Small Offset Parabolic Reflector Antenna Design and Analysis Wojciech J. Krzysztofik # #
Wroclaw University of Technology, Faculty of Electronics Engineering, Institute of Telecommunications, Teleinformatics & Acoustics, Wybrzeze Wyspianskiego 27, 50-370 Wroclaw, Poland,
[email protected]
Abstract— Complete radiation pattern of a focus-fed offset parabolic reflector antenna is presented. Forward radiation and wide-angle radiation is calculated using the geometrical theory of diffraction. Effects of the offset angle and the feed pattern asymmetry on the cross-polar isolation are presented. Design criteria of an offset reflector satisfying the WARC-DBS requirements for receiving antenna, and for a given feed radiation pattern are presented. It is also shown how to determine the
across the aperture of the antenna for a given reflector feed configuration. Then a procedure for computing the antenna far-field patterns from the aperture distribution is required.
antenna noise temperature experimentally, using direct satellite signal. I. INTRODUCTION The performance of the front-fed parabolic arrangement is impaired by the unavoidable blocking of the aperture by feed and supporting structures. However, by using an offset parabolic (not including the apex) the feed can be kept clear of the reflected beam, since it do not block the aperture. Another its important advantages over its symmetric counterpart are mainly the scanning capability and the reduction of interaction between the primary feed and the reflector. These advantages are paid by the higher level of cross-polar radiation for linear polarization and the beam shift for circular polarization [1, 2, 3]. Increasing interest in the use of the reflector antennas for Direct Broadcast Satellite (DBS) ground station (home) reception, has emphasized the need to study closely its microwave and geometrical (mechanical) properties.
Fig. 1. Geometry of an offset parabolic reflector
The far-field radiation arising from a known tangential electric field distribution in an infinite plane can be determined exactly. In dealing with the offset reflector, the infinite surface is chosen as the x´ y plane and the electric fields outside of the projected aperture region are assumed negligible. An electromagnetic field distribution is introduced around the boundary of the projected aperture to satisfy the continuity criterion, and thus the predicted radiation fields satisfy the radiation condiII. BASIC EQUATIONS FOR COMPUTING ANTENNA PATTERN tions in the forward hemisphere. The neglect of the electric One of the important problem is the knowledge of the rela- fields outside of the projected-aperture region is acceptable tionship between the reflector shape, the field distribution of providing that the dimensions of the aperture are large relative the primary feed, and the antenna radiation pattern. to the electrical wavelength (d/λ>10). The tangential electric field distribution within the proConsider an offset parabolic reflector excited at its focus whose geometry configuration is shown in Figure 1. The ba- jected-aperture region is determined by use of the physical sic parameters of reflector are shown as the focal length (F) of optics approximation. the parent parabolic, the offset angle (γo), the half of the angle That is, the electric field E r reflected from the offset re( θ ∗ ) subtended by the reflector as viewed from the focal point, flector is obtained from (1) an aperture diameter d (diameter of the projected circular E r = 2(1n ⋅ E i ) ⋅ 1n − E i aperture of the main reflector), the ratio (F/D) of focal length where E i is the incident electric field (is taken as the primaryto diameter of parent (symmetrical) reflector (so called shape coefficient of the reflector). The physical contour of the re- feed radiation) at the reflector, and 1n is the surface unit norflector is elliptical but its projection into the x´ y plane pro- mal. When the phase centre of primary-feed is located in the duces a true circle. general vicinity of the reflector geometric focus, the incident To calculate the radiation patterns of reflector antennas we fields at the reflector can be expressed in the form, need analytical expressions for the feed pattern and the fields
