How do you calculate free-space path loss at a given frequency and distance?

• A. Lp(dB) = 20 log10(4πR/λ) with λ = c/f
• B. Lp(dB) = 20 log10(R) + 20 log10(f) - 147.55
• C. Lp(dB) = 10 log10(Pr/Pt)
• D. Lp(dB) = 4πR/λ

Answer: (A)

Free-space path loss describes how the signal strength fades simply due to the wave spreading out in open space, and in decibels it depends on distance and wavelength. The standard expression in dB is Lp(dB) = 20 log10(4πR/λ), where R is the separation between transmitter and receiver and λ is the wavelength. If you use the relationship λ = c/f, you can rewrite this as Lp(dB) = 20 log10(4πR f / c). This form is equivalent to the common frequency-based version, which can be expanded to Lp(dB) ≈ 20 log10(R) + 20 log10(f) - 147.55 when f is in hertz and R is in meters (the constant comes from 20 log10(4π/c)).

Why this is the best choice: it directly expresses how loss scales with distance and wavelength (or frequency) in a compact, exact form. The other options either omit the logarithmic relation or express a power ratio incorrectly. For example, using 10 log10(Pr/Pt) would give the log of the received-to-transmitted power, not the standard free-space path loss in dB, and the form 4πR/λ is a linear ratio, not a dB measure.