Question

1) A Hertzian dipole antenna is a short conducting wire carrying an approximately constant current over its length If such a dipole is placed along the z-axis with its midpoint at the origin, and if the current flowing through it is i(t) ż lo cosot, assume I to be sufficiently small so that the observation point is approximately equidistant to all points on the dipole; that is, assume RR then the corresponding magnetic field is described by: olk2 sin e (a) what is the result for E and H field in the far field (kR>>l ) (ie, drop term l/(kR)2 or higher). Use the far field result for Hto determine E. (b) Determine the time-averaged Poynting vector in the far field. (c) Determine the direction of the radiating electromagnetic power and how it depends on R and 0 (d) Draw a sphere of radius R around the dipole antenna. Calculate the total average power flowing out of the sphere (e) Assume the Hertzian dipole has an impedance of 75 2. If you attach this dipole as the load to a 50-Ω transmission line that has an additional λ/4 transmission line of impedance Z02 between the first TL and the load determine the magnitude of Zo2 that will maximize the power delivered to the load? (f) Assume the circuit fromn (e) is attached to a genertor of voltage V= 100 cos (2π x 1067) V and internal impedance of 50 Ω. Use the fact that the power delivered to the load equals the total power radiated by this dipole antenna to rewrite the electric and magnetic fields in (a) in terms of only R and Q

Answer 1

solution k R 2 2 LA

502 50x15 1o50 15 าตั้ 61, 23 yr 2. 200