A radiated power of 5 W is produced by a resonant antenna. Its directional radiation intensity represented by: U = B0cos3θ (W/unit solid angle) 0 ≤ θ ≤ π/2; 0 ≤ ϕ ≤ 2πFind the(a) maximum power density (in W/m2) at a distance of 1500m (assuming far field distance).(b) Directivity of the antenna (dimensionless and in dB)(c) Gain of the antenna with an efficiency of 85% (dimensionless and in dB)
Question
A radiated power of 5 W is produced by a resonant antenna. Its directional radiation intensity represented by: U = B0cos3θ (W/unit solid angle) 0 ≤ θ ≤ π/2; 0 ≤ ϕ ≤ 2πFind the(a) maximum power density (in W/m2) at a distance of 1500m (assuming far field distance).(b) Directivity of the antenna (dimensionless and in dB)(c) Gain of the antenna with an efficiency of 85% (dimensionless and in dB)
Solution
(a) The maximum power density (Smax) in the far field of an antenna can be calculated using the formula:
Smax = P/(4πr²)
where P is the radiated power and r is the distance from the antenna. Substituting the given values:
Smax = 5W/(4π(1500m)²) = 1.77 x 10^-9 W/m²
(b) The directivity (D) of an antenna is the ratio of the maximum intensity (Umax) to the average intensity (Uavg). The maximum intensity is given by B0 (since cos3θ is maximum at θ=0) and the average intensity can be calculated by integrating U over the solid angle and dividing by the total solid angle (4π).
The directivity in dB can be calculated by taking 10 times the log base 10 of the directivity.
(c) The gain (G) of an antenna is the product of its directivity and its efficiency (η). Substituting the given values:
G = D * η = D * 85%
The gain in dB can be calculated by taking 10 times the log base 10 of the gain.
Note: The values of B0, Umax and Uavg are not given in the problem, so I can't calculate the numerical values of D and G.
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