Path Loss & SNR

You find the ( here used ) formulas in THE SATELLITE handbook, ARRL edition ( ISBN 0-87259-658-3 8-12 & 8-13 ). These calculations deliver good results.

First we calculate the path loss ( dB ).

Path loss is : 32.4+20logf+20logrho.

Note : in this site you can find a small script ( JAVA ) which calculates this formula above. To see : click here

f is the used ( up or down ) frequency ( MHz ) and rho is the slant range ( km ).

Second the power sum, ps ( dBmW ).

Power sum is : actual transponder power ( dBmW ) plus satellite antenna gain ( dBi ) plus ground station antenna gain ( dBi ) minus path loss ( dB ).

Remark : use dBi if comparing iso, for instance a 0.5 wave dipole in free space delivers ca 2.15 dBi. An antenna with a gain of 6 dBd has 8.15 dBi. Iso and the 0.5 wave dipol are standards.

Third the total received noise power, trnp ( dBmW ) and ( at the end ) the Signal Noise Ratio, SNR ( dB ), see THE SATELLITE handbook or below.

Signal Noise Ratio is : ps minus trnp.

If you want to analyse the own situation : below you find the required formulas.

Calculation total received noise : Ptrn ( trnp above ).


k is the Boltzmann factor 1.38•10to(-20) in mW/Hz•K (K=273+C), Trs is the resulting system temperature in K, B is the bandwidth in Hz. Remark : 10logk delivers a -198.6 value.

Calculation resulting system temperature : Trs.

The receive system noise ( a hardware result ), cosmic noise ( received by the antenna ) and earth radiated noise going into the lobs of the antenna. ( for instance earth radiated noise at a temperature -5C=268K ). Attention, Trs expressed in temperature, see below.


Tr is the receive system temperature in K, Tsky is the temperature of the sky in K. Tsky is 'seen' by the antenna.

Calculation receive system temperature : Tr.


Ta is the ambient temperature ( hardware ) in K, Ft is the system noise figure in dB, concerning the coax, preamp(s) and input(s) in the circuit. Figure 11.3 ( 11-2 ), in the satellite handbook, explains more. Very clear is : every module must be on the right place ! The part ( in the formula above ) : 10to(Ft/10) is the system noise factor fT.

Calculation Signal Noise Ratio : SNR.


Prs is the received signal power, the power sum, ps ( see above ).

You find some calculations ( examples ) in : the VUSat transponder ( fourth submenu button ). And a script ( JAVA ) which calculates all the formulas, described. Also reachable via the fifth submenu button.