I-Shaped Metamaterial Using SRR for Multi-Band Wireless Communication

: A novel I-shaped metamaterial (ISMeTM) using split-ring resonator (SRR) for multi-band wireless communication is presented in this paper. The proposed ISMeTM unit cell structure is designed using the three-square split-ring resonators (SSRRs) and I-shaped copper strip at the center. The size of the proposed ISMeTM is 10 × 10 × 1.6 mm 3 while utilizing the FR-4 dielectric substrate material. The analysis of various array arrangements, variation in the ring gap, variation in strip length, and the variation in strip width is performed to achieve the optimum results for multi-band operation. The effective permittivity, permeability, and refractive index of the unit cell have been analyzed. The design and simulation of the ISMeTM unit cell and arrays are performed using the Computer Simulation Technology (CST) Studio Suite and MATLAB. The equivalent circuit of the ISMeTM is designed using the Advanced Design System (ADS) software. The split ring’s inner loop’s gap functions as a capacitor, while the metallic ring itself functions as an inductor. Electric resonance is created by the interaction between the split ring and the electric ﬁeld. The interaction of magnetic ﬁelds with metallic loops during EM propagation in the structure causes the magnetic resonance. The variation in dimensions of the structure causes the variation in the inductance and capacitance, which causes the variation in resonant frequency. The proposed design is optimized after several parametric analyses. A comprehensive analysis of 1 × 2, 2 × 2, and 2 × 4 array is also investigated. The results conﬁrm the multi-band operation of the proposed ISMeTM. The proposed ISMeTM is suitable for the multi-band C/X/Ku-band microwave applications.


Introduction
The demand for multi-band operational metamaterials (MeTMs) has increased substantially because of the rapid growth of wireless communication applications. MeTMs are artificially engineered structures which have distinct electromagnetic properties not found in regular materials [1]. Certain materials display negative permittivity and permeability which are not present in nature. In 1945 and 1968, Mandel'shtam and Veselago proposed the concepts the Left Hand Medium (LHM) materials which exhibited negative permittivity and permeability [2,3]. They also presented the general properties of electromagnetic wave propagation in such materials.
A metallic structure with negative permeability was presented by Pendry et al. [4] in 1996. He, in collaboration with other researchers [5], also created metallic SRR which is a non-magnetic structure. Furthermore, in 2000, Smith et al. [6] designed the SRR, proposed by Pendry, on a printed circuit board (PCB) by integrating the SRR with set of copper strips. The electric permittivity (ε) and the magnetic permeability (µ) were extracted and analyzed. Transmission-line-based MeTMs was proposed in by Iyek et al. [7] and Caloz et al. [8]. As a result of their distinct electromagnetic characteristics, numerous researchers have proposed and presented several MeTMs for various uses. The application areas of MeTM include design of electromagnetic absorbers [9], multi-band elements [10],

MeTM Unit Cell Geometry and Design
The geometrical configuration of the proposed ISMeTM unit cell and its simulated model are illustrated in Figure 1. A perfect electric conductor (PEC) is used for the metallic part and it is designed on the FR-4 dielectric substrate. The dielectric constant and loss tangent (tanδ) of the FR-4 substrate material are 4.3 and 0.025, respectively. The thickness of the substrate and the thickness of the annealed copper used for the SRR are 1.6 mm and 0.035 mm, respectively. The primary function of splits in the ring resonators is to ensure that the inductance and capacitance interact with one another to determine the operating frequency. The unit cell's total optimum size is 10 × 10 × 1.6 mm 3 (sw × ls × s h ). The parameters of the ISMeTM unit cell are presented in Table 1. The configuration and the comprehensive analysis of the MeTM properties is carried out using the Finite Integration Technique (FIT)-based electromagnetic CST simulator.
of the substrate and the thickness of the annealed copper used for the SRR are 1.6 mm and 0.035 mm, respectively. The primary function of splits in the ring resonators is to ensure that the inductance and capacitance interact with one another to determine the operating frequency. The unit cell's total optimum size is 10 × 10 × 1.6 mm 3 (sw × ls × sh). The parameters of the ISMeTM unit cell are presented in Table 1. The configuration and the comprehensive analysis of the MeTM properties is carried out using the Finite Integration Technique (FIT)-based electromagnetic CST simulator.

