Above is an archived extract of a spreadsheet that was very popular in the ham community, both with antenna designers and sellers and end users (buyers / constructors). It shows a column entitled G/T which is actually the hammy calculation. The meaning possibly derives from (Bertelsmeier 1987), he used G/Ta.

Ta is commonly interpreted by hams to be Temperature – antenna. It is true that antennas have an intrinsic equivalent noise temperature, it relates to their loss and physical temperature and is typically a very small number. But as Bertelsmeier uses it, it is Temperature – ambient (or external), and that is how it is used in this article.

Let’s calculate the G/Ta statistic for the three scenarios in Do I ‘need’ a masthead preamp to work satellites on 2m? – space noise scenario.

Above is a calculation of the base scenario, G/T=-29.74dB/K.

Also shown in this screenshot is G/Ta=-23.98dB/K.

Above is a calculation of the masthead amplifier scenario, G/T=-25.21dB/K.

Also shown in this screenshot is G/Ta=-23.98dB/K.

Above is a calculation of the LNA at the receiver scenario, G/T=-25.754dB/K.

Also shown in this screenshot is G/Ta=-23.98dB/K.

Scenario | G/T (dB/K) | G/Ta (dB/K) |

Base | -29.74 | -23.98 |

With masthead LNA Gain=20dB NF=1dB | -25.21 | -23.98 |

With local LNA Gain=20dB NF=1dB | -25.75 | -23.98 |

Note that G/Ta is the same for all three configurations, it does not contain the important information that differentiates the performance of the three configurations.

Importantly, you cannot derive G/T from G/Ta without knowing either G or Ta (and some other important stuff), the G/Ta figure by itself cannot be ‘unwound’… so if you select an antenna ranked on a G/Ta value (even if mislabeled), the ranking of ‘real’ G/T may be different depending on many factors specific to your own scenario, ie the one with the better G/Ta might have the poorer G/T.

- Bertelsmeier, R. 1987. Equivalent noise temperatures of 4-Yagi-arrays for 432MHz. DUBUS..
- Duffy, O. 2006. Effective use of a Low Noise Amplifier on VHF/UHF. VK1OD.net.
- ———. 2007. Measuring system G/T ratio using Sun noise. VK1OD.net.
- ———. 2009. Quiet sun radio flux interpolations. https://owenduffy.net/calc/qsrf/index.htm.
- ITU-R. 2000. Recommendation ITU-R S.733-2 (2000) Determination of the G/T ratio for earth stations operating in the fixed-satellite service .

Base scenario is a low end satellite ground station:

- 144MHz;
- terrestrial noise (satellite with omni antenna);
- IC-9700, assume NF=4.8dB;
- omni antenna;
- 10m of LMR-400.

A metric that may be used to express the performance of an entire receive system is the ratio of antenna gain to total equivalent noise temperature, usually expressed in deciBels as dB/K. G/T is widely used in design and specification of satellite communications systems.

G/T=AntennaGain/TotalNoiseTemperature 1/K

Example: if AntennaGain=50 and TotalNoiseTemperature=120K, then \(G/T=\frac{50}{120}=0.416 \text{ } 1/K\) or -3.8 dB/K**.**

The utility of G/T is that receive S/N changes dB for dB with G/T, in fact you can calculate S/N knowing G/T, wavelength, bandwidth and the field strength of the signal (Duffy 2007).

\(Signal/Noise=S \frac{\lambda^2}{4 \pi} \frac{G}{T} \frac1{k_b B}\) where:

S is power flux density;

λ is wavelength;

k_{b} is Boltzmann’s constant; and

B is receiver equivalent noise bandwidth

Usage in this article is consistent with the industry standard meaning of G/T given at (ITU-R. 2000) (as opposed to the meaning used by some Hams who have appropriated the term for their own purpose).

Note this is not the bodgy G/T figure used widely in ham circles.

Ambient noise temperature Ta is an important factor in calculation of G/T. Ta depends on frequency, the environment, the antenna’s ability to reduce off boresight noise, and the on-boresight noise. For the purposes of this discussion let’s assume total ambient noise for the given omni satellite scenario at 144MHz is 1500K.

Above is a calculation of the base scenario, G/T=-33.41dB/K.

