Calculate theoretical reach of radio devices

In this page it is explained the theoretical method to calculate the point-to-point transmission distance between two radio devices in optical sight (LOS) without obstacles. In a radio system of the type shown in the figure:

We can hire:

PRx=PTx-CL+GTx-FSLP+GRx-CL

In which :

PRx [dBm] = Potenza ricevuta 
PTx [dBm] = Potenza trasmessa
CL [dB] = Perdita del cavo (se esiste)
GTx [dBi] = Guadagno dell'antenna trasmittente
GRx [dBi] = Guadagno dell'antenna ricevente 
FSPL [dB] = Free Space Path Loss,
ovvero attenuazione del segnale in spazio aperto 
(vedi tabella)

It is also remembered that the equation for the calculation of the FSPL is the following:

FSPL = 32.4 + 20*Log F + 20*Log R

In which:

F [MHz] = Frequenza Operativa 
R [km] = Distanza tra le antenne

In the table below are shown some typical values ​​of attenuation FSPL as a function of distances and frequencies.

Distance [km] FSPL [dB]
@169MHz @434MHz @868MHz @2.4GHz @5.4GHz
0.5 70.94 79.05 85.15 93.98 101.03
1 76.96 85.07 91.17 100 107.05
2 82.98 91.09 97.19 106.02 113.07
4 89 97.11 103.21 112.05 119.09
8 95.02 103.13 109.23 118.07 125.11
10 96.96 105.07 111.17 120.00 127.05
12 98.54 106.65 112.75 121.59 128.63
16 101.04 109.15 115.25 124.09 131.13
20 102.98 111.09 117.19 126.02 133.07

The same equation is represented in graphical form in the figure below:

From the table and the graph, we can see that for every increase of 6dB FSPL corresponds to a doubling of distance. It is also important in the calculation to maintain a safety margin of at least 5-6dB.

Taking for example a radio link made with Maxstream XStream X24-009 radiomodem equipped with 2.1dBi dipole antennas, we could hypothesize a LOS radio range of:

FSPL = PTx+GTx-PRx+GRx = 17+2.1+105+2.1 = 126.2dB

to this value must be removed 6dB of safety margin:

126.2-6 = 120.2dBm Correspondents in the table and in chart a 10km.

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