Graphene, which is an extraordinary material with many unique properties and superiorities, has been extensively investigated in optical, mechanical, thermal, and electrical fields,^[1–3] including transparent conductors for touch screens,^[4,5] flexible electronics,^[6] interconnects,^[7] surface plasmon polaritons (SPPs) waveguides,^[8,9] phase shifters,^[10] and absorbers.^[11–13] Thanks to the dynamical tunability of graphene conductivity that results from its field effect by applying adequate bias electrostatic, the reconfigurable graphene-based antenna has also attracted growing attention.^[14–20] In the previous efforts, graphene was applied to planar or planar array with periodic units in the design of leaky-wave antennas (LWA),^[15,16] reflector antennas,^[17,18] and low-profile antennas.^[19,20] Graphene is usually used for antennas in two forms: 1) acting as an actual radiation part, which, however, leads to a low radiation efficiency due to the loss caused by the real part of graphene surface conductivity;^[21,22] 2) being employed as a parasitic component, which enhances the radiation performance owning to diminish the loss.^[23,24]

Recently, the graphene impedance surface is frequently presented to improve the performances of various antennas. These researches are mainly concentrated on THz and optical frequencies and are rarely involved in microwave range. However, with the development of art methods, large graphene flakes and graphene transferred onto flexible substrates can be produced. The technical progress makes it possible to develop graphene-based antenna with high performance in microwave frequencies.^[25,26]

In the microwave band, graphene has an outstanding characteristic, i.e., the real part of the surface impedance (R_e(Z_s) = R_e(1/σ_s)) of graphene is very high without bias and becomes lower when the bias electrostatic increases. Therefore, graphene can act as a high impedance surface (HIS) on low bias electrostatic or a low impedance surface (LIS) on high bias electrostatic.^[14] Moreover, the R_e(Z_s) varies from a few ohms to thousands of ohms. This means that the surface resistance realizes a metal–insulator transition. These characteristics have been employed to develop some novel antennas, such as smart antennas.^[14] These previous antennas, however, have obvious disadvantages of a narrow bandwidth and a limited tunable range of radiation direction, which extremely limit their practical application.

In this paper, we propose a cylindrical graphene coating (CGC) in microwave range, which is made of graphene transferred onto the inner surface of SiO₂ substrate (the relative permittivity is ɛ_r) and a set of independent polysilicon pads located outside the cylinder. Furthermore, we design an ultra-wideband pattern reconfigurable antenna which consists of a monopole and the CGC. The proposed antenna has high radiation performance in an ultra-wideband because of the characteristic of the metal–insulator transition of the graphene coating. Meanwhile, the antenna realizes directional radiation, whose direction can be continuously adjusted in the entire azimuth, or omnidirectional radiation.

The rest of this paper is arranged as follows. The surface impedance of the graphene in microwave range is presented in Section 2. In Section 3, the design of a 3D ultra-wideband pattern reconfigurable antenna with CGC is given. In order to demonstrate the ultra-wideband and reconfigurable radiation characteristics of the proposed antenna, numerical results are analyzed using the transmission line (TL) model and simulated using CST software respectively in Section 3. Finally, the conclusions are drawn in Section 4.

Graphene can be regarded as an infinitesimally thin surface, whose surface conductivity σ_s in the absence of magnetostatic bias and spatial dispersion is analytically expressed using the well-known Kubo formula^[27]

For T = 300 K, τ = 0.1 ps, Γ = 1/τ, and v_f = 9.5 × 10⁵ m/s, we obtain the surface impedance of graphene depending on frequency from Eqs. (1)–(4) by changing the biased electrostatic, as shown in Fig. 1. One can obtain the following conclusions. 1) The intraband contribution is dominant, which means that the interband term can be neglected. 2) The real part of the surface impedance remains approximately constant and is far larger than the image part. This means that the surface reactance can also be ignored. 3) The surface impedance becomes lower with the biasing electrostatic increasing and the real part varies from thousands of ohms to a few ohms. This causes the surface resistance metal–insulator transition of the surface resistance. Therefore, a reconfigurable antenna can be constructed by adjusting the graphene’s metal–insulator transition, which is tuned by the biased electrostatic.

Fig. 1.

