Calculation of the Mutual Coupling Parameters and Their Effects in 1-D Planar Almost Periodic Structures

Abstract

Abstract-This paper proposes a new modal analysis based on Floquet's theorem which is needful for the study of a 1-D periodic phased array antenna excited by arbitrary located sources. This analysis requires an accurate estimation for calculation of the mutual coupling parameters (for example: mutual impedances or admittances . . . ) between the array elements and their effects integrating a large planar radiating structure. Two different formulations are suggested, in spectral and spatial domains, to solve the problem and to calculate the coupling coefficients between the neighbouring elements in a periodic environment. Important gain in the running time and used memory is obtained using Floquet analysis. One numerical method is used for modeling the proposed structures: the moment method combined with Generalized Equivalent Circuit (MoM-GEC).

Floquet Modal Analysis to Modelize and Study 2-D Planar Almost Periodic Structures in Finite and Infinite Extent With Coupled Motifs

“…It is possible to express the excitation source by a non-uniform field [1,20]. Based on Floquet states or Floquet eigen modes, we will identify all proper phases shift of the unit cell surrounded by others cells.…”

“…[10,15,22,23]. Many numerical techniques have been invested in this context, and their goal is to solve partial differential equations with periodic boundaries conditions, for instance the finite element method (FEM), the method of moment (MoM) and finite-difference time-domain (FDTD) [1,15,27].…”

“…But this work considers a new original modal approach based on the Floquet's theorem to facilitate the treatment of this kind of structure [1,3,4,21]. The modal description of the impressed field has been given in spectral domain one, and the radiated fields have discrete spectra in the wavenumber space.…”

“…For solving this problem, we propose adopting an integral method based on the generalized equivalent model and using the Floquet modes written as a group of excitation sources. This proven Floquet modal technique allows to considerably reduce the running time and used memory observed by other conventional methods [1,26]. This paper is structured as follows.…”

“…To begin with, the Finite Fourier Transform (FFT) and spectral decomposition are given. Next, in Section 3 the studied problem is formulated by an integral equation based on the formalism of the admittance (or impedance) operator using Generalized Equivalent Circuit (GEC) cited in [1,3]. Then, in Section 4 numerical results are presented and discussed for many applications.…”