It shows four steps to achieve the final design of the printed slot antenna with tapered V-shaped slots. The simulated results for four designs 1, 2, 3, and 4 are introduced in section IV.
The printed antenna is composed of the tapered slots with V-shaped arms. When two tapered V-shaped slots embed on the patch, an extra inductance and capacitance between the arms of the V-shaped patch are acquired to broad the bandwidth with two resonances. Fig. 5 plots the structure of the design method. It demonstrates the comprehensive model with three steps to achieve an optimized printed design with enhanced features. At first, the novel wideband AMC design in 7.85-12.24 GHz (43.7%) for X-band operation is presented. In second stage, the printed slot antenna with the CPW feed in X-band (8.24-11.13 GHz) for wideband applications are introduced. Finally, by combining and loading a novel wideband AMC reflector into wideband printed array an antenna with tapered V-shaped slots for wideband communications (4.47-13.32) is implemented. Fig. 6 shows the photographs of the fabricated configurations of the antenna. The measured far-field setup and testing the radiation patterns of the antenna in the anechoic chamber is provided. A transmit (TX) antenna as a standard horn antenna is selected and the proposed antenna is located as a receiving (RX) antenna. The antenna (RX) is located at the far-field distance 2D 2 /λ from the horn antenna and it is spined by a mechanical retainer for testing the radiation patterns in various directions. To achieve the power reception without variation, the amplifiers are used. To measure the S-parameters, the network analyzer of Agilent 8720C is used. The RF vector network analyzer operates in 50 MHz-20 GHz. Meanwhile, the gain of the antenna is tested in comparison with the reference horn antenna (G ref ) in terms of dBi. Also, the gain of the antenna (G Relative ) compared to the reference antenna is measured. Eventually, the aggregate of G ref and G Relative for all frequencies is computed to attain the gain of the antenna. There is a little difference between the simulated and measured results of S-parameters, radiation patterns, gains, and efficiencies.

III. PROPOSED EQUIVALENT TRANSMISSION LINE MODEL
The proposed equivalent circuit model of the present design is depicted in Fig. 7. The circuit model of L 1 C 1 for conventional patch antenna is calculated [12] and [14]: The proposed model of the array is introduced by utilizing the impedance model of wideband antennas [39]. It consists of two sections with the same 100-impedance matching. Two same 100-sections are connected in parallel to achieve 50-input impedance. Accordingly, the V-shaped slots of a broadband antenna are modeled by multiple RLC parallel cells in series (Z in1 ), as seen in Fig. 7 (a). The impedance Z in1 for one V-shaped slot through the transmission line of M 2 connects to another V-shaped slot branch. Two V-shaped slots of one 100-branch are coupled with C c to the AMC surface by an RLC resonator (see Fig. 7 (b)). The AMC surface is modelled by LC elements.
The  [12]: The real part is considered simply the values of RLC parameters: Based on the formula (12), the simulation outputs of the array design by HFSS are inserted into the input VOLUME 11, 2023  impedance which acquired from the presented model. The optimized parameters are provided R k , L k , and C k by using a least-square and curve-fitting techniques.