E i = ( Aθ ⋅ 1θ + Aφ ⋅ 1φ ) exp[ jk ( R1 − ρ )] / ρ
(2)
where Aθ, Aφ are the primary-feed principal plane radiation patterns; R1 is a phase-compensation term that accounts for small offset in the primary-feed location, and ρ = 2 F /(1 + cosθ cosθ 0 − sin θ sin θ 0 cosφ ) is the distance between a point on reflector surface and the reflector geometric focus. The physical-optics aperture-field method was selected in preference to the surface-current method since it leads to the more simple mathematical expressions, and offers a significant reduction in the required computational effort [2]. For an incident field polarized in the y-direction, reference polarization (called co-polar) E co and orthogonal polarization (cross-polar) E cr are defined, respectively, by
E co = E Ψ sin Φ ⋅ 1Ψ + EΦ cos Φ ⋅ 1Φ
(3)
E cr = E Ψ cos Φ ⋅ 1Ψ − EΦ sin Φ ⋅ 1Φ and total E-field is given as E = E co + E cr
(4) (5)
The model employs a conventional spherical co-ordinate system (R, Ψ, Φ) with origin at the centre of the reflector projected-aperture (Fig. 1), and makes use of spatial Fourier transform formulation for the radiation from an infinite surface. The normalized radiation patterns of the offset antenna may be expressed directly in terms of a linear co-polar field component Eco and a cross-polar component Ecr in the matrix form as [1] t 2 sin 2Φ ⎤ ⎡ Fco ( Ψ, Φ )⎤ ⎡ Eco ⎤ 1 + cos 2Ψ ⎡1 − t 2 cos 2Φ ⎥⎢ ⎥ ⎢ E ⎥ = 2 F (0,0) ⎢ 2 1 + t 2 cos 2Φ ⎦ ⎣ Fcr (Ψ, Φ ) ⎦ co ⎣ cr ⎦ ⎣ t sin 2Φ (6)
where t = tan Ψ/2, and the functions Fco, Fcr are the spatial Fourier transforms of the co-polar and cross-polar components of the tangential electric field in the projected aperture plane. The Fourier transforms are the transverse components of the vector
Fi ( Ψ, Φ ) =
2πθ *
∫ ∫ ε exp[− jkRsi nΨ ]ρ i
2
si nθ dθ dφ
(7)
0 0
where R = ρ [(sin θ cos θ 0 cos φ + sin θ 0 cos θ ) cos Φ − sin θ sin Φ sin φ ] is the distance from general point in the projected-aperture plane to a far-field point, and the tangential electric field components εi distributed in the projected-aperture are expressed directly trough the radiation characteristics of the primaryfeed (Aθ, Aφ) by the matrix expression as
⎡ε co ⎤ ⎡a − b⎤ ⎡ Aθ ⎤ , ⎢ε ⎥ = K ⎢ b a ⎥ ⎢ A ⎥ ⎣ ⎦⎣ φ ⎦ ⎣ cr ⎦ where K = − exp[ jk ( R1 − 2 F )] / 2 F
(8)
;
a = (cos θ 0 + cos θ ) sin φ
;
; b = sin θ sin θ 0 − cos φ (1 + cosθ cosθ 0 ) R1 ≈ Δ t sin θ cos(φ − φ0 ) + Δ z cosθ ; Δ t , Δ z are the small transverse and axial offsets in the primary-feed location, respectively; φ0 is the angle (measured to the x axis in the xy plane) denotes the plane of the offset. To predict the overall antenna radiation pattern it is necessary to specify the primary-feed directivity characteristics ( AΘ , AΦ ) and to compute the two-dimensional integrals of the Fourier transforms Fi ( Ψ, Φ ) . The feed is the element that connects the source and/or receiver of electromagnetic radiation by way of a transmission line, such as waveguide, to the antenna. Number of antennas for illuminating reflectors, e.g. pyramidal horn and conical horn antennas (smooth-walled and corrugated), slots, dipoles, etc. are used. More typically, aperture antennas are fed by conical corrugated horn radiators. Horn patterns can often be approximated by Gauss error functions or by the cos N (θ ) function (Fig. 2). H-plane 10.95 GHz + 11.85 GHz ◊ 12.4 GHz Δ cos8θ
Fig. 2. Example of measured and approximated patterns of primary fed
So that, for a horn pattern linearly polarized in the ydirection , we can write
g (θ ) ≈ A cos N (θ )(sin φ ⋅ 1θ + cos φ ⋅ 1φ ) ⋅ exp( −ikρ ) / ρ =
(9) = ( Aθ ⋅ 1θ + Aφ ⋅ 1φ ) ⋅ exp( −ikρ ) / ρ where N is a constant (ranging from one to perhaps 500) and the co s N (θ ) pattern is assumed to be zero for θ > θ*. The horn pattern is assumed to be a function of θ only, independent of φ, and the polarization that of a Huygens source. The primary parameters that the designer can control are • the degree of offset (through γ0), • the aiming of the feed antenna (i.e., the angle θ0), and • field taper on reflector edge (feed radiation pattern).
