Development of Double C-Shaped Left-Handed Metamaterial for Dual-Band Wi-Fi and Satellite Communication Application with High Effective Medium Radio and Wide Bandwidth

Abstract

The development and improvement of the dual-band 802.11ac standard Wi-Fi and wide bandwidth satellite communication devices are currently research subjects that have garnered significant interest. In this paper, double C-shaped two split-ring resonator (SRR) bounded unit cells were developed, which are applicable for S, C, and X band applications, including dual-band Wi-Fi communication devices and satellite communication applications for its effective medium ratio (EMR) of 15.6, which results in a 2.4 GHz resonance frequency and wide bandwidth (S21 < −10 dB) of 1650 MHz at an 11.5 GHz resonance frequency. A copper resonator and the popular substrate material Rogers RT 5880 (thickness of 1.575 mm) were adopted for analyzing the characteristics of this unit cell. The $8\times 8 {\mathrm{mm}}^2$ structure was designed and simulated using a commercially available electromagnetic simulator CST (Computer Simulation Technology) Studio Suite 2019, which was utilized at four resonance frequencies: 2.4 GHz, 5.6 GHz, 8.93 GHz, and 11.5 GHz. The electric field, magnetic field, and surface current distribution were examined by modifying the metamaterial unit cell design structure, showing effective results. To confirm the CST simulation results, the newly designed double C-shaped double-negative metamaterial (DNG) was also simulated with the Ansys High-Frequency Structure Simulator (HFSS) and compared with the extracted results. The suggested metamaterial is advised for usage in Wi-Fi and satellite communication applications for superior long-distance communication performance and efficiency with the compactness of the structure.

1. Introduction

In recent decades, metamaterials have received a lot of attention in the scientific community because of their extraordinary electromagnetic properties. In microwave engineering, metamaterials are used to build manmade dielectric electromagnetic waves [1] that are being controlled. The development of metamaterials is inextricably linked to the progress of manmade material design that interacts with microwave, radio, and optical frequency bands. The double negative (DNG) metamaterial is known as the negative index metamaterial (NIM); they are also sometimes referred to as left-handed metamaterials (LHM), which exhibit negative electric permittivity and negative magnetic permeability. In a particular frequency range, a metamaterial can act as a single negative metamaterial that shows only negative permittivity or negative permeability [2,3]. These unusual features are not typically encountered in nature. Tweaking the metamaterial design can provide the electromagnetic field a large range of potentiality including the development of substrates [4], reconfigurable antennas [5], absorbers [6,7,8], microwave devices such as Wi-Fi, GPS [9], imaging [10], study of SAR reduction [11], metamaterial sensor [12], filter [13], perfect lens [14], perfect tunneling [15], optics [16,17,18], invisible cloaking [19], radar and satellite communication [20], information metamaterial [21], terahertz metamaterial [22,23], programmable modulator [24]; these benefits afford metamaterials wide applicability in many fields.

It is highly requested in many application fields to design the required system for high performance with better device compactness and higher bandwidth capacity. EMR refers to the design’s compactness and effectiveness in long-distance communication systems, which can be added to the design’s novelty. In this literature, recent progress on EMR-based metamaterial design is discussed. In 2017, a double C shape metamaterial was developed by Faruque et al. [25]. The frequency bands were S, C, and X-band, the dimension of that unit cell was $12\times 12{ \mathrm{mm}}^2$, and the EMR was 7.427. In the same year, Marathe et al. [26] reported a very compact size metamaterial design with a higher EMR of 11.5. The size of the reported open delta loops-based metamaterial was $6\times 6 {\mathrm{mm}}^2$. Another double L shape [27] metamaterial was designed two years later in 2019. The structure was $10\times 10{ \mathrm{mm}}^2$ in dimension and developed for long-distance, military, and satellite communication applications. The EMR of that proposed metamaterial was lower than the previous one of 3.9. In 2020, Afsar et al. [28] proposed a new inverse epsilon-shaped metamaterial unit cell that has a higher EMR of 12.61, where the unit cell was $10\times 10 {\mathrm{mm}}^2$ in dimension and the resonance frequencies were in the S, C, and X bands. The developed metamaterial was suggested for distance radar communication and satellite communication applications. In the same year, more research was established on the metamaterial unit cell EMR properties. Sifat et al. [29] developed a hook C-shaped metamaterial design with a higher EMR of 12.78. The compactness of that design also established the effective electric field characteristics under the S band. The dimension of that design was $8\times 8 {\mathrm{mm}}^2$ and the metamaterial was highly suggested for airport surveillance radar systems. In the same year, Islam et al. [30] designed a new square circle shape metamaterial with the dimension of $8\times 8{ \mathrm{mm}}^2$. The metamaterial unit cell with a higher EMR of 14.3 presents its effectiveness and compactness for airport surveillance radar systems. In the following year, 2021, Islam et al. [31] developed a compact-sized semi-circle-shaped meander-lines-based metamaterial unit cell that operates under S, C, X, and Ku bands. The EMR and the dimension of the unit cell were 15.1 and $8\times 8{ \mathrm{mm}}^2$ respectively.

