antennas 97
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Antennas 97
97
Aperture Antennas
Reflectors, horns.High GainNearly real input impedance
Huygens’ Principle
Each point of a wave front is a secondary source ofspherical waves.
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Equivalence Principle
Uniqueness Theorem: a solution satisfying Maxwell’sEquations and the boundary conditions is unique.
1. Original Problem (a): 2. Equivalent Problem (b): outside ,
inside , on , where
3. Equivalent Problem (c): outside , zerofields inside , on , where
To further simplify,Case 1: PEC. No contribution from .Case 2: PMC. No contribution from .
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Infinite Planar Surface
To calculate the fields, first find the vector potential dueto the equivalent electric and magnetic currents.
In the far field, from Eqs. (1-105),
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Since in the far field, the fields can be approximate byspherical TEM waves,
Thus the total electric field can be found by
Let be the aperture fields, then
Let
Use the coordinate system in Fig. 7-4, then
and
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or in spherical coordinate system
Using Eq. (7-8), we have
If the aperture fields are TEM waves, then
This implies
Full Vector Form
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Techniques for Evaluating Gain
Directivity
From (7-27), (7-24), (7-61)
Thus, for broadside case,
Total power
Then,
In general, for uniform distribution
If
then
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where are the directivity of a line source due to respectively. the main beam direction
relative to broadside.
Gain and Efficiencies
where : aperture efficiency
: radiation efficiency. (~1 for aperture antennas)
: taper efficiency or utilization factor.
: spillover efficiency. is called : illuminationefficiency.
: achievement efficiency. : cross-polarization efficiency. phase-error efficiency.
Beam efficiency
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Simple Directivity Formulas in Terms of HPbeam width
1. Low directivity, no sidelobe
2. Large electrical size
3. High gain
Rectangular Horn Antenna
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High gain, wide band width, low VSWR
H-Plane Sectoral Horn Antenna
Evaluating phase error
thus the aperture electric field distribution
where is defined in (7-108), (7-109)
Directivity
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Figure 7-13: universal E-plane and H-plane pattern with factor omitted, and
Figure 7-14: Universal directivity curves.
Optimum directivity occurs at and
From figure 7.13,
E-Plane Sectoral Horn AntennaThe aperture electric field distribution
See (7-129) for the resulting Directivity
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Figure 7-16: universal E-plane and H-plane pattern with factor omitted, and
Figure 7-17: Universal directivity curves.
Optimum directivity occurs at and
From figure 7.13,
Pyramidal Horn Antenna
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The aperture electric field distribution
Optimum gain
Design procedure:1. Specify gain , wavelength , waveguide
dimension , .2. Using , determine from the following
equation
3. Determine from
4. Determine , by ,
5. Determine , by ,
6. Determine , by ,
7. Verify if and , by
,
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Reflector Antennas
Parabolic Reflector
Parabolic equation:
or
Properties1. Focal point at . All rays leaving , will be
parallel after reflection from the parabolic surface.2. All path lengths from the focal point to any
aperture plane are equal.3. To determine the radiation pattern, find the field
distribution at the aperture plane using GO.
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Geometrical Optics (GO)
Requirements1. The radius curvature of the reflector is large
compared to a wavelength, allowing planarapproximation.
2. The radius curvature of the incoming wave fromthe feed is large, allowing planar approximation.
3. The reflector is a perfect conductor, thus the reflectcoefficient .
Parabolic reflector:Wideband.Lower limit determine by the size of the reflector.
Should be several wavelengths for GO to hold.Higher limit determine by the surface roughness of
the reflector. Should much smaller than a wavelength.Also limited by the bandwidth of the feed.
Determining the power density distribution at theaperture by
where ,
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PO/surface current method
PO and GO both yield good patterns in main beam andfirst few sidelobes. Deteriorate due to diffraction bythe edge of the reflector. PO is better than GO for offsetreflectors.
Axis-symmetric Parabolic Reflector Antenna
For a linear polarized feed along x-axis, the pattern canbe approximate by the two principle plan patterns asbelow.
where , are E-plane and H-plane patterns.
If the pattern is rotationally symmetric, then . Wehave
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Also, the cross-polarization of the aperture field ismaximum in the .
For a short dipole, , ,
At , only x component exists.
F/D increases, cross-polarization decreases.
Since the range of decreases as F/D increases, theterm .
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Approximation formula
Normalized aperture field
Thus,
whereEI=edge illumination (dB) =20 log CET=edge taper (dB)=-EIFT=feed taper (at aperture edge) (dB)=Spherical spreading loss at the aperture edge
Example 7-8,1. Estimate EI by the radiation pattern of the feed at
the edge angle of the reflector.2. Calculate due to the distance from the feed to
the edge.3. Estimate ET at the aperture by adding the EI and
. 4. Look up Table 7-1b for n=2.
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Offset Parabolic Reflectors
Reduce blocking loss.Increase cross-polarization.
Dual Reflector Antenna
Spill over energy directed to the sky.Compact.Simplify feeding structure.Allow more design freedom. Dual shaping.
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Other types
Design example1. Determine the reflector diameter by half-power
beam width. For -11 dB edge illumination,
2. Choose F/D. Usually between 0.3 to 1.0.3. Determine the required feed pattern using
model.
Example 7-9