fresnel zone formula with constant of 17.3 why?

[STINGERX]

as you can see in the attached image below:

edit: no λ on the second formula!!!!
for the first formula, all of d are in [m]
f is in [Hz]

for the second formula,
all of d are in [km]
f is in [GHz]

but i still can't figure out how to get this constant of 17.3?
tried to do this:
(move from m to km
*1/10^3
and from Hz to GHz)
*1/10^9

 

[Angophora]

The first formula is the square root of a ratio.

The second formula you posted is not quite right. The correct formula is Fn = 17.3 * SQRT(distance * (path_length - distance) / (Frequency_GHz * path_length))

The 17.3 comes out of converting the wavelength to a frequency (wavelength = speed of light / frequency) and taking the constant out of the square root. If you square 17.3 you get 299.29 which is close to the speed of light in meters per second, 299,792,458. The constant is divide by 1000 to get the answer in meters rather than km when the distances are in km. The constant should be 17.31451581766005 but it is pointless using so many decimal places, so it is rounded to 17.3

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This link provides some background on microwave link calculations

http://www.piscespacific.org/livesite/files/Link_Budget_Calculation.pdf