EME Link Budget & Analysis Tool (1-100 GHz)
Gerald Ihninger OE2IGL ... Salzburg Mar 2023 (v231031)
Joachim Köppen DF3GJ ... Kiel Oct 2022
Why a new EME calc tool?
To get most reliable results all currently known dependencies are included.
At higher frequencies and/or smaller beam width additional dependencies must be taken into account.
Atmospheric loss, Ruze loss, beam pointing loss on moon, fill factor for sun/moon noise, beam width factor (BWF) for Tx/moon/Rx combination, libration spreading depends on BWF,... .
It is based on the article Radar Studies of the Moon by J.V.Evans in J.Res. National Bureau of Standards, Section D, p.1637 (1969),
available at https://nvlpubs.nist.gov/nistpubs/jres/69D/jresv69Dn12p1637_A1b.pdf , in particular on equation (2).
How to get best results or how to reduce unknown parameters? A step by step instruction:
Unknown parameters are mainly Tx power, Rx noise figure, dish efficiency/gain, spillover temp and real edge taper.
If you have a matched feed then use -11 dB as edge taper.
If possible make a Tx power measurement near your feed or use best estimation.
Make a sky profile measurement and use Joachim's tool to get a very accurate NF of your system. This method takes atmospheric attenuation into account.
Or make a cold noise (sky zenith), hot noise (absorber at ground temperature in front of the feed) measurement with the dish (not only with feed).
Check Y-Gnd in this EME tool and adjust RF noise figure until measured and calculated Y-Gnd are equal. Don't forget to enter weather conditions and elevation.
Make a moon noise measurement and adjust "used antenna efficiency" until SNR matches measured SNR. Max. efficiency is a good estimation if you have a very well matched feed. Surface roughness loss has a big influence at higher frequencies.
If possible make a moon echo measurement and adjust/check "Tx power" until SNR matches measured SNR.
Make a DL0SHF moon beacon measurement and check calculated SNR.
Now you are ready to make high accuracy SNR calculations with other stations.
Sun/Moon data:longitude [E]latitude [N]
day of year
Time [UTC] :
Sun (only optical refractive elevation corr.) RaDec AzEl Ang.Diameter [deg]
Moon (only optical refractive elevation corr.) RaDec AzEl Phase [0 = Full Moon] angle to Sun [clockwise from top] Distance [km] Ang.Diameter [deg]
Lunar reflectivity ε
Moon noise temp., add temp
Days after full moon
RX refrac.corr. elevation [°]
RX LOS atmosph.attenuation
UTC YY/MM/DD hh:mm:ss
Isotropic path loss (radar equation)
Path loss (corrected for beam widths)
ε * gainTX * gainRX
TX power [W]
Received signal power
RX NoiseFigure [dB], temp
RX bandwidth [kHz]
RX noise power
Received Moon noise
Sky+CMB, zenith+CMB temp
Spillover temp., add. spillover
RX main beam effic. ηMB, ηF
Spatial polarization, pol.loss
The link budget of an EME communication is described by the radar range equation
PRX = PTX GTX GRX
λ² A ε / (64 π³ d²TX d²RX)
with the transmitter power PTX, the gains
GTX, GRX of transmitting and receiving antennas, the wavelength λ, the area A = π R²moon
of the target (the lunar disc), the reflectivity ε ≈ 0.07 of the lunar soil, and the distances
dTX, dRX between Moon and antennas.
In this equation, the target is taken to subtend a small angle compared to the HPBWs of both antennas. Not taken into account are the elevation-dependent attenuation on the path
through the Earth atmosphere at either end and any variation of the lunar reflectivity across the face of the Moon.
The (imaginary) isotropic antennas will fully and evenly illuminate the lunar disc as well as receive the reflected signal from the entire disc.
This is expressed in the overall EME isotropic path loss
The gains of real antennas compensate this loss. But at higher frequencies and/or with large antennas the radiation patterns may become comparable or even more narrow than the
Moon. Then it is necessary to take into account:
if the transmitting antenna's HPBW is smaller than the Moon's angular diameter, the lunar disc is only partially illuminated, as the power in the beam of the
transmitting antenna will be concentrated in a 'bright' spot on the lunar disc. Only this spot will contribute to the reflected signal.
if the receiving antenna's HPBW is smaller the angular size of the illuminated spot, it can receive only some part of the power reflected by the Moon.
if the receiving antenna's HPBW is smaller than the Moon, it picks up only some part of the Moon's thermal noise.
The correction factor to the radar range equation which deals with how well the antenna beams cover the Moon as well as each other is computed from the radiation
patterns, and thus may appropriately be called the Beam Width Factor:
BWF = ∫ ΦTX(x,y) ΦRX(r) dx dy / (π R²moon)
For a better understanding it is useful to split up the BWF into two factors:
measures how much of the lunar disc is illuminated by the transmitting antenna. Note that the illumination factor is quite different from the Moon's filling factor
in the transmitting beam, which is the fraction of beam power received by the Moon.
