Reducing the Mutual Coupling of Cylindrical Circular Microstrip Antennas (CCMAs) Array Using EBG Structure

: A theoretical study to design a conformal microstrip antennas was introduced in this work. Conformal microstrip antennas define antennas which can be conformed to a certain shape or to any curved surface. It is used in high-speed trains, aircraft, defense and navigation systems, landing gear and various communications systems, as well as in body wearable. Conformal antennas have some advantages such as a wider-angle coverage compared to flat antennas and low radar cross-sectional (RCS) and they are suitable for using in Radome. The main disadvantage of these antennas is the narrow bandwidth. The FDTD method is extremely useful in simulating complicated structures because it allows for direct integration of Maxwell's equations depending on time. The 1x2 cylindrical circular microstrip antennas array is designed and simulated vertically via Finite Difference Time Domain (FDTD) method where can directive antenna be achieved through antennas array design. Mutual coupling between the antennas in the array and the different separation between them were studied. The circular patch is excited by a probe feed method for several reasons including providing less spurious radiation from the probe current, in addition to the simplicity in theoretical engineering installation and practical manufacturing. It is well known that the values of the coupling are decreased as the distance separation increased. Cylindrical circular microstrip antenna with resonant frequency operating is 3.5GHz for TM 01 mode, several parameters like return loss, band width, and input impedance are calculated. Also, for isolated coupling, mutual coupling coefficients, directivity gain, for different separations between the centers of the two adjacent circular patches in terms the wave length operating are calculated. Moreover, the electromagnetic band gap EBG structure is used for reducing the mutual coupling created by the surface waves in order to enhance the antenna's performance in an array has become smaller than before. The proposed EBG is a three triangular-shape equal sides metallic structure, utilizing the inter-element spacing in an array. The less value of S 12 is − 69dB for the spacing between the two centers of patches is 102.84mm . BW percentage increased to 34.3% and the directivity is enhanced also. Additionally, simulations were done using MATLAB 2017b.

A theoretical study to design a conformal microstrip antennas was introduced in this work. Conformal microstrip antennas define antennas which can be conformed to a certain shape or to any curved surface. It is used in high-speed trains, aircraft, defense and navigation systems, landing gear and various communications systems, as well as in body wearable. Conformal antennas have some advantages such as a wider-angle coverage compared to flat antennas and low radar cross-sectional (RCS) and they are suitable for using in Radome. The main disadvantage of these antennas is the narrow bandwidth. The FDTD method is extremely useful in simulating complicated structures because it allows for direct integration of Maxwell's equations depending on time. The 1x2 cylindrical circular microstrip antennas array is designed and simulated vertically via Finite Difference Time Domain (FDTD) method where can directive antenna be achieved through antennas array design. Mutual coupling between the antennas in the array and the different separation between them were studied. The circular patch is excited by a probe feed method for several reasons including providing less spurious radiation from the probe current, in addition to the simplicity in theoretical engineering installation and practical manufacturing. It is well known that the values of the coupling are decreased as the distance separation increased. Cylindrical circular microstrip antenna with resonant frequency operating is 3.5GHz for TM 01 mode, several parameters like return loss, band width, and input impedance are calculated. Also, for isolated coupling, mutual coupling coefficients, directivity gain, for different separations between the centers of the two adjacent circular patches in terms the wave length operating are calculated. Moreover, the electromagnetic band gap EBG structure is used for reducing the mutual coupling created by the surface waves in order to enhance the antenna's performance in an array has become smaller than before. The proposed EBG is a three triangular-shape equal sides metallic structure, utilizing the inter-element spacing in an array. The less value of S 12 is − 69dB for the spacing between the two centers of patches is 102.84mm. BW percentage increased to 34.3% and the directivity is enhanced also. Additionally, simulations were done using MATLAB 2017b.