potential degradation of service and co-channel/satellite interference [8]. We will discuss procedure of the gain to noise ratio (G/T) (figure of merit) obtained by making use of prevailing television carriers [6], [7]. Generally a G/T characterisation is a C/N measurement via a calibrated filter having a known noise equivalent bandwidth. This filter can be that of spectrum anaThe feed radiation pattern is assumed with a -10 dB lyser if the carrier used is pure or has little modulation, or a beamwidth of ±θ*, this led to a feed taper (edge illuminations) TV filter, if a TV carrier is used. It is the latter method that we of -10 dB (exactly: -10.1 dB and -14.6 dB on horizontal and shall describe here as this has been used to characterise the vertical reflector edges, respectively). This was for the case of above-mentioned antenna. The configuration of the measured set up contains AUT (Antenna Under Test), LNB ( Low Noise d = 0.55 m; F/D = 0.326; γ0 = 420; θ*= 720, and the feedBlock) with down converter, and spectrum analyser (Tekpattern maximum pointed to bisect the angle subtended by the tronix -TEK 2710 ). reflector. The main advantage of this method is that space segment is always available in the form of TV carriers (Fig. 3), entailing III. NUMERICAL AND EXPERIMENTAL RESULTS routine G/T measurements throughout the operational life of Results of numerical calculations, together with experi- the antenna. ments, and ITU-R-standards for the radiation patterns are ploted in Fig.3. We investigated the influence of the above parameters on cross polarisation, gain, and sidelobe level, using the geometrical diffraction based on presented theory, and adopted in computer code OFFREFAN. Scattering from support structures was not modelled, but for an offset configuration, these are typically negligible.
ITU-R
ITU-R
a)
a)
ITU-R
b) Fig. 3. Computed and measured far-field radiation co-polar pattern in E- and H-plane (a) and cross-polar pattern in E-plane (Φ=90o) (b) of the offsetparabolic reflector antenna of diameter d = 0.55 m
Comparison of theoretical end experimental ([4], [5]) data shows a favourable agreement. In both polarisations antenna satisfies requirements of ITU-R WARC-DBS (Geneva 1977). IV. G/T MEASUREMENT The need to verify RF performance of an Earth Station antenna for satellite telecommunications prior to commencement of operational activities is paramount in order to secure any
b) Fig. 4. Spectra of TV-signals from satellites ASTRA 1A(a), and EUTELSATII (b), received in Wroclaw (Poland) using the offset parabolic reflector antenna model OG-66
The procedure would thus be that the AUT measures the TV carrier level with the antenna pointed to the satellite. The power level, says Ps, is recorded. Next the antenna is depointed to clear sky and a new power meter readings (Pcs) is noted. The satellite EIRP is assessed by the co-operating station and the G/T value is obtained as follows:
G / T = ( Ps − Pcs ) − EIRP + Lbf + Lat + Lrsd + BNeq − k (10)
where: (Ps-Pcs) [dBm] is the power meter readings ; Lbf, Lat, Lrad are the free space , atmospheric, and radiometer losses, respectively; BNeq is an equivalent noise bandwidth; and k [dBW/kHz] is the Boltzmann´s constant. Antenna noise temperature TA have been estimated theoretically and verified experimentally by means of direct satellite signal measurements. We have made use of the existing TV carriers within the ASTRA and EUTELSAT II space segments (Fig. 4) to assess the G/T figure of an offset parabolic reflector antenna and compared this to traditional methods. In Table 1, the measured geometrical, and electrical parameters of WISI Model OG 66 parabolic reflector antenna, are presented.