Above is a calculation of the masthead amplifier scenario, G/T=-31.99dB/K.

Scenario | G/T (dB/K) |

Base | -33.41 |

With masthead LNA Gain=20dB NF=1dB | -31.99 |

The first finding is that adding a masthead LNA with 20dB gain and 1dB NF makes only a small difference to G/T and hence S/N, just 1.4dB in this case.

The foregoing analysis assumed a linear receive system, no intermodulation distortion. Now let’s talk about the real world.

Some LNAs are sold without specifications, those that have meaningful NF and Gain specifications are usually based on laboratory measurements with no interfering signals.

When attached to an antenna, the out of band signals will give rise to noise due to intermodulation distortion, so the NF in-situ might be poorer than specification NF. Indeed, the IMD noise can be so great as to deliver worse G/T with the LNA.

One way of reducing IMD noise is to limit the amplitude of interfering signals arriving at the LNA active device, and front end filtering is one possible solution.

Be aware that lots of hammy Sammy LNA designs have very little front end selectivity, relying upon the narrow band response of a high gain antenna. When these are used with low gain tuned antennas, or worse, broadband antennas like Discones, the IMD noise can be huge.

On the other hand, there are LNAs available with a very narrow front end filter… but they cost a lot more.

The benefit / necessity of front end filtering depends on your own IMD scenario.

- Duffy, O. 2006. Effective use of a Low Noise Amplifier on VHF/UHF. VK1OD.net.
- ———. 2007. Measuring system G/T ratio using Sun noise. VK1OD.net.
- ———. 2009. Quiet sun radio flux interpolations. https://owenduffy.net/calc/qsrf/index.htm.
- ITU-R. 2000. Recommendation ITU-R S.733-2 (2000) Determination of the G/T ratio for earth stations operating in the fixed-satellite service .

Base scenario is a low end satellite ground station:

- 144MHz;
- satellite;
- IC-9700, assume NF=4.8dB;
- high gain (narrow beamwidth antenna);
- 10m of LMR-400.

A metric that may be used to express the performance of an entire receive system is the ratio of antenna gain to total equivalent noise temperature, usually expressed in deciBels as dB/K. G/T is widely used in design and specification of satellite communications systems.

G/T=AntennaGain/TotalNoiseTemperature 1/K

Example: if AntennaGain=50 and TotalNoiseTemperature=120K, then \(G/T=\frac{50}{120}=0.416 \text{ } 1/K\) or -3.8 dB/K**.**

The utility of G/T is that receive S/N changes dB for dB with G/T, in fact you can calculate S/N knowing G/T, wavelength, bandwidth and the field strength of the signal (Duffy 2007).

\(Signal/Noise=S \frac{\lambda^2}{4 \pi} \frac{G}{T} \frac1{k_b B}\) where:

S is power flux density;

λ is wavelength;

k_{b} is Boltzmann’s constant; and

B is receiver equivalent noise bandwidth

Usage in this article is consistent with the industry standard meaning of G/T given at (ITU-R. 2000) (as opposed to the meaning used by some Hams who have appropriated the term for their own purpose).

Note this is not the bodgy G/T figure used widely in ham circles.

Ambient noise temperature Ta is an important factor in calculation of G/T. Ta depends on frequency, the environment, the antenna’s ability to reduce off boresight noise, and the on-boresight noise. For the purposes of this discussion let’s assume total ambient noise for the given satellite scenario at 144MHz is 250K.

Above is a calculation of the base scenario, G/T=-29.74dB/K.

Above is a calculation of the masthead amplifier scenario, G/T=-25.21dB/K.

Above is a calculation of the LNA at the receiver scenario, G/T=-25.754dB/K.

Scenario | G/T (dB/K) |

Base | -29.74 |

With masthead LNA Gain=20dB NF=1dB | -25.21 |

With local LNA Gain=20dB NF=1dB | -25.75 |

The first finding is that adding a masthead LNA with 20dB gain and 1dB NF makes a small difference to G/T and hence S/N, 4.5dB in this case.

Note that there is only a small degradation in moving the LNA from masthead to local to the transceiver. There are additional reliability / maintenance issues with masthead located amplifiers… particularly if high performance narrow band front end filtering is used. It is much more practical to house a coaxial resonator (‘can’ in repeater parlance) in the shack that at the masthead.

