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A planar magnetoinductive (MI) waveguide loaded rectangular microstrip patch antenna is presented and discussed. The MI waveguide consists of two planar metamaterial split squared ring resonators (SSRRs) placed in between two microstrip lines. The backward wave propagation takes place through this structure. The rectangular microstrip patch antenna is magnetically coupled to the MI waveguide. The unloaded rectangular microstrip patch antenna resonates at 37.10 GHz. When loaded with planar MI waveguide, its resonant frequency is reduced to 9.38 GHz with the bandwidth and gain of 44% and 4.16 dBi respectively. In loaded condition, the dimension of antenna is 12.50 mm × 3.70 mm (0.390 λ × 0.115 λ). The appreciable bandwidth is achieved in such a small size antenna. The pass band frequency of MI waveguide is predicted by using the theoretical model of dispersion equation. The effective medium theory is used to verify the metamaterial characteristics of SSRR. The simulated results and theoretical calculations are also presented. The results show that the proposed method can be used to design compact and high bandwidth microstrip patch antennas.

In 1967, the Russian physicist Viktor Veselago presented the properties of artificial materials named as metamaterials. These materials possess negative permeability (μ) and negative permittivity (ε) that support the backward wave propagation of electromagnetic waves [

Recently, metamaterial is used to load the microstrip patch antennas as superstrate and substrate to enhance the gain, bandwidth, directivity as well as to achieve miniaturization [6-7,15-18]. Pai Yen Chen and Andrea Alu (2010) proposed a dual band elliptical patch antenna partially loaded with negative permeability (μ) metamaterial and reported that such loading enhances the bandwidth and miniaturize the antenna [_{020} mode is reported by partially metamaterial loaded rectangular patch antenna [

E. Shamonina et al. investigated the phenomenon of magnetoinductive waves in one, two and three dimensional periodic structure of SRRs. In one dimensional axially arranged structure or lattice the wave propagation is forward whereas it is backward in planar orientation. In their work, the dispersion relations are also presented indicating the range of frequencies for which propagation is possible whereas other frequencies get stopped or rejected. The authors reported that the frequency range over which the effective permeability varies rapidly from high positive value to high negative value is the pass band of magnetoinductive waves [9-11]. Ilya V. Shadrivov et al. experimentally demonstrated the propagation of magnetoinductive electromagnetic waves in an array of SRRs operating at microwave frequencies. In this work, the transverse and longitudinal orientation of the SRRs array is used. The SRRs are excited by separate antennas in which the bandwidth changes dramatically as the coupling coefficient between the resonators is varied. In longitudinal array, the forward wave propagation takes place whereas the transverse geometry supports backward wave propagation [

The objective of this paper is to present a squared split ring resonator (SSRR) based MI waveguide loading technique to load the rectangular microstrip patch antenna to enhance its bandwidth and to reduce the size. In the proposed work, rectangular microstrip patch antenna is loaded with planar MI waveguide consisting of metamaterial SSRRs. Initially, metamaterial characteristics of the SSRR unit cell are verified and it is found that the SSRR endows negative permeability (μ-negative). In loading condition, the rectangular microstrip patch is excited by coaxial feed. The MI waveguide is closely placed near to the rectangular microstirp patch. Due to magnetic coupling the electric field gets induced in MI waveguide and ultimately the SSRR elements get excited. This excitation makes the SSRRs to exhibit the metamaterial characteristics. After loading, the rectangular microstrip patch antenna shows reduction in its resonant frequency that is miniaturization is accomplished as well as the bandwidth is appreciably enhanced. In this paper, both effective medium theory as well as magnetoinductive wave analysis is used to validate the work.

The paper is structured into five sections. The sketch and detailed geometrical dimensions of the proposed planar MI waveguide loaded rectangular microstrip patch antenna with the design of metamaterial SSRR unit cell is presented in Section 2. In Section 3, the metamaterial properties of SSRR are verified using effective medium theory. The simulation results of unloaded and MI waveguide loaded rectangular microstrip patch antenna are also presented and analyzed in this section. In Section 4, the theoretical aspects related to dispersion relation and equivalent circuit analysis are discussed to validate the obtained results. Finally, the paper is concluded in Section 5.

