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 ).

Ptrn(mW)=k•Trs•B=>Ptrn(dBmW)=10log(k•Trs•B)=10logk+10logTrs+10logB.

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.

Trs=Tr+Tsky.

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.

Tr=Ta[10to(Ft/10)-1].

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.

SNR(dB)=Prs(dBmW)-Ptrn(dBmW).

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.