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Electromagnetic Waves and Antennas combined - Chapter 22

Coupled Antennas Trong tính toán hiệu ứng khớp nối lẫn nhau giữa ăng ten tuyến tính chặt chẽ khoảng cách đều nhau, chúng ta cần phải biết các lĩnh vực sản xuất bởi một ăng-ten ở khoảng cách gần. Các lĩnh vực được tạo ra bởi một ăng-ten dây mỏng với hiện tại I (z) được làm việc trong Sec. 14,4. Chúng tôi tóm tắt những kết quả này ở đây. Tất cả các thành phần lĩnh vực có thể thu được từ những kiến thức của các thành phần-z của vector tiềm năng Az từ (z, ρ): . | 22 Coupled Antennas 22.1 Near Fields of Linear Antennas In calculating mutual coupling effects between closely-spaced linear antennas we need to know the fields produced by an antenna at near distances. The fields generated by a thin wire antenna with current I z were worked out in Sec. 14.4. We summarize these results here. All held components can be obtained from the knowledge of the z-component of the magnetic vector potential Aziz py. Il e Az z p I z dz 4tt J-h R 22.1.1 where h is the half-length of the antenna h 2 and the geometry is shown in Fig. 22.1.1. We have used the approximate thin-wire kernel because it differs little from the exact kernel for distances p a typically when p ầ 5a. Fig. 22.1.1 Fields of a thin wire antenna. 906 22. Coupled Antennas Then the non-zero held components Ez Ep H f can be constructed from the two alternative sets of formulas jwpeEz S2zAz k2 Az jwpeEp SpSzAz pHộ SpAz jwpeEz s2 Az k2Az Sp pH p ju epEz JuieEp 22.1.2 As a first approximation we will assume that the current I z is sinusoidal. This is justified only when the antenna length is near half a wavelength A 2. Most coupled antenna arrays that are used in practice such as Yagi-Uda satisfy this condition. We note also that the near fields resulting from the sinusoidal current assumption do not satisfy the correct boundary conditions on the surface of the antenna that is the condition z z p 0 at z 0 and p a. In Sec. 22.2 we consider an improved approximation of the near fields that addresses these issues. Thus for now we will assume that Hz ogj . Z Imsin k h- z 22.1.3 sinkh where we distinguish between the current Io at z 0 and the maximum current Im Io sinkh. For half-wavelength antennas we have kh 7T 2 Io Im and the current becomes I z Io cos kz. In principle one could insert Eq. 22.1.3 into 22.1.1 and perform the required integrations to get Az. However for the purpose of determining the fields this is not necessary. Combining 22.1.1 and 22.1.2 we obtain jvopeEz z p d Az .