Development of Metamaterial Inspired Non-Uniform Circular Array Superstate Antenna Using Characteristic Mode Analysis

Abstract

In this work, using characteristic mode analysis, a multi-layered nonuniform metasurface structured antenna has been optimized. The driven patch of square structure and the parasitic patch elements of circular radiating cross-slotted meta-structure are used in the proposed model. The modal significance characteristic angles and surface currents are analyzed based on characteristic mode to optimize the nonuniform structures. The antenna is resonating between 5.5–6.1 GHz, covering WLAN applications with an average gain of 7.9 dBi and efficiency greater than 90%. Transient mode, terminal mode, and eigenmode-based analyses are performed on the proposed design, and comparative analysis has been presented in this work. The prototype model fabrication and real-time measurement analysis with simulation results matching are presented for application validation.

1. Introduction

Nowadays, the demand for novel wideband antennas is attracting more and more attention from researchers towards wireless services such as WiMAX, Wi-Fi, and WLAN. The world has to put its efforts into the development of a wireless 5G system with the integration of advanced communication modules [1]. So, the researchers have to endorse a new design approach for the fifth-generation wireless systems, which must fulfill the needs such as higher data rates, reliability, and good connectivity [2,3]. On the other hand, the design challenges need to be addressed, and more focus should be on compatibility with the environment. The major challenge in the design of working communication systems will depend on the efficiency of the antenna system. The antenna needs to be reliable, and adoptable and should have high gain bandwidth with good impedance matching. The microstrip antenna technology is more suitable and preferable to cater to these needs with design simplicity and ease in impedance matching. Compared to other conventional antennas, the microstrip patch antennas are very popular due to their light weight, ease of fabrication, lower cost, and also provide wideband characteristics.

One of the promising techniques to achieve the wideband characteristics is in the antenna structure loading a metasurface-layer, which leads to an increase in the bandwidth and also reduces the size of the antenna [4,5]. Normally the natural materials exhibit positive permittivity ϵ[r], permeability µ[r], and refractive index but metamaterials exhibit negative properties [6]. The metamaterial-based patch antenna for the improvement of bandwidth has been studied by Wu [7]. The metasurface is considered a kind of two-dimensional metamaterial structure that contains a layer of electrically small scatters arranged in order by using certain rules [8]. Painam designed a circular microstrip patch antenna loaded with a metamaterial, and the size of the antenna is reduced to 74% compared to other conventional microstrip antennas [9]. A non-uniform metasurface layer is formed by adjusting the cells of the antenna to improve the overall radiation performance [10,11,12,13]. The unit cell size in a non-uniform metasurface layer is gradually increased from center to outwards and achieved a wide bandwidth of 33.1% by Feng [14]. The wideband filtering of the antenna is achieved by adjusting the size of unit cells on two sides of the y-axis [15]. In [16], the column unit cell size is adjusted on x-axis to achieve the wideband characteristics of an antenna. Due to the lack of sufficient theoretical basics, the arrangement of unit cells in a non-uniform metasurface layer to accomplish the wideband characteristics is a tedious and time-consuming task.

Considering the defects and difficulties in the above-mentioned design methods, there is a need for more physical insights into the antenna design by engineers. The characteristic mode analysis (CMA) is the most popular and efficient method which is proposed by Garbacz [16] and modified by Harrington and Mautz [17,18,19] to optimize the antenna performance characteristics. The characteristic mode analysis (CMA) furnishes an in-depth physical insight into the antenna design aspect and its radiating properties. In recent years, using characteristic mode analysis, different types of antennas are designed for various commercial and military communication applications, such as ultra-wideband antennas [20,21,22] and metasurface antennas [23,24,25]. In [26], a novel miniaturized metasurface unit cell is proposed, and using this miniaturized unit cell, a 4 × 4 array antenna structure is composed. The design is analyzed using the theory of characteristic modes and realized circular polarization. In [27], 4 × 4 non-uniform array antenna is designed with H-shape patch array elements. The current distributions of metasurface and radiating properties are analyzed and obtained wide impedance bandwidth of 38.8%. In [28], to realize the dual-band operation, a non-uniform 3 × 3 array antenna is designed using square shape patch elements.

