| Christoph Petermann | Homepage |
|
Free Space Pathloss Calculation and EME link budget |
Part 1 - JAVA application
DOWNLOAD !
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
Pr=------------------------------
( 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 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 */
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
http://home.t-online.de/home/df9cy.petermann AND 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
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 Mio.km
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
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
© 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
|
GO (back) and visit my homepage