1、 Report ITU-R S.2196(07/2010)Methodology on the modelling of earth station antenna gain in the region of the antenna main-lobe and the transition region between the minimum angle of the reference antenna pattern and the main-lobeS SeriesFixed satellite serviceii Rep. ITU-R S.2196 Foreword The role o
2、f the Radiocommunication Sector is to ensure the rational, equitable, efficient 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 adopte
3、d. The regulatory and policy functions of the Radiocommunication Sector 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 Po
4、licy for ITU-T/ITU-R/ISO/IEC referenced in Annex 1 of Resolution ITU-R 1. 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
5、 for ITU-T/ITU-R/ISO/IEC and the ITU-R patent information database can also be found. Series of ITU-R Reports (Also available online at http:/www.itu.int/publ/R-REP/en) Series Title BO Satellite delivery BR Recording for production, archival and play-out; film for television BS Broadcasting service
6、(sound) BT Broadcasting service (television) F Fixed service M Mobile, 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
7、 between fixed-satellite and fixed service systems SM Spectrum management Note: This ITU-R Report was approved in English by the Study Group under the procedure detailed in Resolution ITU-R 1. Electronic Publication Geneva, 2010 ITU 2010 All rights reserved. No part of this publication may be reprod
8、uced, by any means whatsoever, without written permission of ITU. Rep. ITU-R S.2196 1 REPORT ITU-R S.2196 Methodology on the modelling of earth station antenna gain in the region of the antenna main-lobe and the transition region between the minimum angle of the reference antenna pattern and the mai
9、n-lobe 1 Modelling of the antenna main-lobe The gain of an elliptical aperture antenna in the main-lobe for a specific angle of rotation with respect to the major axis depends on both the off-axis angle and the D/ ratio for the plane of interest1. The derivation which follows is the simplified case
10、that assumes the antenna major axis dimension of the antenna aperture is parallel to the GSO plane2. Models for calculating the D/ ratio for the plane of interest for other antenna shapes and for elliptical antennas which do not conform to this simplified case can also be developed. The model for th
11、e simplified case of an elliptical antenna is developed below: The dimensions of the antenna aperture in the GSO plane and the plane perpendicular to the GSO plane can be related to one another and to the equivalent diameter using the defined ratio K where: eqGSODKD = (1) KDDGSOGSO=(2) where: GSOD i
12、s the antenna dimension in the geostationary orbit plane; GSODis the antenna dimension in the plane perpendicular toGSOD;eqD is the equivalent circular diameter of the physical antenna; K is the ratio of the perpendicular dimensionsGSOD to GSODand the antenna boresight is normal to the plane contain
13、ing the dimensions GSOD and GSOD. For elliptical antenna pattern, the values of DGSOand DGSOcan be applied to an ellipse equation to calculate the antenna dimension D in the plane of interest. Figure 1 shows the relationship between D (represented by dotted line) and the ellipse in the plane of inte
14、rest given by the angle . 1The plane of interest is the plane passing through the antenna boresight and the direction of interest. 2The term “GSO plane”, which is used throughout shall be interpreted as the plane containing the tangent to the part of the GSO arc aligned with DGSO(see Figure 1) and t
15、he earth station. 2 Rep. ITU-R S.2196 FIGURE 1 and are the dimensions of major axis and minor axes respectively of the elliptical antenna. Replace the semi-major axis a and semi-minor axis b of the ellipse equation with 2GSODand2GSODrespectively, so that in rectangular coordinates: 1222222=+GSOGSODy
16、Dx(3) Assuming the major axis of the antenna is aligned with the geostationary orbit plane and represents the angle of rotation in a counter-clockwise direction about the main beam direction, the antenna “dimension” (of the antenna aperture in the plane parallel to the boresight axis, passing throug
17、h the direction of interest and the boresight axis) can be expressed as a function of the rotation angle . Therefore, x and y in (3) can be expressed as: = cosRx (4) = sinRy (5) where: D the dimension, in metres, of the antenna aperture in the plane of interest as shown in Figure 1; R the “radius” o
18、f the antenna aperture in the plane of interest (=D/2); the angle, in degrees, between the plane containing the boresight and the dimension DGSOand the plane of interest, where the plane of interest passes through the boresight and the direction of interest (see Figure 1). GSODGSODbDGSODGSOR aDRep.
