Final answer:
The received signal power in a free space communications system is determined using the Friis transmission equation, which takes into account the transmit power, antenna gains, signal frequency, and distance between the antennas. By substituting the given values into the equation, the received signal power is calculated to be 0.0144 W.
Step-by-step explanation:
To determine the received signal power in a free space communications system, we can use the Friis transmission equation:
Pr = Pt * (Gt * Gr * (λ/4πR)2)
Where:
-
- Pr is the received power
-
- Pt is the transmit power (2W)
-
- Gt and Gr are the transmit and receive antenna gains (40 dB)
-
- λ is the wavelength of the signal (c/f = (3e8)/(2.5e9) = 0.12 m)
-
- R is the distance between the antennas (100 m)
Converting dB to linear scale:
40 dB = 10^(40/10) = 10,000 (transmit and receive antenna gains)
Substituting the values into the equation:
Pr = 2 * (10,000 * 10,000 * (0.12/4π*100)2)
Simplifying the equation gives: Pr = 0.0144 W
Therefore, the received signal power in this free space communications system is 0.0144 W.