The foregoing analysis assumed a linear receive system, no intermodulation distortion. Now let’s talk about the real world.

Some LNAs are sold without specifications, those that have meaningful NF and Gain specifications are usually based on laboratory measurements with no interfering signals.

When attached to an antenna, the out of band signals will give rise to noise due to intermodulation distortion, so the NF in-situ might be poorer than specification NF. Indeed, the IMD noise can be so great as to deliver worse G/T with the LNA.

One way of reducing IMD noise is to limit the amplitude of interfering signals arriving at the LNA active device, and front end filtering is one possible solution.

Be aware that lots of hammy Sammy LNA designs have very little front end selectivity, relying upon the narrow band response of a high gain antenna. When these are used with low gain tuned antennas, or worse, broadband antennas like Discones, the IMD noise can be huge.

On the other hand, there are LNAs available with a very narrow front end filter… but they cost a lot more.

The benefit / necessity of front end filtering depends on your own IMD scenario.

For satellite work, a low gain antenna will tend to have higher Ta by virtue of side lobe contribution, and so the improvement seen above might be diminished a little.

Terrestrial ambient noise is much higher, and the improvement would be considerably less. Likewise for an omni satellite antenna. In both cases, the improvement in G/T might be less than 1dB with the same masthead LNA… download the spreadsheet and explore.

As mentioned Ta is frequency dependent, so the case for 432MHz might be quite different than the above case. In particular, the choice of masthead mounting becomes clearer on higher frequencies.

- Duffy, O. 2006. Effective use of a Low Noise Amplifier on VHF/UHF. VK1OD.net.
- ———. 2007. Measuring system G/T ratio using Sun noise. VK1OD.net.
- ———. 2009. Quiet sun radio flux interpolations. https://owenduffy.net/calc/qsrf/index.htm.
- ITU-R. 2000. Recommendation ITU-R S.733-2 (2000) Determination of the G/T ratio for earth stations operating in the fixed-satellite service .

Despite efforts to make the transition transparent, some code in some calculators turned out to be less reliable on the new site and some changes made to make them reliable. QSRF was the main troublesome app, but is now stable and the update service has been improved to two hourly in the revision.

It is a quite complex web site, and a huge amount of work, some 10,000+ files, several databases, lots of custom PHP applications, and subtle but significant changes in PHP and apache environments.

Hopefully it has been worth the work (~150h) in terms of reliable affordable service for the future. The new hosting environment is certainly easier to work with and properly supports remote secured access… so that has to be good.

]]>With a change in hosting and the changes to adapt to supported and unsupported features, one of the positives is that the ‘short term’ fetching of data on which Quiet solar radio flux interpolations calculator is based is now happening two hourly at 5 minutes past the even hours.

If you wish, you could email SWPC.Webmaster@noaa.gov thanking them for their service and encouraging them to restore the rad.txt and 45day_rad.txt files to HTTP access quickly.

The data remains available on an FTP server, but my web server cannot access it for security reasons, and it would be unacceptably slow anyway.

I wrote to NOAA and they replied promptly:

You wrote to request restoring the 45day_rad.text and rad.txt to be accessible via HTTP. We are working to make a number of our products currently available only via FTP also available via our services at http://services.swpc.noaa.gov/text/. The files you’ve requested will be among those, but I do not yet have a schedule for the update.

As you can see, there is no time given for what ought to be a fairly trivial fix to restore availability under HTTP, albeit on a different URL.

In the mean time, I have implemented a temporary measure to take a snapshot of the FTP server’s file once per day (midday Sydney time) which should be up to date for the previous UTC day.

If you wish, you could email SWPC.Webmaster@noaa.gov thanking them for their service and encouraging them to restore the rad.txt and 45day_rad.txt files to HTTP access quickly.

The factor I is λ^2*Φ/(8*π*k) where λ is wavelength of the measurement, Φ is solar flux at **that** wavelength, k is Boltzmann constant.

The authors give a set of approximations for I in terms of solar flux at 10.7cm, based they say on a polynomial curve fit on experimental data. They do not give further information on their approximations.

Above is a scatter diagram of observations at the Palehua observatory during 2011 of solar flux at 2695MHz and 410MHz.

