EME path budget

Empirically, hams have measured the EME path budget at about 252dB at 144MHz. If this is dBd, I’d agree. My calculations show a -2.5dB margin, making EME at 144MHz tricky. As I show below, the margin improves to 16dB at 432MHz, and to 27dB at 1296MHz, making EME progressively easier at higher frequencies.

I’ve set out my calculations below for Earth-Moon-Earth communications. And there’s a description of the path loss calculation on an adjacent page. I’ll update this sheet and the loss rationale page as my understanding grows.

I’ve done three path budgets – for 144MHz, 432MHz and 1296MHz.

Simply scan down the table for each frequency and focus on the Margin result at the bottom. Then read on.

The EME path budget

Transmission losses
Antenna gain at TX [1]202428dBi144MHz: 4 x 8-element Yagi array. 432MHz: 4 x 14-element Yagi array. 1296MHz: 2.4m dish.
Free Space Loss (FSL) [2]-387-395-414dBiAt apogee, as 2 x [32.4 + 20log f + 20log d].
Moon reflection loss [3]-12-12-12dBAs 10log[6.5%], Rho, reflection coef. = 6.5%
Billboard or passive reflector gain [4]143161181dBAs 20log((πd)22).
Path loss [5] as [2] + [3]+ [4]-256-246-245dBiCompares favourably with the oft-quoted 252dB.
Libration fading loss000dBVaries from -23dB to +10dB. Sporadic. Avoid periods of fading. See adjacent paper.
Sky noise degradation000dBVaries as sky background. From 2dB to 12dB. Avoid pointing at a noisy sky.
Scintillation loss000dBVariations in the path refractivity.
Moonrise ground gain000dB6dB when Moon is just above horizon.
Rotation (de-polarisation) loss000dBFaraday rotation as wave transits ionosphere.
Antenna gain at RX [6]202428dBi144MHz: 4 x 8-element Yagi array. 432MHz: 4 x 14-element Yagi array. 1296MHz: 2.4m dish.
Feeder loss at RX [7]000dBFrom array to RX. Balanced by the cascaded noise figure with the low-noise amplifier in place.
Total gains minus total losses [8] as [1] + [5] + [6] + [7]-216-204-189dBSum of losses and gains from FSL down.
System Value
Receiver threshold [9]-159-159-159dBWThe 2.5kHz sensitivity of a typical ham rig.
bandwidth gain [10]
282828dBBandwidth factor as 10log (2500/50), plus JT65 coding gain. See bibliography.
Antenna system threshold degradation or improvement [11]-0.5*2*2*dBConsidering cascaded noise figure with the low-noise amplifier in place. See bibliography. See System noise. See note below.
Effective JT65 threshold [12] as [9] – [10] – [11]-186.5-189-189dBW
TX output power [13]272727dBWAs 500W RF at antenna.
System Value [14] as [12] + [13]213.5216216dBAs the maximum loss between TX output and RX input for viable operation.
Margin [15] as [14] + [8]-2.51627dBSystem Value minus total loss
EME path budget: slightly negative margin at 144MHz, 16dB at 432MHz, 27dB at 1296MHz

* Bibliography from 2005 suggests that this might be a bit light – if the noise figures of modern receivers have not improved much since, the improvement from use of an LNA with a noise figure of around 0.5dB will possibly give a 4-5dB improvement in each case.

Margin for viable comms

So, given a margin of -2.5dB, EME will work at 144MHz for less than 50% of time with two stations running 500W transmitters, four-stack arrays and JT65. Things will, of course, improve to give a 0dB margin at perigee. See elsewhere a discussion on how variables aggregate to yield a chance of communication.

This EME path budget calculation illustrates that the communication at 144MHz is on a knife edge. If hams allow losses to creep in by using poor feeder, if a lesser transmission system is used, or if lower RF power is used, the path will be available for small percentages of time when conditions are more favourable than normal.

Conversely, at perigee, and perhaps with improvements like increased power, a few dB become available and the chance of communications improves. That’s why bigger stations at 144MHz give more operational certainty – and why a marginal station (like that described here) will need to rely on bigger stations for QSOs.

At 432MHz

At 432MHz on the other hand, the antenna gain available for the same sort of antenna size is about 4dB more. Since the billboard reflector gain is a function of 1/λ2, a reduction in wavelength from 2metres to 70cm gives a huge increase in gain from 143dB to about 161dB. So, despite the Free Space Path loss rise on using 432MHz, a margin of about 16dB is available.

EME is a lot easier on 432MHz than on 144MHz with a moderate chance of success.

At 1296MHz

And at 1296MHz, the billboard reflector gain more than compensates for the increased Free Space Path Loss. I’ve used a 2.4m dish with a gain of 28dBi as something typical for a typical garden. All other parameters from references and the IC-9700 handbook are the same as the lower bands. The result is a heightened margin of 27dB.

EME is considerably easier at 1296MHz with a high chance of success, though the kit is more complex and costly.

Other variable losses

There are also several fading mechanisms that may conspire to thwart success in both cases. Some hams call those collectively, degradation. I haven’t discussed those. They’re all set to zero in the above budgets, illustrating the most optimistic state. For a viable path the margin should be significantly above zero to accommodate this fading and avoidance . The fading mechanisms, and the fade margins needed, are discussed elsewhere on this site.

As a final note, I’ve not included anything for pointing loss – the loss resulting from imperfect pointing of the antenna (at the moon). The gain of all antenna types used falls away off the bore sight. Pointing will be more difficult at higher frequencies as beamwidths narrow, and hence loss through imperfect pointing will rise with frequency. More on this later.