TESIS

ABSTRACT
Beginning from the differential and integral form of the Maxwell equations, the wave
equation and its solution are obtained. The properties of the fields of the electromagnetic
waves were obtained as: propagation velocity, phase velocity, and polarization as well as
the transformation of the electromagnetic wave when it is propagated through different
mediums.
In order to use the numeric technique called Finite Difference Time Domain (FDTD), the
Maxwell equations were girded following the Yee technique. We built the algorithm and
defined FDTD equations in two and three dimensions. The numeric stability analysis and
the propagation velocity in the mesh were done in two dimensions.
To solve the reflection problem originated by the boundaries of the discrete space, the
Perfectly Matched Layers (PML) technique was used. The reflection coefficient results for
Transversal Electric (TE) and Transversal Magnetic (TM) polarization using a continuous
wave and pulses as source are shown.
Using the Green’s theorem, the far field equation from the near field values was obtained.
The near values were calculated by FDTD. The analysis was developed for both
polarizations.(TE and TM).
We applied these techniques to design a parabolic cylindrical antenna. Due to the reflector
curvature, it was necessary to use the stairs technique to adapt the FDTD mesh to the
parabola. We calculated the near field and diffracted field from the reflector. The solutions
from FDTD were obtained also in the frequency domain, for that, we applied the discrete
Fourier Transformed.
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