While these frequencies are not exactly those used in (Bertelsmeier & Magnin 1992), they are in almost the same ratio as 2800MHz and 432MHz (their formula 3), but displaced about 4% lower in frequency. They probably have very similar characteristics to 2800MHz vs 432MHz.

Examining the chart, there is obviously some relationship between the values, but the question are what is it, and more importantly, how strong is that relationship.

Fitting a simple linear relationship gives the formula SF410=0.1431*SF2694+19.936 as shown on the chart, but the more interesting statistic is the correlation coefficient R^2=0.1954. It is generally accepted that strong relationships are indicated by R^2>0.8, and that below that, any relationship is weak. The R^2 for this curve fit at 0.1954 is stunningly low and indicates to me that there will be large uncertainty in using the linear model.

Nevertheless, I have calculated the RMS error in using the model to predict the 341 data points in the original dataset, and it is 16.7SFU. This is an appalling error which in terms of calculated flux around 40SFU is an error of 3.8dB at 1σ confidence interval, even worse at higher confidence.

Let us compare the G/T calculated by (Bertelsmeier & Magnin 1992) for the most recent solar observations (27/04/14) given a Y factor of 6dB.

Above is the raw data from NOAA.

Above are the interpolated flux values at 432 and 1296MHz using Quiet sun radio flux interpolations.

Above the results of calculation from the same set of solar observations using the methods of (Bertelsmeier & Magnin 1992) (B&M) and (Duffy 2007),(Duffy 2009), (Duffy 2014), (Duffy 2014b) (D). There is around 4dB difference, quite substantial.

On the basis of this analysis, I would expect (Bertelsmeier & Magnin 1992) to be subject to similar uncertainty, and the uncertainty is too large to be used to verify small improvements or otherwise in a system.

Their approximations may account apparent errors in many analyses done by Hams, and may be embedded in calculation tools that users apparently do not understand and have not verified.

- Duffy, O. 2007. Measuring system G/T ratio using Sun noise. VK1OD.net (offline).
- ———. 2009. Quiet sun radio flux interpolations. https://owenduffy.net/calc/qsrf/index.htm.
- ———. 2014. Measuring G/T. https://owenduffy.net/blog/?p=1490.
- ———. 2014b. Calculate G/T from Sun noise Y measurement. https://owenduffy.net/calc/sf2gt.htm.
- Bertelsmeier, R and Magnin, P. 1992. Performance evaluation for EME systems In DUBUS 3/92. http://dpmc.unige.ch/dubus/9203-3.pdf(accessed 29/04/14).
- ITU-R. 2000. Recommendation ITU-R S.733-2 (2000)Determination of the G/T ratio for earth stations operating in the fixed-satellite service .

The first system he describes is 4 x ZB7013 Yagis with claimed gain of 22.65dB, and measured Sun/ColdSky of 4.5dB at SF=68SFU.

We can calculate the G/T from these observations, G/T=-7.15dB/K.

If we assume the gain figure is correct, then the system noise temperature is 10^(G/10-G/T/10)=10^(22.65/10–7.15/10)=955K. This is an awful system noise figure.

The next system uses a single EF7015 Yagi with claimed gain of 17dB, and measured Sun/ColdSky of 4.0dB at SF=70SFU. (I note he states SFI=70 which questions whether he is giving solar flux at 432MHz… but lets hope it was a typo).

We can calculate the G/T from these observations, G/T=-8.08dB/K. It is not much worse than the higher gain 4 x ZB7013 system.

If we assume the gain figure is correct, then the system noise temperature is 10^(G/10-G/T/10)=10^(17.0/10–8.08/10)=322K. Though only a third of the previous case, this is still a relatively high system noise figure… perhaps double of what you might like.

The next system uses 4x EF7015 Yagi with claimed gain of 22.94dB, and he suggests Sun/ColdSky of 10.0dB at SF=70SFU. (I note he again states SFI=70 which questions whether he is giving solar flux at 432MHz… but again lets hope it was a typo).

We can calculate the G/T from these observations, G/T=-0.33dB/K. It is quite a leap from the 1 x EF7015 system, and it is not clear that he actually measured 10dB. Lets assume that he did, that he is not just making wild estimates (and a 8dB improvement would be a wild estimate).

