An Innovative Compact Split-Ring-Resonator-Based Power Tiller Wheel-Shaped Metamaterial for Quad-Band Wireless Communication

A split-ring resonator (SRR)-based power tiller wheel-shaped quad-band ℇ-negative metamaterial is presented in this research article. This is a new compact metamaterial with a high effective medium ratio (EMR) designed with three modified octagonal split-ring resonators (OSRRs). The electrical dimension of the proposed metamaterial (MM) unit cell is 0.086λ × 0.086λ, where λ is the wavelength calculated at the lowest resonance frequency of 2.35 GHz. Dielectric RT6002 materials of standard thickness (1.524 mm) were used as a substrate. Computer simulation technology (CST) Microwave Studio simulator shows four resonance peaks at 2.35, 7.72, 9.23 and 10.68 GHz with magnitudes of −43.23 dB −31.05 dB, −44.58 dB and −31.71 dB, respectively. Moreover, negative permittivity (ℇ) is observed in the frequency ranges of 2.35–3.01 GHz, 7.72–8.03 GHz, 9.23–10.02 GHz and 10.69–11.81 GHz. Additionally, a negative refractive index is observed in the frequency ranges of 2.36–3.19 GHz, 7.74–7.87 GHz, 9.26–10.33 GHz and 10.70–11.81 GHz, with near-zero permeability noted in the environments of these frequency ranges. The medium effectiveness indicator effective medium ratio (EMR) of the proposed MM is an estimated 11.61 at the lowest frequency of 2.35 GHz. The simulated results of the anticipated structure are validated by authentication processes such as array orientation, HFSS and ADS for an equivalent electrical circuit model. Given its high EMR and compactness in dimensions, the presented metamaterial can be used in S-, C- and X-band wireless communication applications.


