Tham khảo tài liệu 'satellite communications part 16', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Satellite coverage optimization problems with shaped reflector antennas 441 Fig. 5. Parabolic reflector antenna a . Parabolic reflector antenna A point b z p belongs to a parabola as shown in Fig. 6 when it is at the same distance from the focus a F 0 and its projection c F p onto the directrix z F which leads to the implicit equation p2 X2 y2 z 4F 4F where F is called the focal distance. The unit normal vector to the parabola can be written as 2Fz pp 2Fz xX yy y 4F2 p2 ự 4F2 X2 y2 9 10 The angle of the normal vector if to z is 9 arctan 11 The direction of a ray from the focus to a point on the parabola can be written as J z F z pp z F 12 so that J A 2zF 2F2 p2 d n -- _ z F y 4F2 p2 _ 2F 74 7 n z 2zF 2F2 4zF z F ự4F2 p2 13 cos 9 442 Satellite Communications Fig. 6. Parabola with focus a F 0 and directrix z -F defined by points b z p . Hence the angle between d and fl is the same as the angle between fl and z. If the reflection is perfect . for electromagnetic waves reflector must be a perfect electric conductor then 9 is the angle of reflection of the ray which equals the angle of incidence so that all reflected rays go towards z. A last notable feature of parabolic reflectors is that the distance traveled by two reflected rays originated from the focus up to a given z za plane are exactly the same and valued to I b a I za z b c I za z F z za z 14 F za Therefore if all rays from the feed are in phase then they will still be in phase after reflecting and reaching z za. This is highly desired considering that an aperture . a bounded region at a given z za is most directive when the field distribution on it is uniform in phase and amplitude. Unfortunately the same does not hold true for the amplitude since the dispersive behavior from the feed up to the reflector attenuates non-uniformly each ray according to the respective distance F z. Fig. 7 shows a parabolic reflector antenna with circular aperture of radius R. The reflector center was displaced H .