19、ITU-R S.2196 3 Replacing x and y in (3) by (4) and (5), and R with D/2, the antenna dimension D in the plane of interest can be expressed as follows: +=222cossinGSOGSOGSODDDD(6) Substitute equation (2) into equation (6), it gives: +=222cos)1(sinKDDGSO(7) To simplify the notation, the denominator of
20、equation (7) is defined as rotation factor F, which is a function of the rotation angle and the DGSOto DGSOratio K. Therefore, FDDGSO= (8) where: +=222cos)1(sin),(KKF (9) For a given antenna, having a major-to-minor axis ratio K, the value of F can be expressed as a function of the rotation angle .
21、Therefore, in a plane of interest of a given antenna, having a major-to-minor axis ratio K, D is simply a function of . 2 Modelling the antenna main-lobe given a side-lobe reference pattern Modelling the transition region between the main-lobe of an antenna and the side-lobe envelope requires knowle
22、dge of the reference pattern depicting the antennas side-lobe envelope. The main-lobe of an antenna and the transition region between the main-lobe and the side-lobe envelope can be modelled for two types of side-lobe reference patterns. The methodologies in this Report may be used with either Recom
23、mendation ITU-R S.465-6 or Recommendation ITU-R S.1855. Although the intersection point in this model where the envelope of the side-lobe reference pattern intersects the antenna main lobe is equal to the main-lobe gain in equation (10), the actual gain in this vicinity may be considerably less. In
24、fact, the first null of a parabolic reflector type antenna occurs very near this intersection point. The actual location of the null will be determined by a number of factors including type of illumination. The antenna main lobe model in equation (10) assumes a uniform illumination resulting in a wi
25、der main lobe and thus results in a conservative estimate of gain at the intersection point. The very small transition region between this intersection point and the minimum angle applicable to the side-lobe reference pattern follows the applicable side-lobe reference pattern. 4 Rep. ITU-R S.2196 2.
26、1 Modelling the antenna main-lobe assuming a side-lobe reference envelope of Recommendation ITU-R S.465-6 2.1.1 Main-lobe definition Using the main-lobe definition that can be found in Annex 3 of RR Appendix 8: 2max0025.0)(= DGG for m m), the intersection that occurs is between the first side-lobe G
27、1and the side-lobe envelope (32 25 log() and is defined by: ()rG = log25321(17) 6.085.15=Dr(18) However, this value is correct provided that ris greater than m. In the case that ris less than m, the intersection (int) between the main-lobe and the side-lobe envelope (32 25 log() is then determined b
28、y solving the following expression: ()int2intmaxlog25320025.0 =DG(19) Figures 2 and 3 below show that intis greater than mfor D/ varying between 45.00 and 54.45, according to the value of the aperture efficiency. Rep. ITU-R S.2196 5 FIGURE 2 FIGURE 3 Minimum value ofD/ for calculation int45.00 47.22
29、 49.2551.1152.8454.4555.9640 45 50 55 60 50 55 60 65 70 75 80 Efficiency (%) D/6 Rep. ITU-R S.2196 Figure 3 shows the minimum value of D/ for which the intersection point (int) of the main-lobe with the side-lobe envelope can be calculated using the expression in (18) where inttakes the value of r.
30、Below these values, intmust be solved for using the expression in (19). The minimum value of D/ is shown as a function of aperture efficiency. In case D/ is smaller than the value shown in Figure 3 for a given efficiency, as it is stated before, the intersection intbetween the main-lobe and the side
31、-lobe envelope (32 25 log() is then determined by solving the expression in (19). The angle of intersection intof the main beam of the antenna with the side-lobe envelope of the antenna can be approximated by a function that takes the form: ()ZDA =intA “least squares” solution to this approximation
32、function, using only values of D/ from 15 to the applicable maximum value of D/ (for a given efficiency), gives different values of the coefficients for A and Z, depending on the efficiency: Efficiency (%) A Z 50 112.6522 1.1142 55 112.6702 1.107960 112.8286 1.1028 65 113.0639 1.098770 113.3417 1.09
33、51 75 113.5527 1.091980 113.8002 1.0891 Figure 4 shows a graphical representation of int. Note that the higher value of aperture efficiency results in a greater value of int. In Figure 4 below, it is assumed that Note 5 of Recommendation ITU-R S.465-6 does not apply. Rep. ITU-R S.2196 7 FIGURE 4 (An
