Antennas 97 Aperture Antennas - ntut.edu.twjuiching/antenna4.pdfAxis-symmetric Parabolic Reflector...
Transcript of Antennas 97 Aperture Antennas - ntut.edu.twjuiching/antenna4.pdfAxis-symmetric Parabolic Reflector...
Antennas 97
Aperture Antennas
Reflectors, horns.High GainNearly real input impedance
Huygens’ Principle
Each point of a wave front is a secondary source of spherical waves.
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Equivalence Principle
Uniqueness Theorem: a solution satisfying Maxwell’s Equations andthe boundary conditions is unique.
1. Original Problem (a): 2. Equivalent Problem (b): outside , inside ,
on , where
3. Equivalent Problem (c): outside , zero fields inside , on , where
To further simplify,Case 1: PEC. No contribution from .
Case 2: PMC. No contribution from .
Infinite Planar Surface
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To calculate the fields, first find the vector potential due to theequivalent electric and magnetic currents.
In the far field, from Eqs. (1-105),
Since in the far field, the fields can be approximate by spherical TEMwaves,
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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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The Uniform Rectangular Aperture
Let the electric field be
Then,
where
Therefore,
At principle planes
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For large aperture ( ), the main beam is narrow, the factor is negligible. The half-power beam width
.
Also,
Example: a Uniform Rectangular Aperture
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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
where are the directivity of a line source due to respectively. the main beam direction relative to broadside.
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Directivity of an Open-Ended Rectangular Waveguide:
Gain and Efficiencies
where : aperture efficiency
: radiation efficiency. (~1 for aperture antennas)
: taper efficiency or utilization factor.
: spillover efficiency. is called : illumination efficiency.: achievement efficiency. : cross-polarization
efficiency. phase-error efficiency.
Beam efficiency
Simple Directivity Formulas in Terms of HP beam width
1. Low directivity, no sidelobe
2. Large electrical size
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3. High gain
Example 7-5: Pyramidal Horn Antenna (aperture efficiency=0.51)Measured gained at 40 GHz: 24.7 dB.A=5.54 cm, B=4.55 cm.
Example 7-6: Circular Parabolic Reflector AntennaTypical aperture efficiency: 55%.Diameter: 3.66 mFrequency: 11.7 GHzMeasured Gain: 50.4 dB.Measured .
1. Computed by aperture efficiency
2. Computed by half power beam width
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Rectangular Horn Antenna
High gain, wide band width, low VSWR
H-Plane Sectoral Horn Antenna
Evaluating phase error
thus the aperture electric field distribution
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where is defined in (7-108), (7-109)
Directivity
Figure 7-13: universal E-plane and H-plane pattern with
factor omitted, and (a measure of the maximum phase
error at the edge)
Figure 7-14: Universal directivity curves.
Optimum directivity occurs at and
From figure 7.13 for optimum case,
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E-Plane Sectoral Horn AntennaThe aperture electric field distribution
See (7-129) for the resulting Directivity
Figure 7-16: universal E-plane and H-plane pattern with
factor omitted, and (a measure of the maximum phase
error at the edge)
Figure 7-17: Universal directivity curves.
Optimum directivity occurs at and
From figure 7.13,
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Pyramidal Horn Antenna
The aperture electric field distribution
At optimum condition:
Optimum gain
For non optimum case,
Design procedure:1. Specify gain , wavelength , waveguide dimension , .
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2. Using , determine from the following equation
3. Determine from
4. Determine , by ,
5. Determine , by ,
6. Determine , by ,
7. Verify if and , by
,
Example 7-7: Design a X-band (8.2 to 12.4 GHz) standard horn fedby WR90 ( )waveguide.Goal: at 8.75 GHz.1. Solve for A: 2. Solve for the rest parameters:
3. Evaluating the gain by Fig. 7-14 and 7-17:
(exact phase error)
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Reflector AntennasParabolic 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.Geometrical Optics (GO)
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Requirements1. The radius curvature of the reflector is large compared to a
wavelength, allowing planar approximation.2. The radius curvature of the incoming wave from the feed is
large, allowing planar approximation.3. The reflector is a perfect conductor, thus the reflect coefficient
.
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 the aperture by
where ,
PO/surface current method
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PO and GO both yield good patterns in main beam and first fewsidelobes. Deteriorate due to diffraction by the edge of the reflector.PO is better than GO for offset reflectors.
Axis-symmetric Parabolic Reflector Antenna
For a linear polarized feed along x-axis, the pattern can beapproximate by the two principle plan patterns as below.
where , are E-plane and H-plane patterns.
If the pattern is rotationally symmetric, then . We have
Also, the cross-polarization of the aperture field is maximum in the. Leads to cross-polarization.
For a short dipole, , ,
At , only x component exists.
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Summary:1. F/D increases, cross-polarization decreases. -7809Since the
range of decreases as F/D increases, the term . 2. Fields inverted because of reflection from conductor.3. Cross-polarization cancels each other on principal plane in the
far field.
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Approximation formula
Normalized aperture field
Thus, (7-208)
whereEI=edge illumination (dB) =20 log CET=edge taper (dB)=-EIFT=feed taper (at aperture edge) (dB)=Spherical spreading loss at the aperture edge
Design procedure of axial symmetrical aperture field: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 7-1 for a suitable n.
Example 7-8: A 28-GHz Parabolic Reflector Antenna fed by circularcorrugated horn.
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Assume , then
Use Table 7.1b for n=2 and interpolate, we have
( measured)
( measured)
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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 the optimum -11 dB edge illumination,
(7-248)
2. Choose F/D. Usually between 0.3 to 1.0.3. Determine the required feed pattern using model.
(7-249)
Example 7-9: From 7-248
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Choose F/D=0.5, then .
From (7.249), find q to approximate the pattern by .
Verify EI=-11 dB, by (7-208).
Note: for feed pattern
Consideration of Gain due to taper and spillover:1. The more taper, the less loss due to spillover, but less taperefficiency .
2. The less taper, the more loss due to spillover, but higher taperefficiency .
3. Optimum efficiency for feed: EI= -11 dB.
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A General Approximate Feed Model for Broad Main Beam andPeak at
Assume
That is the feed pattern
For symmetrical feed,
The value of is chosen to match the real feed pattern at (usually
) by
Then,
For symmetrical feed, the illumination efficiency , the spill overefficiency , the feed gain and EI are computed by
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