1、 Recommendation ITU-R SA.1345-1(01/2010)Methods for predicting radiation patternsof large antennas used for space research and radio astronomySA SeriesSpace applications and meteorologyii Rec. ITU-R SA.1345-1 Foreword The role of the Radiocommunication Sector is to ensure the rational, equitable, ef
2、ficient and economical use of the radio-frequency spectrum by all radiocommunication services, including satellite services, and carry out studies without limit of frequency range on the basis of which Recommendations are adopted. The regulatory and policy functions of the Radiocommunication Sector
3、are performed by World and Regional Radiocommunication Conferences and Radiocommunication Assemblies supported by Study Groups. Policy on Intellectual Property Right (IPR) ITU-R policy on IPR is described in the Common Patent Policy for ITU-T/ITU-R/ISO/IEC referenced in Annex 1 of Resolution ITU-R 1
4、. Forms to be used for the submission of patent statements and licensing declarations by patent holders are available from http:/www.itu.int/ITU-R/go/patents/en where the Guidelines for Implementation of the Common Patent Policy for ITU-T/ITU-R/ISO/IEC and the ITU-R patent information database can a
5、lso be found. Series of ITU-R Recommendations (Also available online at http:/www.itu.int/publ/R-REC/en) Series Title BO Satellite delivery BR Recording for production, archival and play-out; film for television BS Broadcasting service (sound) BT Broadcasting service (television) F Fixed service M M
6、obile, radiodetermination, amateur and related satellite services P Radiowave propagation RA Radio astronomy RS Remote sensing systems S Fixed-satellite service SA Space applications and meteorology SF Frequency sharing and coordination between fixed-satellite and fixed service systems SM Spectrum m
7、anagement SNG Satellite news gathering TF Time signals and frequency standards emissions V Vocabulary and related subjects Note: This ITU-R Recommendation was approved in English under the procedure detailed in Resolution ITU-R 1. Electronic Publication Geneva, 2010 ITU 2010 All rights reserved. No
8、part of this publication may be reproduced, by any means whatsoever, without written permission of ITU. Rec. ITU-R SA.1345-1 1RECOMMENDATION ITU-R SA.1345-1 Methods for predicting radiation patterns of large antennas used for space research and radio astronomy (1998-2010) Scope This Recommendation d
9、escribes methods to be used in predicting the radiation patterns of large antennas used for space research and radio astronomy taking into consideration the reflector surface distortion effects in modelling the antenna radiation pattern. The ITU Radiocommunication Assembly, considering a) that in ma
10、ny cases reflector antennas used by space research and radio astronomy are similar in that they are of large diameter and operate at frequencies up to tens of GHz; b) that because of the large distances required to achieve conventional far-field conditions (2D2/), standard antenna test range or anec
11、hoic chamber measurements are inappropriate, however the predictions of radiation patterns for very large antennas can in some instances be validated by calibrated measurements; c) that many potential sources of terrestrial based interference to the two services will be in the near-field of the ante
12、nna; d) that accurate models and associated software are becoming available for the prediction of antenna radiation patterns in both the near-field and the far-field, and also for situations which involve interaction with additional reflectors or undesirable obstacles, recommends 1 that where a choi
13、ce of the most appropriate modelling technique is required for predicting the gain pattern of large reflector antennas, the methods described in Annex 1 and tabulated below should be used: Recommended analysis techniques Sector I Forward axial sector Physical optics Sector II Far sidelobes Geometric
14、al theory of diffraction/ uniform theory of diffraction and induced field ratio Sector III Backlobes Geometrical theory of diffraction/uniform theory of diffraction FIGURE 1 Sectors for reflector analysis 1345-01Feed or subreflectorSectorIIIIII IIIIVReflectorIISector IV Rear axial sector Equivalent
15、edge currents Rec. ITU-R SA.1345-1 2 2 that with respect to modelling techniques involving measurement, the description of the methods in Annex 2 should be used as a guide in selecting the most appropriate method; 3 that in determination of the significance of the mechanical characteristics of the a
16、ntenna to be modelled, the following factors should be taken into account: a) scattering by the feed support struts in determining the sidelobe levels; b) spill-over of the radiation direct from the feed; and c) surface distortions. Annex 1 Suitability of various electromagnetic modelling methods to
17、 predict the gain and radiation patterns of large antennas 1 Introduction There are a large number of techniques available for solving electromagnetic problems. Each technique may have advantages for modelling particular problems but may be impracticable for other problems. This annex considers the