where: D is the antenna directive gain, ηr ,η p ,η f − ph ,ηra − ph ,η sa − ph ,η f ,ηc are, respectively, all losses due to: radiation, polarization, phase of primary fed characteristic, random and systematic phase errors in the antenna aperture field distribution, feeding line between primary fed and down-converter, and the coating surface protecting the reflector. The estimated numbers of different losses of designed antenna are shown in Table 2. TABLE 2. ANTENNA LOSSES, GAIN, AND HPBW Parameter ηr ,dB ηp ,dB ηra-ph ,dB ηsa-ph ,dB ηc ,dB ηtotal ,dB Efficiency D, dB G, dB HPBW, deg
TABLE 1. ANTENNA GEOMETRICAL AND ELECTRICAL PARAMETERS Parameter Diameter, d [m] Ellipse Main Axis [m] Focal Length, F [m] Aperture Angle, θ* [deg] Offset Angle, γ0 [deg]
Producer Data 0.55 -
Measured 0.55 0.60 0.589 72.36 42.37
G [dBi] Effeciency HPBW [deg] FSLL [dB] G/T [dB]
35 13
34.1 0.71 3.3 -23 14.4
In Fig. 5, the calculated radiation patterns of an offset parabolic antenna OG-66 are presented. E/E
max
[dB] 20 co-polar
0
cros-polar -20
Frequency, GHz 10.95 11.3 11.7 -0.96 -0.89 -0.92 -0.11 -0.11 -0.11 -0.1 -0.1 -0.1 -0.18 -0.2 -0.24 -0.15 -0.15 -0.15 -1.5 -1.45 -1.52 0.708 0.716 0.705 36.27 35.55 35.85 34.77 34.10 34.33 3.08 3.34 3.25
VI. CONCLUSIONS It is verified numerically that aperture field integration can predict radiation fields of offset parabolic reflectors that are close to the measured results, if the aperture integration surface is chosen to cap the reflector. We conclude that as long as the necessary precautions evoked above are achieved, good qualitative results of G/T measurements can be obtained. The accuracy associated with this type of measurement is +/-0.6 dB. Taking into account the losses in the antenna structure, the antenna gain was estimated with good accuracy with respect to measurements.
-40
REFERENCES -60
[1]
-80
-100 -12
-10
-8
-6
-4
-2
0
2
4
6
8
10
12
Ψ [deg]
[3]
Fig. 5. Calculated radiation pattern of OG-66 antenna
V. ANTENNA GAIN – LOSSES BILANS An offset parabolic reflector illuminated axially-symmetric, always produces an orthogonal radiated field component. It means if part of power radiated by primary fed is useless. The phase errors in the aperture field are due to: imprecise pattern of primary-fed, the reflector surface and shape tolerance, shifting of primary-fed phase centre with respect to reflector focus, etc. The real an offset parabolic reflector antenna can be characterized with an equivalent power gain as follows:
G = D η rη p η
f − ph
η ra − ph η sa − ph η f η c
[2]
(11)
[4] [5] [6]
[7] [8]
[9]
A.W. Rudge, “Multiple-Beam Antennas: Offset Reflectors with Offset Feeds”, IEEE Transactions on Antennas & Propagation, vol.AP-23, pp. 317-22, May 1975 H. Matsuura, K. Hongo, “Comparison of Induced Current and Aperture Field Integration for an Offset Parabolic Reflector”, i.b.i.d, vol. AP-35, pp. 101-105, January 1987. W. Stutzman, M. Terada, “Design of Offset-Parabolic-Reflector Antennas for Low Cross-Pol and Low Sidelobes”, IEEE Antennas and Propagation Magazine, vol. 35, No. 6, pp. 46-49, December, 1993. A.W. Rudge, K. Milne, A.D. Olver, P. Knight, eds, The Handbook of Antenna Design, Peter Peregrinus Ltd., vol. 1, London, GB, 1982 A.W. Love, ed., Reflector Antenna, IEEE Press, New York, US,1978 B.J. Kasstan, An Ideal Test Range for Accurate Earth Station Antenna Measurements, Six International Conference on Antennas & Propagation, ICAP´ 89, Coventry, United Kingdom, Part 1: Antennas, 473-7, 1989 D.J. Bem, Satellite Radiocommunication, (in Polish), Communication & Telecommunication Publications, Warsaw, Poland, 1990 W.J. Krzysztofik, Z. Langowski, W. Papierniak, Design of an Offset Parabolic Reflector Antenna for Direct Reception of TV-Satellite, Scientific Report, Wroclaw University of Technology, Wroclaw, Poland,1992 ITU-R, “Final Acts of the World Administrative Conference for Planning of Broadcast Satellite Service in Frequency Band 11.7-12.5 GHz (in Region 1), and 11.7-12.2 GHz (in Regions 2 and 3), Geneve 1977
