SOLVED Numerical's - Antenna Theory - Page 4.

9) A Hertzian dipole at the origin in free space has dl = 20 cm and I = 10 cos2π10⁷t A, find |E_θs| at the distant point (100, 0, 0).


SOLUTION:

λ = c / f = ( 3 x 108 ) / (107) = 30 m

At (100, 0, 0), r = 100 m & θ = π / 2

10) A 2-A source operating at 300 MHz feeds a Hertzian dipole of length 5 mm situated at the origin. Find E_s and H_s at (10, 30°, 90°).

SOLUTION:


                   λ = c / f = (3 x 108) / (3 x 108) = 1m

                   β = 2π / λ = 2π

                  At r = 10, θ = 30^o , φ = 90^o

                   λ = 120π = 377 m

                   E_θs = η H_φs = 94.25 mV/m


11) An antenna can be modelled as an electric dipole of length 5 m at 3 MHz. Find the radiation resistance of the antenna assuming a uniform current over its length.

SOLUTION:

          dl = 5 m

          λ = c / f = (3 x 10⁸) / (3 x 10⁶) = 100 m

          dl / λ = 5 / 100 = 1/20

         Now since dl / λ = 1/20 < 1/10

          R_rad = 80π² (dl/λ)²

                  = 80π² / 400 = 1.974Ω



12) A half-wave dipole fed by a 50 Ω transmission line, calculate the reflection coefficient and the standing wave ratio.
SOLUTION:

For a half wave dipole antenna,

                                                Z_in = 73 + j42.5