In the Friis transmission equation, what does the factor (λ/(4πR))^2 represent?

• A. The transmitter's efficiency factor.
• B. The free-space path loss factor that depends on wavelength and distance.
• C. The receiver's noise figure.
• D. Antenna mismatch factor.

Answer: (B)

The key idea here is how signal strength fades as it travels through free space. The factor (λ/(4πR))^2 captures that propagation loss due purely to geometry and the wave’s wavelength. At distance R, the radiated power spreads over a sphere with area 4πR^2, so the power flux is Pt Gt divided by that area. The receiving antenna only picks up a portion of that flux, determined by its effective aperture A_eff, which for a matched antenna is A_eff = (λ^2 Gr)/(4π). Multiplying the flux by A_eff gives the received power: Pr = Pt Gt Gr (λ^2)/(4πR)^2, which is the same as Pt Gt Gr (λ/(4πR))^2. So this term represents the free-space path loss: it decreases with distance as 1/R^2 and depends on wavelength. The remaining factors (the antenna gains) account for how well the antennas capture and direct that power.