Question

A mobile base station (BS) in an urban environment has a power measurement of 35 μW at 275 m from the BS. If the propagation follows an inverse cube power law, what would be a reasonable power value, in μW, to expect at 1.1 km from the BS?

A. (5.72 × 10^{-2}) μW
B. (1.09 × 10^{-3}) μW
C. (2.17 × 10^{-1}) μW
D. (4.22 × 10^{-3}) μW

Answer 1

Using the inverse cube power law, the power at 1.1 km from the mobile base station (BS) in an urban environment is estimated to be 0.546875 μW. Among the options provided, the closest approximation is (2.17 × 10^{-1}) μW which is answer C.

Step-by-step explanation:

In an urban environment, a mobile base station (BS) has a power measurement of 35 μW at a distance of 275 m. When considering the inverse cube power law for propagation, the power at a new distance can be calculated by the formula:

P2 = P1 * (d1/d2)^3

Where P1 is the initial power, d1 is the initial distance, P2 is the power at distance d2. Plugging in the given values:

P2 = 35 μW * (275 m / 1100 m)^3

P2 = 35 μW * (1/4)^3

P2 = 35 μW * 1/64

P2 = 0.546875 μW

Upon reviewing the options provided, none of them exactly match the calculated value. Since P2 must be less than 35 μW and option C (2.17 × 10^{-1} μW) is the only one that is less than 35 μW and closest to the calculated value, it is the most reasonable approximation.

Therefore, the correct answer is:

C. (2.17 × 10^{-1}) μW