If we assume the gain figure is correct, then the system noise temperature is 10^(G/10-G/T/10)=10^(22.94/10–0.33/10)=212K. System noise is getting closer to what might be expected.

With G/T around 0dB/K, it is at the low end of 432MHz EME station performance, G/T up to nearly 10dB/K would represent the state of the art from 4 x Yagi systems (though more than twice as long).

It is a common practice amongst Hams to use 10.7cm flux measurements as the flux density at other frequencies. This is wrong, and if the solar flux values quoted in (Haefner 2010) are 10.7cm flux measurements, then the above results will be wrong as flux at 432 might be more like 30-50% of the 10.7cm flux. He has not given dates for the experiments, so I cannot check archives. The simple fact is that there is no reliable accurate way to preduct solar flux at 432MHz from flux at 10.7cm, examination of historical data will demonstrate that fact.

To use Sunspot number (SSI, T index) give even worse error.

Sometimes the uncertainty can be resolved by calculating a solution assuming that solar flux was given for 10.7cm and testing its feasibility. If that is done for the 1 x EF7015 scenario, and we assume solar flux was around 30SFU, then system noise temperature would be around 140K which is quite believable and it does not help to resolve the ambiguity about the author’s meaning of solar flux values.

It seems Hams boast Sun/ColdSky Y factors without understanding that they have no stand alone value, but they are very useful if the solar flux at the frequency of observations is known and the G/T figure calculated.

If I was a betting person, I would bet on Ham behaviour and that all the solar flux observations were in fact for a frequency of 2800MHz, more than 6 times that of the Sun Y factor measurements.

- Duffy, O. 2007. Measuring system G/T ratio using Sun noise. VK1OD.net (offline).
- ———. 2009. Quiet sun radio flux interpolations. https://owenduffy.net/calc/qsrf/index.htm.
- ———. 2014. Measuring G/T. https://owenduffy.net/blog/?p=1490.
- Haefner, A. 2010. 432MHz EME with a small Antenna In DUBUS. http://www.g0ksc.co.uk/DJ3JJ.pdf(accessed 27/04/14).
- ITU-R. 2000. Recommendation ITU-R S.733-2 (2000)Determination of the G/T ratio for earth stations operating in the fixed-satellite service .

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The report shows solar flux at 1296MHz to be 106SFU.

On returning the model form, the solar flux at 10.7cm has been updated to 127SFU in agreement with the previous form. There is no sign that the solar flux at 1296MHz has been copied back.

We have a model at 1296MHz:

- after fetching current solar flux, it is shown as 127 @10.7cm;
- antenna gain is 30dB (upper right);
- Tsys=60K (red text at middle left);
- Y factor for Sun/ColdSky is shown as 12.31dB.

From these we can calculate G/T=gain-10*log(Tsys)=12.22dB/K.

We can also calculate the solar flux at 1296MHz that would give rise to a 12.22dB Y measurement for a system with G/T=12.22dB/K (ITU-R S.733-2). The solar flux is 63SFU, about half of what is shown on the form (admittedly labelled as @10.7cm), and nothing like its reported 106SFU at 1296MHz.

There appears to be some secret magic used here, (McArthur 2008):

This has been a significant break through as previous calculations were only accurate over a small sfu range. The ability to perform this calculation with complete accuracy has been the â€œHoly Grailâ€ I had been trying (unsuccessfully) to achieve for many years.

The correct Y factor for 106SFU @ 1296MHz for a system with G/T=12.22dB/K is 14.49dB, not 12.13dB as shown in EMRCalc v9.09.

I have not raised this with the EMRCalc’s author, why would I bother when he says (McArthur 2008):

The figures calculated by the software are â€œfirst principlesâ€ and if you do not get close to those predicted then it is your system and not the software that is the problem!

- ———. 2007. Measuring system G/T ratio using Sun noise. VK1OD.net (offline).
- ———. 2009. Quiet sun radio flux interpolations. https://owenduffy.net/calc/qsrf/index.htm.
- ———. 2014. Measuring G/T. https://owenduffy.net/blog/?p=1490.
- McArthur, D. 2008. Sun noise and measurements. http://www.vk3um.com/Documents/SunNoise_Measurements.pdf (accessed 26/04/2014).
- ITU-R. 2000. Recommendation ITU-R S.733-2 (2000)Determination of the G/T ratio for earth stations operating in the fixed-satellite service .