The U-NII (Unlicensed National Information Infrastructure) radio band [32], which was established by the United Federal Communications Commission, is part of the microwave frequency spectrum from 5.150 to 7.125 GHz. This frequency band is used by WLAN devices and wireless ISPs. Wireless ISPs generally use a 5.825–7.725 GHz band span. In March 2021, U-NII provided a total of eight ranges, which were segmented as U-NII-1–U-NII-8. U-NII-1 to U-NII-4 ranges are for 5 GHz WLAN, which are 802.11 a and later standards; U-NII-5 to U-NII-8 areas are for 6 GHz WLAN, which are 802.11 ax standards; UNII-2 is divided into three sub-range sections through A to C. Licensed amateur radio operators are authorized to use 5.650–5.925 in the USA. Due to a shared IEEE standard, many countries use similar bands for wireless communication. The European HiperLAN standard operates in the same frequency band as the U-NII. The U-NII-1, U-NII-2A, and U-NII-3 bands are also used for Wi-Fi as well, being used both indoors and outdoors for higher bandwidth capacity. The concept of dual-band Wi-Fi comes from the need for extra data capacity and coverage; the dual-band architecture of 2.4 GHz and 5.6 GHz bands in gateways and end notes have become the most popular. The users are allowed to connect more devices to the Internet using the 5 GHz spectrum in a more effective way when a home mesh system with several routers is used to cover a bigger area; the UNII band 5.6 GHz can be worked as a dedicated communications connection between the two routers, speeding up the overall system using a dual-band [33] configuration.

In this study, two SRR-constrained double C-shaped metamaterials are presented for S, C, and X band applications. The proposed design provides a unique shape with a miniaturized size: a dimension of 0.0156λ × 0.0156λ. The proposed metamaterial produced quadruple resonance covering for Wi-Fi and satellite communication applications. Moreover, it can provide a wider bandwidth of 1.65 GHz at 11.5 GHz. The developed double C-shaped left-handed metamaterial exhibited a highly effective medium ratio (EMR) of 15.6 that showed compactness, which is relatively high in this regard compared to the recently proposed metamaterials. The S band is very popular with a 2.4 GHz resonance frequency for Wi-Fi and other applications such as mobile services, satellite communications, and optical communications. The C band with 5.6 GHz resonance frequency can be used for dual-band Wi-Fi communication along with the 2.4 GHz. It is also applicable in WLAN/WiMAX and radar applications with its large bandwidth of 600 MHz. The other two resonance frequencies, 8.93 GHz and 11.5 GHz are also highly applicable for long-distance communication devices. The 11.5 GHz under the X band has a high bandwidth of 1650 MHz, which can be employed in long-distance satellite communication applications. Metamaterials are presently a prominent focus of study to build lightweight, small, and low-cost devices for improving radar and satellite application functionality. The proposed unit cell was developed with the high-performance Rogers RT5990 substrate and the design is achieved with an EMR of 15.6, which is better than the existing works. Moreover, the demonstration is observed with the suggested design’s compactness and effectiveness. The CST studio suite 2019 and the finite integration technique (FIT) were used to design and analyze the considered metamaterial properties that are broadly described in this manuscript.

2. Design of the Metamaterial Unit Cell

In the unit cell construction, a mutually linked double C-shaped metal with an interconnected double SRR was proposed. The design structure is shown in Figure 1a, which presents the geometric structure of the metamaterial unit cell with a front view of the structure. The design of the proposed metamaterial unit cell was implemented with a Rogers RT5990 substrate with a dimension of $8\times 8 {\mathrm{mm}}^2$ and a substrate thickness of $1.575 \mathrm{mm}$. The dielectric constant and loss tangent of the substrate is $\mathsf{\epsilon }$_r = 2.2 and $\delta$= 0.0009, respectively. The used copper coating has a thickness of 0.035 mm and a width of 0.4 mm, with an electrical conductivity of $\sigma =5.8\times {10}^7 \mathrm{S}/\mathrm{m}$. The double SRR attached double C-shaped metamaterial schematic and 3D diagram are shown in Figure 1b–d. Figure 1b exhibits the layers of the metamaterial unit cell where there is a substrate layer and a copper coating layer; Figure 1c shows the perspective view of the unit cell; Figure 1d indicates the side view of the design. The unit cell consists of two square SRR bounded with two C-shaped interconnected parts. The design is achieved with modification of the position, length, and width of the shapes by several numerical simulations executed in the CST Microwave Studio Suite (2019).

Figure 2 represents the design progress from beginning to end; Figure 3 represents the transmission coefficients and reflection coefficients from the different design structures. The design was attempted with an outer SRR, which is shown in Figure 2a-Design 1. The gap between the edge of the substrate and the outer SRR is 0.2 mm. The length, width, and height of the very first SRR are 7.6 mm, 7.6 mm, and 0.035 mm, respectively. There is a split gap of 0.2 mm at the top-right side of the SRR. When the incident wave is propagated on the device, the resonance is observed there by the SRR as the conducting part of the SRR shows inducting properties and the split gap creates the capacitance. As shown in Figure 3a, there are three resonances of transmission coefficient found because of the outer SRR at 3.53 GHz, 10.29 GHz, and 13.42 GHz.

