Consider an antenna transmitting a power of 5W at 900MHz. Calculate the received power at a distance of 2km if propagation is taking place in free space.
8.8 x 10^-10 W
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P3.2. Consider an antenna transmitting a power of 5W at 900 MHz. Calculate the
received power at a distance of 2km if propagation is taking place in free space.
In a cellular system, diffraction, reflection, and direct path take different amount of time for the signal to reach an MS. How do you differentiate and use these signals? Explain clearly. Compute the level crossing rate with respect to the rms level for a vertical monopole antenna, assuming the Rayleigh faded isotropic scattering case. The receiver speed is 20 km/hr and the transmission occurs at 800 MHz.
To calculate the received power at a distance of 2km in free space, you can use the Friis transmission equation. This equation relates the transmitted power, the transmitter and receiver antenna gains, the wavelength, and the distance between the transmitter and receiver.
The Friis transmission equation is given by:
Pr = Pt * ((Gt * Gr * λ^2)/ (4π * R)^2),
Where:
Pr is the received power
Pt is the transmitted power
Gt is the transmitter antenna gain
Gr is the receiver antenna gain
λ is the wavelength of the signal
R is the distance between the transmitter and receiver
In this case, the transmitted power (Pt) is 5W, and the distance (R) is 2km = 2000m. The frequency given is 900MHz, so we can calculate the wavelength (λ) as λ = c/f, where c is the speed of light (approximately 3 x 10^8 m/s) and f is the frequency in hertz.
λ = (3 x 10^8 m/s) / (900 x 10^6 Hz)
≈ 0.333 m
Assuming there are no losses in the transmission, we can neglect the antenna gains (Gt and Gr), and the Friis transmission equation simplifies to:
Pr = Pt * (λ^2/ (4π * R)^2)
Plugging in the values we have:
Pr = 5W * ((0.333m)^2 / (4π * 2000m)^2)
≈ 4.63 x 10^-5 W
Therefore, the received power at a distance of 2km in free space would be approximately 4.63 x 10^-5 W.