Which expression is the correct free-space path loss formula in decibels?

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Multiple Choice

Which expression is the correct free-space path loss formula in decibels?

Explanation:
In free-space, the signal loses power purely due to spreading, described by Pt/Pr = (4πR/λ)^2 from the Friis equation. Converting this to decibels means PL(dB) = 10 log10(Pt/Pr) = 10 log10((4πR/λ)^2) = 20 log10(4πR/λ). So the correct expression is PL(dB) = 20 log10(4πR/λ). The other forms would either invert the ratio, omit the squaring, or misplace the logarithmic factor, which would give an incorrect loss value.

In free-space, the signal loses power purely due to spreading, described by Pt/Pr = (4πR/λ)^2 from the Friis equation. Converting this to decibels means PL(dB) = 10 log10(Pt/Pr) = 10 log10((4πR/λ)^2) = 20 log10(4πR/λ). So the correct expression is PL(dB) = 20 log10(4πR/λ). The other forms would either invert the ratio, omit the squaring, or misplace the logarithmic factor, which would give an incorrect loss value.

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