It is observed that the four resonance frequencies are in three different bands, the S, X, and Ku bands, respectively. The reflection coefficient is shown in Figure 3b, where two strong resonances are observed at 5.2 GHz and 12.6 GHz. In Figure 2b-Design 2, when the second outer SRR is introduced at the inner part of the existing SRR, we observed there is a left shifting of the resonance frequencies. The updated transmission coefficients are 3.4 GHz, 9.2 GHz, and 12.9 GHz—see Figure 3a; the updated reflection coefficients are 4.6 GHz and 11.3 GHz—see Figure 3b. In Figure 2c-Design 3, the C-shape SRR is introduced at the inner part of the existing two SRRs; we find that a new resonance frequency is added with a strong bandwidth at 8.7 GHz.

The new transmission coefficient is shown in Figure 3a along with the other resonance frequencies, 3.4 GHz, 8.7 GHz, 9.2 GHz, and 12.8 GHz, respectively. The new reflection coefficient at 10.8 GHz is also compared in Figure 3b with the other frequencies, 4.5 GHz, 10.8 GHz, and 11.2 GHz, respectively. In Figure 2d-design 4, we introduce a new C-shape SRR in the very inner part of the whole structure and we find almost the same resonance frequencies over the transmission coefficient (S21) in Figure 3a and reflection coefficients (S11) in Figure 3b. The transmission coefficients and reflection coefficients are 3.4 GHz, 8.7 GHz, 9.2 GHz, and 12.8 GHz and 4.5 GHz, 10.8 GHz, and 11.2 GHz, respectively. Finally, in Figure 2e-Proposed design, we interconnect the C-shape SRRs to make a double C-shape and interconnect the outer two SRRs. The outer two SRRs and the inner double C-shape are interconnected with a metallic stripe; as a result, we obtain tremendous results with a strong lower frequency in this compact size structure. The new design is adopted with the frequencies shifted towards the lower frequencies where the mutual coupling is introduced and magnitudes are changed. The shifted transmission coefficients are 2.4 GHz, 5.6 GHz, 8.9 GHz, and 11.5 GHz with a magnitude of −32.77, 38.28, −26, and −44.7 dB, respectively, which are shown in Figure 3a; the reflection coefficients are 2.8 GHz, 6.14 GHz, 9.1 GHz, and 12.6 GHz with a magnitude of −35.9, −14.8, −17.54, and −7.04 dB, respectively, which are shown in Figure 3b. We also observed that the resonance frequency under the Ku band is shifted towards the X band. The resonance frequencies are found under the S, C, and X bands in the proposed structure. The parameters and dimensions of the proposed unit cell are shown in

Table 1. Proposed unit cell parameters values.

Parameter	a & b	l & w	l1 & l2	l3	l4	w1 & c3	w2
Value	8	7.6	2.3	5.8	3.4	1.7	4.9
Parameter	w3	w4	g1,g2,g3,g4	c1 & c2	c4	c5	m
Value	5.8	0.8	0.2	3.4	2	0.9	0.2

.

The metallic part of the design was tweaked until we obtained good results in the computer simulation technology (CST) studio suite (2019). In this study, different substrates were utilized with different thicknesses, dielectric constants, and loss tangents. The design began with a single SRR on the FR-4 substrate and ended with two SRR bounded double C-shaped metallic copper coatings on the Rogers RT5880 substrate. The outer two SRRs are interconnected and there is a connection with the inner design of the double C-shaped metallic part. The inner metallic parts relate to each other at the top and bottom area, where they appear as a bold C shape. The width and length of the double C shape are w3 and l3, respectively. The width of the outer C is denoted by c1, and the length of the outer C is denoted by c2. The inner C shape is denoted by c3, c4, which are the width and length of the inner C shape, respectively. The free space between the head and tail of the C shape is identified by g4.

The whole double C shape is attached to an SRR where l3 is denoted for the length. The SRR has two split gaps at the top and bottom area; the length is 0.02 mm for each gap denoted by g2 and g3. The single SRR-attached design is also bounded with another SRR, and they are interconnected with two metallic parts; the metallic part is denoted by m. The height and width of those connectors are identified as m = 0.2 and g4 = 0.5, respectively. The gap length between the two SRRs is 0.5 mm. The length and width of the most outer SRR are denoted by l and w. Finally, the whole copper coating structure is placed over a Roger RT5880 substrate, which has a length and weight that are denoted by a and b. The transmission coefficient (S21) and reflection coefficient (S11) of the designs are shown in Figure 3 based on the design evaluation. The results of the polarization angle and the incident angle of the incident wave are shown in Figure 4. Figure 4a displays the S21 comparison for distinct incident wave polarization, indicating that the suggested metamaterial design has a similar response in different circumstances. This polarization angle effect is analyzed by varying the polarization angle, Φ, from 0° to 90°, with four identical steps. The S21 response was also observed from different angles of the incident wave, which is represented in Figure 4b. The effect of this oblique incidence is analyzed by varying the incident angle, θ, from 0° to 90°. The transmission coefficient is unaffected by changes in polarization and incident angle, demonstrating that the suggested design structure has a consistent response for every angle of incidence. As a result, the suggested metamaterial structure is insensitive to changes in polarization and oblique incidence angle.