_{r} = 2.4 mm and width W_{r} = 2 mm respectively that is co-axially fed at the location x = –1.2 mm and y = 1.2 mm. The waveguide structure consists of two microstrip lines which are inductively coupled by means of two split squared ring resonator array for effective propagation of magnetoinductive waves. The position of SSRRs is parallel to microstrips along the waveguide line of symmetry. The distance between microstrip line and SSRR array is g_{m} = 0.15 mm. The SSRRs are transversely oriented between the two

microstrip lines that constitute a finite length planar waveguide structure. The rectangular microstrip patch antenna is placed in the proximity to the waveguide at a distance g_{w} = 0.25 mm. The length of microstrip lines is L_{m} = 10.25 mm and width W_{m} = 0.50 mm.

To realize the magnetoinductive waves, the ratio of resonant wavelength to the structure period should be of the order of 10 [_{1} = 5 mm and the overlapping length of inner strip l_{2} = 4.6 mm. The gap at split of the strips (g), the separation between inner and outer strips (s) and width of the strips (w) are in the order of g = s = w = 0.2 mm.

The side length dimensions of the strips are; x_{1} = 2.4 mm and x_{2} = 2 mm respectively. The dimension of the SSRR at its resonant frequency 4.09 GHz is 0.033 λ x 0.068 λ. This antenna is designed and simulated on RT Duriod 5880 substrate of thickness h = 3.175 mm and dielectric constant ε_{r} = 2.2. In this work, method of moment based IE3D electromagnetic simulator of Zeland software incorporation, Fremont, USA is used to simulate the antenna.

The SSRR and the designed antenna are simulated using IE3D of Zeland Software Incorporation. At the outset attempt is made to realize or verify the metamaterial characteristics of SSRR in the defined frequency band. _{11})_{ }and transmission coefficient (S_{21}) characteristics of an isolated SSRR unit cell. _{r}) in the frequency range 3.5 GHz to 5.5 GHz. Thus, the SSRR is single negative that is explicitly μ-negative (MNG) metamaterial.

The average cell size of SSRR unit cell is smaller than λ_{g}/4 which satisfies the condition of effective homogeneity [_{r}) and permittivity (ε_{r}). The effective medium parameters are derived from the reflection and transmission coefficient parameters (S-parameters) using Nicolson-Ross-Weir (NRW) approach [4-7]. The expressions of Equations (1) and (2) are used to determine these effective medium parameters.

where k_{0} is wave number, d is the thickness of substrate, V_{1} and V_{2} are the composite terms to represent the addition and subtraction of S-parameters. In SSRR, the factor k_{0}d = 0.266 which is 1 [4-7]. The values of V_{1} and V_{2} are estimated using Equations (3) and (4).

By using the obtained S-parameters, mathematical equations and MATLAB code the metamaterial characteristics have been verified [4-7].

From

_{11})_{ }characteristics of the unloaded rectangular microstrip patch antenna resonates at frequency f_{r} = 37.10 GHz with the bandwidth and gain of 15% and 0.5 dBi respectively. Hence, to decrease the resonant frequency and to increase the gain as well as bandwidth in the same dimensions of the rectangular microstrip patch antenna; it is loaded with planar MI waveguide. _{11}) of the rectangular microstrip patch antenna loaded with MI waveguide. The loaded antenna resonates at 9.38 GHz with the bandwidth of 44%. This is considerably a high bandwidth in such a compact size antenna. In the loaded antenna structure the spacing between neighbouring SSRRs is small consequently the mutual coupling is increased. In this antenna the directivity of 7.5 dBi is achieved. In general, for efficient radiation the electrical size of the antenna at resonant frequency 9.38 GHz should be equal to λ/2 that is 16 mm (at λ = 32 mm). In loaded condition the size of the proposed antenna is 12.50 mm x 3.70 mm (0.390 λ x 0.115 λ). The design of two long strips of the SSRR forms the two capacitors which cancel the electric dipoles associated with them at the resonance condition. Hence, in this antenna the cross-polarization gets reduced.

From

The dispersion relation of magnetoinductive waves propagating in the SSRR array of MI waveguide is expressed by Equation (5) [7-14].

where M is the mutual inductance between adjacent SSRR, a is periodicity of the array, L is the inductance of resonant element, ω is angular frequency and k is the wave number. The resonant frequency (ω_{0})_{ }of an isolated SSRR unit cell is expressed by Equation (6) [7,13-14].

where L and C are the equivalent inductance and capacitance of SSRR respectively.

The inductance (L) is estimated by modifying the mathematical equations expressed in [20-21]. Equation (7) is used to calculate the value of “L”.

where ρ is the filling ratio expressed as

, L_{1avg} is average length of the SSRR expressed by, and N is number of rings.