In this work, a new multi-layered design is proposed and also optimized for the metamaterial-inspired 3 × 3 non-uniform array antenna using characteristic mode analysis (CMA). The antenna modeling and the simulation performance characteristics are realized on the commercial electromagnetic tool HFSS and presented in the subsequent sections.

The proposed design is analyzed in modal analysis, terminal, transient, eigenvalue, and characteristic mode analysis. All analysis method results for a particular design are placed in this article. Characteristic mode analysis significance is clearly presented and shows how modes are resonating with respect to all parameters, such as modal significance, eigenvalue, and characteristic angle in the subsequent sections.

2. Antenna Design

The side and top views of the proposed metamaterial-inspired non-uniform array antenna design are presented in Figure 1. The designed antenna contains a non-uniform metasurface, patch antenna on two substrates named sub1 and sub2. Both the substrates of circular shape are designed with the height of ‘h’ and radius of ‘R’. The substrate material used in the design is PDMS material having a loss tangent of 0.013 and relative permittivity of 2.7 and the conducting material used in the antenna design is copper. The ground plane also has the same radius as ‘R’ and covers the sub2 bottom part.

The rectangular patch is printed on the sub 2 with a length of ‘Lp’ and width of ‘Wp’. To achieve 50 Ω impedance matching, a coaxial feeding technique is used, and a coaxial feed probe is located on the y-axis at a distance of 4 mm from the origin. According to the top view of antenna geometry shown, a non-uniform metasurface is designed with an array of 3 × 3 unit cells, and the space maintained between the unit cells on the metasurface is 2 mm. Each unit cell covers an area of U_L × U_W and contains a circular radiating element of radius ‘r’. To improve the coupling effect between the non-uniform metasurface layer and radiating antenna, the circular copper element is cut symmetrically into two parts by a slot width of ‘Ws’ and other cuts of having length ‘Lc’ and width of ‘Wc’. The angle ‘Ө’ is defined as a rotation angle, which is the angle made between the x-axis and the center of the slot. The unit cells placed at the center and all four corners are having a counterclockwise direction of rotation angle and the remaining unit cells are having the opposite direction of the rotation angle. The proposed antenna dimensions are given in

Table 1. The non-uniform array antenna dimensions (unit: mm).

R	h	Lp	Wp	r	Ws	Lc	Wc	Ө	Uw	UL
27.5	2	13.27	13	6	2	2	2	40°	14	14

.

Figure 2 represents modal, terminal, and transient analysis characteristics of the designed antenna array. It has been noticed that the transient mode analysis is contributing lesser bandwidth in comparison with the modal and terminal analysis and the impedance bandwidth of 52% is only attained for the transient analysis, whereas for other two, an impedance bandwidth of 105% has been obtained.

The eigenmode analysis with respect to five modes of Mode 1, Mode 2, Mode 3, Mode 4, and Mode 5 has been presented in Figure 3. This is giving clear evidence regarding the resonant frequencies for each mode as per the operating frequency is concerned.

3. Unit Cell Design

The proposed array antenna unit cell structure has been presented in Figure 4. The unit cell with the port assignment and the cross-sectional view with respect to dimensional characteristics are presented in Figure 4a,b. Figure 5 and Figure 6 represent the corresponding unit cell analysis parameters with respect to permittivity and permeability. The functional representation of these two parameters at the resonating band with negative values can be observed from the obtained results. The metamaterial behavior of the proposed design with negative characteristics gives strong motivation for the applicability of the given structure in the desired band.

4. Characteristic Mode Analysis

The analysis of characteristic mode became a popular method to design the microstrip patch antenna, which provides more physical insight into antenna resonance and radiation analysis. The characteristic modes are current modes that are associated with eigenvalues that can be calculated numerically for arbitrarily shaped perfect electric conducting bodies (PEC). The theory of characteristic modes is dependent only on the shape and size of a conducting object and is independent of any kind of excitation to achieve good performance of an antenna design. The CMA provides an inevitable approach for an antenna design, which is more efficient than cut-and-try methods or time-consuming optimizations [29]. The design of the antenna can be performed in two steps using characteristics. In Step 1, the size and shape of conducting elements are optimized. In Step 2, based on the current distributions provided by CMA, a suitable feeding configuration is chosen to excite desired characteristic modes. If the size of the element is changed, then the resonant frequency and radiating properties also will change. The derivations of characteristic modes and their various applications in antenna design are presented in [30]. The characteristic currents are derived by using eigenvalue equation,

$$X\left[{\overrightarrow{J}}_n\right]={\lambda }_{n}R\left[{\overrightarrow{J}}_n\right]$$

