It is often more convenient to express distance in m rather than m and frequency in Hz rather than Hz. Rewrite the equation for free space loss, = 20 log + 20 log − 147.56 , using the new dimension units.

L (in dB) = 20 log f + 20 log d + 32.44

with f in MHz and d in Km

Explanation:

L(in dB) = 20 log f + 20 log d - 147.56 dB

with f in Hz and D in m

MHz = 10⁶ Hz

And

Km = 10³ m

L(in dB) = 20 log f + 20 log d - 147.56 dB

L = 20 log [10⁶f] + 20 log [10³d] - 147.56

L = 20 log 10⁶ + 20 log f + 20 log 10³ + log d - 147.56

From the law of logarithms,

Log 10⁶ = 6

Log 10³ = 3

L = (20×6) + (20×3) + 20 log f + 20 log d - 147.56

L = 20 log f + 20 log d - 147.56 + 120 + 60

L (in dB) = 20 log f + 20 log d + 32.44

Hope this Helps!!!

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