Introduction
Metamaterial is a congress of non-natural physical structures designed to achieve advantageous and uncommon electromagnetic properties. The effective properties of metamaterials are defined and measured in terms of permittivity (ε) and permeability (µ) [1,2]. A hypothetical ε-negative and µ-negative metamaterial termed DNG or LHM metamaterial was introduced in 1968 by Russian physicist Victor Veselago [3]. The unique properties of this metamaterial have drawn the attention of scientists all over the world for various applications in the microwave frequency range [4][5][6]. Nowadays, microwave-based applications are used in filtering [7], hidden cloaking [8], SAR reduction [9], absorber design [10], bandwidth enhancement [11], etc. A unit cell itself cannot acts as a complete metamaterial but is a systematic periodic array of metal-dielectric-metal or dielectricmetal structure upon a host substrate [12]. An S-shaped metamaterial with an EMR of 4.8 was designed for sensing applications in the microwave range [13]. A dual-band flexible metamaterial was designed on a nickel aluminate (NiAl2O4) substrate with a 42% aluminum concentration and dimensions of 12.5 × 10 mm 2 , covering the X and Ku bands [14]. Recently, a metamaterial was reported that a contained rectangular-shaped SRR. This metamaterial was utilized to sense concrete, temperature and humidity [15]. Islam et al. in [16] introduced a SNG metamaterial that shows triple band resonance for microwave application. Moreover, Smith et al. proposed a three-dimensional metamaterial built on reedy wire, along with a split-ring resonator [17]. In numerical simulation, the MM exhibited a double-negative characteristic with a wideband spectrum. A triple-band polarization-dependent MM with dimensions of 8 × 8 mm 2 was designed on an RT6002 substrate and yielded at 0.92 GHz, 7.25 GHz and 14.83 GHz, covering the S, C and Ku bands [18]. A tri-band MM with dimensions of 10 × 10 mm 2 and a Greek key shape was designed on an RT 5880 dielectric. In numerical simulation, it showed triple resonance peaks at 2.40, 3.50 and 4.0 GHz [19]. An epsilon-negative, delta-shaped metamaterial comprising an SSR (square ring resonator) exhibited tri-resonance crests that covered the C and X bands [20]. Another triple-band metamaterial with dimensions of 5 × 5 mm 2 was presented by Liu et al. in 2016 [21] with an RCER (reformed circular electric resonator). This MM with a low (5.45) effective medium ratio (EMR) was resonant in the frequency ranges of 9.70 GHz to 10.50 GHz and 15 GHz to 15.70 GHz.
A different metamaterial with a pie-shaped metallic resonator surrounded by an SRR was presented in [22]. This tri-band MM was designed on a substrate with dimensions of 8 × 8 mm 2 and covered the microwave S, C and X bands. An SRR-based triple-band metamaterial was designed with a double circular ring [23]. This multiunit cell-based MM was resonant at 5.6 GHz of Wi-MAX and 2.45 of WLAN. In 2019, Almutairi et al. [24] designed a metamaterial based on a CSRR (complementary split-ring resonator) with dimensions of 5 × 5 mm 2 . It showed resonance at 7.5 GHz with an EMR of 8. Moreover, an SNG metamaterial with dimensions of 5 × 5 × 1 mm 3 which comprising a concentric ring, along with a cross line, was designed on an FR-4 substrate [25]. It exhibited dual resonance peaks at 13.9 GHz and 27.5 GHz and was used to enhance the performance of a microstrip transmission line. A metamaterial was designed on an elliptical graphene nanodisk with a periodic pattern on a thin SiO 2 dielectric layer, as reported in [26]. Recently, two ceramic dielectrics were synthesized using MGa 2 O 4 (M = Ca, Sr) and LiF for to enhance the gain and performance of antennae [27,28]. An MM was designed using critical coupling at the gaps of two SRRs for total broadband transmission electromagnetic (EM) waves in a C-band application [29]. A cadmium sulfide (CdS) nanocrystalline coating with conducting polyaniline was designed to synthesized polyaniline-coated CdS nanocomposites characterized by UV-vis absorption [30]. In 2022, Amali et al. designed a nanocomposite using a potentiostatic method, which offered excellent electrocatalytic activity for nitrite oxidation [31].
In his research article, we present a new metamaterial that is an aggregation of three modified octagonal rings, along with a split-ring resonator. This power tiller wheel-shaped MM is compact in size, with an EMR of 11.61. In numerical simulation, it exhibits quadband resonance peaks at 2. 35, 7.72, 9.23 and 10.68 GHz, covering the S, C and X bands. Moreover, it also exhibits negative permittivity (ε) and a negative refractive index (n), with simultaneous near-zero permeability (µ). Such characteristics can be applied to comprehend various electronic components with different features and utilities. The main aim of this simple but first-hand design is to target versatile uses in wireless communication. The simulated results are verified by validation processes, confirming the reliability, consistency and efficiency of the proposed metamaterial. The ADS simulated result using a circuit model and Ansys HFSS 3D high-frequency software (high-frequency structure simulator) results show excellence harmony with the CST results. Figure 1a shows the front view of the unit cell, which is labeled with symbols. It is a new combination of three different octagonal rings surrounded by a split-ring resonator (SRR). A popularly used dielectric Rogers RT 6002 with dimensions 11 × 11 mm 2 and a thickness of 1.524 mm is used as a substrate. The dielectric constant, thermal conductivity and tangent loss of RT6002 are 2.94, 0.6 W/m/K and 0.0012, respectively. Copper (annealed) with an electrical conductivity of 5.96 × 10 7 Sm −1 is used for all resonators of the upper layer. The outer and inner radii of the first octagon are R 1 = 4.3 mm and R 2 = 3.8 mm, respectively, whereas the radii of the second octagon are r 1 = 3.3 mm and r 2 = 2.8 mm, respectively. Each split gap (g) of the octagon is 0.40 mm. The outer and inner radii of the smallest octagon are r 3 = 1.5 mm and r 4 = 0.75 mm, respectively. These three octagons (OSRRs) are placed at the center an SRR with dimensions of 10.40 × 10.40 mm 2 and a split gap (G) of 0.50 mm. The three octagons are attached to each other by four metal strips with a length of 3 mm and a width of 0.40 mm.