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	Fig. 1. Frequency dependence of graphene parameters. (a) Total and intraband term of surface resistance and surface reactance. (b) Surface resistance and surface reactance of intraband term for different Eb.

The configuration of the proposed antenna and its front-penetrative view are shown in Figs. 2(a) and 2(b), respectively. The number N of the polysilicon pads is set to be 36 and each polysilicon pad is labeled with an integer i (1 ≤ i ≤ 36) the graphene sheet is then correspondingly divided into 36 subdomains and each subdomain is also labeled with i. Throughout this study, the order of i in the Cartesian coordinate system remains unchanged, as shown in Fig. 2(b). It is well known that the bias electrostatic E_bi is decided by the applied DC voltage V_DCi, and furthermore the surface impedance for the i-th subdomain of the cylindrical graphene-based coating is controlled by the bias electrostatic E_bi (see Eq. (3)). Therefore, we can control the surface impedance of graphene for each subdomain by changing the DC voltage V_DCi freely.

Fig. 2.

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Fig. 2. (a) The proposed reconfigurable antenna using a CGC with the radius of d, (b) the front-penetrative view of the proposed configuration, and (c) an example of the binary code. The polysilicon pads (yellow in the insert) are used to control the graphene conductivity σs as a function of the bias electrostatic by applied DC voltage VDCi. All dimensions are in millimeters: Gh = 20, the length l of the monopole and its ground diameter are 4.5 and 40, respectively. The distance between the pads satisfies g << s. The polysilicon pads and the SiO2 substrate (with the thickness of t) are excluded in the subsequent simulation because of their extremely thin profile.[16]

In the fabrication of the proposed antenna, 36 pairs of wires can be used to bias the graphene. The two terminations of one end of each pair insert into a small hole on the ground of the antenna near the coating and connect the graphene and pad by conductive silver paste, and these of the other end connect the DC power. It is obvious that the variohm should be joined between graphene and the DC power to change the DC voltage and bias the corresponding subdomain graphene. It is worth pointing out that 1) 36 variohms are needed, 2) these variohms should be placed in the back of the antenna’s ground, and 3) the electric potentials of all the terminations connecting graphene are equal. Therefore, the loss effect of the wire can be neglected if all the wires in the front of the antenna’s ground are very short.

In this work, we will use two states: 1) LIS with a smaller surface impedance for the graphene with a relative high bias electrostatic; and 2) HIS with a larger surface impedance for the graphene with a low bias electrostatic. For convenience in following description, the LIS and the HIS are denoted by binary codes “1” and “0”, respectively. As shown in Fig. 2(c), for example, the case of the subdomains from 1^st to 18^th being LIS and the rest being HIS is coded as

3.1. The ultra-wideband impedance characteristics of the proposed antenna

The TL method and the ABCD transmission matrices are used to analyze the ultra-wideband impedance characteristics of the proposed antenna. As shown in Fig. 2(a), when the monopole is loaded by an excitation source, the electromagnetic wave can be radiated from it and propagate in the free space between the monopole and CGC, the current is then induced on the graphene of CGC, and finally the radiated wave spreads across the free space outside the CGC. Therefore, the proposed antenna can be seen as a TL model with four cascaded networks, as shown in Fig. 3.

The transmission line (its length and characteristic admittance are d and Y₀ = 1/120π S, respectively) in section (ii) is the equivalence of the free space between the monopole and the coating, Y_mp in section (i) represents the admittance of the monopole, and Y_g in section (iii) and Y_L in section (iv) represent the admittances of graphene and the outer free space, respectively. The Y_mp is mainly determined by the length l of the monopole, and then it can be used to obtain the inherent resonant frequency f₀ (or the inherent resonant wavelength λ₀) of the monopole. For l = 4.5 mm, f₀ is approximately equal to 15 GHz, that is, l ≈ 0.225λ₀.

Fig. 3.

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	Fig. 3. The TL model of the antenna.

