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Free Space Pathloss Calculation and EME link budget

by DF9CY Christoph Petermann ©

Part 1 - JAVA application


Please let me know, if you like this calculator. The JAVA source code of EME System Calculator is also availbale for you here. This ZIP File contains the CLASS Files AND the JAVA File.

The latest version however is integrated into the VMT software package.

Part 2 - EXCEL Spreadsheet

How do I calculate the effective range of my station in free space environment ? The solution is quite simple: Add all known parameters of your station, take the formula for free space path loss and don't forget the Boltzmann konstant.

I have added a Microsoft EXCEL (Version 5 or 7) spreadsheet EME System Sheet, where you can enter or modify all parameters and see immediately the effect on the result. This spreadsheet works correct and takes care of all noise contibutions to your system. Moon noise cannot be calculated.

Part 3 - Fundamentals

Propagation on the earth's surface is a different problems and this adds a number of restrictions.

Moonbounce propagation adds other difficulties:

The virtual diameter of the moon is ca. 0.5° it is a certain fraction of the whole sphere. Therefore an additional loss of around 50 dB has to be introduced. Doing so you will come to the general RADAR equation:

     a * Pt * Gr * Gt * La^2
      ( 4 * PI )^2 * d^2

a: cross section of target
Pr: receive power
Tr: transmit power
Gr: gain of receive antenna
Gt: gain of transmit antenna
La: Lambda = wavelength
d: distance to target

Here is the "dB" version:

Pr [dB] = Pt + Gr + Gt + 10 * log (a) + 20 * log (f) + 40 log (d) - 103.4

   d in km
   a in m^2
   f in MHz

The reflectivity of the moon is only 7%

Here is a calculation example for standard free space propagation:

Noise power calculation
Definition: Noise Power NP = 4 * KTB / (4*R) = KTB


   K  = Boltzmann konstant    = 1.38E-23 J/K
   B  = Bandwidth in Hertz
   T  = Ambient temperature   = use 290 K (Kelvin!) 
                                /* no Celsius or Fahrenheit ...*/
   NF = Noise Figure in dB      /* ideally should be 
                                 transformed to Noise temperature !!! */

   SNR= Signal to Noise Ratio for detection

Definition: Pathloss Pl = 32.45 + 20*log(f) + 20*log(d)


   f  = Frequency in MHz
   d  = distance in kilometers

Antenna gains should be given in dBi, that means dB over an isotropic
radiator. IF your gain is in dBd /* db over halfwave dipole */ 
then add 2.14 dB to your value.

Here is an example from the EXCEL speadsheet:

Free space path loss calculation (April 1997)                                       


Christoph Petermann     09.04.1997                              
Pommernweg 11                                       
D24229 Schwedeneck                               


The framed fields may be changed only !                                     

Signal to Noise Ratio / Sensitivity Limit                                       


Noise Power P = 4 k T B / ( 4 R ) = k T B                                   
Bandwidth B [Hz] =                    1,0E+02 Hz                        
Boltzmann Konst. [ J/ K]=             1,38E-23 J /K                     
Temperature [K] =                     290,00 K                      
Noise Power [dBm]@290K                -153,98 dBm                       

My systems Signal to Noise Ratio:                                   

SNR [dB]                              5,00 dB                       
Receiver Noise figure                 0,30 dB                       
Receiver Noise temperature            20,74 K                       
Losses prior to LNA                   0,20 dB                       
Losses in Noise Temperature           13,67 K                       
Antenna temperature (Sky)             20,00 K                       
All system Noise Temperature          40,94 K                       
Noise Power [dBm]@T_sys                -162,48 dBm                      
Sensitivity [dBm]@T_sys               -157,18 dBm                       

Calculation of maximum possible Free Space Range                                     

Transmit antenna gain                 35,00 dBi Gain over isotropic                 
Receive antenna gain                  35,00 dBi                     
Transmit power                        60,00 dBm                     
         equal to                     30,00 dBW                     
         equal to                     1000,00 Watt                      
Receive Sensitivity                   -157,18 dBm                       
Frequency                             1296,00 MHz                       

Maximum path loss incl. antenna gains                                   

         Pl=                          287,18 dB                     
         Range out of Pl=32.45+20log(f)+20log(d)                                    
         R=                           4206                       

EME Pathloss for a given frequency                                       

         Frequency                    1296,00 MHz
         Moon distance                386000,00 km
         Moon diameter                3400,00 km
         RADAR Equation               53,14 dB
         reflectivity of Moon surface 7,00 %

         Pathloss                     277,15 dB

         Expected Signal to noise ratio 
                                      10,03 dB


PL=32.45 + 20*log(Moondistance * 2) + 20*log(f)
   + Spherical loss from RADAR equ. + reflectivity loss                 

reflectivity loss : the moons' surface reflects only 7% to the earth                    
RADAR Equation: the virtual moon represents only a fraction of the total sphere.                    
Therefore an additional loss must be introduced. 
This is called in general the RADAR EQUATION                

© C.Petermann DF9CY June 1997                       

"References: VHF/UHF Manual; ARRL Publications et al."                      

The calculations are valid for free space only                      

Text and All Images are Copyright by Christoph Petermann DF9CY

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