Cosecant Squared Pattern Synthesis for Reflector Antenna Using IWO A. R. Mallahzadeh 1 , P. Taghikhani 2 , A. H. Ghasemi 3 , J. Rashed Mohassel 4 1,2 College of Engineering, Shahed University Tehran, Iran {mallahzadeh, taghikhani}@shahed.ac.ir 3 Université Paris Ouest La Défense amir.h.ghassemi@gmail.com 4 Department of Electrical Engineering, Tehran University Tehran, Iran jrashed@ut.ac.ir Abstract— A method based upon Invasive Weed Optimization (IWO) Algorithms is described for the synthesize of double- curvature reflector surface to produce from a point source a shaped beam in one plane and pencil beam in the perpendicular plane. The method used the optimization algorithm to construct reflector surface by finding its central section curve. The synthesize procedure of this type antenna is discussed and the simulation results of a model antenna with a cosecant squared beam are shown and compared with Geometrical optics based method. I. INTRODUCTION Search radar antenna system often employs a shaped beam antenna which has a cosecant-squared pattern in the elevation plane and narrow pattern in the transverse plane. Doubly curved reflector antenna is a classical antenna for this purpose. The synthesis procedure based upon conservation of energy and the simple laws of geometrical optics (GO) has been described in details by many authors [1-6]. This method creates a differential equation or an integral equation that need to be solved numerically. Solving these equations need different parameters such as the parameter related to size of reflector that is arbitrary or an initial guess necessary for solving equation that has to be found. These requirements make antenna synthesize complicated and inflexible to achieve extra features like low sidelobe level or low ripple in shaped region. Recently, there has been a considerable attention paid to optimization algorithms in solving antenna problems. Therefore, to reduce the complexity and inflexibility of previously used methods, the authors employ the ability of optimization algorithm to create a new synthesizes method. This method uses IWO as an efficient, simple and fast optimization algorithm method which was first extracted by [7], and successfully has been used in antenna design problems [8,9]. In this paper basic concept of GO synthesis is reviewed briefly and then a classical doubly curved reflector with a cosecant squared pattern will be designed and simulated. Fig. 1 Central vertical Curve parameters Simulated results show that the new method has better accomplishments in cosecant squared region. II. GEOMETRICAL OPTICS SYNTHESIZE In order to shape reflector antenna’s surface to have a prescribed elevation pattern the proper central vertical section must be found. Central curve is illustrated in Fig. 1. Consider that the phase center of feed is located at origin O.  is the angle of incident ray with respect to  and  is the angle of reflected ray. The angle between incident and reflected rays, , can be determined as follows:  (1)  is the distance from origin to central curve. Clearly  and  are functions of  (i.e.  and  ). The differential equation of the central curve is [1-3]         (2) In this equation,  and  are both unknown. If know , then  can be determined. This equation couldn’t be         O Feed Point Proceedings of the 5th European Conference on Antennas and Propagation (EUCAP) 1258