Link budget - Tutorial - FSL dB calculation?

[flong]

Hi

With respect to the calculation of the Free Space loss on Page 15 of this tutorial

In going from

FSL = (4 * Pi * r / (wavelength))^2

to

FSL = 32.4 + 20* Log (r) + 20* Log (f)

Where does the 32.4 come from ?

I assumed it would be

20 * Log ( 4 * Pi / (Speed of Light) )

which comes out at -147 dB.

Thanks
Finbarr

[chico128]

The 32.4 comes from all the constants in the equation and fall out from the engineering units used.

The equation in logs is:
Loss = 20*log10(4*pi) + 20*log10(r*10^3) - 20*log10(3*10^8) + 20*log10(f*10^6)
Where lamda has been converted to c/f.

This specifies f requency (f)is in MHz, and distance (r) in Km.
If you now group all the constants:
20*log10(4*pi) + 20*log10(10^3) - 20*log10(3*10^8)+20*log10(10^6)
you will end up with the number 32.44.

chico

[nanatanjung]

There is another equation for 32.4 constant configure :

FSL = 10 log ( 4 x pi x r / lamda )²

whereby lamda = c / f

c = 3 x 10^8 (speed of light)
f = 1 x 10^6 (Medium frequency)
r = 1 x 10^3 (kilometer)

FSL = 10 log ( 4 x 3.142 x (1 x 10^3) / 300 )²
= 32.44

Nanatanjung