3. Metamaterial Simulation and Methodology

The various models were utilized to investigate different property parameters for the metamaterial. The CST Microwave Studio simulation software was used to realize the performance and compute the S-parameters of the proposed unit cell. The finite integration technique (FIT), including simulation and analysis, was used in this study following from Reference [34]. The numerical approach of the FIT is used to extract the transmission coefficient (S₂₁) and reflection coefficient (S₁₁), which indicate return loss and insertion loss, respectively. The two waveguide ports are utilized to generate electromagnetic waves and transmitted in the Z-axis direction. The boundary conditions are realized to induce the negative electric and negative magnetic responses to the X and Y-axis. The polarization happens while propagating the incoming electromagnetic wave through the E-field and H-field. The X-axis is approved as a perfect electric conductor and the Y-axis as a perfect magnetic conductor. For free space simulation, a frequency domain solver-based simulation was utilized. This metamaterial structure implies the equivalent LC circuit where the split gap acts as a capacitor and the resonator strip plays as an inductor. The inductance of the acting inductor and capacitance of the acting capacitor were modified with the width of the metallic part and the split gap. The simulation was performed from the 1 GHz to 14 GHz microwave range. The boundary conditions and the wave ports are shown in Figure 5.

The property of effective permittivity (ε_r), permeability (μ_r), and refractive index ($\eta$) are extracted from the S-parameters using the Robust technique [35]. Throughout the whole procedure, Equations (1)–(7) were performed to calculate the parameters [36]. From Equations (1) and (2), the reflection coefficient (S₁₁) and transmission coefficient (S₂₁) can be formed.

$$S_{11}=\frac{R_{01} (1-{℮}^{i2n{k}_{0}d})}{1-R_{01}{}^2 {℮}^{i2n{k}_{0}d}}$$

(1)

$$S_{21}=\frac{(1-R_{01}{}^2){℮}^{in{k}_{0}d}}{1-R_{01}{}^2 {℮}^{i2k_{0}d}}$$

(2)

where $R_{01}=\frac{z-1}{z+1}$.

The metamaterial is identified as a passive medium. In such a situation, the real component and the imaginary portion of the refractive index and impedance are determined in the following manner.

$$\mathrm{z} \left(\mathrm{real}\right)\ge 0$$

(3)

$$\eta \left(\mathrm{imaginary}\right)\ge 0$$

(4)

The refractive index $\left(\eta \right)$ and the impedance (z) are derived from Equations (1) and (2),

$$z=\pm \sqrt{\frac{{\left(1+S_{11}\right)}^2-S_{21}{}^2}{{\left(1-S_{11}\right)}^2-S_{21}{}^2}}$$

(5)

$${℮}^{ink0d}=X \pm i\sqrt{1-X^2}$$

(6)

where $X=\frac{1}{2S_{21}\left(1-S_{11}{}^2+S_{21}{}^2\right)}$.

$\eta$ denotes refractive index value and can be achieved from Equation (7) using Equation (6)

$$\eta =\frac{1}{k_{0}d}\{[{[\ln ({℮}^{in{k}_{0}d})]}^{″}+2m\pi ]-i{[\ln ({℮}^{in{k}_{0}d})]}^{\prime }\}$$

(7)

where m denotes an inextricable link to the index of ${\eta }^{\prime }$ and k denotes the free space wave vector. The thickness of the proposed structure is denoted by d. The imaginary component of η is known just once, while the real part is complicated by the subfunctions of the logarithm function. To calculate the true fraction of effective parameters, the usual extraction procedure is utilized. From the effective parameter analysis, the resonance frequencies are displayed. The real part of the effective parameters is determined using the conventional extraction procedure. The effective parameter analysis reveals the resonance frequencies. The negative effective permeability is influenced by a series of gaps, which are added together to form a narrow band gap where permittivity and permeability emerge close to the resonance frequency, and the real value of the effective permittivity, permeability, and refractive index can be calculated using Equations (8)–(10) [37].

$${\mathsf{\epsilon }}_{\mathrm{r} }=\frac{\mathrm{c}}{\mathrm{j}\mathsf{\pi }\mathrm{fd}}\times \frac{\left(1-{ \mathrm{V}}_1\right)}{\left(1+{ \mathrm{V}}_1\right)}$$

(8)

$${\mathsf{\mu }}_{\mathrm{r}}=\frac{\mathrm{c}}{\mathrm{j}\mathsf{\pi }\mathrm{fd}}\times \frac{\left(1-{ \mathrm{V}}_2\right)}{\left(1+{ \mathrm{V}}_2\right)}$$

(9)

$${\mathsf{\eta }}_{\mathrm{r}}=\frac{\mathrm{c}}{\mathrm{j}\mathsf{\pi }\mathrm{fd}}\times \sqrt{\frac{{\left({\mathrm{S}}_{21}-1\right)}^2-{ \mathrm{S}}_{11}{}^2}{{\left({\mathrm{S}}_{21}+1\right)}^2-{ \mathrm{S}}_{11}{}^2}}$$

(10)

The obtained resonance frequencies are 2.4 GHz, 5.6 GHz, 8.93 GHz, and 11.5 GHz in the proposed structure. The final structure is developed by changing many structures with the variation of the resonance frequencies. The bandwidths are also varied due to their design pattern. According to the different design structures, the transmission-based resonance frequencies are 2.4 GHz, 5.6 GHz, 8.93 GHz, and 11.5 GHz, respectively. The variation of the designs at their different resonance frequencies and bandwidths are shown in

Table 2. Proposed unit cell parameters values.