The beam overlap factor
beam_overlap = ∫ ΦTX(x,y) ΦRX(x,y) dx dy / ∫ ΦTX(x,y) dx dy
indicates the degree by which the transmitting and receiving beam patterns overlap on the lunar disc.
As before, all integrals are taken over the lunar disc. It is worth noting that if both beams have the same width and smaller than the lunar disc, the overlap
factor is 0.5 for any width. Hence, having the same narrow beam in both antennas alone is responsible for a 3 dB loss in the signal level.
The Reflectivity of the Moon can be taken to be constant across the lunar disc (default) or to vary with distance from the disc centre as estimated for
this frequency from measurements (derived from Fig.10 in Evans(1969), and other works).
The image of the Moon can be displayed with:
illumination of the Moon by the transmitting antenna
relative intensity of the reflected power
relative intensity of the received signal
The intercepted power fraction is the part of the power
which is captured by the Moon.
The illuminated fraction is the part of the lunar disc which
is illuminated by the transmitting antenna.
The received fraction (BWF) or Beam Width Factor is the ratio
of the power from the illuminated spot received by the receiving antenna's beam
and the illuminated fraction of the Moon. This factor is smaller than 1,
and describes the additional loss due to the use of beams narrower than the Moon,
in comparison with the received power estimated from the radar range equation.
The isotrop. path loss (radar equation) is the path loss computed with the radar
range equation and isotropic antennas, and is what one would expect for a fully and
evenly illuminated Moon, observed by a large beam receiving antenna.
The path loss, corrected for beam widths also includes the losses due to
the smaller antenna beams.
The entire sky contributes to noise from the thermal emission
by the Earth atmosphere, and from the Cosmic Microwave Background radiation.
For the radiation pattern of each antenna one may select among these shapes:
evenly illuminated circular dish
Rather than performing tedious calculations with the detailed radiation pattern, it is
convenient to distinguish three parts in it:
The Main beam or lobe is directed to the target. Its fraction in the whole pattern
is described by the (main) beam efficiency ηB. A lower value of η implies
that the antenna picks up more ground noise via side and back lobes, which results in
a lower S/N ratio. If the reflector's surface is not smoother than about a tenth of the
wavelength, these uneven structures cause scattering from the main beam into all other
directions, and a corresponding loss (Ruze's equation). Side lobes are lobes next to the main beam. Here the antenna is less sensitive,
but it may well pick up a strong source, like the Sun, which then would render the measurements
useless. Further away from the main lobe, there can be angles where the antenna feed
looks beyond the rim of the dish and picks up noise from the ground or buildings
behind the dish ("spill-over"). Back lobes are the angles opposite the main beam. Here the antenna receives
noise from the ground, when it points to the sky.
Light green fields are inputs required from the user. Hit the Enter key to display the new results.
When a parameter is outside the range of validity for the approximations used in this tool, its fields is marked yellow.
Enter date, time, frequency and weather conditions.
Select stored "locator-call-band" Tx and Rx systems from drop down menu or set your desired locator and Tx/Rx system.
"max. antenna efficiency is calculated/shown. Enter your "used antenna efficiency" that matches reality as best as possible.
Select "use (real) time locked TX/RX elevation for:" for moon or sun if you want to use calculated moon or sun elevation automatically. Then, for the moon it is possible to track S/N in real time.
Field "sun temp" should be 0. The tool automatically uses published standard sun temperatures for all frequency ranges. Sometimes it is necessary to adjust
sun temperature in case of sun activity at frequencies < 20 GHz. Then you can use the field "sun temp". Enter a sun temp until you have reached SFU at your frequency. Sun Radio Flux is a great help to find SFU values the last 45 days.
Older data (since 2002) can be fould in Joachim's Sun Radio Flux file or use his
These standard sun brightness temperatures/flux are used (black body radiation and A.O. Benz), optical solar disk with a diameter of 32', center temperature is lower:
10368 MHz : 12950 K, 292 SFU (depends strongly on sun activity)
24048 MHz : 10475 K, 1270 SFU
47088 MHz : 8840 K, 4110 SFU
76032 MHz : 7840 K, 9500 SFU
122250 MHz: 6960 K, 21800 SFU
241920 MHz: 5860 K, 71800 SFU
To calculate the dish gain loss due to a mesh grid then enter wire diameter and grid spacing >0 mm.
Y-Gnd measurement: Make a cold sky noise measurement at zenith (elevation = 90°) with a dish. Don't use only the feed.
At higher frequencies the atmospheric loss is too high and sky noise is not constant over elevation.
Due to the high HPBW of the feed not only the (lowest) sky noise in zenith is measured.
For hot noise measurement use an absorber (e.g. Eccosorb HR-25) at ground temperature in front of the feed. Use only this method because formula in background is optimized for this.