(1)

where ${\lambda }_n$ represents the eigenvalues, ${\overrightarrow{J}}_n$ are nothing but the eigen currents or eigen functions, n is the mode order and R and X are the real and imaginary parts of impedance matrix is [31],

$$\mathrm{Z}=\mathrm{R}+\mathrm{JX}$$

(2)

The eigenvalue is one of the utmost essential parameters because its magnitude provides valuable information about the resonant frequency and radiation information of the characteristic mode [32,33]. Consider a mode is resonating, the eigenvalue (${\lambda }_n)$ associated with a mode is zero, i.e., $\left|{\lambda }_n=0\right|$, it is stated that the mode radiates more efficiently when the magnitude of the eigenvalue is smaller.

when ${\lambda }_n$ = 0, the mode is externally resonant.

• ${\lambda }_n$ > 0, the mode is inductive, which means the energy is stored in a magnetic field.
• ${\lambda }_n$ < 0, the mode is capacitive, which means the energy is stored in an electric field.

The second important parameter in characteristic mode analysis is the characteristic angle, it is an angle that represents the phase lag between the electric field and surface current on a conductor object [34,35]. Mathematically, it is represented as,

$${\alpha }_n=180-{\tan }^{-1}{\lambda }_n$$

(3)

• When ${\alpha }_n$ = 180 deg, the mode is externally resonant.
• When 90 deg < ${\alpha }_n$ < 180 deg, the mode is inductive.
• When 180 deg < ${\alpha }_n$ < 180 deg, the mode is capacitive.

Modal significance is the parameter used in CMA to find the resonant frequency and radiating bands of a specified mode. It is represented as,

$$\mathrm{MS}=\frac{1}{\left|1+J{\lambda }_n\right|}$$

(4)

In characteristic mode analysis a mode can be considered resonant when ${\lambda }_n=0$, MS = 1 and ${\alpha }_n$ = 180.

The frequency vs. characteristic angle plots are presented in Figure 7. The rotation angle of the circular slots is varied from 0 deg to 90 deg and −20 deg to −60 deg and analyzed the change in characteristic angle and presented the resonant frequency for the particular mode in

Table 2. Mode resonating frequencies with respect to characteristic angle.

Angle	Ө = 0°	Ө = 20°	Ө = 40°	Ө = 60°	Ө = 90°	Ө = −20°	Ө = −40°	Ө = −60°
Mode 1	5.6	3.7	5.0	5.0	5.49	3.7	4.7	5.09
Mode 2	5.7	5.4	5.5	6.1	-	4.48	5.8	-
Mode 3	-	5.6	-	-	-	-	-	-

. In Mode 1 for a rotation angle of 0 deg, the resonant frequency is varied between 3.7 to 5.6 GHz. In Mode 2, the resonant frequency varied between 4.4 to 6.1 GHz and at 90 deg and −60 deg, there is no resonance from the antenna. In Mode 3 for only a rotation angle of 20 deg, the antenna resonates at 3.8 GHz and for other angles, there is no resonance from the antenna.

The model significance analysis for the proposed antenna structure with reference to frequency of operation is indicated in Figure 8. Mode 1, Mode 2 and Mode 3 are analyzed with resonant frequency and presented the same in this section.

The change in the rotation angle of the slots in the radiating element varied from 0 degrees to 90 degrees and from −20 degrees to −60 degrees. For 20 degrees there are three resonant frequencies for three modes at 3.7, 5.4, and 3.8 GHz, respectively.

For 90 degrees and −60 degrees, there is only a single resonant frequency at 5.4 and 5 GHz, respectively. For 0, 20, 40, 60, −20, and −40 degrees, both Mode 1 and Mode 2 provide different resonant frequencies of operation from

Table 3. Mode resonating frequencies with respect to modal significance.