Design Parameters of the Metamaterial and Simulation Setup
Materials 2023, 16,1137 3 of 24 Figure 1a shows the front view of the unit cell, which is labeled with symbols. It is a new combination of three different octagonal rings surrounded by a split-ring resonator (SRR). A popularly used dielectric Rogers RT 6002 with dimensions 11×11 mm 2 and a thickness of 1.524 mm is used as a substrate. The dielectric constant, thermal conductivity and tangent loss of RT6002 are 2.94, 0.6 W/m/K and 0.0012, respectively. Copper (annealed) with an electrical conductivity of 5.96 × 10 7 Sm −1 is used for all resonators of the upper layer. The outer and inner radii of the first octagon are R1 = 4.3 mm and R2 = 3.8 mm, respectively, whereas the radii of the second octagon are r1 = 3.3 mm and r2 = 2.8 mm, respectively. Each split gap (g) of the octagon is 0.40 mm. The outer and inner radii of the smallest octagon are r3 = 1.5 mm and r4 = 0.75 mm, respectively. These three octagons (OSRRs) are placed at the center an SRR with dimensions of 10.40×10.40 mm 2 and a split gap (G) of 0.50 mm. The three octagons are attached to each other by four metal strips with a length of 3 mm and a width of 0.40 mm.  Table 1. Proper boundary conditions are applied to attain the expected results from the proposed metamaterial design. The electromagnetic radiation propagates along the z coordinate, whereas the perfect electric conductor (PEC) and the perfect magnetic conductor (PMC) propagate along the x coordinate and y coordinate, respectively. It is noteworthy that the width of the SRR (t), as well as that of the first two octagons, is 0.50 mm, whereas the width of the smallest octagon (e) is 0.75 mm. The perspective view and the simulation setup of the proposed MM are depicted at Figure 1b,c respectively. The symbolic presentations of the design parametric values of the projected unit cell are given in the Table 1. Proper boundary conditions are applied to attain the expected results from the proposed metamaterial design. The electromagnetic radiation propagates along the z coordinate, whereas the perfect electric conductor (PEC) and the perfect magnetic conductor (PMC) propagate along the x coordinate and y coordinate, respectively.

Extraction Process of Medium Parameters
To extract the various properties of the material, the S-parameters model of the postprocessing module of CST can be deployed [32]. This software is applied to obtain information associated with the three important characteristics of permittivity (ε r ), permeability (µ r ) and refractive index (n r ) of the proposed unit cell of metamaterial to realize EM properties [33]. Moreover, the refractive index, S parameters (reflection and transmission coefficient) and impedance can be correlated with the help of Equations (1)-(5) of the robust retrieval method described in [34]. (1) (2) Here, impedance is expressed as: where S 11 = reflection coefficient, and S 21 = transmission coefficient. Then, The electromagnetic wave is fixed to propagate along the z direction, together with the perfect electric and the magnetic fields, which are applied as boundary conditions along the x and y directions, respectively. Additionally, the relative permittivity (ε r ) and relative permeability (µ r ) can be derived from Equations (6) and (7), respectively, using the Nicolson-Ross-Weir (NRW) technique [35].
Permeability, µ r = c jπfd where c = speed of light, f = frequency and d = the thickness of the substrate. MATLAB codes are written based on Equations (6) and (7). The values of the material parameters extracted through the NRW technique are verified and compared with the results of numerical simulation.

Design Hierarchy
The chronological development of the proposed metamaterial unit cell is shown in the Figure 2. The design architecture and its morphology are set up to achieve the highest performance possible. An iterative method is applied to record feedback of the unit cell in order to determine the transmission coefficient (S 21 ). Design 2(a) comprises a split-ring resonator (SRR) along with an octagonal ring on the substrate layer. It yields resonance at 2.44 GHz, 8.67 GHz and 10.84 GHz. Another comparatively smaller octagonal ring of the same width is added to the first design, which is shown in the Figure 2b. In CST simulation, it exhibits quad-band resonance peaks at 2.51 GHz, 8.55 GHz, 9.50 GHz and 11.02 GHz. Again, to test the enhancement of the bandwidths, a small octagon with a width of 0.75 mm is placed at the center of the previous structure, which is shown in Figure 2c Table 2. Figure 3 shows the numerical results of S 21 for all design steps.
for the proposed MM. The simulated results of the S21 from Figures 2(a-e) are shown in the Table 2. Figure 3 shows the numerical results of S21 for all design steps. S-, C-,X-

Effect of Substrate Materials
Proper dielectric selection is an important task for any metamaterial design. An investigation is conducted to observe the response of different substrate materials. Commercially available flame-retardant FR-4 material, along with two Rogers dielectrics, RT 5880 and RT 6002, are taken into consideration. Three individual substrates are simulated by keeping the resonator structure unchanged. First, dielectric FR-4 shows resonance at 2.04 GHz, 6.66 GHz, 7.97 GHz and 9.42 GHz, with very low magnitudes. Secondly, Rogers RT 5880 yields triple-band resonance peaks at 3.7 GHz, 8.67 GHz and 11.33 GHz, whereas RT6002 shows quad-band resonance peaks at 2.35 GHz, 7.72 GHz, 9.23 GHz and 10.68 GHz, with satisfactory magnitudes and moderate bandwidths. The simulated results cover the S, C and X bands. The transmission coefficients ( ) for the three substrate materials are shown in Figure 4.

