Wireless Communication Basics
With transmit and receive antenna gains of 0 dBi, which is closest to the free-space path loss when a 2.4 GHz radio wave (wavelength 0.125 m) travels 100 m through free space?
- A40 dB
- B60 dB
- C80 dB
Show answer and explanation
Answer: C. 80 dB
Free-space path loss is the rate at which power weakens between isotropic antennas as it spreads out spherically with distance, given by L = (4πd/λ)². With d = 100 m and λ = 0.125 m, 4πd/λ ≈ 1.0×10⁴, so L = 20·log₁₀(1.0×10⁴) ≈ 80 dB. In dB, the loss grows by about 6 dB each time the distance doubles and by 20 dB each time it increases tenfold. In this formula, at the same distance the loss is larger at higher frequency (shorter wavelength).
- A. This is calculated with 10·log₁₀ instead of 20·log₁₀. The loss is the square of (4πd/λ), so 20·log₁₀ is taken to convert it to dB.
- B. This is the value for a distance of 10 m. Cutting the distance to one tenth reduces the loss by 20 dB.
- C. Correct. 20·log₁₀(4π×100/0.125) ≈ 80 dB.