Structure	Design 1	Design 2	Design 3	Design 4	Proposed design
Resonance frequencies	3.53, 10.29, 13.42 GHz	3.41, 9.19, 12.9 GHz	3.41, 8.72, 9.25, 12.87 GHz	3.43, 8.77, 9.25, 12.85 GHz	2.4, 5.6, 8.93, 11.5 GHz
Magnitude in dB	−40.79, −47.37, −34.61	−42.49, −44.98, −38.36	−41.38, −35.89, −35.68, −40.44	−39.9, −35.11, −39.9, −23.43	−32.27, −38.28, −25.99, −44.7
Bandwidth Span (under −10 dB)	3.25–3.8, 9.38–11.1, 13.2–13.8	3.1–3.6, 8.3–9.8, 12.5–13.36	3.18–3.6, 8.27–8.88, 9.0–9.7, 12.55–13.19	3.19–3.6, 8.28–8.87, 9.0–9.7, 12.5–13.15	2.3–2.49, 5.27–5.87, 8.81–8.98, 10.61–12.26

, which indicates the evolution of the designs and the outcome of the proposed design from the design evolution. The magnitudes and bandwidth spans of the different design patterns are also attached to Table 2.

4. Equivalent Circuit and Design Analysis

Numerous approaches can be taken for remodeling the equivalent circuit. The lumped equivalent circuit approach is one of the approaches that consider the microwave elements, including the inductance, resistance, capacitance, and conductance [38]. The metallic conductor is addressed with the inductor property when the equivalent circuit model is developed. The capacitive impact is represented by the split gap. Every SRR serves as a combination of inductance L and capacitance C. The split ring acts as a resonator, resonating at a specific frequency. The proposed structure is based on double SRR with some modifications. The length and spacing of the ring resonator may be adjusted to modify the resonance frequency.

$$f=\frac{1}{2\pi \sqrt{LC}}$$

(11)

The total inductance L and capacitance C of the proposed unit cell can be achieved from Equations (12) and (13), respectively [39].

$$L=0.01\times {\mu }_0\left\{\frac{2{\left(d+g+h\right)}^2}{{\left(2w+g+h\right)}^2}+\frac{\sqrt{{\left(2w+g+h\right)}^2+l^2}}{\left(d+g+h\right)}\right\}t$$

(12)

$$C={ϵ}_0\left[\frac{2w+g+h}{2\pi {\left(d+h\right)}^2}\ln \left\{\frac{2\left(d+g+h\right)}{\left(a-l\right)}\right\}\right]t$$

(13)

where ${\mu }_0=4\pi \times {10}^{-7}$ H/m, ${\mu }_0=8.854\times {10}^{-12} \mathrm{F}/\mathrm{m}$, h = thickness of the substrate, d = split distance, l = resonator length, w = resonator width, t = thickness of the copper resonator, and g = split gap of the ring.

The equivalent circuit of the unit cell and the S21 response from the CST and ADS simulator are illustrated in Figure 6.

Table 3. Circuit components and values of the components.

Capacitor	Value (pF)	Inductor	Value (nH)	Capacitor	Value (pF)	Inductor	Value (nH)
C1	0.2	L1	0.5	C6	1.45	L6	1.61
C2	1.5	L2	0.258	C7	0.775	L7	0.85
C3	0.85	L3	1.33	C8	0.76	L8	0.408
C4	1.8	L4	4.42	C9	4.405
C5	1.02	L5	1.5

represents the values of the circuit components. The inductances L1 and L2 with the collaboration of capacitances C1 and C2 indicate the model of the equivalent circuit of the outer SRR of the design. At the same time, inductances L3 and L4 and capacitances C3 and C4 represent the inner SRR as an equivalent circuit. The outer and inner SRR relate to two metallic stripes, which are represented with the LC combination of L7, C7, and L8, C8, respectively. The inductances and capacitances of the Double C shape are indicated by the components of L5, L6, C5, and C6. This part of the circuit is related to the inner SRR, whereas component C9 is made by the split gap. The simulation software Advanced Design System (ADS) was used to determine the values of these circuit components; the acquired values are characterized in Table 3. These values are considered from the unit cell resonances of S21. It can be seen in Figure 6b that both results show slight variations, as the ADS simulator was used to provide the estimated structure of the lumped elements with manual fitting and lower boundary values, whereas the CST simulator used the finite integration method with a computing mesh algorithm. After studying the unit cell design and equivalent circuit model, the responsible components that trigger the resonance at a certain frequency are identified. The L1, L3, C1, C3, L8, and C8 are responsible for the resonance of 2.4 GHz, whereas the L3, C3, L7, and C7 represent the resonance of 5.6 GHz. The resonance of 8.93 GHz is responsible for the components of C9, L5, and C5. The resonance frequency at 11.5 GHz is triggered by the components of L6 and C6. Controlling the values of these components can change the resonance frequencies.