18、techniques used for the modelling of reflector antennas and considers their suitability for analysis of the large reflector antennas typically used for space research and radio astronomy. 2 Analytical and numerical methods 2.1 Method of moments The method of moments is a mathematical technique for s
19、olving inhomogeneous linear equations of the type: Lf = g (1) where L is usually a linear integro-differential operator, and the functions f and g are elements of Hilbert spaces. In this equation, g is known and the idea is to invert L to obtain the unknown function f = L1g. The procedure involves a
20、 technique that transforms the operator equation (1) to a system of linear algebraic equations. To this end, the unknown function f is expanded in a series of basis functions fn with unknown constant coefficients Cn. Substituting this back into equation (1), and taking the inner product of both side
21、s with a set of known testing functions wm reduces equation (1) to a simple matrix equation of the form: Ax = b (2) where A and b are given by the inner products Amn= wm, Lfn, bm= wm, g, and x is the vector of unknown coefficients Cn. Equation (2) is easily solved for x using elementary numerical me
22、thods which then yields f. Rec. ITU-R SA.1345-1 3In order to apply this technique to reflector analysis, it is necessary to formulate the problem in the form of equation (1). This is accomplished by expressing the field scattered by the antenna as an integral of the unknown surface currents on the r
23、eflecting surface. Invoking the electromagnetic boundary condition that the tangential component of the total electric field be zero on a perfect conductor yields an equation for the unknown surface current density JSin the form of equation (1): ( )iSEuIJu =+nnjSGkS02d(3a) which is a Fredholm integr
24、al equation of the first kind. Here: un: unit normal to the surface I: unit dyadic given by zzyyxxuuuuuuI +=G : free space scalar Greens function, given by: rreGrrjk=4with r and r distances for the source and observation points respectively Ei: incident electric field k = 2/0: free space wave number
25、. Equation (3a) can be solved by dividing the surface into small patches over each of which JSis expanded as a sum of current components along two orthogonal directions. Alternatively, the reflector may be modelled in the form of a wire grid. This has the advantage that the scattered field can then
26、be expressed as a one dimensional integral of current flowing along the wire. For the case of a thin wire segment along the z-direction defined by the unit vector uz, the appropriate equation of the form (1) can be given by: () ()()( )izzzGzIkzIj Euu =+ d/120(3b) where the prime denotes the derivati
27、ve. Equation (3b) is solved for the unknown current distribution by expanding it in a suitable set of basis functions. In principle, this is the most accurate of all known methods used in electromagnetic scattering analysis. The formulation of the governing equation is exact, and extremely accurate
28、solutions can be obtained by a suitable choice of basis and testing functions. In addition, struts, feed, subreflector and supporting structures can all be integrated into the problem. Well-defined surface irregularities on the reflector can be similarly modelled. The technique essentially fragments
29、 the complete structure into tiny linear or planar segments, on each of which a boundary condition directly derived from Maxwells equations is applied by brute force. This results in a coupled system of equations in which electromagnetic interaction of every segment with every other segment is autom
30、atically accounted for. The method is, therefore, capable of predicting the complete antenna pattern at all points in space, taking into account the effect of antenna support and related sub-systems. Herein lies the difficulty: assuming a wire grid solution, if the reflector is modelled with M wire
31、segments, and the current in each is represented by N basis functions, this would, in general, lead to a system of MN linear equations in as many unknowns, requiring the numerical evaluation of (MN)2integrals to obtain the elements of the coefficient matrix. Typically, 10 to 20 segments per waveleng
32、th with 3 basis functions per segment are needed for an accurate representation of the currents, leading to a system with over 650 unknowns per square wavelength of the reflecting surface. Rec. ITU-R SA.1345-1 4 In practice, however, some simplifications can be effected. In the case of focus-fed axi
33、-symmetric reflectors, circular symmetry can be exploited to significantly reduce the number of unknown coefficients. In addition, Kirchoffs current law can be invoked at wire junctions to relate some of the unknown constants. In numerical electromagnetics code (NEC), a well-known commercially avail