The ABCD matrices for sections (ii) and (iii) are expressed as

Then, the chain transmission matrix of the above two sections is derived as

Therefore, the input admittance of in Fig. 3 can be written as

where

From Fig. 1, Y_g in the microwave region can be considered as real numbers. The cascaded networks (ii), (iii), and (iv) illustrate the coupling relationship between the monopole and the graphene-based coating. From Eq. (8), it can be derived that there are a serial of coupling resonances when (i.e. tan(β_nd) = 0), and then the corresponding coupling frequencies may be determined as

where c₀ is the speed of the electromagnetic wave in the free space, and n is the order of the coupling frequency. The f₁ corresponds to the first-order or major coupling frequency, while the other f_n denotes the high-order coupling frequency. From Eq. (9), we can see that the coupling frequencies vary as a function of the radius d of the CGC.

To investigate the influence of radius d on the impedance bandwidth of the proposed antenna, we simulate the reflection coefficient using commercial software CST Microwave Studio with all the surface impedances of the 36 subdomains of graphene (see Fig. 2(a)) being 300 Ω, as shown in Fig. 4(a).

Fig. 4.

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	Fig. 4. Simulated S11. (a) The monopole and the proposed antenna for different d. (b) The proposed antenna for different Zs.

Figure 4 shows that there are many resonant frequencies, where the first frequency (f₀) is mainly determined by the length of the monopole and the others (f_n, n = 1, 2, 3, …) are caused by the coupling resonance of the monopole and the CGC. These coupling frequencies can also be obtained from Eq. (9). In order to validate it, we compare the coupling frequencies calculated by Eq. (9) with those extracted from the simulations (see Fig. 4(a)), as listed in Table 1, where f_n−tlm and f_n−cst are the coupling frequencies obtained from Eq. (9) and CST, respectively. It is obvious that the coupling frequencies calculated from Eq. (9) agree well with those simulated by CST, and then the accuracy and the effectiveness of the above analysis are validated. In Table 1, f_2−cst for d ≤ 8.5 mm and f_3−cst for d ≤ 10 mm are higher than 35 GHz, thus they are not exhibited in Fig. 4(a); f_3−cst for d ≤ 8.5 mm are not listed because they are very inconspicuous in the simulated results; f_1−cst for d ≥ 10 mm are also not listed because it is drowned in the inherent resonance. By optimizing the coupling resonance of the antenna, the multiple resonance frequencies can be brought closer,^[29–32] and the ultra-wideband impedance characteristic is then obtained. Figure 4(a) shows that an ultra-bandwidth of 52.5% is realized when d = 7.5 mm.

Table 1.

Table 1.

Table 1. Coupling frequencies (GHz) and the relative error (%) simulated by TL method and CST for different d (mm). . d f1−tlm f1−cst Error f2−tlm f2−cst Error f3−tlm f3−cst Error 6.5 23.1 23.3 0.87 46.2 45.6 1.30 69.2 – – 7.5 20.0 20.0 0.00 40.0 40.5 1.25 60.0 – – 8.5 17.7 18.0 1.70 35.3 36.1 2.27 53.0 – – 10 15.0 – – 30.0 31.0 3.33 45.0 46.1 2.44 20 7.5 – – 15.0 15.8 5.33 22.5 23.0 2.22

Table 1. Coupling frequencies (GHz) and the relative error (%) simulated by TL method and CST for different d (mm). .

Moreover, when all of the surface impedances of the 36 subdomains of graphene have the same value and the values are 60 Ω, 300 Ω, 500 Ω, and 1 kΩ, respectively, the reflection coefficients of the proposed antenna are displayed in Fig. 4(b), which shows that the widest relative bandwidth increases to 58.5% when Z_s equals to 500 Ω. This implies that the graphene with 500 Ω matches the monopole to free space better.^[33]

The above investigations are based on the same impedances; namely, the impedance of LIS is equal to that of HIS for each subdomain of graphene. For example, for four curves in Fig. 4(b), the impedance of each subdomain is equivalent to 60 Ω, 300 Ω, 500 Ω, and 1 kΩ, respectively. In order to further study the influence of the surface impedance on the performance of the proposed antenna, we define R_LIS–R_HIS as the different impedance counterpart of LIS and HIS, that is the LIS and HIS having different impedances. Here, the LIS and HIS are coded by (see Fig. 2(c)), and R_LIS–R_HIS are respectively 5–377 Ω, 5–1000 Ω, 5–5000 Ω, 50–5000 Ω, and 377–5000 Ω, we simulate the reflection coefficients for these five cases, as shown in Fig. 5(a). We can clearly see that R_LIS–R_HIS has great influence on the bandwidth of the antenna. When R_LIS–R_HIS is 5–5000 Ω, the antenna occupies the greatest bandwidth. On the other hand, the coupling resonance becomes stronger and stronger with the decrease of R_LIS–R_HIS, which means that the metallicity of the graphene is more obviously.