Effect of Substrate Materials
Proper dielectric selection is an important task for any metamaterial design. An investigation is conducted to observe the response of different substrate materials. Commercially available flame-retardant FR-4 material, along with two Rogers dielectrics, RT 5880 and RT 6002, are taken into consideration. Three individual substrates are simulated by keeping the resonator structure unchanged. First, dielectric FR-4 shows resonance at 2.04 GHz, 6.66 GHz, 7.97 GHz and 9.42 GHz, with very low magnitudes. Secondly, Rogers RT 5880 yields triple-band resonance peaks at 3.7 GHz, 8.67 GHz and 11.33 GHz, whereas RT6002 shows quad-band resonance peaks at 2.35 GHz, 7.72 GHz, 9.23 GHz and 10.68 GHz, with

Unit Cell Dimension Optimization
Various sizes of unit cell for the same dielectric (RT6002) and for the same metal (copper annealed) are inspected to select the appropriate size of the proposed metamaterial. First, the unit cell is simulated with substrate dimensions of 13 × 13 × 1.524 mm 3 , exhibiting quad-band resonance at 2.58 GHz, 7.60 GHz, 9.47 GHz and 10.36 GHz. Secondly, it is simulated with a unit cell with dimensions of 12 × 12 × 1.524 mm 3 , showing quad-band resonance peaks with a small decrement of resonance frequencies. Lastly, it is simulated for dimensions of 11 × 11 × 1.524 mm 3 , showing quad-band resonance at 2.35 GHz, 7.72 GHz, 9.23 GHz and 10.68 GHz, with a better progression of bandwidths. Figure 5 demonstrates the simulated results for the selected sizes of the unit cell.

Unit Cell Dimension Optimization
Various sizes of unit cell for the same dielectric (RT6002) and for the same metal (copper annealed) are inspected to select the appropriate size of the proposed metamaterial. First, the unit cell is simulated with substrate dimensions of 13 × 13 × 1.524 mm 3 , exhibiting quad-band resonance at 2.58 GHz, 7.60 GHz, 9.47 GHz and 10.36 GHz. Secondly, it is simulated with a unit cell with dimensions of 12 × 12 × 1.524 mm 3 , showing quad-band resonance peaks with a small decrement of resonance frequencies. Lastly, it is simulated for dimensions of 11 × 11 × 1.524 mm 3 , showing quad-band resonance at 2.35 GHz, 7.72 GHz, 9.23 GHz and 10.68 GHz, with a better progression of bandwidths. Figure 5 demonstrates the simulated results for the selected sizes of the unit cell.

The Effect of Field Propagation Direction
A change in transmission coefficient (S 21 ) is observed with varying electric field and magnetic field direction. Figure 6 demonstrates the simulation setup for changing the field propagation. Initially, electric field (Ex) propagates along the X direction, and the magnetic field (Hy) is applied to the Y direction. The simulation result shows quad-band resonance peaks at 2.35 GHz, 7.72 GHz, 9.23 GHz and 10.68 GHz. If the fields are interchanged with each other, the simulated results show two resonance peaks at 4.58 GHz and 8.38 GHz. Figure 7 illustrates the simulated results for propagation in the ExHy and HxEy directions. magnetic field direction. Figure 6 demonstrates the simulation setup for changing the fi propagation. Initially, electric field (Ex) propagates along the X direction, and the m netic field (Hy) is applied to the Y direction. The simulation result shows quad-band r onance peaks at 2.35 GHz, 7.72 GHz, 9.23 GHz and 10.68 GHz. If the fields are int changed with each other, the simulated results show two resonance peaks at 4.58 G and 8.38 GHz. Figure 7 illustrates the simulated results for propagation in the ExHy a HxEy directions.