34、able suite of moment method software that uses equation (3b), the current I(z) in each segment is represented as the sum of three terms a constant, a sine and a cosine. Of the three coefficients, two are eliminated by the conditions that charge and current be continuous at wire junctions leaving onl
35、y one constant, which determines the current amplitude, to be determined by matrix methods. For this representation to be adequate, the length of each wire segment needs to be less than /10, producing over 220 segments per square wavelength of the reflecting surface. For a 100 diameter reflector, in
36、 the absence of symmetry, this method would require determination of about 1.8 million elements in the coefficient matrix A, followed by the inversion of a 1 340 1 340 complex matrix. If the sub-systems and support structures are also modelled, it would result in a significantly larger system of equ
37、ations. Apart from CPU time, computer memory resources also increase rapidly with reflector size. The method is, therefore, computationally intensive, and is not a viable technique for electrically large reflectors. Typical maximum size for which the method of moments can be successfully applied is
38、10. If circular symmetry is exploited, reflectors as large as 25 may be analysed. These limits are continuously extended with powerful computer machines becoming available but it is doubtful whether they can be applied to large reflector antennas, at least in the near future. 2.2 Aperture field meth
39、od The aperture field method is based on a theorem which states that if S is a closed surface enclosing a finite collection of sources , then the field due to at any arbitrary point exterior to S can be expressed in terms of integrals of field vectors Eaand Haover S, where the subscript a refers to
40、the tangential component. Thus, if S is chosen to be a sphere enclosing the antenna, then a spherical near-field scanning set-up can be used to measure the magnitude and phase of Eaand Haover S, and from this the field of the antenna at every point in space outside S can be computed. However, measur
41、ing the near-field over a complete spherical surface surrounding a large reflector is very difficult, if not impossible, to carry out in practice. An alternative is to determine the fields over S by analytical techniques, but with complex sub-systems this is often an intractable problem and various
42、approximations need to be invoked. One such approximation, called the aperture field method (see Fig. 2a), is based on the assumption that Eaand Haare non-zero over only a finite sector of S. This is justified in the case of a large class of focus-fed convex reflectors where there exists a finite cl
43、osed contour which circumscribes the family of all specularly reflected rays from the illuminated side of the reflector. The projection along the reflected ray paths on S defines a sector A S, bounded by , over which Eaand Haare computed using the laws of geometrical optics, with Ea= 0 and Ha= 0 ove
44、r S A. This prescription specifies a sharp discontinuity along which is inconsistent with Maxwells equations. To overcome this difficulty, electric and magnetic charge densities are postulated along in accordance with the equation of continuity. With this, the field scattered by the reflector is giv
45、en by the expression: ()()() ()SGjjanananAsd1+=EuHuHuE (4) Rec. ITU-R SA.1345-1 5where: un: outward unit normal to A G : free-space scalar Greens function. Equation (4) forms the fundamental result of the aperture field method, and applies equally to both near- and far-fields exterior to S. In the f
46、ar-field sector of the antenna, some simplifications can be effected in equation (4) which significantly eases its computational complexity. Its main drawback, however, is the discontinuity postulated along which is then overcome by a purely artificial construct. Apart from making the formula consis
47、tent with Maxwells equations, the addition of electric and magnetic charge densities along does not make it any more accurate. In actual usage, however, equation (4) is often reduced to a scalar integral by a suitable choice of S, as discussed in 2.3. It is in this form that the method is better kno
48、wn. FIGURE 2 The aperture field method 2.3 Scalar radiation integral/projected aperture method The projected aperture method (see Fig. 2b), is essentially a simplification of the aperture field method discussed in the previous section. The surface S is taken to be made up of an infinite plane P (cho
49、sen on the radiating side of the reflector) closed at infinity by an infinite hemisphere on the source side, thereby enclosing the antenna. The field over the hemispherical sector vanishes (in view of the radiation condition) and the right hand side of equation (4) reduces to a surface integral over P. With some mathematical manipulation this can be transformed into a scalar radiation integral: SnGFnFGEPsd= (5) Rec. ITU-R SA.1345-1 6 where F stands for any Cartesian component of