5. Parametric Study: Changing Effects of Length and Split Gaps

The length and split gap are the most important property for metamaterial performance. Because of the split gap and length, the inductance and capacitance are altered. The metamaterial’s resonance frequencies are affected by the modification of the split gaps. The split gap in SRR has the most influence on the proposed metamaterial unit cell’s response. Due to the relationship between capacitance and resonance frequency, the change in capacitance value impacts the resonance of the unit cell. The split gaps g1 and g3 are modified on the proposed unit cell for analyzing the resonance results. The split gap g1 is designed in the outer SRR and g3 is developed in the inner SRR. In this study, the lengths of these two split gaps are varied once at a time, whereas the lengths of the other split gap remain fixed. The effects of changing the split gaps are shown in Figure 7. The split gap g1 has an effect on the resonance at 5.6 GHz, 8.93 GHz, and 11.5 GHz, which is shown in Figure 7a. As the split gap g1 decreases from higher gap length to lower gap length, the capacitance increases steadily; this causes the resonance frequency to trend toward the lower values by following Equation (11). The impact of changing the split gap g3 in the inner SRR is shown in Figure 7b. The modification of capacitance value due to the change in g3 causes a minor resonance to exist around 2.4 GHz, though the variation of the resonance frequency is lesser when compared to the effect of the change of g1. The split gap g3 in the inner SRR shows its impact around the resonances within 7 GHz and 14 GHz. As a result, the split gaps play an important role in regulating the modulator’s capacitance, and the resonance frequency may be controlled by modifying the gap length. The effect of changing the length of the metamaterial design is also observed in this study. l1 and l2 represent the length of the outer and inner SRR copper parts of the design, respectively. The length modification strongly affects the inductance and influences the resonance of the proposed metamaterial. The resonance shifting results based on the modification of the length of the outer and inner SRR are shown in Figure 7c,d, where the lengths are tweaked until we obtained the desired resonances.

6. Results and Discussion

In this part, the metamaterial property of the proposed design is extracted and analyzed to identify the feature of the introduced design. The EMR on the design evolution is also analyzed here along with the discussion. The array was designed, and the property analysis of the metamaterial array is also introduced here. The metamaterial was used as an array most of the time; thus, it was also necessary to examine the performance of various arrays of metamaterial because of the validity of the design. The frequency hopping properties of the outer two SRRs were explored using numerical simulation by mirroring the unit cell position in the array. In this part, the metamaterial’s performance is compared to some current research works.

6.1. Electric Field, Magnetic Field, and Surface Current Analysis

With the help of mathematics and physics, the electric field distribution at resonance frequencies of 2.4 GHz, 5.6 GHz, 8.9 GHz, and 11.5 GHz was investigated. The propagation constant ($\gamma$) of the medium is responsible for frequency ($\omega$), permittivity ($\epsilon$), permeability ($\mu$), and conductivity ($\sigma$). The propagation constant of the medium is adopted by E-field propagation. For the E-field, we may obtain the Helmholtz equation [40] from Equation (14).

$${\nabla }^2{E}_m-{\gamma }^2{E}_m=0$$

(14)

E_m indicates the propagation of electric field and $\gamma$ indicates propagation constant.

$$\left|{\gamma }^2\right|=\omega \mu \sqrt{{\sigma }^2+{\omega }^2{\epsilon }^2}$$

(15)

Equation (14) can be generated by combining the given parameters and form to Equation (16), where it is satisfied with a linear homogeneous differential equation.

$$\left[\frac{d^2}{d{z}^2}-{\gamma }^2\right]E_{xm}\left(z\right)=0$$

(16)

At a resonance frequency, Equation (16) gives the properties to the electric field. In Figure 8, the E-field distribution over the outer SRRs is seen while simulating wave propagation along the z-axis. The properties of electric fields are also observed in the inner double C shape area of the metamaterial unit cell. At different resonances, for the proposed quad resonance frequencies, a high-intensity E-field produces a significant dipole moment when mutual coupling occurs, and this moment is shared equally by the symmetric and asymmetric parts of the structure. We adjusted the planned unit cell with a connecting slab based on the E-field. The introduced copper metallic slab inductor was placed in the gap between the outer two SRR areas at 1.7 mm from the left and 4.9 mm from the right of the outer SRR. We also introduced another metallic stripe at 4.9 mm from the left and 1.7 mm from the right of the outer cell between the two outer SRR gap. Fortunately, the feedback is produced by the electric field and resonance frequencies after connecting the two outer SRRs. There is another connecting slab used between the inner SRR and double C shape gap, which also shows effective results on electric field distribution. This modifying technique of the metallic part in the unit cell is inspired by Ahamed et al. [41]. The resonance frequencies are implemented in this design at 2.4 GHz, 5.6 GHz, 8.9 GHz, and 11.5 GHz; the bandwidth was observed at or below −10 dB and achieves distinguished results, which can be discussed further in the study.

