|
EME free-space path-loss calculation
Original calculator was DF6CY's Excel sheet: df9cy-eme-pathloss.xls
Results:
| |
|
|
|
|---|
Receiver signal-to-noise ratio, and sensitivity limit
|
|---|
| | Rx bandwidth: | 100 | Hz |
|---|
| | Rx temperature: | 290 | Kelvin [K] |
|---|
| | Internal Noise Power: | -154.0 | dBm |
|---|
| |
My system Signal to Noise Ratio:
|
|---|
| | Wanted SNR: | 5.0 | dB |
|---|
| | Rx Noise Figure: | 2.00 | dB |
|---|
| | Rx Noise Temperature: | 169.6 | Kelvin [K] |
|---|
| |
|---|
| | Losses prior to LNA: | 0.20 | dB |
|---|
| | .. as Noise Temperature: | 13.7 | Kelvin [K] |
|---|
| |
|---|
| | Antenna (Sky) temp: | 20.0 | Kelvin [K] |
|---|
| |
|---|
| | Sum of Noise Temps: | 203.3 | Kelvin [K] |
|---|
| | .. as noise power: | -155.5 | dBm |
|---|
| |
|---|
| | Rx Sensitivity: | -153.5 | dBm |
|---|
Calculation of maximum possible Free Space Range:
|
|---|
| | Tx Antenna Gain: | 30.0 | dB |
|---|
| | Rx Antenna Gain: | 30.0 | dB |
|---|
| |
|---|
| | Tx power: | 30.0 | dBm |
|---|
| | | 0.0 | dBW |
|---|
| | | 1.000 | W |
|---|
| |
|---|
| | Rx Sensitivity: | -153.5 | dBm |
|---|
| |
|---|
| | Frequency: | 2.450 | GHz |
|---|
| |
|---|
| | Path Loss Budget, including antenna gains: |
|---|
| | | 243.5 | dB |
|---|
| |
|---|
| | One Way Range of Free Space Path Loss Budget,
millions of kilometers: |
|---|
| | | 14.600 | M km |
|---|
EME round-trip computation:
|
|---|
| | Frequency: | 2.450 | GHz |
|---|
| |
|---|
| | Moon diameter: | 3400 | km |
|---|
| | Moon distance: |
|---|
| | @ Apogee: | 406700 | km |
|---|
| | @ "mean": | 384400 | km |
|---|
| | @ Perigee: | 356400 | km |
|---|
| | Moon (RF) alebo: | 7.0 | % |
|---|
| |
|---|
| | RADAR Equation: |
|---|
| | @ Apogee: | 53.6 | dB |
|---|
| | @ "mean": | 53.1 | dB |
|---|
| | @ Perigee: | 52.5 | dB |
|---|
| |
|---|
| | EME Path Loss: |
|---|
| | @ Apogee: | 283.6 | dB |
|---|
| | @ "mean": | 282.6 | dB |
|---|
| | @ Perigee: | 281.3 | dB |
|---|
| |
|---|
| | Expected roundtrip Signal-to-Noise ratio: |
|---|
| | @ Apogee: | -40.1 | dB |
|---|
| | @ "mean": | -39.1 | dB |
|---|
| | @ Perigee: | -37.8 | dB |
|---|
Above all decibel values are with one decimal, all others are with 2-3 significant numbers due to the accuracy (or lack, thereof) of the input values.
That is: 12.34567, and 0.001234567 should be considered as 12.3 and 0.00123 respectively!
The computation method:
Source for this page
# Rx Noise Power = k T RxBW; T = 290 K
#$RxTemp = 290.0; # 290 Kelvins
$k = 1.38E-23; # Bolzman constant
$MoonDist3 = 406700.0; # Apogee distance
$MoonDist2 = 384400.0; # "Mean" distance
$MoonDist1 = 356400.0; # Perigee distance
$MoonReflectivity = 0.07;
## This is quite good value for any frequency 10 thru 30 000 MHz.
$RxNoisePwr = 10.0 * log10($RXBW * $RxTemp * $k) + 30.0; # dBW -> dBm
$RxNFTemp = (10.0 ** ( $RXNF * 0.1)) * $RxTemp - $RxTemp;
$RxLossTemp = (10.0 ** ( $RXLOSS * 0.1)) * $RxTemp - $RxTemp;
$SysNoiseTemp = $ANTTEMP + $RxNFTemp + $RxLossTemp;
$SysNoisePower = 10.0 * log10($RXBW * $SysNoiseTemp * $k) + 30.0; # dBW -> dBm
$RxSensitivity = $SysNoisePower + $RXNF;
# [ TXPOWER in dBm ]
$PathLossBudget = $RXANTGAIN + $TXANTGAIN + $TXPOWER - $RxSensitivity;
# Path Loss Range in millions of kilometers..
# FREQ in GHz, must convert to MHz..
$PathRangeGM = 10.0 ** (($PathLossBudget - 32.45 -
20 * log10($FREQ * 1000.0))/20) / 1E6;
$EMERadarEQ = 10.0 * log10( 4.0 * $MoonDist ** 2
/ ($MOONDIAM ** 2 / 4));
$EMEPathLoss = ( 32.45 + # Magic RADAR constant..
20 * log10($FREQ * 1000.0) + # FREQ in MHz, raised to 2nd
# power after taking the log..
20 * log10($MoonDist * 2.0) + # Twice the distance, and
# raised to 2nd power after
# taking the log..
$EMERadarEQ -
10 * log10( $MoonReflectivity ));
$ExpectedEMEsnr = $PathLossBudget - $EMEPathLoss;
EME path-loss graph per frequency:
Tom A. Clark, W3IWI
Note: The graph above (and the math behind it) does differ from calculations given above, and is giving circa 10 dB smaller path-loss, than what is calculated above..
Matti Aarnio <matti.aarnio@zmailer.org>; OH2MQK
| 
