Antenna Design, Parabolic Reflector

I. Theory

1. Optics-based Antennas

- Reflector antennas

- Lens antennas

Figure: Optical antennas. Left = lens antenna, right = parabolic reflector antenna. From C. A. Fernandes et al. in Handbook of Antenna Technologies, Z. N. Chen et al. Ed. Springer, 2016

- Various types of reflector antennas

Figure: Reflector antennas in various forms. After P. Hazdra.

2. Parabolic Reflector Antenna

- Theory of operation: conversion of a spherical wave into a planewave

- Ray path length independent of the ray angle

Figure: Geometry of a parabolic reflector. After P. Hazdra

- Various types of the reflector antenna

- Origin at the reflector apex

- F-A-A' path length = F-B-B' path length

- Origin at the focal point

- Space taper

- Feed-oriented geometrical equations

3. Parabolic Reflector Antenna Design Procedures

- Maximum efficiecny condition

Figure: Feed illumination loss and spillover loss. After P. Wade

Figure: Optimum edge taper in the reflector illumination. From P. Hazdra

- Feed taper due to spherical wave spreading

Figure: Spherical wave spreading loss

- Gain speficied

- Calculate the reflector diameter assuming 50% efficiency (when realized).

- Design a feed and find its 10-dB half-beamwidth .

- Design a parabolic reflector.

z: axial distance from the apex

x: radial distance from the apex

- Simulate the reflector illuminated by the feed.

Full-wave simulation

Full-wave symmetrical simmulation: 1/2, 1/4 of the structure applying the field symmetry

Simulation using the far field of the feed

- Analyze the reflector performance.

Figure: 3D gain patterns of a 15-wavelength parabolic reflector. After P. Hazdra

Figure: Cartesian gain patterns of a 15-wavelength refelctor antenna. After P. Hazdra

4. Feed Design

- Sidelobe level of a circular aperture

Uniform circular aperture:

: direcitivity

a : aperture radius

SLL = -17.6 dB : sidelobe level

Uniform rectangular apertuer:

SLL = -13.3 dB

- Tapered aperture

Figure: Performance of tapered circular apertuers. After W. L. Stutzman.

- Feed types

Horns for the Cassegrain reflector

Circular waveguides for the prime-focus parabolic reflector

- Feed performance

10-dB beamwidth

E- and H-plane pattern symmetry

Cross polarization level

Phase center

- Feed gain pattern in 3D

Figure: 3D gain pattern of a circular waveguide feed. From P. Hazdra

- Feed gain pattern in Cartesian

Figure: Cartesian gain pattern of a circular waveguide feed. From P. Hazdra

- Feed phase pattern

Figure: Phase pattern of a circular waveguide feed. From O. Garcia-Perez.

- Cicular waveguide feed

Good E- and H-plane pattern symmetry when the waveguide diameter is 0.65 wavelength.

Backlobe supperssion: Use a quarter-wave choke around the aperture

E-plane slits (two of them): To improve the pattern symmetry

5. Reflector Antenna Analysis

5.1 Radiation pattern calculation

1) 1D aperture integration

- Axi-symmetric case:

: reflector's pattern angle

: feed's pattern angle

- Calculation of Bessel function J₀(x):

Single-precision Fortran

Modification of Abramowitz & Stegun for 0.001 accuracy

2) 2D aperture integration

3) Feed blockage modeling

4) High-frequency methods

- PO

- Ray methods: GTD, PTD, UTD

- Effects of the aperture blockage

Efficiency decrease due physical blockage: simple formula available

Sidelobe increase: simple formula available

Feed diffraction/scattering efficiency loss: graph available

- Main reflector rim diffraction

Backlobe increase at 180°: main reflector rim diffractions add in phase.

Reduction of rim diffraction:

Rim edge: rolled, castellated, serrated

5.2 Efficiency calculation

- Maximum directivity

: maximum possible directivity

A_p : antenna aperture's physical area

- Realized directivity

: antenna aperture efficiency

: feed blockage efficiency

: feed diffraction efficiency

: feed amplitude taper efficiency

: feed phase efficiency

: feed spill-over efficiency

: feed cross-polarization efficiency

: implementation efficiecy. Main reflector surface error, feed dielectric loss, feede reflection loss

- Feed mismatch or reflection efficiency

- Feed lockage efficiency:

- Amplitude taper efficiency:

- Phase error efficiency:

- Spill-over efficiency:

- Cross-polarization efficiency:

- Efficiency in dB

Efficiency	Decibel (dB)
1.0	0
0.9	– 0.46
0.8	– 0.97
0.7	– 1.55
0.6	– 2.22
0.5	– 3.01
0.4	– 3.98
0.3	– 5.23

5.3 Accurate analysis of reflector antennas

- High-frequency methods-based commercial software package

Grasp

ICARA

- Full-wave analysis package

CST Studio

HFSS

FEKO

- Literature

1) Milligan: p. 65

20-lambda parabolic reflector with -12dB taper illumination

Sidelobe around 100°: due to feed spillover

PO: accurate up to 120 degrees off axis

PTD: accurate up to 180 degrees off axis

2) Yurduseven(11-ieee):

ARM (analytical regularization method): 2-D problem, E-polarized wave diffraction by arbitrary shaped, smooth and PEC cylindrical obstacles

3) Oguzer(95-ieee)

a: main reflector radius

b: feed radius

5.4 Front-to-back ratio estimation

Milligan, p. 399

G : antenna gain

T : feed taper ( > 0)

G_f : feed gain

6. Reflector Antenna Product Specs.

ETSI Class 2/3

Dia 0.6m

Pol single

Freq: 7.75-8.5GHz

Gain: 30.4-31.6dB

Beamwidth: 4.5°/4.5°

X-pol: 30dB

F/B: 54dB

VSWR: -16dB (1.37:1)

7. Reflector Antenna Examples

Figure: A 26-m prime-focus parabolic reflector antnena and a 12-m AuScope VLBI antenna at the Mount Pleasant Radio Observatory (Australia). From Wikipedia

Figure: High-performance backfire feed. From Garcia-Perez.

Figure: Left = General Dynamics uPak C060QDA 60-cm reflector antenna for SATCOM on the move (SOTM) operating at Ka, Ku, and X bands. Right = Skytech 30-cm ADE reflector for SOTM (Rx 10.7-12.75 GHz, Tx 13.75-14.5 GHz)

Figure: Gain patterns of a 10.3-λ backfire fed parabolic reflector antenna. From Kildal, IEEE T-AP, 45(7), 1997

References

[1] T. A. Milligan, Modern Antenna Design, 2nd Edition, IEEE-Wiley, 2005.

[2] W. L. Stutzman and G. A. Theiele, Antenna Theory and Design, 3rd Edition, Wiley, 2013