A GSM1800 cell tower antenna is transmitting 20W of power in the frequency range of 1840 to 1845MHz. The gain of the antenna is 17dBi. Find the power density at a distance of 50m. Select one:a. 31.8m W/m2b. 41.8m W/m2c. 21.8m W/m2d. 51.8m W/m2
Question
A GSM1800 cell tower antenna is transmitting 20W of power in the frequency range of 1840 to 1845MHz. The gain of the antenna is 17dBi. Find the power density at a distance of 50m. Select one:a. 31.8m W/m2b. 41.8m W/m2c. 21.8m W/m2d. 51.8m W/m2
Solution
To solve this problem, we need to use the formula for power density (S) in free space:
S = P * G / (4 * π * r^2)
where:
- P is the power of the antenna (20W),
- G is the gain of the antenna (17dBi, which needs to be converted to linear scale),
- r is the distance from the antenna (50m).
First, we need to convert the gain from dBi to linear scale. The formula to convert dBi to linear scale is:
G_linear = 10^(G_dBi/10)
So, G_linear = 10^(17/10) = 50.1187
Now we can substitute P, G and r into the formula for S:
S = 20W * 50.1187 / (4 * π * (50m)^2)
Solving this equation gives us the power density in W/m^2.
Let's calculate it:
S = 20W * 50.1187 / (4 * π * (50m)^2) = 0.0318 W/m^2
So, the power density at a distance of 50m from the antenna is 0.0318 W/m^2 or 31.8 mW/m^2.
Therefore, the correct answer is a. 31.8m W/m^2.
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