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Above is his graphical summary of the measurements.

This article concentrates on just the measurements of K5SO station and the underlying model.

It is worth noting that the observations of all three stations fall within less than 25% of the range shown in the graph… so most of the graph is an extrapolation, and over a relatively huge range.

K5SO gives a model for the behaviour, it is SN(dB)=10*log(((0.72*(SF-64))+47)/A).

Note that he defines SF to be the solar flux at 2800MHz whereas the noise measurements are made at 1296MHz.

This expression can be simplified to SN(dB)=10*log((0.72*SF+0.92)/A), or as a simple ratio SN=(0.72*SF+0.92)/A =0.72/A*SF+0.92/A …(eqn 1).

For the purpose of this article, I will refer to K5SO’s quantity SN as Y, the ratio of noise pointing at the Sun to that pointing to cold sky.

The power received when pointing to the Sun includes both noise due to the Sun itself (lets call it Th) plus other noise, external and internal to the system (lets call that Tc).

So, Y=(Th+Tc)/Tc=Th/Tc+1 …(eqn 2).

Note the similarity of form of eqn 2 and eqn 1. That suggests that K5SO’s factor of 0.92/A is in fact 1.

Above is a comparison of the two formulas. A value of A=0.55 has been used to calibrate to K5SO’s curve.

So, we now know that Th/Tc=0.72/0.55*SF=1.31*SF. The factor 1.31 accounts for station antenna gain, and Sun noise at 2800MHz relative to system noise (Tc) at 1296MHz. That implies that there is a constant relationship between received Sun noise at 1296MHz and that at 2800MHz… but is there?

Above is a comparison of SF at 1415MHz compared to 2695MHz as measured at Learmonth observatory over 45 days in 2014. Clearly there is not a fixed relationship between them (they are produced in different parts of the chromosphere), and there is likely to be a somewhat similar variation in solar flux at 1296MHz compared to 2800MHz if one was to measure it.

Using 2800MHz SF just adds statistical noise. Whilst solar flux is not measured in these observatories at 1296MHz, they measure a number of frequencies and It should be better to use a sensible interpolation of those measurements.

Above is a plot of the distribution of the ratio of solar flux at 1415MHz to 2695MHz for the same data. This variation would give rise to 3σ uncertainty of 0.5dB, a little worse probably for the actual case of 1296MHz from 2800MHz, a significant amount which can easily be reduced subtantially by a better projection of 1296MHz from the observatory data.

K5SO gets a Y factor of about 21dB when 2800MHz solar flux is 100SFU. If we were to assume that at that time, solar flux at 1296MHz was say 85SFU, we can calculate G/T=20dB/K (making a beamwidth correction for a 39dB dish). Assuming antenna gain to be 39dB, that indicates a system noise temperature (Tc) of 78K which is credible.

W2UHI’s gain is probably around 36dB, G/T is probably around 16dB/K and assuming antenna gain of 36dB implies a system noise temperature (Tc) of 102K which is again believable.

Similarly, VK7MO’s gain is probably around 28dB, G/T is probably around 9dB/K and assuming antenna gain of 28dB implies a system noise temperature (Tc) of 113K which is again believable.

So, above is a graph similar to K5SO for a family of G/T values. The graph is constructed using the technicque and formulas given in Measuring G/T. (One must apply a beamwidth correction factors for narrow beamwidth antennas, and in the above chart that is calculated based on G/T and an assumed system noise temperature Ts.)

The similarity of the above chart and K5SO’s shows that conventional theory underlies K5SO’s experimental observations.

- Duffy, O. 2006. Effective use of a Low Noise Amplifier on VHF/UHF. VK1OD.net (offline).
- ———. 2007. Measuring system G/T ratio using Sun noise. VK1OD.net (offline).
- ———. 2009. Quiet sun radio flux interpolations. https://owenduffy.net/calc/qsrf/index.htm.
- ———. 2014. Measuring G/T. https://owenduffy.net/blog/?p=1490.
- K5SO 2007. Sun noise. http://www.k5so.com/Using_sun_noise.html (accessed 24/04/14).