For the given R_LIS–R_HIS, such as 5–5000 Ω, the different binary codes of LIS and HIS may affect the impedance bandwidth of the proposed antenna. To verify this, we take binary codes of , , , , , and as examples to simulate the reflection coefficient, as shown in Fig. 5(b). We observe that there are two resonances, which correspond to the inherent resonance and the first-order coupling resonance, and the two resonances are influenced by the subdomain number of LIS. In detail, the coupling resonance becomes strong whereas the inherent resonance becomes weak with the increase of the subdomain number of LIS. Because of its multiple resonance characteristic, the proposed antenna can operate in ultra-wideband by optimizing the geometric parameter.^[31] It is worthy to note that, in this design, the optimized relative bandwidth of 67% is achieved for the binary code of and LIS–HIS of 5–5000 Ω.

Fig. 5.

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	Fig. 5. The S11 of the monopole and the proposed antenna surrounded by the CGC with (a) the same binary code and (b) different binary.

3.2. Pattern reconfiguration characteristics of the proposed ultra-wideband antenna

As described above, the graphene acts as a metallic plate for the lower impedance, this is used to control the radiation pattern of the antenna. Fortunately, the size and position of the metallic plate can be modified by controlling the biased voltage V_DCi, which results in the tunability of the radiation pattern of the antenna. In order to demonstrate this, we set R_LIS–R_HIS as 5–5000 Ω and simulate the radiation patterns for different binary codes of LIS and HIS, as shown in Figs. 6 and 7. From Fig. 6(a), we can see that when the code is set as (namely all the surface impedances of the 36 subdomains are 5000 Ω), the antenna is omnidirectional with the gain of 2.81 dB, corresponding to the radiation of the monopole. However, for the other codes as shown in Figs. 6(b)–6(d), the antenna gives directional radiation and its directivity is changed when the code is altered, implying tunability of radiation pattern. Furthermore, we also observe that the elevation angles of the main lobe vary between 20° and 30° in the whole frequency range (see Fig. 7), showing perfect radiation performance.

Fig. 6.

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	Fig. 6. 3D radiation pattern under the conditions of (a) at 14 GHz, (b) at 14 GHz, (c) at 18 GHz, and (d) at 22 GHz.

Fig. 7.

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	Fig. 7. The (a) E-plane and (b) H-plane radiation patterns along the main beam corresponding to Fig. 6.

In order to further investigate the radiation performance of the antenna, we simulate the H-plane half-power beam (HPBW) for different numbers of the LIS subdomains, as shown in Fig. 8. When the number of the LIS subdomains is 18, 12, and 6, the HPBW is 79.1°, 97.9°, and 151.5°, respectively, which implies that the H-plane HPBW of the antenna increases with the reduction of the number of the LIS subdomains. Actually, the increment of the number of the LIS subdomains is to enlarge the size of the metallic plate, and hence the HPBW can be effectively reduced. Therefore, it is convenient to control the HPBW of the antenna by changing the number of the LIS subdomains.

Fig. 8.

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	Fig. 8. The H-Plane radiation patterns with different numbers of LIS subdomains at 14 GHz.

We have proposed an ultra-wideband pattern reconfigurable antenna with graphene-based coating in microwave region. The antenna is a coaxial hollow dielectric monopole coated by a cylindrical graphene-based impedance surface. A transmission line method has been used to validate the ultra-wideband impedance characteristic. By changing the bias voltages applied to the graphene, the proposed antenna can work in the directional mode orienting in arbitrary azimuth or omnidirectional mode. Furthermore, the gain of the proposed antenna increases compared to that of the monopole without the graphene coating. The pattern reconfiguration and the optimized relative bandwidths of 67% (for directional mode) and 58.5% (for omnidirectional mode) are obtained, which extends the applications of the proposed antenna significantly.