## Reference Designer Calculators

### Free Space Ptha Loss Formula Derivation

Free Space Path loss is directly proportional to the square of the distance between the transmitter and the receiver and inversly proportional to the square of the wavelength of the frequency of transmission. .

$$FSPL = \left(\frac{4pd}{λ}\right)^2$$ $$= \left(\frac{4πdf}{c}\right)^2$$

Where,

λ is the signal wavelength (in metres),
f is the signal frequency (in hertz),
d is the distance from the transmitter (in metres),
c is the speed of light

In terms of dB the equation translates to
$$FSPL(dB) = 10 log_{10}\left[\left(\frac{4πf}{c}\right)^2\right]$$ $$= 20 log_{10}\left(\frac{4πdf}{c}\right)$$ $$= 20 log_{10}\left(\frac{4πdf}{c}\right)$$ $$= 20 log_{10}\left(\frac{4π}{c}\right)+20 log_{10}(d)+20 log_{10}(f)$$