Calculation of Total Radiated Power

Given: Directive gain = 6 dB, Total radiated power = 16 kW

We know that the directive gain of an antenna is given by the formula:

G(dB) = 10 log10 [P(rad)/P(iso)]

Where P(rad) is the power radiated by the antenna and P(iso) is the power that would be radiated by an isotropic radiator (an ideal point source that radiates uniformly in all directions) if it were driven with the same input power as the antenna.

We can rearrange this formula to find the radiated power:

P(rad) = P(iso) x 10^(G(dB)/10)

Substituting the given values, we get:

P(rad) = P(iso) x 10^(6/10)
16 kW = P(iso) x 3.981

Therefore, the power radiated by the antenna (P(rad)) is 3.981 times the power that would be radiated by an isotropic radiator (P(iso)).

Calculation of Electric Field Amplitude

We can use the Friis transmission formula to calculate the electric field amplitude at a distance of 8 km from the antenna in the direction of maximum gain.

The Friis formula relates the power received at a distance (Pr) to the power transmitted by the antenna (Pt), the gain of the transmitting antenna (Gt), the gain of the receiving antenna (Gr), the wavelength of the signal (λ), and the distance between the antennas (d).

Pr = (Pt x Gt x Gr x λ^2) / (16π^2 x d^2)

In this case, we can assume that the receiving antenna has a gain of 1 (since we are interested in the field strength in free space). Therefore, the formula simplifies to:

Pr = (Pt x Gt x λ^2) / (16π^2 x d^2)

We need to find the power received at a distance of 8 km from the antenna. We know that the power radiated by the antenna is 16 kW. We also know that the wavelength of the signal is given by:

λ = c/f

Where c is the speed of light (3 x 10^8 m/s) and f is the frequency of the signal.

Assuming that the frequency of the signal is in the UHF range (around 500 MHz), we get:

λ = 3 x 10^8 / 500 x 10^6 = 0.6 m

Substituting the values, we get:

Pr = (16 x 10^3 x 3.981 x 0.6^2) / (16π^2 x 8 x 10^3)^2
Pr = 7.073 x 10^-12 W

The power received is very small, but we are interested in the electric field amplitude (E) rather than the power. We know that the power received is related to the electric field amplitude by the formula:

Pr = (E^2 x 4π x d^2) / λ^2

Solving for E, we get:

E = sqrt[(Pr x λ^2) / (4π x d^2)]

Substituting the values, we get:

E = sqrt[(7.073 x 10^-12