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Lenses are used to collimate incident
energy to prevent it from spreading in undesired directions. Luneburg
lenses are broadband. These kinds of lenses are usually used in
microwave frequencies. They are used in antenna constructions, radar
calibrations, satellite systems and they are expected to be used in
future in some of the internet communication systems.
Corrugated horn antennas are a type of
horn antennas developed for achieving high efficiency. Horn antennas are
used in satellite systems, radar applications, etc. and are the main
type of feeders of reflector and lens antennas.
Theoretical Background
Luneburg lens is a spherically symmetric structure with variable
refracting index, decreases radially out from the center. Luneburg lens
creates two conjugate foci outside of the lens. Each point on the
surface of an ideal Luneburg lens is the focal point for parallel
radiation incident on the opposite side. Placing grooves on the walls of
a horn antenna is implemented so that the same boundary conditions to
all polarizations are achieved and that the field distribution is
tapered at the aperture in all the planes. Same boundary conditions
eliminate the spurious diffractions at the edges of the aperture. Main
characteristics of Luneburg lenses are
• Broad band,
• Dielectric lens influences the signal transition.
WIPL-D Simulation
An antenna model which consists of a Luneburg lens and a corrugated
horn, simulated using WIPL-D Pro 3D EM solver, is presented here. Full
model is shown in Fig. 1. Quarter model, where dielectric layers can be
clearly seen, is shown in Fig. 2. The variable refracting index is
approximated by using five layers of dielectrics with different
electrical properties. The corrugated horn model is shown in Fig. 3. Our
aim is to inspect simulation times and memory requirements, radiation
pattern and near field at the operating frequency. Operating frequency
is 1414 MHz (D band – NATO band classification).
Radiation pattern in 3D and a phi cut are given in Figs 4-5,
respectively. The diagram shows relatively high directivity and low
side-lobes, as expected. Please note that the theta angle is measured
with respect to the xOy plane.
Distribution of the near field is shown in Fig. 6. The focusing effect
of the lens is clearly seen where a spherical EM wave comes into the
lens originating from the horn while on the other side it is transformed
into a plane wave.
Number of unknowns and simulation time are given in Tab. 1. Computer used for these calculations is Intel® Core2 Quad CPU @ 2.83 GHz, 8 GB RAM.
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Figure 1. Luneburg lens and
corrugated horn antenna |
Figure 2. Quarter model of
Luneburg lens and corrugated horn antenna |
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Figure 3. Corrugated horn antenna |
Figure 4. 3D radiation pattern |
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Figure 5. Radiation pattern in
phi-cut |
Figure 6. Near field |
Table 1. Analysis characteristics
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Number of unknowns |
Time [sec] |
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17174 |
256 |
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Conclusion
This kind of antenna is usually very difficult for simulation using a
rigorous computational electromagnetics code. However, WIPL-D Pro
successfully analyses the antenna using MoM thanks to sophisticated
techniques such as higher order basis functions. Simulation times are
very short comparing to other computational methods of similar accuracy.
This makes WIPL-D Pro an excellent tool for tackling very challenging
lens antenna designs.
Results given here by WIPL-D Pro coincide with theoretical expectations.
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