Analysis of Electromagnetic Field and Surface Current
The upper layer of the proposed metamaterial unit cell contains resonant assemblies composed of split gaps and metallic conductors. The split gaps and conductors play the roles of capacitors and inductors, respectively. Electromagnetic force is exerted on the resonators due to the interaction between time-varying EM fields and the unit cell. The induction current flows from one resonator to another through the capacitive split gaps, which are smaller than the wavelength of the incident EM wave. Produced electric and magnetic moments influence the transmission ability and change the material characteristics such as permittivity and permeability. The surface current distribution of the presented MM is illustrated in Figure 8, predicting that at a low-resonance frequency of 2.35 GHz, the outer ring subsidizes a higher amount of current. At the lower frequency, the inductive reactance is also low because the outer ring contributes a low impedance route. A significant amount of current flow decreases in the first outer ring at the second resonance frequency of 7.72 GHz because an increase in impedance occurs with the increase in frequency. At this frequency, non-uniform and random movement of current is detected in bars connecting the octagons, which eventually reduces the overall current flow. In the two inner octagons, current flow is reduced because of the neutralization of two opposite flows. For the same reasons, current flow becomes insufficient at a resonance frequency of 9.23 GHz, and high current flow is observed through the edges of all horizontal sides of all rings compared to the previous two positions. It is also noteworthy that a substantial amount of current is contributed by the two horizontal sides of the outer ring, owing to lower impedance applied by the split gap at a resonance frequency of 10.68 GHz.

Analysis of Electromagnetic Field and Surface Current
The upper layer of the proposed metamaterial unit cell contains resonant assemblies composed of split gaps and metallic conductors. The split gaps and conductors play the roles of capacitors and inductors, respectively. Electromagnetic force is exerted on the resonators due to the interaction between time-varying EM fields and the unit cell. The induction current flows from one resonator to another through the capacitive split gaps, which are smaller than the wavelength of the incident EM wave. Produced electric and magnetic moments influence the transmission ability and change the material characteristics such as permittivity and permeability. The surface current distribution of the presented MM is illustrated in Figure 8, predicting that at a low-resonance frequency of 2.35 GHz, the outer ring subsidizes a higher amount of current. At the lower frequency, the inductive reactance is also low because the outer ring contributes a low impedance route. A significant amount of current flow decreases in the first outer ring at the second resonance frequency of 7.72 GHz because an increase in impedance occurs with the increase in frequency. At this frequency, non-uniform and random movement of current is detected in bars connecting the octagons, which eventually reduces the overall current flow. In the two inner octagons, current flow is reduced because of the neutralization of two opposite flows. For the same reasons, current flow becomes insufficient at a resonance frequency of 9.23 GHz, and high current flow is observed through the edges of all horizontal sides of all rings compared to the previous two positions. It is also noteworthy that a substantial amount of current is contributed by the two horizontal sides of the outer ring, owing to lower impedance applied by the split gap at a resonance frequency of 10.68 GHz.  Time-varying charge flow is mainly responsible for generating magnetic field accor ing to the Amperes law in association with Faraday's law of induction, which, in tur produces an electric field due to electromagnetic interaction [36]. The induced E field an H field can be inspected using the Maxwell's curl Equations (8)- (12), as presented in [37 Horizontal magnetic field component: ( Produced electric field related to the magnetic field: ( where the vector operator is expressed as: Equations (8) and (9) are not sufficient to explain why the two fields interact wi materials. Two more equations are required to overcome these limitations [38].
(1 (1 The material properties of permittivity ℇ and permeability µ in Equations (1 and (12) are complex parameters and real in the case of isotropic lossless material. A viv observation magnetic field and electric field for the four resonance frequenci (2.35, 7.72, 9.23 and 10.68 GHz) are illustrated in Figures 9 and 10, respectively. The inte sity of the magnetic field and polarity depend on the amount of current and its flow d rection. The H-field distribution in Figure 9 shows that at locations in the unit cell whe the current density is high, the magnetic field is also high. As shown by the patterns of H field and E-field distribution in Figures 9 and 10, if the magnetic field changes towards a increment, then the electric field changes inversely. The changing tendency of magnet and electric fields is determined according to Equations (8) and (9). Furthermore, as eve split gap of the unit cell of the proposed MM acts as a capacitor, the electric field intensi in the split gap is increased. Time-varying charge flow is mainly responsible for generating magnetic field according to the Amperes law in association with Faraday's law of induction, which, in turn, produces an electric field due to electromagnetic interaction [36]. The induced E field and H field can be inspected using the Maxwell's curl Equations (8)- (12), as presented in [37].
Horizontal magnetic field component: Produced electric field related to the magnetic field: where the vector operator is expressed as: ∇ =î ∂x ∂t +ĵ ∂y ∂t +k ∂z ∂t (10) Equations (8) and (9) are not sufficient to explain why the two fields interact with materials. Two more equations are required to overcome these limitations [38].
The material properties of permittivity (ε) and permeability (µ) in Equations (11) and (12) are complex parameters and real in the case of isotropic lossless material. A vivid observation magnetic field (H) and electric field (E) for the four resonance frequencies (2.35, 7.72, 9.23 and 10.68 GHz) are illustrated in Figures 9 and 10, respectively. The intensity of the magnetic field and polarity depend on the amount of current and its flow direction. The H-field distribution in Figure 9 shows that at locations in the unit cell where the current density is high, the magnetic field is also high. As shown by the patterns of H-field and E-field distribution in Figures 9 and 10, if the magnetic field changes towards an increment, then the electric field changes inversely. The changing tendency of magnetic and electric fields is determined according to Equations (8) and (9). Furthermore, as every split gap of the unit cell of the proposed MM acts as a capacitor, the electric field intensity in the split gap is increased.