The equivalent capacitance (C) of an isolated SSRR unit cell is calculated by dividing it into two sections as; the upper and lower two strips as fingers of an interdigital capacitor (C_{I}) and secondly the parallel plate capacitance (C_{s}) between two inner strips. Therefore, the capacitance (C) is estimated using Equation (8).

The inter-digital capacitance (C_{I}) is calculated using Equation (9) [

(pF) (9)

where N_{I} is the number of fingers of inter-digital capacitor.

(pF/μm) (11)

For calculations of A_{1} and A_{2} the dimensions of the SSRR are considered in μm.

Similarly, the parallel plate capacitance between two inner strips (C_{s}) is estimated using Equation (12) [

where ε_{0} is the permittivity of free space (8.854 x 10^{–}^{12} F/m), A is modified factor (A = 60), t is the thickness of metal strips, and d_{m} is the distance between two inner strips.

By using equivalent circuit theory and above mathematical equations, the estimated values of equivalent circuit elements are; inductance L = 7.45 nH and capacitance C = 0.211 pF respectively. Theoretically, from these values the resonant frequency (f_{r}) of SSRR unit cell is found to be 4.03 GHz. The simulated resonant frequency of an isolated SSRR unit cell is f_{r} = 4.09 GHz (

The mutual inductance M between two neighbouring SSRRs of the array is calculated using Equation (13) [

The estimated mutual inductance is M = –0.224 nH and the coupling coefficient of is 0.030. Here, the minus sign indicates the backward wave propagation in planar configuration of the SSRR array. Thus, from equation (5) the dispersion relation is negative indicating the propagation of backward wave in planar configuration causing to pass the lower resonant frequencies beyond which the propagation is not possible. The dispersion relation (5) is modified to determine pass band of MI waveguide and ultimately the resonant frequency of loaded antenna is expressed by Equation (14) beyond which there is no propagation.

Therefore, through the MI waveguide the propagation of resonant frequency 4.09 GHz at good matched condition in the pass band (3.5 GHz to 5.5 GHz) of MI waveguide takes place. In the same frequency band the effective permeability is negative which also validates the pass band of MI waveguide [9-11] beyond this band there is no propagation. Thus, the loaded rectangular microstrip patch antenna should resonate at 4.09 GHz by decreasing its resonant frequency 37.10 GHz in unloaded condition. But due to loading effect, there is magnetic coupling between rectangular microstrip patch antenna and planar MI waveguide that result to develop the mutual induction between these two elements. Due to this effect the pass band frequency of MI waveguide and ultimately the resonant frequency of loaded rectangular microstrip patch antenna is shifted to 9.38 GHz by a coupling coefficient of, where M' is the mutual inductance between the rectangular microstrip patch antenna and MI waveguide. L' is the inductance of rectangular microstrip patch antenna. Further, equation (10) is modified by incorporating the factor by considering the effect of magnetic coupling and expressed by Equation (15).

The mutual inductance M' is calculated by using Equation (16).

The inductance of rectangular microstrip patch antenna L' is computed by using its equivalent circuit and expressed by Equation (17) [23,24].

where ω_{r} = 2πf_{r}; f_{r} is the design frequency, and C_{p} is the parallel capacitance in the equivalent circuit given by Equation (18) [23,24].

where y_{0} is the Y-coordinate of the feed point.

The estimated values of inductance L' and mutual inductance M' are 1.25 nH and 0.247 nH respectively. Therefore, in the loaded condition due to magnetic coupling effect the resonant frequency is shifted to 9.32 GHz which is closely matching with the simulated resonant frequency 9.38 GHz of the MI waveguide loaded rectangular microstrip patch antenna (

This paper presents a new approach to enhance the bandwidth and reduce the size of microstrip patch antenna. The theoretical explanation using effective medium theory, dispersion relation and equivalent circuit agrees well with the simulated results. A good agreement is observed in terms of resonant frequency and bandwidth with the simulated results thus validating the approach. In future, the authors intend to carry out experimental measurements and to propose such approach in ISM band for wearable wireless devices.

The authors sincerely express their gratitude to the anonymous reviewers for their valuable comments. The support of Director, National Institute of Technical Teachers’ Training and Research (NITTTR), Chandigarh, India is thankfully acknowledged. J. G. Joshi is highly indebted to the Director, Directorate of Technical Education (M.S.), India and Principal, Government Polytechnic, Pune, India for sponsoring him to pursue the full time Ph.D. under AICTE sponsored Ph.D. QIP (POLY) Program.