Because it is not easy to track the moon with very accuracy (~0.01°) for BOTH antennas at higher frequencies/ bigger dishes we suffer from an increased loss.
For a good tracking system use "Position x,y on Moon" of -0.035°/-0.035° and +0.035°/+0.035° as worst case. For a standard tracking system use -0.1°/-0.1° and +0.1°/+0.1°.
Search for next maximum margin of S/N EME in the future after activation of "locked elevation: MOON" and using button "timestep +30min".
This depends on S/N EME and decoder threshold based on libration rate. The tool automatically searches for the next time slot with maximum "S/N EME - decoder threshold" and shows the date/time.
This function is usful for extreme EME at 47 GHz or with small dishes or low Tx power.
Assumptions & limitations:
For frequencies above 1 GHz.
Type of feed has a big influence on illumination (and spillover) efficiency. The feed has to match dish f/D and edge taper. If you have a sub-optimal feed ηi*ηs is below 81.5%.
Because of this the tool uses theoretical efficiency -5% to be more realistic. Theoretical efficiency is calculated with gaussian beam and edge taper of -10 dB to get max. 81.5%.
Product ηi*ηs defines HPBW of the dish. Additional efficiences doesn't influence HPBW but will further reduce dish gain.
Because there are often misleading wordings, relations and consequences on efficiencies please read more about antenna efficiency theory in my antenna basics
and feed pattern, dish illumination
If there is a simulated feed pattern available, resulting ηi and ηs should be used to get more reliable end results.
Dish forward efficiency ηF is also needed. It is quoted that it is feed efficiency (= 1 - ηs - 1% to 2% efficiency loss due to dish rim scatter).
As long as simulated/measured ηs has not been entered I use a fixed value of 0.85 which fits most cases.
Clear sky weather for sun/moon noise measurement without any thick atmospheric inversion layers
Lunar reflectivity and moon temperature data are from the 60's, 70's and 80s. There aren't newer data available and all these data have great variation.
A summary of these data and a simulation model is available here "moon brightness temperature"
For prime focus and offset dish
Drop down menu for locators-calls with stored system data
HPBW depend on edge taper/beam shape factor (illumination and spillover efficiency)
Sun temp curve fit (based on A.O.Benz)
Moon temp formula depending on moon cycle and most reliable scientific values from the 60s to now
Changing moon reflectivity over surface (curve fit by Joachim Köppen)
Tx, Rx beam pointing accuracy on moon and resulting loss
Beam width factor (BWF) and resulting signal loss for 2-way EME
Fill factor for moon/(sun) S/N measurement
S/N formulas for prime focus/offset dish
If polarization rotation is not compensated you have to add polarization loss to S/N. Values are shown if "use (real) time locked TX/TX elevation for:" for moon is used
Calculation of dish center - rim distance (half-angle dish opening) and necessary feed taper for given dish edge taper
Calculation of atmosph. attenuation ITU-R P.676-10 (09/2013), Appendix 2 until 350 GHz
Calculation of G/T including system noise temperature
Calculation of mesh grid loss (based on T.Y.Otoshi)
Max. achievable dish efficiencies based on gaussian beam and all other losses
Use illumination and spillover efficiency from simulated or measured feed pattern instead of gaussian beam
Correct frequency spreading due to moon libration, Rx,Tx beam width and sun/moon diameter
Decoder threshold for SSB, CW, Q65
Azimuth, elevation, distance ... of sun, moon for given location and date/time
Calculator from QTH locator into latitude, longitude
Spillover temp based on f/D, offset angle and elevation
Because of stronger water vapor changes in atmosphere radio waves are bended stronger than VIS waves (higher refraction). Astronomical formula uses VIS refractive correction.
I use refractive correction for radio waves to get most accurate elevation data (error max. 0.01°).
Some (mainly unknown) parameters are not locked. You can play with these parameters
Tx/Rx elevations can be coupled/locked to sun or moon elevation to analyze manually, standard is free elevation input
Live modus (auto play) to see & follow S/N in real time
Search for maximum margin of S/N EME in the future. More under hints.
Map with "illumination of the Moon by the transmitting antenna" or "relative intensity of the reflected power" or "relative intensity of the received signal", and Rx beam width
Button for echo mode (Rx=Tx)
Button for swap mode (Rx<=>Tx)
For a better understanding of moon temperature over moon phases see here.
More EME tools from Joachim DF3GJ see here.
More about antenna related topics from Joachim DF3GJ see here.
What's about clouds and rain?
There are a lot of useful papers from ITU-R.
Clouds are not really a big problem. At 10 GHz cloud loss is 0.001 dB/km.
The biggest problem is rain or invisible rain in clouds. Fog is relevant above 47 GHz.
At 47 GHz cloud loss is 0.04 dB/km for less fog.
At 47 GHz cloud loss is 0.085 dB/km for medium fog (vis 300 m).
At 47 GHz cloud loss is 0.85 dB/km for thick fog (vis 50 m).