Theoretical Model and Equivalent Circuit of the ISMeTM
The proposed ISMeTM metal structure was designed on an FR-4 dielectric substrate layer. The time-varying EM field changes over time. The electron density engulfs the MeTM structure. Metal bars have been used to enhance the formation of a new distinct electromagnetic wave. The sensing response is handled by the metallic ring, while the split gap between the rings provides a strong electric field for the design. The transmission line approach was utilized to analyze the ISMeTM unit cell, which allows an individual

Theoretical Model and Equivalent Circuit of the ISMeTM
The proposed ISMeTM metal structure was designed on an FR-4 dielectric substrate layer. The time-varying EM field changes over time. The electron density engulfs the MeTM structure. Metal bars have been used to enhance the formation of a new distinct electromagnetic wave. The sensing response is handled by the metallic ring, while the split gap between the rings provides a strong electric field for the design. The transmission line approach was utilized to analyze the ISMeTM unit cell, which allows an individual strip or patch to duplicate an RLC series circuit. The passive LC circuit, which is connected to the resonance frequency. The equivalent circuit of the proposed ISMeTM is presented in Figure 2 which consists of the capacitance-and inductance-generating resonance on the proposed ISMeTM unit cell. The resonance frequency (f re ) is expressed as [33,34]: where L E and C E represent the inductance and capacitance of the structure, respectively. Similarly, the split ring's inner loop's gap functions as a capacitor, while the metallic ring itself functions as an inductor. The electric resonance in the structure is created by interaction of the split ring and electric field while the interaction of magnetic fields with metallic loops during EM propagation in the structure causes magnetic resonance. strip or patch to duplicate an RLC series circuit. The passive LC circuit, which is connected to the resonance frequency. The equivalent circuit of the proposed ISMeTM is presented in Figure 2 which consists of the capacitance-and inductance-generating resonance on the proposed ISMeTM unit cell. The resonance frequency (fre) is expressed as [33,34]: where and represent the inductance and capacitance of the structure, respectively. Similarly, the split ring's inner loop's gap functions as a capacitor, while the metallic ring itself functions as an inductor. The electric resonance in the structure is created by interaction of the split ring and electric field while the interaction of magnetic fields with metallic loops during EM propagation in the structure causes magnetic resonance. The total capacitance between the ring gap (Cg) can be defined as the capacitor of the parallel plate (Cpl) which compensate for the fringing field by extending the parameters plate width and thickness and is expressed as [35]: where 0 denotes the free space permittivity. h, w, and g represent the height, width, and gap of the ring, respectively. The inductance of the SSRR can be derived from the inductance of a rectangular loop [36]. By using a rectangular cross-sectional area with the conductor of a rectangular loop [37], we have: The total capacitance between the ring gap (C g ) can be defined as the capacitor of the parallel plate (C pl ) which compensate for the fringing field by extending the parameters plate width and thickness and is expressed as [35]: where ε 0 denotes the free space permittivity. h, w, and g represent the height, width, and gap of the ring, respectively. The inductance of the SSRR can be derived from the inductance of a rectangular loop [36]. By using a rectangular cross-sectional area with the conductor of a rectangular loop [37], we have: where h and w are the height and width of the rectangular loop, respectively. h c and w c denote the height and the width of the conductor's cross section, respectively. The length and the width of the SSRR for the proposed ISMeTM structure R 1 and R t = R, and the weighting factor ρ e = 1 − g/4R Equation (4) is used to analyze the perimeter of the SSRR. By rewriting Equation (4) we have, The parameter values for µ 0 and ε 0 are 8.854 × 10 −12 F/m and 4π × 10 −7 H/m, respectively. In the equivalent circuit presented in Figure 2, C1, C2, C3, C4, C5, C6, C7, and C8 are the capacitors, and L1, L2, L3, L4, L5, L6, and L7 are the inductors. The circuit is designed using the ADS software.

