Consider an Antenna Transmitting a Power of 10 W at 900 MHz. Calculate the Received Power at a Distance of 2 km if Propagation is taking place in Free Space.

Solution:

Given Data:

P_t = 10W
f = 900 MHz
d = 2 km = 2000 m

P_r = ?

While Propagation take place in a free space so assume:

G_t = G_r = 1 dB

So here

_{Pr = (Pt*Gt*Gr*λ²)/(4πd)²}

While

λ = c₀/f

=(3*10⁸)/(900*10⁶)
=0.0033*10²

λ = 0.33 m

So,

P_r = (10 * 1 * 1 * (0.33)²)/(4 * 3.14 * 2000)²
=(10 * 0.1089)/(25132.741)²
=1.089 / 631654675.92

P_r = 1.72 * 10^-9W

While in dBm

P_r = 10 * log₁₀(P_r) + 30

= 10 * log₁₀(1.72 * 10^-9) + 30
= 10 * (-8.763) + 30

P_r = -57.63 dBm

While in dBW:

P_r = 10 * log₁₀ (1.72 * 10^-9/1)

P_r = -87.63 dBW

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