34、gle of main-lobe intersection shown for 15 (D/) 150) It is proposed to base the definition of inton an efficiency of 0.75 as higher efficiencies result in a greater angle of intersection with the main-lobe. Furthermore, the values of the coefficients A and Z in the general expression for intin equat
35、ion (20) are rounded to three significant digits such that the approximation expression of intwill result in a conservative estimate such that it is not less than the value of intderived by numerical solution. Rounding the values of the coefficients of both A and Z “up” to the closest three signific
36、ant digits, such that A = 114 and Z = 1.09, will achieve this goal. The minimum angle, mindefining the intersection between the main-lobe and the first side-lobe or the side-lobe envelope as defined in Recommendation ITU-R S.465-6 can thus be defined by: = 09.16.0min114;85.15DDMax(20) 2.1.3 Antenna
37、pattern for side-lobes The side-lobes definition can be found in Recommendation ITU-R S.465-6. The value to be used for minis the one defined in the section 2.1.2. G = 32 25 log dBifor min 54.5: 2max0025.0)(=DGG for m m) and the angles mand rare given in expressions (38) through (44) below: Main-lob
38、e: G () = Gmax 0.00252Dfor m(36) First side-lobe: G() = G1 for mm) (40) where: 1max)/(20 GGDm= degrees (41) 6.085.15=Drdegrees (42) 10 Rep. ITU-R S.2196 2.2.2 Note on first side-lobe gain and the transition region for larger antennas The expression for the first-side-lobe gain (G1) provided in equat
39、ion (40) is the same as that found in RR Appendix 7 (assuming = 0) for the case of D/ 100. For large values of D/, there is no intersection of the main beam with the side-lobe envelope described by the expression 29-25 log(). In this case it is appropriate to use the expression for rin equation (42)
40、 for calculating the intersection of the side-lobe envelope with a first side-lobe gain G1given by equation (40). For D/ m) to use the expression for rthat is derived from the intersection with the more relaxed (higher) formulation of first side-lobe gain given by the expression in (40) (assuming =
41、0) above. In the case of smaller values of D/, the intersection of the main beam with the side-lobe envelope can be calculated by equating the right-hand sides of equations (36) and (38) and (assuming = 0) solving for intin equation (43) below: ()int2intmaxlog25290025.0 =DG (43) Figure 5 below shows
42、 that intis greater than rfor D/ varying between 61.12 and 72.19, according to the value of the aperture efficiency. FIGURE 5 The maximum value of D/ can be solved similarly for other values of efficiency. The solved values of D/ for efficiencies ranging from 50% to 80% are shown in Figure 6. intrep
43、resentation0.01.02.03.04.05.06.07.015 30 45 60 75 90 105 120 135 150Diameter-to-wavelengthOff-axisangle()(eff. = 0.50)(eff. = 0.75)intintrD/ = 61.12D/=72.19Rep. ITU-R S.2196 11 FIGURE 6 In order to calculate the boundary condition, where the main-lobe region ends and the reference pattern begins, on
44、ce again assuming = 0, it is necessary to consider both cases: 1) the case of larger values of D/, where there is no intersection of the main beam with the side-lobe described by the expression 29-25 log(), and 2) the case of smaller values of D/, where the intersection of the main beam expression i
45、s approximated by the maximum value given by the expression 15.85(D/)0.6and that given by the expression in the form ()ZDA =int. Consideration of these two cases will allow the determination of intover a wide range of D/. A “least squares” solution to this approximation function, using only values o
46、f D/ from 15 to the applicable maximum value of D/ (for a given efficiency), gives different values of the coefficients for A and Z, depending on the efficiency: Efficiency (%) A Z 50 114.9835 1.0812 55 115.5134 1.078260 116.0325 1.0756 65 116.5338 1.073570 117.0145 1.0716 75 117.4740 1.069980 117.8
47、726 1.0684 It is proposed to base the definition of intat which the side-lobe envelope begins on an efficiency of 0.75 as higher efficiencies result in a greater angle of intersection with the main-lobe. Furthermore, the values of the coefficients A and Z in the general expression ( ()ZDA =int) are
48、rounded to three significant digits such that the approximation expression of intwill result in 61.1263.3665.4067.2969.0470.6772.196065707550 55 60 65 70 75 80Maximum value of /D for calculation intD/Efficiency (%)12 Rep. ITU-R S.2196 a conservative estimate such that it is not less than the value of intderived by a numerical solution. Rounding the values of the coefficients of both A and Z “up” to the closest three significant digits, such that A = 118 and Z = 1.06, will achieve this goal. Thus, the expression for calculating the minimum angle for which the use of the side
