Last Updated on January 18, 2025 by John Berry
Using first principles, I calculate the round-trip EME path loss at 245dBi at 144MHz. My calculations show a 10dB margin, making EME at 144MHz possible between two well equipped stations. Below I calculate an EME path budget for the three ‘beginner’ bands. As I show, the margin improves to 15dB at 432MHz, and to 7dB at 1296MHz (with a 1.9m dish).
For every dB of positive margin, the received signal will rise above the minimum of -28 (dB with respect to the 2.5kHz bandwidth noise). So, stations equipped as I’ve described will, all other things being equal, enjoy signal reports of -18 at 144MHZ, -13 at 432MHz, and -21 at 1296MHz. This is bourn out in practice.
I’ve set out my calculations below, 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.
Simply scan down the table for each frequency and focus on the Margin result at the bottom. Then read on.
The EME path budget
| Parameter | Value | Value | Value | Unit | Comment |
|---|---|---|---|---|---|
| Frequency | 144 | 432 | 1296 | MHz | |
| Transmission losses | |||||
| Antenna gain at TX [1] | 20 | 22 | 23 | dBi | 144MHz: 4 x 8-element Yagi array. 432MHz: 4 x 14-element Yagi array. 1296MHz: 1.9m dish*. |
| Free Space Loss (FSL) [2] | -375 | -395 | -414 | dBi | At apogee, as 2 x [32.4 + 20log f + 20log d]. |
| Moon reflection loss [3] | -12 | -12 | -12 | dB | As 10log[6.5%], Rho, reflection coef. = 6.5%*** |
| Billboard or passive reflector gain [4] | 143 | 162 | 181 | dB | As 42.9 + 40log f + 20log Ae, where Ae is the effective area. An effective area of 70% of disk is assumed. |
| Path loss [5] as [2] + [3]+ [4] | -245 | -245 | -245 | dBi | Compares favourably with the oft-quoted 252dB (which may not include correction for effective area). |
| Libration fading loss [A] | 0 | 0 | 0 | dB | Varies from -23dB (loss) to +10dB (gain). Sporadic. Avoid periods of fading. |
| Sky noise degradation [B] | 0 | 0 | 0 | dB | Varies as sky background. From 2dB to 12dB. Avoid pointing at a noisy sky region. |
| Amplitude scintillation fading [C] | 0 | 0 | 0 | dB | Small variations in the refractivity of the tropospheric part of the path. |
| Moonrise/moonset ground gain [D] | 0 | 0 | 0 | dB | 6dB when Moon is just above horizon. |
| Geometric rotation polarisation loss [E] | 0 | 0 | 0 | dB | Since a horizontally polarised wave can be received vertically polarised. |
| Faraday rotation loss [F] | 0 | 0 | 0 | dB | Polarisation rotation as wave transits ionosphere. |
| Antenna gain at RX [6] | 20 | 22 | 23 | dBi | 144MHz: 4 x 8-element Yagi array. 432MHz: 4 x 14-element Yagi array. 1296MHz: 1.9m dish. |
| Feeder loss at RX [7] | 0 | 0 | 0 | dB | From array to RX. Balanced by the presence of the low-noise amplifier. |
| Total gains minus total losses [8] as [1] + [5] + [6] + [7] | -205 | -201 | -199 | dB | Sum of losses and gains from FSL down. Is Total Loss. |
| System Value | |||||
| Receiver threshold [9] | -159 | -159 | -159 | dBW | The 2.5kHz sensitivity of a typical ham rig for 0dB signal to noise. |
| Coding/ bandwidth gain [10] | 28 | 28 | 28 | dB | Bandwidth factor as 10log (2500/50), plus JT65 coding gain. See bibliography. |
| Antenna system threshold degradation (-ve) or improvement (+ve) [11] | -1** | 2** | 2** | dB | Considering system noise with the low-noise amplifier in place. See bibliography. See note below. |
| Effective JT65/Q65 threshold [12] as [9] – [10] – [11] | -188 | -189 | -189 | dBW | Including threshold degradation. |
| TX output power [13] | 27 | 27 | 17 | dBW | As 500W RF at antenna at 144MHz and 432MHz, and 50W at 1296MHz. |
| System Value [14] as [12] – [13] | 215 | 216 | 206 | dB | As the maximum loss between TX output and RX input for viable operation. |
| Margin [15] as [14] + [8] | 10 | 15 | 7 | dB | System Value minus Total Loss |
| Typical indicated received signal as [15] minus [10] | -18 | -13 | -21 | dB | As indicated in applications like WSJT-x. |
* Regulators may demand a larger dish size in the future as a condition of secondary use of the 23cm band. This is to control inter-service interference. They may demand a minimum of 3m (30dBi) as agreed at WRC-23. The dish must be elevated at >15 degrees to the horizon.
** Bibliography from 2005 suggests that this might be a bit light. Typically ham rigs have relatively poor front end noise figures. Use of a mast-head mounted LNA with a noise figure of around 0.5dB will possibly give a 4-5dB improvement in each case.
*** There has been some work done to determine the Moon’s reflection coefficient with frequency – up to 11% at 1296MHz is proposed by one author. But there’s no conclusion so 6.5% is assumed.
Comments on the calculations
The margins and received signals shown above are the best that can be expected. This assumes the fairly good stations described in the Comments column.
The path loss rises with frequency. We know that. And the Moon becomes a better reflector as frequency rises: the electrical size rises as the wavelength reduces. That’s logical. So the increasing loss is balanced by the improved reflection.
And I’ve included a calculation for the effective reflective area of the Moon, assuming that only the inner 70% is effective. But that may be optimistic. It’s difficult to see what others have used in their calculations. If it’s less, the EME path budget will be further constrained.
See my adjacent page for details. Values are rounded up or down as appropriate.
Margin for viable comms
So, given a margin of 10dB, EME will work at 144MHz for a decent percentage of time with two stations. However, those stations must run 500W transmitters, four-stack arrays and JT65. Things will, of course, improve at perigee. See elsewhere a discussion on how variables aggregate to yield a chance of communication. And a low noise amplifier at the mast head is always needed on receive to overcome feeder losses.
This EME path budget calculation illustrates that reliable communication at 144MHz is possible. If hams allow losses to creep in by using poor feeder, if a lesser transmission system (such as CW) is used, or if lower RF power is used, the path will be more susceptible to degradation.
Conversely, at perigee the chance of communications improves despite degrading effects. And bigger stations at 144MHz give more operational certainty. It’s why a marginal station (like that described here) will need to rely on bigger stations for QSOs when conditions are less than optimal.
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 162dB. So, despite the Free Space Path loss rise on using 432MHz, a margin of about 15dB is available.
EME on 432MHz is more likely, with more in hand to overcome degradation.
At 1296MHz
And at 1296MHz, the billboard reflector gain again compensates for the increased Free Space Path Loss. I’ve used a 1.9m dish antenna with a gain of 20dBi 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 margin of 10dB. Use of a 3m dish at both ends improves the margin to a whopping 30dB with a received signal of +2dB (above 2.5kHz bandwidth noise).
EME is considerably easier at 1296MHz with a higher chance of success, though the kit is more complex and costly.
Other variable losses in the EME path budget
There are several fading mechanisms yielding loss over optimum that may conspire to thwart success in all cases ([A], [B], [C], [E] and [F]). Some hams call those collectively, degradation. Sprinkle a bit of any or all of these effects and the result is catastrophic for communications. I also assume that there’s no ground gain [D]. These variables are discussed separately on other pages. They’re all set to zero in the above budgets, illustrating the most optimistic state (most pessimistic for ground gain). 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.