Equivalent LC Circuit of the Unit Cell
An estimated electrical equivalent circuit is drawn and executed by ADS to validate the CST results of the proposed metamaterial. The unit cell is designed with a combination of both metal strips and some split gaps. Every metal strip represents a conductor, whereas every split gap represents a capacitor [39]. In the microwave band, metallic conductor copper can be treated as a perfect conductor that can ignore the ohmic losses [40]. Therefore, the whole unit cell is represented by an LC resonance circuit. The inductance and the capacitance are the main parameters of an LC circuit, denoted by and , respectively. Using these two parameters, resonance frequency can be calculated by applying Equation (13).
The quasi-state theory can be applied to measure the capacitance within a distance or in a split gap in a circuit [41].
where ℇ is the permittivity in free space, ℇ is the relative permittivity, is the crosssectional area of the conducting strip and is the split gap. The inductance of a rectangular metal bar can be calculated according to Equation (15) [42]. .
. (15) where is the correction factor, w is the width, is the length and is the thickness of the strip.
An equivalent LC circuit of the proposed MM is illustrated in Figure 11. The whole equivalent circuit comprising eleven (L1 to L11) inductors and twelve (C1 to C12) capacitors is simulated by ADS software. The first resonator on the upper layer is a split-ring resonator (SRR), as indicated by (L1, C1) and (L2, C2), contributing the first resonance frequency of 2.39 GHz, whereas (L3, C3) and (L4, C4) are used for the first octagon that belongs to 7.23 GHz. On the contrary, the second octagon is replaced by (L5, C5) and (L6, C6), which partially contribute to the frequency of 9.21 GHz. C7 and C8 are the coupling capacitors. The joining metal bars and associate gaps are represented by (L9, C10) and (L10, C11), whereas L11 is used for the small central octagon. These components are jointly responsible for the resonance frequency of 10.72 GHz. A comparison between two transmission coefficients that are determined by CST and ADS is shown in Figure 12.

