Horn Antenna Design Rhea Vanessa Acut Gerfel Philip Gonzales
1 INTRODUCTION This report documents the design of a portable outdoor antenna range, as well as design and fabrication, and measurement techniques of practical antennas for TV Rece ption. ABS-CBN Sports and Action Iligan is on Channel 26. The Program operates between 542MHz to 548MHz. A rectangular waveguide and a pyramidal hor n are designed and built for 542 – 548MHz frequency. Both antennas are designed for maximum radiation with minimal ohmic loss. There are several important facors taken into the design of these two antennas, such as skin depth factor, cut-off frequency, and the structure of the radiating element.
2 SKIN DEPTH FACTOR , AND CUTOFF FREQUENCY The material used for building the waveguide and the pyram idal horn is aluminum with thickness of 0.5486 of a millimeter. Aluminum has high electrical conductivity; its conductivity is second copper and the cost is significantly cheaper. This insures the radio wave transmitted in the waveguide is properly reflected and surface current on the waveguide does not produce much Ohmic loss. To ensure the copper used in construction is thick enough for a 1.2MHz electromagnetic wave to propagate with the least amount of attenuation, the skin depth must be calculated. The skin depth or the depth of penetration of a conductor:
√
The aluminum used in the construction is approximately 548.6 micrometers, which is much thicker than the skin depth. This ensures the waveguide will not be lossy. Radio waves can propagate in many different modes in a rectangular waveguide. For our purpose, the dominant mode of transverse electric propagation is selected. This TE10 mode has the lowest attenuation of all modes in a rectangular waveguide and its electric field is vertically polarized. In order to design the dimension of the waveguide, we must calculate the cut-off frequency for the dominant mode of propagation. For 1.2GHz wave to propagate inside the waveguide, the cutoff frequency must be lower then the mode of propagation. Plotting the attenuation of the transverse electromagnetic wave in the dominant mode within the waveguide will give us a good idea of the cut-off frequency to choose.
3 THE WAVEGUIDE Horn antennas are typically fed by a section o f a waveguide, as shown in Figure 4. The waveguide itself is often fed with a short dipole, which is shown in red in Figure 4. A waveguide is simply a hollow, metal cavity. Waveguides are used to guide electr omagnetic energy from one place to another. The waveguide is a rectangular waveguide of w idth b and height a, with b > a.
4 FIELDS AND GEOMETRICAL PARAMETERS FOR HORN ANTENNA Antenna texts typically derive very complicated functions for the radiation patterns of horn antennas. Since the pyramidal horn antenna is the most popular, we'll analyze that. The E-field distribution across the aperture of the horn antenna is what is responsible for the radiation. The radiation pattern of a horn antenna will depend on B and A (the dimensions of the horn at the opening) and R (the length of the horn, which also affects the flare angles of the horn), along with b and a (the dimensions of the waveguide). These parameters are optimized in order to taylor the performance of the horn antenna, and are illustrated in the following Figures.
Figure 5. Cross section of waveguide, cut in the H-plane.
Figure 6. Cross section of waveguide, c ut in the E-plane.
Observe that the flare angles (flare angle in the E-plane and flare angle for horn antenna) depend on the height, width and length of the horn antenna.
Given the coordinate system of Figure 6 (which is centered at the opening of the horn), the radiation will be maximum in the +z-direction (out of the screen).
The E-field distribution across the opening of the horn antenna can be approximated by:
The above equation states that the far -fields of the horn antenna is the F ourier Transform of the fields at the opening of the horn.
5 DESIGN Horn antennas are basically apertures with an electric field across them, which gives rise to the radiation. Now, we can model an electric field as a "magnetic surface current" Ms: [18]
In [18], is a unit vector perpendicular to the surface. The far field results can then be calculated using [18] in place of Js, and replacing the electric field with the magnetic field. That is, we can calculate E directly from Js, and H directly from Ms. In addition, since we are looking at radiated fields, we can calculate E from H, or H from E as:
[19]
In Equation [19], characteristic impedance of free space is a constant (about 377 Ohms), k nown as the characteristic impedance of free space, and is the direction of propagation for t he plane wave. The horn antenna geometry affects its antenna gain. For a desired antenna gain, there are tables and graphs that can be consulted in antenna handbooks that describe the optimal geometry in terms of the length and aperture size of the horn. However, this optimal geometry is only valid at a single frequency.
Since horn antennas are to operate over a wide frequency band, they are often designed to have optimal gain at the lowest frequency in the band. At higher frequencies, the geometry is no longer optimal, so the E-field across the aperture is not optimal. However, the horn's aperture becomes electrically larger at higher frequencies (the aperture is more wavelengths long as the frequency increases or the wavelength decreases). Consequently, the loss of an optimal aperture field is offset by an electrically larger horn, and the antenna again actually increases as the frequency incre ases.
6 REFERENCES 1. “New method for optimum design of pyramidal horn antennas”, Leandro de Paula Santos
Pereira; Marco Antonio Brasil Terada, Antenna Group, Electrical Engineering De pt., University of Brasilia 2. Antennas, Antenna Basics, Antenna Gain . http://www.antenna-
theory.com/antennas/aperture/horn.php
3. Pyramidal Horn Antenna, ETS-Lindgren Inc. 4. Horn Antenna, http://en.wikipedia.org/wiki/Horn_antenna
