The power output of the transmitter is 130W. In dBW, it is approximately 21.97 dBW, and in dBm, it is approximately 51.04 dBm. The path loss for a distance of 30 km and a frequency of 6 GHz is approximately 89.546 dB. The received power in dBm is approximately 34.494 dBm, and in milliwatts, it is approximately 244.687 mW.
Step-by-step explanation:
To calculate the power output in dBW, we use the formula:
Power (dBW) = 10 * log10(Power (W)) The power output is given as 130W, so:
Power (dBW) = 10 * log10(130) = 21.97 dBW
To calculate the power output in dBm, we use the formula:
Power (dBm) = 10 * log10(Power (mW)) Since 1W = 1000mW, we convert the power output to mW:
Power (mW) = 130 * 1000 = 130,000 mW
Power (dBm) = 10 * log10(130,000) = 51.04 dBm
The path loss can be calculated using the formula:
Path Loss (dB) = 20 * log10(d) + 20 * log10(f) + 20 * log10(4 * Pi / c) Where d is the distance (30km), f is the frequency (6 GHz), and c is the speed of light (3 * 10^8 m/s).
Plugging in the values, we get:
Path Loss (dB) = 20 * log10(30,000) + 20 * log10(6 * 10^9) + 20 * log10(4 * Pi / (3 * 10^8))
Path Loss (dB) ≈ 20 * 4.477 + 20 * 9.778 + 20 * -0.973 = 89.546 dB
The received power can be calculated using the formula:
Received Power (dBm) = Transmitter Power (dBm) + Transmitter Antenna Gain (dBi) + Receiver Antenna Gain (dBi) - Path Loss (dB)
Plugging in the values, we get:
Received Power (dBm) = 51.04 + 58 + 15 - 89.546 = 34.494 dBm
The received power in milliwatts can be calculated using the formula:
Received Power (mW) = 10^(Received Power (dBm) / 10)
Plugging in the value, we get:
Received Power (mW) = 10^(34.494 / 10) ≈ 244.687 mW