Equivalent LC Circuit of the Unit Cell
An estimated electrical equivalent circuit is drawn and executed by ADS to validate the CST results of the proposed metamaterial. The unit cell is designed with a combination of both metal strips and some split gaps. Every metal strip represents a conductor, whereas every split gap represents a capacitor [39]. In the microwave band, metallic conductor copper can be treated as a perfect conductor that can ignore the ohmic losses [40]. Therefore, the whole unit cell is represented by an LC resonance circuit. The inductance and the capacitance are the main parameters of an LC circuit, denoted by (L) and (C), respectively. Using these two parameters, resonance frequency ( f ) can be calculated by applying Equation (13).
The quasi-state theory can be applied to measure the capacitance within a distance or in a split gap in a circuit [41].
where ε o is the permittivity in free space, ε r is the relative permittivity, A is the crosssectional area of the conducting strip and d is the split gap. The inductance of a rectangular metal bar can be calculated according to Equation (15) [42].
where K G is the correction factor, w is the width, l is the length and t is the thickness of the strip. An equivalent LC circuit of the proposed MM is illustrated in Figure 11. The whole equivalent circuit comprising eleven (L1 to L11) inductors and twelve (C1 to C12) capacitors is simulated by ADS software. The first resonator on the upper layer is a split-ring resonator (SRR), as indicated by (L1, C1) and (L2, C2), contributing the first resonance frequency of 2.39 GHz, whereas (L3, C3) and (L4, C4) are used for the first octagon that belongs to 7.23 GHz. On the contrary, the second octagon is replaced by (L5, C5) and (L6, C6), which partially contribute to the frequency of 9.21 GHz. C7 and C8 are the coupling capacitors. The joining metal bars and associate gaps are represented by (L9, C10) and (L10, C11), whereas L11 is used for the small central octagon. These components are jointly responsible for the resonance frequency of 10.72 GHz. A comparison between two transmission coefficients that are determined by CST and ADS is shown in Figure 12.

Results and Discussion
CST microwave studio is deployed to simulate the proposed metamaterial in the frequency range 1-14 GHz. Figure 13 demonstrates the scattering parameters (reflection and transmission coefficients). Numerical simulation yields four resonance frequencies at 2.35, 7.72, 9.23 and 10.68 GHz with magnitudes of −43.23 dB, −31.05 dB, −44.58 dB and −31.71 dB, respectively. These frequency bands cover the S, C, and X bands. Moreover, the response for the reflection coefficient shows at 3.33 GHz, 7.92 GHz and 10.39 GHz with magnitudes of −36.30 dB, −13.84 dB and −15.23dB, respectively. It is evident that every resonance of the transmission coefficient is followed by bandwidths of 0.36 GHz, 0.46 GHz, 1.42 GHz and 0.30 GHz at the concerned S, C, and X bands, respectively. It is also evident that each resonance of the transmission coefficient is tracked by a reflection coefficient minimum. Subsequently, the frequency of each value of minimum is always lower than the concerned value of the minimum frequency. In this regard, it can be concluded that every resonance can be treated as electrical resonance in the proposed metamaterial unit cell [43]. The permittivity ℇ , permeability µ and refractive index extracted by applying the RRM (robust retrieval method) in CST and

Results and Discussion
CST microwave studio is deployed to simulate the proposed metamaterial in the frequency range 1-14 GHz. Figure 13 demonstrates the scattering parameters (reflection and transmission coefficients). Numerical simulation yields four resonance frequencies at 2. 35, 7.72, 9.23 and 10.68 GHz with magnitudes of −43.23 dB, −31.05 dB, −44.58 dB and −31.71 dB, respectively. These frequency bands cover the S, C, and X bands. Moreover, the response for the reflection coefficient (S 11 ) shows at 3.33 GHz, 7.92 GHz and 10.39 GHz with magnitudes of −36.30 dB, −13.84 dB and −15.23dB, respectively. It is evident that every resonance of the transmission coefficient (S 21 ) is followed by bandwidths of 0.36 GHz, 0.46 GHz, 1.42 GHz and 0.30 GHz at the concerned S, C, and X bands, respectively. It is also evident that each resonance of the transmission coefficient (S 21 ) is tracked by a reflection coefficient (S 21 ) minimum. Subsequently, the frequency of each value of S 21 minimum is always lower than the concerned value of the S 11 minimum frequency. In this regard, it can be concluded that every resonance can be treated as electrical resonance in the proposed metamaterial unit cell [43]. The permittivity (ε), permeability (µ) and refractive index (n) extracted by applying the RRM (robust retrieval method) in CST and NRW in MATLAB are shown in Figures 14-16, respectively. Figure 14 shows that the permittivity of the designed MM varies from the positive value to the negative. Again, the values of S 21 begin when the magnitudes of permittivity fluctuate from maximum to minimum values. Moreover, the starting positive minimum value of µ occurs at the minimum resonance frequency shown in Figure 15. This tendency continues over the whole resonance frequency range. A graph of the refractive index is presented in Figure 16, which reveals negative refractive indices in the frequency ranges of 2.  GHz. The negativity of refractive index is a function of frequency that can be utilized to increase the gain and directivity of antennae, whereas the ε-negative property is deployed to enhance the bandwidth [44,45]. Finally, a brief comparison is shown on the basis of some important parameters in Table 3.