Design Methodology
In microwave communication application, various factors must be considered to provide multi-band operating frequencies. To increase the efficiency and effectiveness of the design for the proposed ISMeTM structure, the configuration is optimized using CST microwave studio. An iterative approach is used to obtain the response of the ISMeTM unit cell. Hence, modifying the resonance frequency is feasible by adjusting the dimensions and thickness of the substrate. However, because of the capacitance and inductance variation, some major parameters such as the length and width of the ring resonator, the ring gap between the rings, spilt gap and the ring length are responsible for producing the multiband operating frequencies. The design steps for the proposed ISMeTM unit cell are shown in Figure 3. The reflection coefficient, transmission coefficient and permittivity for various design steps are shown in Figure 4a-c, respectively. In design step-a, double copper wire cut was introduced into the outer ring. From the S21 graph, it can be observed that the resonant frequencies are 6.4, 10.02 and 11.82 GHz. A second copper ring is introduced to the unit cell and four resonances at 6.23, 7.81, 10.17, 11.98 and 14.68 GHz are realized for design step-b. A third copper ring is introduced into the structure in design step-c. This design produces six resonances at 6.32, 7.81, 9.98, 11.46, 12.21 and 15.67 GHz. In design step-d (ISMeTM), an I-shaped metallic structure is introduced into the internal ring of the unit cell. Furthermore, seven resonances are obtained at 6.31, 7.79, 9.98, 10.82, 11.86, 13.36 and 15.5 GHz. The parameters for various design steps are summarized in Table 2.

Design Methodology
In microwave communication application, various factors must be considered to provide multi-band operating frequencies. To increase the efficiency and effectiveness of the design for the proposed ISMeTM structure, the configuration is optimized using CST microwave studio. An iterative approach is used to obtain the response of the ISMeTM unit cell. Hence, modifying the resonance frequency is feasible by adjusting the dimensions and thickness of the substrate. However, because of the capacitance and inductance variation, some major parameters such as the length and width of the ring resonator, the ring gap between the rings, spilt gap and the ring length are responsible for producing the multi-band operating frequencies. The design steps for the proposed ISMeTM unit cell are shown in Figure 3. The reflection coefficient, transmission coefficient and permittivity for various design steps are shown in Figure 4a-c, respectively. In design step-a, double copper wire cut was introduced into the outer ring. From the S21 graph, it can be observed that the resonant frequencies are 6.4, 10.02 and 11.82 GHz. A second copper ring is introduced to the unit cell and four resonances at 6.23, 7.81, 10.17, 11.98 and 14.68 GHz are realized for design step-b. A third copper ring is introduced into the structure in design step-c. This design produces six resonances at 6.32, 7.81, 9.98, 11.46, 12.21 and 15.67 GHz. In design step-d (ISMeTM), an I-shaped metallic structure is introduced into the internal ring of the unit cell. Furthermore, seven resonances are obtained at 6.31, 7.79, 9.98, 10.82, 11.86, 13.36 and 15.5 GHz. The parameters for various design steps are summarized in Table 2.