Modal Significance (MS = 1)	Ө = 0°	Ө = 20°	Ө = 40°	Ө = 60°	Ө = 90°	Ө = −20°	Ө = −40°	Ө = −60°
Mode 1	5.6	3.7	5.0	5.0	5.49	3.7	4.7	5.09
Mode 2	5.7	5.4	5.5	6.1	-	4.48	5.8	-
Mode 3	-	5.6	-	-	-	-	-	-

.

The eigenvalue analysis with respect to resonant frequency is presented in Figure 9 for different angles of rotation.

Table 4. Mode resonating frequencies with respect to eigenvalue.

Eigenvalue (${\mathsf{\lambda }}_{\mathit{n}}=0)$	Ө = 0°	Ө = 20°	Ө = 40°	Ө = 60°	Ө = 90°	Ө = −20°	Ө = −40°	Ө = −60°
Mode 1	5.6	3.7	5.0	5.0	5.49	3.7	4.7	5.09
Mode 2	5.7	5.4	5.5	6.1	-	4.48	5.8	-
Mode 3	-	5.6	-	-	-	-	-	-

. Except for 90 deg and −60 deg, single resonant mode and for 20 deg triple resonant modes are observed. A similar kind of observation is attained for eigenvalues from Table 4 and modal significance analysis from Table 3.

The surface current distribution analysis of the designed antenna for different rotation angles is presented in Figure 10. The circular orientation of current elements’ direction in all the cases gives evidence of polarization diversity, and in each unit cell, the strength of the current is consistent. The direction of current in Mode 1 is along the y-axis and in Mode 2 is along the x-axis.

The three-dimensional and 2D gain plots of the current antenna are presented in Figure 11. The gain plots at different resonant frequencies of various modes are analyzed and presented. At 5.4 GHz of Mode 2 (Ө = 20°), a maximum gain of 7.5 dB is attained. At 5.5 GHz of Mode 2 (Ө = 40°), a maximum gain of 7.7 dB is attained. At 5.6 GHz of Mode 1 (Ө = 0°), a maximum gain of 7.8 dB is attained. At 5.7 GHz of Mode 2 (Ө = 0°), a maximum gain of 7.9 dB is attained. At 5.8 GHz of Mode 2 (Ө = −40°), a maximum gain of 8.1 dB is attained. At 6.1 GHz of Mode 2 (Ө = 60°), a maximum gain of 8.2 dB is attained.

Figure 12 providing the simulated and measured reflection coefficient of the antenna with perfect matching between them. The gain and efficiency plot in Figure 13 provides average gain of 7.9 dBi and an efficiency of more than 90%.

Figure 14 provides the measurement setup of the proposed antenna. The comparative analytical study of the proposed model with the literature is tabulated in

Table 5. Comparison of proposed and other antenna designs (NR: not reported, DB: dual band).

Reference	Dimensions (mm × mm)	Bandwidth (GHz)	Average Gain (dBi)	Average Efficiency
[5]	132 × 132	5.71–5.88	13.7	NR
[15]	78 × 78	4.20–5.59	8.2	95%
[32]	80 × 60	3.27–4.66	7.7	NR
[33]	60 × 60	4.9–5.1	11.6	NR
[34]	27.5 × 27.5 × π	5.07–5.94	7.63	>80%
[35]	20 × 20	9.798–10.202 14.09–15.91	8.24 9.65	82% 87%
Proposed	27.52 × π	5.5–6.1	7.9	>90%

. The gain and efficiency are showing better performance characteristics when compared with existing antenna models.

5. Conclusions

A non-uniform slotted array with a multilayer structured antenna is designed in this work for WLAN communication applications. Characteristic mode analysis has been examined to optimize the antenna performance characteristics as per the application specification. The slotted structure metamaterial characteristics are analyzed for the designed model with respect to negative permittivity and negative permeability at the targeted operating band. Characteristic angle, modal significance parameters, and eigenvalues are analyzed and presented with respect to the resonant frequency in the current work. An average gain of 7.9 dBi, impedance bandwidth of 105%, and efficiency of more than 90% is attained with good matching between simulation and measurement results.