The electric field (E-field), magnetic field (H-field), and surface current distribution of the proposed metamaterial were analyzed for quad resonance frequency and are shown in Figure 8, Figure 9 and Figure 10. At the resonance frequency of 2.4 GHz, a strong electric field is seen at the top-right area of the metallic part of the structure, including two outer SRRs; there is an electric field also observed in the inner split of the outer SRRs at the bottom-left area due to the capacitive effect in Figure 8a. At the same time, the magnetic field is observed in the inner double C shape area on the left side of the structure in Figure 9a, where it indicates the opposite reaction from the electric field. Figure 10a shows that a higher surface current is observed in those areas where the magnetic field is present.

These characteristics fulfill the criteria of Maxwell’s equation. At the resonance frequency of 5.6 GHz in Figure 8b, there is a strong electric field observed at both the top-right and bottom-left outer SRR area. At the same resonance frequency, the magnetic field is also observed strongly at the top-left area where the two outer SRRs are connected in Figure 9b. A strong surface current flow is observed in the same area where the magnetic field occurred—see Figure 10b. This high current concentration creates a powerful magnetic dipole through the top-right and bottom-left outer SRR. At the resonance frequency of 8.9 GHz, in the metamaterial unit cell structure, a strong electric field is observed in both the outer two SRRs and the inner double C shape. In the meantime, a strong magnetic field is observed at the connecting strip between the outer SRR and the inner double C shape part—see Figure 9c. The surface current flow is observed in the same area where the strong magnetic field exists in Figure 10c. At the resonance frequency of 11.5 GHz, a strong magnetic field appears at the split gap between the outer SRR and inner SRR in Figure 9d. A dense magnetic field is observed throughout the structure where there is less of an electric field. A strong magnetic field appears in the inner SRR bottom-left area because of the low impedance path—see Figure 9d. At the same time, the surface current flow is observed in the same area where the magnetic field density is achieved.

6.2. Metamaterial Unit Cell Property Extraction Analysis

The transmission coefficient (S21) and reflection coefficient (S11) obtained from the CST studio suite 2019 are plotted in Figure 11a. The results were analyzed using MATLAB code from Equations (6) and (13) to determine the relative permittivity, relative permeability, refractive index, and impedance. The graphs are plotted in Origin Pro 2018 using the exported data from MATLAB. Figure 11b shows the negative permittivity in four separate range frequencies of 2.42–2.71 GHz, 5.64–6.15 GHz, 8.9–9.1 GHz, and 11.57–12.64 GHz, respectively. Another resonance frequency is seen near 6.2 GHz, whereas the other four indicate a strong contribution to negative permittivity characteristics. The positive permittivity imaginary obtains the metamaterial behavior criteria. In Figure 11c, the permeability graph is plotted where three district areas are identified with negative permeability of near 2.4 GHz, 5.5 GHz, and 11.2 GHz, which strongly established itself as a double negative metamaterial. To confirm the results from the CST simulator, another popular simulator, the Ansys High-Frequency Structure Simulator (HFSS), was utilized to extract the transmission coefficient (S21) and reflection coefficient (S11) data under the simulator’s proper setup conditions. The compared results of the S21 and S11 from the CST and HFSS simulator are illustrated in Figure 11e. They have almost the same results, which validates the design structure of the metamaterial unit cell.

The refractive index is plotted in Figure 11d, which indicates the negative refractive index (real) in the frequency range of 2.4–2.74 GHz, 5.6–6.1 GHz, 8.9–9 GHz, and 11.5–12.6 GHz. The imaginary part of the refractive index indicates positive values in the frequency range of 2.4–2.7 GHz, 5.6–6.1 GHz, 8.9–9 GHz, and 11.6–12.6 GHz, respectively. The incident wave within the metamaterial structure decreases when the refractive index has a positive imaginary value. For the validation of the suggested design, the extracted results from the HFSS simulation software are also compared with the CST simulator, which is illustrated in Figure 11e. The magnitude negative values of the S21 from the HFSS are slightly higher than in the CST simulator, where the resonance frequencies are placed at almost the same points. The S11 values from the HFSS simulator are slightly shifted right than the CST results. This comparison establishes the validity of the design structure based on different simulation software, which is mostly popular for microwave simulations. The simulated S21 phase of the metamaterial unit cell and different size array is shown in Figure 11f.

6.3. Metamaterial Array Analysis

In this study, four different sizes of array structures were investigated. The examination was held under consideration of the resonance and different characteristics of the array at different positions. To evaluate the effects of coupling between the unit cell, different layouts of an array need to be described. We call it mirror positioning when one unit cell is positioned as a mirror to its neighbor unit cell. Moreover, we can classify the array evolution into two types: (A) without mirror positioning; (B) with mirror positioning—inspired by Reference [29]. The top and bottom positions of the two-unit cells were used to place them face to face in a mirror positioning array. In Figure 12, two different types of positioning 1 × 2 sized arrays are illustrated; Figure 12a indicates the without mirror positioning array (the normal placement); 12b indicates the mirror positioning array where the top unit cell is mirrored horizontally in its place. Another scenario is presented in Figure 12c,d, where a 2 × 1 sized array is examined, where 12 c indicates a general positioned unit cell and 12d indicates a transformed unit cell on top position where it transformed to 180° in the Z-axis at its position. The transmission coefficients from that without mirror positioning and transformed positioning yield almost similar results to that of the metamaterial array characteristics. In normal unit cell placement in 1 × 2 sized arrays, the resonance frequencies shifted to 2.63 GHz, 5.8 GHz, 8,2 GHz, and 11.8 GHz from 2.4 GHz, 5.6 GHz, 8.93 GHz, and 11.5 GHz, respectively. It is also observed that with mirror positioning, the resonance frequencies in the same sized array shift back to 2.43 GHz, 5.64 GHz, 9.93 GHz, and 11.55 GHz. The same shifting is occurred in the 2 × 1 sized transformed positioning array structure. Utilizing this mirror positioning, the 2 × 2 and 4 × 4 sized metamaterial arrays are formed and shown in Figure 12e,f, respectively. The graph visualization of transmission coefficients of different-sized metamaterial arrays is shown in Figure 13.