Methodology for Extracting the Unit Cell's Effective Medium Parameters
The effective parameters of the proposed ISMeTM unit cell can be determined by placing the structure between two waveguides (ports) such that the electromagnetic wave (EM) has magnetic field along the y-axis and electric field in the direction of the x-axis. Thus, the wave is propagated at the z-axis. This means that the first port acts as the reflecting signal's transmitting port, while the second port acts as the signal's receiving port. In addition, a tetrahedral mesh from frequency domain solver has been used for simulating the unit cell and array structure. The impedance has been set to 50 Ω. The operating frequency range is from 2 to 18 GHz. Figure 1b shows the simulation arrangement of the proposed ISMeTM unit cell inside the waveguide. The effective medium ratio depends on the unit cell dimension and the wavelength must be less the working wavelength. The reflection coefficient (Γ) can be expressed as [38]: The scattering parameters S 11 and S 21 can be calculated as follows: from Equations (3) and (4), where Z 0 , Z, S 11 and S 21 represent the impedance, the interface reflection coefficient, the reflection coefficient, and the transmission coefficient, respectively. The complex electric permittivity and complex magnetic permeability can be positive or negative in different combinations [39]. The Nicolson-Ross-Weir (NRW) method is adopted to determine the effective electric permittivity (ε r ), magnetic permeability (µ r ) and relative refractive index (η r ) of the proposed ISMeTM unit cell. The effective permittivity and permeability can be expressed as [40,41]: The refractive index η r can be obtained as: where, k 0 = w c = 2π f c and e jnk o s h = S 21 where f, k 0 , m, c and s h represent the operating frequency, the wave number, the branch index, the speed of light and the substrate thickness, respectively. Equations (6)- (13) have been used to analyze the scattering parameters of the ISMeTM unit cell and array.

ISMeTM Unit Cell Analysis
This section discusses the analysis of the proposed ISMeTM unit cell parameters. The Nicolson-Ross-Weir method has been used to extract the MeTM parameters. Detailed electromagnetic characteristic in terms of permeability, permittivity, relative index and the scattering parameters of the MeTM are shown in Figure 5. The CST Microwave Studio software is used to investigate the performance of the proposed ISMeTM. The analysis validates that the effective magnetic permittivity (ε r ) is negative, the electric permeability (µ r ) is positive, and relative refractive index (η r ) is positive and negative within the same resonance frequency bands. As a result, these characteristics show that the proposed ISMeTM unit cell shows SNG metamaterial properties. The structure is designed to produce multi-band operation. Due to the compact nature of the ISMeTM, it can be utilized in antenna design for improving antenna performance. The proposed ISMeTM can also be used in satellite communications, WiFi devices, weather radar systems, surveillance etc. be used in satellite communications, WiFi devices, weather radar systems, surveillance etc.
The S-parameters and the effective parameters of the proposed ISMeTM unit cell are presented in Figure 5a, b, respectively. The obtained simulated S21 parameter of ISMeTM shows the resonance frequencies at 6.31, 7.79, 9.98, 10.82, 11.86, 13.36 and at 15.5 GHz in the C/X/Ku-bands. ). The proposed structure shows the wideband operation and the maximum fractional bandwidth of 51.67% is achieved. Hence, the proposed structure can be used for wideband applications for different bands. From Figure 5b it can be observed that the ISMeTM produces the SNG characteristics for the frequency ranges ). The proposed structure shows the wideband operation and the maximum fractional bandwidth of 51.67% is achieved. Hence, the proposed structure can be used for wideband applications for different bands. From Figure 5b it can be observed that the ISMeTM produces the SNG characteristics for the frequency ranges 5.46-6.29, 11.6-11.8, 13.8-15 and 15.8-16.8 GHz. The analysis validates the following: the values of the effective electric permittivity (ε r ) are negative; those of the magnetic permeability (µ r ) are positive; and relative refractive index (η r ) are positive and negative within the same resonance frequency bands. As a result, these characteristics show that the proposed ISMeTM unit cell shows the MeTM properties. The proposed ISMeTM is useful for medical devices, optical filters, remote aerospace applications, and electromagnetic cloaking etc.