IV. SIMULATION AND EXPERIMENTAL RESULTS WITH DETAILED DISCUSSION
The finite element and Floquet theory are applied in HFSS to realize the reflection properties of the AMC unit cell. Fig. 8 (a) shows the AMC reflection phase by propagating the normal TE/TM waves. The simulated result of 7.85-12.24 GHz (43.7%) for normal TE/TM waves is obtained at the resonance of 10.14 GHz. Fig. 8 (a) displays the reflection phases of the AMC for various oblique incident waves (θ) from 0 • to 45 • in two polarization plates (ϕ = 0 • , 90 • ). Also, the simulation results of the AMC design evolution based on Fig. 4 is displayed in Fig 8 (b). It reveals that four designs A, B, C, and D cover the bandwidths of 8. 39-9.81, 8.56-10.42, 8.25-11.48, and 7.85-12.24 GHz, respectively.
The simulation and measurement S-parameters of the proposed printed antenna without AMC are provided in Fig. 9. The antenna without AMC is measured in 8.24-11.13 GHz (29.8%) for S 11 < −10 dB. According to Fig. 9, the proposed antenna with the AMC surface displays a −10 dB bandwidth of 100% in 4.47-13.32 GHz from the measurement results. Therefore, the array with the AMC exhibits a bandwidth improvement of 70% versus the antenna without the AMC. The simulated S 11 of the equivalent transmission line model achieves the operating band in 4.50-13.30 GHz, according to Fig. 9. Therefore, it is comprehended that the proposed equivalent circuit model with respect to the measured result predicts the wideband operation as well. Fig. 10 demonstrates the results of the design evolution based on Fig. 4. For this purpose, four cases are considered in Fig. 4 to obtain the final design. According to Fig. 10, four designs 1, 2, 3, and 4 result in bandwidths of 8. 8-10.7, 8.96-11, 8.92-11.12, and 8.24-11.13 GHz, respectively. The overall size of the antenna without the AMC is 2.17λ L , 2.19λ L and 0.044λ L , respectively. Besides, the overall size of the antenna with the AMC is 1.17λ L , 1.19λ L , and 0.055λ L , respectively. Thus, by applying the AMC the reduction of the size of 109.4% achieves compared to the antenna without the AMC. Also, Fig. 10 compares the effect of V-shaped slots (Design 4) with respect to the tapered slots (Design 3) for enhancing the bandwidth and impedance matching. Fig. 11 demonstrates the results of the S-parameters for the antenna with four AMC designs based on Fig. 2. According to Fig. 11, the printed antenna with four designs A, B, C, and D result in impedance bandwidths of 8.10-12.51, 6.94-12.71, 6.14-13.28, and 4.47-13.32 GHz, respectively.
The effect of the variations of patch sizes and the capacitance of C in the equivalent model for the unit cell in the AMC periodic surface is investigated in Fig. 12 (a). The simulation results are done by HFSS for the proposed design and ADS for the proposed equivalent model. As shown, by increasing the size of the unit cell and consequently, increasing the capacitance of C in the model, the bandwidth is enlarged until it achieves the optimum value of C = 0.54 pF. Also, the effect of the variations of height and the inductance of L in the equivalent model for the unit cell in AMC periodic surface is plotted in Fig. 12 (b). As shown, by passing the height of the unit cell and consequently, the inductance of L in the model, form the optimum value of L = 0.026 nH, the bandwidth decreases. Fig. 13 displays the current distribution on the patch of the antenna at various resonances of 5.7 GHz and 10.4 GHz. At 5.7 GHz, the current density focuses on the feeding system and at 10.4 GHz it concentrates around tapered slots. The V-shaped slots are more effective on creating new resonances at higher frequencies. For this reason, the current density concentrates around the slots at 10 GHz compared to the lower frequency of 5.7 GHz. The measured and simulated radiation patterns for the suggested design in the xz-and yz-planes are exhibited in Fig. 14. According to Fig. 14, the radiation pattern at 10.4 GHz is more directional than that at 5.7 GHz. That is due to this fact that applying the AMC surface to printed slot antenna affet on lower frequencies by creating new resonances. Therefore, the radiation patterns have a wider beamwidth at lower frequencies. The maximum gain of the antenna with AMC whole the operational band is 12.3 dBi, according to Fig. 15. Hence, the gain at the frequency band is considerably improved.

V. CONCLUSION
The 2 × 2 printed slot array with tapered V-shaped slots loaded by a 7×7 AMC structure demonstrates the low-profile wideband antenna with -10 dB measured impedance bandwidth of 4.47-13.32 GHz (100%). The novel planar AMC design is presented to show a wide frequency band in 7.85-12.24 GHz (43.7%) with acceptable stability within the AMC bandwidth. The 2 × 2 printed array by loading the AMC compared to the antenna without AMC shows good impedance matching (-40 dB), good compactness (almost 110%) and improved bandwidth up to 100%. The total size of the printed design is selected 79.1 × 80 × 3.7 mm 3 (1.17λ L ×1.19λ L ×0.055λ L ). Moreover, the uni-directional radiation patterns and an enhanced gain of 12.3 dBi are acquired. Meanwhile, the proposed equivalent circuit model is introduced to foreseen the wideband operation for the input reflection coefficient as well. The obtained S 11 of the proposed model shows the frequency band in 4.50-13.30 GH by utilizing the impedance model of the wideband antennas.