Introduction:
Recently, communications have developed widely and the microstrip antennas array played a curial role in this developing due to its multitasking possibilities which made it have many advantages in several applications. One of them, in highperformance spacecraft, is satellite and missile applications 1 .
As known, a conformal antenna is defined as an antenna that can be compatible with a specific shape or on any curved surface by just changing the shape of the antenna ground plane. Additionally, the patch can be rolled on the base without getting any unacceptable changes in its radiation characteristics and does not cause an additional drawback 2 .
The conformal antennas are divided into a singly curved (such as cylindrical antennas) and doubly curved (such as spherical antennas), depending on how many curvatures the geometry has. Generally, conformal antennas have some advantages such as special angular coverage, wideband and lower radar cross-section(RCS) 3 . The directive gain of the single element has a low value and provides a relatively wide radiation pattern. Some applications demand the design of antennas with high directive gain characteristics. The directive antenna can be achieved by antennas array design. Important parameters must be calculated at stages of the conformal microstrip arrays design such as the effect of the mutual coupling between the elements 4 . Conformal microstrip arrays are used widely in a miscellaneous application 5 such as satellite arrays, antennas of an aircraft, and wearable networks 6 . The configuration of a directional cylindrical circular microstrip antenna CCMA array requires that the identical elements of CCMAs can be placed with an adjacent spacing between the elements. However, the closeness of the elements causes a mutual coupling between the elements due to the electromagnetic EM interaction between the elements which influenced the radiating properties. When the mutual coupling has a significant value then it affects the performance of the array including directivity, return loss and bandwidth, with a little negative effect on both near and far field patterns and the radiation efficiency. In other words, the current in each element changed depending on the amount of the mutual coupling between the elements. Thus, it is necessary to take into account the effect of mutual coupling while analyzing the arrays 7 .
The radiation of the surface wave increases as the dielectric constant and substrate thickness increases 8 , hence, this radiation may be controlled by various methods such as restricting the substrate size or adding a photonic band gap modal .The surface waves can be suppressed by utilizing the electromagnetic band gap EBG structures which reduce the mutual coupling and enhance the performance of antenna 8 .An EBG structure can be defined as the fabricated periodic objects that prevent the propagation of EM waves with a certain band of frequency over the incident angles and for all polarization cases 9 .The main challenge of tactical communication systems is the accessibility of relevant information on the particular operating environment required for the determination of the waveform's ideal use. The propagation model focuses mainly on broadcasting and wireless communication with a high directivity antenna 10 .The current work has played a vital role in enhancing CCMA's performance. In other words, the EBG structure is used for reducing the mutual coupling created by the surface waves in order to enhance the antenna's performance in an array has become smaller than before by reducing the mutual coupling between the array elements. Also, for isolated coupling, mutual coupling coefficients, directivity gain, for different separations between the centers of the adjacent circular patches in terms the wave length operating will be calculated .The inter-element spacing in an array can be utilized to put the proposed EBG.
Several EBG structures are used for mutual coupling reducing and bandwidth enhancement such as EBG structure with T-shaped slot (EBGT) and EBG structure with Opposite L-shape slot Loading T-shaped slot (EBGTL) in order to reduction the mutual coupling between radiating elements in such array(S 12 = −32.19 , = 4.76% and the directivity 7.7 dB 7 . A rectangularshape metallic structure with four periodic inverted H-shape slots, as a EBG structure is proposed by the researcher 8. The mutual coupling coefficients between the elements of the array S 12 = −52.7 and BW= 2.99% while directivity about 14.9 dB .

Cylindrical Circular Microstrip Antennas (CCMAs)
Antennas on singly surface curved are the easiest conformal antennas. It is the most obvious in non-planar geometry. Especially, the cylindrical antennas are commonly used in conformal antenna applications such as aerospace, communication systems and in many experimental radars 3 . Our study is concentrated on cylindrical conformal microstrip antenna with a circle patch or which is known cylindrical circular microstrip antenna (CCMA) 11 .
The basic structure of CCMA is shown in Fig.1. The excitation was chosen by a probe feed method for several reasons including providing less spurious radiation from the probe current, in addition, to the simplicity in theoretical engineering installation and practical manufacturing. The coaxial feed consists of two conductors, the outer conductor is connected with the ground plane while the inner conductor extends through the dielectric substrate reaching to the patch. The essential feature of this type of feeding methods is that the feed can be placed at any required position within the patch aimed to obtain the impedance matching 8 . The ground plane of the CCMA is a metal cylinder of radius (a). The dielectric substrate is of dielectric constant ε r and having thickness h extends around the body of the ground plane. The circular metal patch is etched on the surface of the substrate 12 .
The ground plane has been assumed infinite along z-axis. The resonant frequency of the circular patch , , for TM mn mode as a function of an  An antenna bandwidth is defined as where f u : upper frequency. f L : lower frequency.

