Question

Problem 3 A communications system operates at 300 MHz. What current is required at the center of the antenna to generate an E field strength of 10 mV/m at a distance of 10 km from the antenna on the horizontal (0 90°) plane, if the antenna is: (a) a Hertzian dipole of length 0.01 λ. (b) a short dipole of lenugth-0.01 A (c) a half-wave dipole

Answer 1

We know that electric field in bar field is given by - E^rightarrow = j I l beta^2 sin theta/4 pi epsilon omega r e^-j beta r - e^j omega t so Vertical-bar E^rightarrow Vertical-bar = I l beta^2 sin theta/4 pi epsilon_0 omega r given f = 300 MHz so lambda = c/f = 3 times 10^8/300 times 10^6 = 1m so beta = 2 pi/lambda = 2 pi given at r = 10 km or 10^4 m E = 10 mv/m or 10^-2 v/m theta = 90 degree (a) By Hertzian dipole for l = 0.01 lambda so l = (0.01) (1) = 0.01 m put values - 10^-2 = (I) (10^-2) (2 pi)^2 sin (90 degree)/4 pi times 10^-9 /36 pi times 2 pi times 300 times 10^6 times 10^4 \r\n 1 = (I) (2 pi) (9)^3/10^-9 times 3 times 10^12 1 = 6 pi I/10^3 So I = 10^3/6 pi = 53.0785 A or I = 53.0785 A \r\n b) For short dipole with l = 0.01 lambda due to it electric field