Result and Discussion
The parametric analysis for the ring gap (g) is carried out and presented in Figure 6. This analysis provides a suitable dimension for the ISMeTM design. It can be observed from Figure 6a that when the dimension of the ring gap (g) is varied, the operating band changes. It can be observed that for g = 0.5 mm and 1 mm the MeTM have the same number of resonance frequencies, while at g =1.5 mm and 2 mm the MeTM have five and six resonance frequencies, respectively. However, the MeTM has its best performance at Crystals 2022, 12, 559 9 of 15 the dimension of g = 0.5 mm. Furthermore, the variation of S21(dB) parameter with the variation of the ring gap (g) is displayed in Figure 6b. At g = 1 mm, 1.5 mm, and 2 mm, the ISMeTM has four and three resonance frequencies, respectively. Thus, when g is at 0.5 mm seven resonances are realized, making it the best dimension for optimal performance of the design. the same resonance frequency bands. As a result, these characteristics show that the proposed ISMeTM unit cell shows the MeTM properties. The proposed ISMeTM is useful for medical devices, optical filters, remote aerospace applications, and electromagnetic cloaking etc.

Result and Discussion
The parametric analysis for the ring gap (g) is carried out and presented in Figure 6. This analysis provides a suitable dimension for the ISMeTM design. It can be observed from Figure 6a that when the dimension of the ring gap (g) is varied, the operating band changes. It can be observed that for g = 0.5 mm and 1 mm the MeTM have the same number of resonance frequencies, while at g =1.5 mm and 2 mm the MeTM have five and six (e) (f) (g) (h) Figure 6. ISMeTM unit cell parameters: (a) variation of S11 with g; (b) variation of S21 with g; (c) variation of S11 with RL; (d) variation of S11 with W; (e) variation of S21 with dielectric constant of the substrate; (f) variation of S21 with sh; (g) variation of permittivity and permeability with ls; (h) variation of permittivity and permeability with sh.
The variation of the strip length (RL) of the unit cell is presented in Figure 6(c). It is observed that the most suitable dimension of RL for the ISMeTM unit cell is 2 mm. Similarly, the strip width (W) of the unit cell is varied and presented in Figure 6d. It can be studied that at W = 0.5 mm the unit cell exhibits the optimum multi-band behavior. The variation of the S21 parameter with the dielectric constant and sh are shown in Figure 6e,f, respectively. From these figures, it can be observed that the center frequencies and the frequency bands can be modified by varying the dimensional parameters of the structure. The variation of permittivity and permeability with ls is shown in Figure 6g. The variation of permittivity and permeability with sh is shown in Figure 6h. From Figure 6g,h, it can be observed that the frequency band with SNG property and the values of permittivity and permeability can be varied by changing the dimensional parameters of the structure. Figure 6. ISMeTM unit cell parameters: (a) variation of S11 with g; (b) variation of S21 with g; (c) variation of S11 with RL; (d) variation of S11 with W; (e) variation of S21 with dielectric constant of the substrate; (f) variation of S21 with sh; (g) variation of permittivity and permeability with ls; (h) variation of permittivity and permeability with sh.

ISMeTM Array Analysis
The variation of the strip length (RL) of the unit cell is presented in Figure 6c. It is observed that the most suitable dimension of RL for the ISMeTM unit cell is 2 mm. Similarly, the strip width (W) of the unit cell is varied and presented in Figure 6d. It can be studied that at W = 0.5 mm the unit cell exhibits the optimum multi-band behavior. The variation of the S21 parameter with the dielectric constant and sh are shown in Figure 6e,f, respectively. From these figures, it can be observed that the center frequencies and the frequency bands can be modified by varying the dimensional parameters of the structure. The variation of permittivity and permeability with ls is shown in Figure 6g. The variation of permittivity and permeability with sh is shown in Figure 6h. From Figure 6g,h, it can be observed that the frequency band with SNG property and the values of permittivity and permeability can be varied by changing the dimensional parameters of the structure.

