Numerical Model for Phase Distribution Characterization of Reflectarray Elements Arslan Kiyani* and M. Y. Ismail Wireless and Radio Science Centre (WARAS), University Tun Hussein Onn Malaysia, 86400 Parit Raja, Johor, Malaysia arslan.kiyani@gmail.com, yusofi@uthm.edu.my Abstract—A mathematical model to obtain a linear progressive phase distribution of six different high performance reflectarray resonant elements in order to realize a planar wave in front of the periodic aperture is formulated in this paper. All the resonant elements under characterization are tuned to operate at X-band frequency range using commercially available CST computer model. The reflection phase curves for each resonant element are then calculated by using analytical equations based on a periodic Method of Moments (MoM). A Figure of Merit (FoM) has been defined for the comparison of reflection phase curves obtained by both simulation and formulation in terms of bandwidth and static phase range performance. It has been demonstrated that among the entire resonant elements triangular loop acquire steepest phase characteristics gradient offering higher static phase range of 190° with minimum bandwidth, whereas rectangular patch element is shown to exhibit smoother phase characteristics gradient giving lower static phase range of 120° with broader bandwidth performance. Furthermore it has been observed that triangular loop depicts the maximum reflection loss of 3.90dB, whereas rectangular patch shows the minimum reflection loss of 0.23dB. Keywords- finite integral method; method of moment; reflectarrays; resonant elements; surface current distribution; static phase range. I. INTRODUCTION Modern wireless technologies demands the deployment of low cost, light weight, high gain and easy to install microstrip antennas for commercial applications such as avionic radar systems and point-to-point communications. Therefore a flat surface reflectarray antenna is gaining attraction as an alternative to conventional curved reflectors and phased arrays [1], [2]. It consists of printed radiating elements on top of the grounded dielectric substrate, illuminated by a feed antenna Microstrip reflectarrays gives the ability of scanning its main beam to large angles from its broadside direction and perform the phase synthesized pattern shaping [3]. However, reflectarray antenna has a crucial limitation in bandwidth performance due to the narrow band of its resonant elements, spatial phase delays [4], [5] and phase errors related to the change in patch size [6]. To overcome the bandwidth limitations thick substrate is proposed in [7]. Unfortunately increasing the substrate thickness degrades the phase range performance. In the reflectarray design the phase range required to be 360° at a given frequency in order to provide a suitable compensation to form a planar wave front across the periodic array of aperture. Various passive approaches and shapes of patch elements have been proposed in the past to achieve the progressive phase delay which include identical patches of variable-length stubs [8], square patches of variable size [9], [10], identical planar elements of variable rotation [11] for circular polarization, cross-dipoles [12], [13] and ring elements [14], [15] to vary the scattering impedance of the elements and eliminate the effect of different path lengths. This work provides a detailed numerical implementation of periodic MoM in order to realize a progressive phase distribution. The mathematical formulation has been derived by considering the material properties of dielectric substrate with geometrical and electrical properties of different reflectarray resonant elements. Moreover the practical validation of the formulation has been carried out by comparing the simulated and formulated phase curves in terms of static phase range performance of individual resonant elements. II. DESIGN METHODOLOGY The considerations focus on the design of X-band reflectarray antenna with six different shapes of resonant elements including rectangular patch, square patch, triangular patch, dipole, square loop and triangular loop aimed for operation at 10GHz. The resonant elements are constructed on top of 1mm thick dielectric substrate Rogers RT/ Duroid 5880 *i r ?404. vcph?20222;+ backed by a conducting ground plane. Fig. 1 shows the design configuration of unit cell reflectarray with different resonant elements. Commercially available CST computer model has been used as a simulation tool to analyze each resonant element with proper infinite boundary conditions. Another important parameter that is required to be taken into account is the distance of excitation port from the resonating elements. The port excitation is placed at a distance qh そ g /4 to incident a vertically polarized (Y-axis) plane wave on the unit cell reflectarray to investigate the scattering characteristics. Whereas, そ g is the guided wavelength which can be calculated by: g reff n n g fl ? *3+ However, 1 2 1 1 1 12 2 2 r r reff h w g g g / - / Ç × ? - - È Ù É Ú *4+ This research work is fully funded by the Prototype Research Grant Scheme (PRGS VOT0904) awarded by the Ministry of Higher Education, Malaysia. *Corresponding Author 1st IEEE International Symposium on Telecommunication Technologies 978-1-4673-4786-0/12/$31.00 ©2012 IEEE 160