Currents on Linear Antennas Trong Sec. 14,4, chúng tôi xác định các lĩnh vực điện từ được tạo ra bởi một phân phối hiện tại vào một ăng-ten tuyến tính mỏng, nhưng đã không thảo luận về cơ chế phân phối hiện tại được thiết lập và duy trì. Trong Chap. 16, chúng tôi giả định rằng các dòng hình sin, nhưng đây chỉ là một xấp xỉ. Ở đây, chúng tôi thảo luận về phương trình tích phân xác định hình thức chính xác của các dòng. Một ăng-ten, cho dù truyền hoặc nhận được, luôn luôn được thúc. | 21 Currents on Linear Antennas Haỉỉén and Pocklington Integral Equations In Sec. we determined the electromagnetic fields generated by a given current distribution on a thin linear antenna but did not discuss the mechanism by which the current distribution is set up and maintained. In Chap. 16 we assumed that the currents were sinusoidal but this was only an approximation. Here we discuss the integral equations that determine the exact form of the currents. An antenna whether transmitting or receiving is always driven by an external source field. In transmitting mode the antenna is driven by a generator voltage applied to its input terminals and in receiving mode by an incident electric field typically a uniform plane wave if it is arriving from far distances. In either case we will refer to this external source field as the incident field ln. The incident field fin induces a current on the antenna. In turn the current generates its own field E which is radiated away. The total electric field is the sum tot E Eln. Assuming a perfectly conducting antenna the boundary conditions are that the tangential components of the total electric field vanish on the antenna surface. These boundary conditions are enough to determine the current distribution induced on the antenna. Fig. depicts a z-directed thin cylindrical antenna of length I and radius a with a current distribution z along its length. We will concentrate only on the z-component Ez of the electric field generated by the current and use cylindrical coordinates. For a perfectly conducting antenna the current is essentially a surface current at radial distance p a with surface density Js z z 2rta where in the thin-wire approximation we may assume that the density is azimuthally symmetric with no dependence on the azimuthal angle cf . The corresponding volume current density will be as in Eq. J r Js z 5 p - a z z 5 p- a - zJz r 856 21. Currents on Linear Antennas Fig. Thin-wire .
