Christoph Petermann Homepage

 Free Space Pathloss Calculation and EME link budget

## by DF9CY Christoph Petermann ©

• Part 1
JAVA application for EME budget calculation
• Part 2
• Part 3
Fundamentals

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.

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.

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
Pr=------------------------------
( 4 * PI )^2 * d^2

a: cross section of target
Tr: transmit power
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

with
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

where:

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)

where

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 */
```

Here is an example from the EXCEL speadsheet:

```
Free space path loss calculation (April 1997)

---------------------------------------------

Christoph Petermann     09.04.1997
Pommernweg 11
D24229 Schwedeneck

www.df9cy.de

---------------------------------------------

The framed fields may be changed only !

Signal to Noise Ratio / Sensitivity Limit

Method

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
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
Transmit power                        60,00 dBm
equal to                     30,00 dBW
equal to                     1000,00 Watt
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 Mio.km

EME Pathloss for a given frequency

Frequency                    1296,00 MHz
Moon distance                386000,00 km
Moon diameter                3400,00 km
reflectivity of Moon surface 7,00 %

Pathloss                     277,15 dB

Expected Signal to noise ratio
10,03 dB

Method

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