FDTD method
Simulation model of FDTD method in timedomain is obtained by solving Maxwell curl equations 12 . FDTD method provides us with an understanding of the propagation of the electromagnetic waves in microstrip antennas. This method is to solve Maxwell's time-dependent equations in the time domain by converting it into finite difference equations. Simulation steps of FDTD method are starts by representing the physical structure depending on material type (conductor, dielectric or boundaries).
The second step is applied Gaussian pulse to simulate all the sources. Then, all the fields (electric and magnetic) are calculated at any increments of time. These fields are recalculated again after each increment until they decay to zero into the system. Finally, the frequency information is extracted by Fourier transformation. Yee supposed that FDTD space are cells of an ∆x∆y∆z-volume and the components of electric and magnetic fields in 3D space are distributed as shown in Fig. 2. Every Efield component is surrounded by four H-field components and every H-field component is surrounded by four E-field components 12 .

Basic Formulation of FDTD
Maxwell's time-dependent equation is used because of the wave front of the input signal is a function of time , and any computed results from a FDTD simulation are in the time domain, where the relationship between the input and output is available. When the FDTD simulation is completed , then, the input and output time functions will be transformed to the frequency domain by using Fourier transform Based on the system of central difference, Maxwell's curl equations can be replaced by a set of finite difference equations. The curl operator is yield to six-coupled scalar equations which equivalent to Maxwell's curl equations in a 3D rectangular coordinate system. These equations can be written as: where represents the electric permittivity in Farad per meter, is the magnetic permeability in Henry per meter , represents the electrical conductivity and ρ′ is the magnetic conductivity.
The FDTD simulation space is bounded, and these radiated or scattered fields will be reflected back into the simulation space when they arrived at the boundary of FDTD space. The perfect matched layer (PML) technique is presented by Berenger 13 , who proposed an absorbing layer designed to absorb EM waves without any reflections 14 . The excitation of the system can be done by Gausses pulse where τ is a damping factor has to value depends on the frequency range of the problem, t 0 is the time delay 15 . The far-field components can be getting by using the equivalence principle and through a nearfield to far-field transformation.

Design of cylindrical circular microstrip antenna (CCMA)
The CCMA is fed by the coaxial probe technique, it is excited with the dominant mode TM 01 . The dimensions of the patch are determined in terms of its resonant frequency formula (eq.1). The cylindrical antenna has a radius (a=10 cm). It is used in the civilian and military fields 10 , especially, for unmanned aerial vehicle which need a broadband antenna. In our study, for a circular patch with its pure shape, the standard operating resonant frequency is 3.5 GHz. The proposed antenna is very suitable for the wireless local area network WLAN applications. WLAN operates at the frequency spectrum 3-10 GHz .In addition, this antenna is used in civilian and military fields, specially, for unmanned aerial vehicle, which need broadband antennas.
The proposed antenna contains RO 3003 material as a dielectric layer with the dielectric constant ε r = 3 and thickness of the substrate is (h=1.5 mm). From Eq. 1 with resonant frequency f r = 3.5GHz, so the radius of patch obtained is equal r eff = 30.19 mm. The simulated results of CCMA with the optimum dimensions are shown in Fig. 3.