Array Metamaterial Results
Different types of array combinations are also simulated to test the coupling ef and to verify the consistency of the results, which is the best way to achieve the expec electromagnetic features. Arrays of the proposed MM with dimensions of 1 × 2 and 2 are shown in Figure 17. These two designs are simulated by the CST and the reflect coefficient (S11), and transmission coefficient (S21) results are presented in Figure 18. variations of resonance frequencies among the unit cell and the 1 × 2 and 2 × 2 arrays given in Table 4, which confirms the consistency of the results.

Array Metamaterial Results
Different types of array combinations are also simulated to test the coupling effect and to verify the consistency of the results, which is the best way to achieve the expected electromagnetic features. Arrays of the proposed MM with dimensions of 1 × 2 and 2 × 2 are shown in Figure 17. These two designs are simulated by the CST and the reflection coefficient (S 11 ), and transmission coefficient (S 21 ) results are presented in Figure 18. The variations of resonance frequencies among the unit cell and the 1 × 2 and 2 × 2 arrays are given in Table 4, which confirms the consistency of the results.

Validation Using HFSS
In order to verify the reliability and consistency of the performance of the proposed MM, the CST result for the transmission coefficient (S21) is authenticated by Ansys HFSS. The simulated result obtained with this software also shows quad-band resonance peaks, with amplitudes remaining nearly unchanged and yielding four resonance peaks at 2.

Validation Using HFSS
In order to verify the reliability and consistency of the performance of the proposed MM, the CST result for the transmission coefficient (S 21 ) is authenticated by Ansys HFSS. The simulated result obtained with this software also shows quad-band resonance peaks, with amplitudes remaining nearly unchanged and yielding four resonance peaks at 2.

Conclusions
In this research article, a quad-band power tiller wheel-shaped ENG meta for S-, C-and X-band applications is presented. The size of the proposed MM uni dimensions of 10 × 10 × 1.524 mm 3 and is based on an RT6002 dielectric substr microwave studio is used to simulate the unit cell, showing quad-band resonan at 2.35 GHz, 7.72 GHz, 9.23 GHz and 10.68 GHz with amplitudes of −43.23 dB −3 −44.58 dB and −31.71 dB, respectively. The simulated results are also validated by tion processes such as an equivalent electrical circuit model, high-frequency sim software (HFSS) and various array orientations. The response and contribution of resonators of the unit cell are inspected by analyzing the E-field, H-field and sur rent distribution for propagated electromagnetic radiation. The important feature mittivity, permeability and the refractive index of the metamaterial are extracte MATLAB. The EMR of the proposed MM is 11.61, which indicates its reliability. culated value of 4 is less than the length (L) of the unit cell, highlighting the c ness of the size of the unit cell. This innovative MM can be deployed to enhance ciency of different microwave devices, owing to its NRI and epsilon-negative cha tics. Moreover, the S, C-and X bands are recurrently used for satellite and radar tions.

Conclusions
In this research article, a quad-band power tiller wheel-shaped ENG metamaterial for S-, C-and X-band applications is presented. The size of the proposed MM unit cell has dimensions of 10 × 10 × 1.524 mm 3 and is based on an RT6002 dielectric substrate. CST microwave studio is used to simulate the unit cell, showing quad-band resonance peaks at 2.35 GHz, 7.72 GHz, 9.23 GHz and 10.68 GHz with amplitudes of −43.23 dB −31.05 dB, −44.58 dB and −31.71 dB, respectively. The simulated results are also validated by validation processes such as an equivalent electrical circuit model, high-frequency simulation software (HFSS) and various array orientations. The response and contribution of various resonators of the unit cell are inspected by analyzing the E-field, H-field and surface current distribution for propagated electromagnetic radiation. The important features of permittivity, permeability and the refractive index of the metamaterial are extracted using MATLAB. The EMR of the proposed MM is 11.61, which indicates its reliability. The calculated value of λ 4 is less than the length (L) of the unit cell, highlighting the compactness of the size of the unit cell. This innovative MM can be deployed to enhance the efficiency of different microwave devices, owing to its NRI and epsilonnegative characteristics. Moreover, the S, C-and X bands are recurrently used for satellite and radar applications.