Extension of forward backward method with DFT based acceleration algorithm for the efficient analysis of large periodic arrays with arbitrary boundaries

Abstract

approaches a constant maximum value for tapers longer than 15 mm. CONCLUSIONPlanar transmission-line impedance transformers with an unconventional multilayered structure obtained by deposition of highdielectric-constant thin films on bulk substrates have been designed and their performance have been compared to those of transformers printed on very high-dielectric-constant ( r ϭ 80) bulk substrates. The propagation characteristics of the tapered lines were investigated using the finite-element method through a commercially available software package. The dispersion effects and impedance variation with respect to frequency were taken into account in the analysis. The response of the proposed structure does not deteriorate significantly with frequency, thus allowing operation in an acceptable range up to 40 GHz. The investigation of the propagation characteristics of short electrical pulses on the unconventional multilayered structure and on very high-dielectricconstant bulk-substrate tapers was carried out, confirming the better performance of the proposed structure. The propagation of very short pulses without substantial distortion was verified. Finally, the effects of the multilayered taper length on the performance were assessed.The newly proposed multilayered structure presented attractive results. The achieved effective dielectric constant is very high, whereas the structure has very low dispersion, thus allowing the construction of compact high-frequency devices. The lines have both simple cross sections and comfortable transversal dimensions for a wide range of impedances, thus leading to less expensive manufacture. The results obtained thus far indicate that this structure may be suitable for many other applications in microwave components. ACKNOWLEDGMENTThis work was supported by the Research and Development Center, Ericsson Telecomunicações S.A., Brazil. [7], and hybrid approaches to reduce the total number of unknowns such as a hybrid combination of MoM with either uniform geometrical theory of diffraction (UTD) [8 -10] or discrete Fourier transform (DFT) [11,12] are useful techniques that are available in the literature.Recently, a DFT-based acceleration algorithm [13] was used in conjunction with stationary (for example, the forward-backward method (FBM)) and nonstationary (for example, biconjugate gradient stabilized method (BiCGSTABM)) iterative MoM (IMoM) [14,15] to reduce the computational complexity and memory storage of the IMoM solution to O(N tot ) in the analysis of electrically large, planar, periodic, rectangular, finite phased arrays of both freestanding and printed dipoles. In this approach (DFTIMoM), contributions to every receiving element in the array are coming from two different regions: namely, the strong region formed by the nearby elements of the receiving element whose contributions are calculated in an element-by-element fashion, and the weak region formed by the rest of the array elements whose contributions are obtained from the DFT representation of the entire current di...