Antena

Revista Científica Periódica - Telecomunicações

ISSN 1516-2338

FDTD method: Analysis of an one-dimensional array of H-plane sectoral horn antennas with dielectric lens
Ronaldo O. dos Santos and Carlos Leonidas da S. S. Sobrinho
Department of Electrical and Computer Engineering, Federal University of Pará (UFPA), P. O Box 8619, 66075-900 Belém, PA, Brazil
Abstract ⎯ The FDTD method isused in the analysis of the radiation characteristics of an onedimensional array antenna. Here, the array elements are two-dimensional H-plane sectoral horns with parabolic dielectric lenses. In this case, the dielectric materials used were chosen so that they have low dielectric constant in order to avoid considerable reflections on the air-dielectric interfaces. The numerical results obtained showthat the distance between the array elements and the lens characteristics, in spite of its low dielectric constant, change the phase distribution and power at the aperture of the array. For a suited choice of these parameters, radiation patterns are obtained with low level of side lobes. Index Terms ⎯ FDTD Method, Horn Antennas,
Dielectric Lenses, array.

II. THEORY The transversal section ofthe bidimensional model for the H-plane sectoral horn to be analyzed in this paper is shown in Fig. 1. For the antenna design, R2 = 8 λ and A = 4 λ were considered. Only the TM mode is considered in our analysis, so that the problem is reduced to the following (Hx, Hy) magnetic components and (Ez) electric component, which are expressed (obtained from Maxwell’s equations) as:

. .

lH
d

Ra

I. INTRODUCTION The finite difference time domain (FDTD) method was introduced by Yee in 1966 [1] , and represents an efficient and simple form of solving Maxwell’s equations when written in time domain – differential form. In Yee’s proposal, the magnetic and electric field components are intercalated in time and space in such a way that there is reciprocity among them. Users of this methodhave progressively increased in the last years because of its low cost implementation, probably on account of new generation appearing of computers and the developing of new numerical techniques which made it possible to use the FDTD method to model open structures [2-8]. The FDTD method has been used in characterizing horn antennas [9-11]. In [9] and [10], the FDTD method is used to determine thefield distribution (phase and amplitude) in the horn opening as well as the radiation pattern for both bidimensional and tridimentional cases, respectively, and in [11] the method (stepped-edge) is introduced and applied in calculating the radiation pattern of various aperture antennas. The use of dielectric lenses to correct the phase and /or power distribution in the horn antenna opening is verycommon and, in [12], experimental results for triangular lenses have been presented, considering low refraction index lenses. The main objective of this paper is to analyze the radiation characteristics of an one-dimensional array antenna, where the array elements are twodimensional H-plane sectorial horns with parabolic dielectrics lenses and is assumed no coupling between the array elements.This structure is then present as a proposal of phase correction and power distribution at the aperture of the array.
28

2α H

A

R2
RH

y . . x

R2 = 8λ A = 4λ

2α H = 28o

α=

λ
4

Figure 1. Two-dimensional H-plane sectorial horn with an one-dimensional array inset.

∂H x 1 ∂E z =− ∂t µ ∂y ∂H y 1 ∂E z = ∂t µ ∂x
∂Ez 1 ⎛ ∂H x ∂H y ⎞ ⎟ = ⎜ − ∂t ε ⎜ ∂y ∂x ⎟ ⎝ ⎠

(1)

Theabove written equations are solved numerically through the FDTD method [1]. To define the FDTD grid (sets the number of cells in each dimension and the cell size), a bidimensional uniform grid with cells dimensioned in space and time as, respectively, λ/20 per λ/20 and ∆t ≤ ∆x / 2c obeying the stability criterion suggested by Courant et al. [13] in the central frequency (fc). The sine modulated...