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analysis of the structure with the hybrid method at f ϭ 9 GHz are shown in Figure 6. Specifically, the radiation patterns in the x-z and y-z planes are plotted in Figures 6(a) and 6(b), respectively. For this analysis, the waveguide is inside an FEM domain and the conducting planes are taken into account by means of PO and PO ϩ PTD (FEM ϩ PO and FEM ϩ PO/PTD labels in Fig. 6, respectively). Obviously, mutual interactions between the conducting planes have been computed using the appropriate HFT (PO or PO ϩ PTD). Agreement between the measurements and the results obtained using the hybrid technique is very good. CONCLUSIONSA novel iterative hybrid FEM-HFT method for the efficient analysis of general scattering and radiation problems has been presented, in which the FEM and the HFT exterior domains are fully coupled. Numerical results obtained with a 3D implementation making use of PO and PTD have been shown. Exponential convergence is achieved. A comparison of the measurements and the numerical results from other authors and methods has been provided, showing very good agreement. ACKNOWLEDGMENTSThe authors would like to thank Leandro de Haro and Jose L. Besada for providing the reflector's geometry and measurements. The measurements were made in the anechoic chamber of the Department of Señales, Sistemas y Radiocomunicaciones, Universidad Politécnica de Madrid, Spain. This work has been supported by the Ministerio de Ciencia y Tecnología, Spain, under projects TIC2001-1019 and TIC2002-02657. Another class of antennas uses a defect or resonator in an EBG material to achieve large directivities and high efficiencies. A generic EBG resonator antenna is shown in Figure 1. It consists of a cavity created by an EBG material and a metallic ground plane. Energy is coupled to the cavity using a feed antenna such as a dipole, slot, microstrip patch, or waveguide. The high directivity of the resonator antenna is due to the angle-dependent transmission from the defect resonator to free space. Measured and theoretical results have been reported for these resonant cavity antennas using 1D [13], 2D [14,15] and 3D [16,17] EBG materials. The 1D version of this resonator device is essentially an extension of previous work carried out on the gain enhancement of printed antennas through the use of multiple superstrates [18]. High-gain resonant-cavity antennas have also been implemented using both metallic partially reflective surfaces [19] and grid reflectors [20].In this paper, we present the theory and experimental results for a 1D EBG resonator antenna that uses a microstrip feed element. The design and analysis presents two major advances compared to other papers presented in the literature [13,18]: (i) the substrates we use to create the EBG material have a low dielectric constant; and (ii) we describe a simple method for accurately predicting the antenna's operating frequency using multilayer theory. The analysis of the low-dielectric-constant EBG materials is an important practical consideration because they are more readily ...

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