The relevant transmission coefficients of the differently sized metamaterial arrays, including their different positioning of the unit cell where the mirror positioning and transformed positioning array, almost achieved the same resonances. The 1 × 2 and 2 × 1 normal positioning arrays fluctuated at their desired resonance frequencies, whereas the mirror positioning array in different sizes 1 × 2, 2 × 1, 2 × 2, and 4 × 4 display almost the same resonance frequencies. For the proposed structure, we are able to discuss the homomorphism [42] of the design. The transmission coefficient results of the unit cell and different arrays vary slightly due to the coupling effect; however, when applied to the mirror symmetry method in an array, the transmission coefficient results of both are the same due to less coupling effect.

6.4. Effective Medium Ratio (EMR) Analysis and Comparison

The effective medium ratio represents the compactness of the unit cell. In

Table 4. Comparison between proposed metamaterial and recently developed metamaterials based on resonance frequencies, dimension, and EMR.

References	Year	Shape	Dimensions (mm)	Resonance Frequencies (GHz)	EMR	Frequency Bands
[25]	2017	Double C	12 × 12	3.36, 8.57, 11.57	7.42	S, C, and X
[26]	2017	Delta loop	6 × 6	4.3, 7.6, 9.8	11.5	C and X
[27]	2019	Double L	10 × 10	7.69, 8.47, 12.04, 13.14	3.9	C, X and Ku
[28]	2020	Inverse-epsilon	10 × 10	2.38, 4.55, 9.42	12.61	S, C and X
[29]	2020	Hook-C shape	8 × 8	2.93	12.78	S-band
[30]	2020	Square-Circle	8 × 8	2.6, 6.3, 9.3	14.3	S, C, and X
[31]	2021	Semi-Circle	8 × 8	2.48, 4.28, 9.36, 13.7	15.1	C, S, X and Ku
Proposed	2022	Double C shaped	8 × 8	2.4, 5.64, 8.93, 11.5	15.6	S, C, and X

, the proposed unit cell is compared with a few of the recent existing works, including references, year of development, shape, dimension, resonance frequencies, EMR, and frequency bands. The presented comparison shows that the proposed design has the highest effective medium ratio. The wavelength at the lowest resonance frequency is divided by the unit cell maximal size to achieve the EMR. A metamaterial unit cell can be either single negative or double negative once the EMR should be larger than 4 in order to establish its efficiency. The EMR is calculated from Equation (17) [29]. The wavelength and dimension are denoted by λ and L.

$$EMR=\frac{\lambda }{L}$$

(17)

According to Table 4, it is observed that the lower dimension of the unit cell with lower resonance frequencies can achieve a higher EMR. Though the material from Reference [26] represents a much smaller size unit cell of $6\times 6{ \mathrm{mm}}^2$ in dimension, it also has a high resonance frequency at a lower band among the compared metamaterial structures. We also obtained two frequency bands, where the double L-shaped unit cell with the dimension of $10\times 10{ \mathrm{mm}}^2$ has three frequency bands, although the EMR is very low. The developed structure competes with the square circle shape structure [30], where the number of bands (S, C, and X bands) are the same, but the following semi-circle shape structure [31] has the same number of resonance frequencies of four. From Reference [29], the unit cell provided only one resonance frequency under the S band. Because of its narrow band, the metamaterial unit cell also provided a high EMR at that point. The proposed unit cell obtains the miniaturization and higher EMR with quad-band resonance frequencies, indicating the metamaterial design was the most effective when compared to all other studies presented in Table 4. The compactness and quad-band properties indicate this metamaterial unit cell can be used for a variety of small-sized devices and could be useful in a wide array of applications.

7. Conclusions

In this study, two SRRs bounded to a double C-shape double-negative left-handed metamaterial were simulated using the CST Microwave Studio Suite 2019. We compared the results with the extracted results from Ansys High-Frequency Structure Simulator HFSS. The equivalent circuit analysis and its electric, magnetic, and surface current distribution analysis were also used rigorously in this study. The resonance frequencies are 2.4 GHz, 5.6 GHz, 8.9 GHz, and 11.5 GHz, indicating the multi-band performance of this device. The high EMR of the device at the lower resonance frequency of 2.4 GHz compared to other existing designs strongly indicates its novelty. The proposed developed structure can be employed in Wi-Fi applications with dual-band facilities. It is also suggested to employ the design in satellite communication applications for its high bandwidth.