Results and Discussion:
Input impedance and resonant frequency Simulation results of the real part (resistance) and imaginary part (reactance) of the input impedance are plotted in Fig. 4. At the moment where the reactance value is zero, the resonant frequency is f r = 3.5GHz and the input impedance is Z in = 50Ω . Return loss(RL) and bandwidth Fig. 5 shows that the calculated value of return loss is (−23.95dB) and the resonant frequency is f r = 3.5GHz. Bandwidth of the microstrip antenna is calculated from Eq. 2. It is calculated from the frequency range at two sides of return loss at -10dB. The percentage of bandwidth is 12.34%.

Design of 1x2 CCMAs Array
The proposed 1x2 array is designed and simulated by FDTD method. Return loss coefficients, mutual coupling coefficients, and resonant frequency are calculated and plotted for different separations between the elements. In addition, the directive gain is calculated. Fig. 6 shows the simulated results for two identical CCMAs. The two patches have the same size and fed individually by a coaxial probe with TM 01 mode. The separation between the centers of the two adjacent patches is 0.9λ where λ=85.7mm is the wavelength corresponds to the resonance frequency operating.
The analysis here is for isolated coupling which is defined as the mutual coupling between two elements only. The beginning was by study the effect of the separation (d) between the centers of two adjacent patches on the performance of the antennas array. The spacing (d) is selected to be in the range 0.9λ − 1.4λ. The mutual coupling coefficients were calculated as a function of this spacing (d).
Values of the return loss coefficients, mutual coupling coefficients, and resonant frequency are shown in Figs. 7 and 8. Fig. 7 shows the values of the return loss for four different spacing (d), while, Fig. 8 shows the values of the mutual coupling. Table 1 shows the effect of the mutual coupling on the parameters of antenna for different separations (d).   From the above results, it is shown that there is no change in the value of resonant frequency as a result of the design of the array. The return loss coefficient S 11 increased as the interspacing between the centers of two adjacent patches increased, whereas, the mutual coupling coefficient S 12 decreased. A better array directivity obtained at d = 1.2λ and S 11 = −41dB. The resonant frequency was not significantly affected by the separation variation.

Design of 1x2 CCMAs Array with EBG structure
Several techniques are used for reducing mutual coupling. In this work, the electromagnetic band gap structure is employed to solve this coupling problem. Electromagnetic band gap (EBG) structure defined as an artificial structure reduces the propagation of the surface waves and its generated currents at special band and frequency for all the incident angles.
The proposed EBG is a three triangular-shape equal sides metallic structure. FDTD method is used to design and simulate EBG structure with side length is 4mm as shown in Fig.9. These dimensions are determined by using the trying and error method. Values of the return loss coefficients, mutual coupling coefficients, and resonant frequency are shown in Figs. 10 and 11. These values are calculated for four different spacing (d). These Figs. show that the return lossS 11 with EBG structure is increased compared with the S 11 of the cases without EBG structure, whereas, the mutual coupling coefficient S 12 is decreased. The less value of S 12 is − 69dB for the spacing between the two centers of patches is 102.84mm. S 12 coefficient less than -32.19dB or -52.7dB for both 7,8, respectively. It can be clear that BW percentage increased to 34.3% compare with earliest studies. Directivity is enhanced also. The effect of EBG structure on the parameters of antenna for different separations is shown in Table 2. The current results can be compared with the earliest studies 7,8 as depicted in Table. 3. The resonant frequency didn't change because of the size both of the two circular patch or ground plane didn't change also due to not using a slots or partial miniaturization, respectively.

Conclusion:
To conclude, the FDTD method has been used to design and simulate 1x2 CCMAs array. The EBG technique has played a vital role in enhancing CCMA's performance. The coefficients of return loss are improved as the distance between the centers of two adjoining patches increased, while the coefficients of mutual coupling are reduced, additionally, better directivity has been acquired at d=1.2λ. Hence, this study confirms that using EBG structure reduces the values of the elements mutual coupling with increasing the coefficients of return loss.

Acknowledgements:
The author wish to thank to University of Al-Qadisiyah/College of Education, Department of Physics, Ministry of Higher Education and Scientific Research of Iraq for finical support this study.