ISMeTM Array Analysis
The performance analysis of the ISMeTM unit cell's 1 × 2 array, 2 × 2array, and 2 × 4 array configurations are presented in this section. The overall dimensions are 10 × 20 mm 2 , 20 × 20 mm 2 , and 20 × 40 mm 2 . To validate the results of the ISMeTM unit cell configuration, the three array configurations are investigated. The Nicolson-Ross-Weir (NRW) is used evaluate the array's effective parameters.
The schematic diagram of 1 × 2 array, 2 × 2array, and 2 × 4 array configuration is presented in Figure 7. The arrays are formed by combining two-unit cells horizontally. The S11 and S21 parameters of the array configurations are simulated for the frequency range of 2-18 GHz, and the same approach is used to retrieve their effective parameters.

ISMeTM Array Analysis
The performance analysis of the ISMeTM unit cell's 1 × 2 array, 2 × 2array, and 2 × 4 array configurations are presented in this section. The overall dimensions are 10 × 20 mm 2 , 20 × 20 mm 2 , and 20 × 40 mm 2 . To validate the results of the ISMeTM unit cell configuration, the three array configurations are investigated. The Nicolson-Ross-Weir (NRW) is used evaluate the array's effective parameters.
The schematic diagram of 1 × 2 array, 2 × 2array, and 2 × 4 array configuration is presented in Figure 7. The arrays are formed by combining two-unit cells horizontally. The S11 and S21 parameters of the array configurations are simulated for the frequency range of 2-18 GHz, and the same approach is used to retrieve their effective parameters. In Figure 8a, the S-parameters S11 (dB) and S21 (dB) are presented for the three array configurations. The 1 × 2 array shows the transmission dips at 6.  In Figure 8a, the S-parameters S 11 (dB) and S 21 Table 3. The frequency ranges for the parameters in the three array structures are nearly identical to the single unit cell, except variation for a few frequency bands. Due to mutual coupling effect between the array elements, there may be little variation in the array characteristics as compared to the unit cell [42]. In the proposed array, it can be observed that the array arrangements show similarities with the unit cell except for a few frequency bands that changes slightly which is due to the mutual coupling effect between the array elements. This occurs when two or more unit cells are vertically oriented on the y-axis. However, the arrays still exhibit multi-band properties.  Table 3. The frequency ranges for the parameters in the three array structures are nearly identical to the single unit cell, except variation for a few frequency bands. Due to mutual coupling effect between the array elements, there may be little variation in the array characteristics as compared to the unit cell [42]. In the proposed array, it can be observed that the array arrangements show similarities with the unit cell except for a few frequency bands that changes slightly which is due to the mutual coupling effect between the array elements. This occurs when two or more unit cells are vertically oriented on the y-axis. However, the arrays still exhibit multi-band properties. The comparative analysis of the proposed ISMeTM is presented in Table 4. From this table, it can be observed that the proposed ISMeTM is low cost, compact in size and produces seven resonances. The proposed ISMeTM is suitable for multi-band C/X/Ku-band applications.  The comparative analysis of the proposed ISMeTM is presented in Table 4. From this table, it can be observed that the proposed ISMeTM is low cost, compact in size and produces seven resonances. The proposed ISMeTM is suitable for multi-band C/X/Kuband applications.

Conclusions
A novel ISMeTM unit cell using the SSRR along with its arrays has been designed, simulated and analyzed in this paper. The structure is designed using copper as its metal strip on a FR-4 dielectric substrate. The SSRRs along with an I-shaped patch is utilized for designing the ISMeTM. The detailed theory and equivalent circuit of the ISMeTM are presented. The proposed structure produced multiple resonances and SNG behavior. The proposed ISMeTM is suitable for use in multi-band microwave applications including C band, X band and Ku band. The design and analysis of 1 × 2, 2 × 2, and 2 × 4 array structure of the proposed ISMeTM unit cell are also investigated. The proposed low-cost and compact ISMeTM are suitable for multi-band satellite communication systems, radar applications, sub-6 GHz 5G applications, ultra-wideband applications, etc.