- 2081 Chaitra · 3 marks
Free space loss (LFS)
Short answer
Free space loss is the power ratio between two isotropic antennas due to spherical spreading only: LFS=(4πd/λ)^2, or LFS(dB)=32.44+20log d(km)+20log f(MHz). It increases 20 dB per decade (6 dB when distance or frequency doubles) and serves as the reference in link budgets.
Explain the antenna parameter: free space loss (LFS).
Free space loss (LFS) is the loss in signal power between two isotropic antennas in free space, caused only by the spreading of the radiated energy over a growing sphere. It is not a loss of energy in the medium (free space is lossless); the receiving antenna simply intercepts a smaller fraction of the total power as distance increases.
Expression
From the Friis equation Pr = Pt·Gt·Gr·(λ/4πd)², putting Gt = Gr = 1:
LFS = Pt/Pr = (4πd/λ)²
LFS(dB) = 20 log(4πd/λ) = 22 + 20 log(d/λ)
LFS(dB) = 32.44 + 20 log d(km) + 20 log f(MHz)
Key features
- Increases by 6 dB each time distance doubles (20 dB per decade).
- Increases by 6 dB each time frequency doubles, because a higher-frequency isotropic antenna has a smaller effective aperture (Ae = λ²/4π).
- It is the reference loss used in every link budget: Pr = Pt + Gt + Gr − LFS − other losses.
Example: For d = 50 km and f = 10 GHz, LFS = 32.44 + 20 log 50 + 20 log 10000 = 146.4 dB.
✓ Answer checked by Claude Opus 5.5 (high effort)
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