## Oscillations and relativistic effects in Galileo broadcast clocks

A few days ago, Bert Hubert, the creator of galmon.eu, discovered a sinusoidal oscillation in the clock drift $$a_{f1}$$ parameter of the broadcast ephemerides of Galileo satellites. This variation has a frequency that matches the orbital period of 14 hours and 7 minutes. At first, I suggested that it might be caused by relativistic effects, which are given by$-\frac{\sqrt{\mu}}{c^2}e\sqrt{A}\sin E,$where $$\mu$$ is the Earth’s gravitational parameter, $$c$$ is the speed of light, $$e$$ is the eccentricity, $$A$$ is the semi-major axis, and $$E$$ is the eccentric anomaly. In fact, the order of magnitude of the oscillations that Bert was seeing seemed to agree with this formula.

However, then I realised that this relativistic effect is not included in the broadcast clock model. It needs to be included back by the receivers. Therefore, it shouldn’t appear at all in the broadcast clock. Something didn’t seem quite right. This post is an in-depth look at this problem.

## QO-100 BPSK beacon frequency measured at Bochum

The experiments about measuring the frequency stability of the local oscillator of the QO-100 NB transponder with a Vectron MD-011 GPSDO I made a few days ago indicated that the Allan deviation of the local oscillator was probably better than $$10^{-11}$$ for $$\tau$$ between 1 and 100 seconds. The next step in trying to characterize the stability of the local oscillator is to use a reference clock which is more stable than the Vectron.

I contacted Achim Vollhardt DH2VA asking him if it was possible to record the downlink of the BPSK beacon at Bochum, so as to have a recording referenced to the Z3801A GPSDO in Bochum, which is much more stable than the Vectron. He and Mario Lorenz DL5MLO have been very kind and they have taken the effort to make a recording for me. This post is an analysis of this recording made at Bochum.

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## More frequency measurements of the QO-100 NB transponder

This post is a follow up to my experiments about measuring the stability of the QO-100 NB transponder local oscillator. I am now using the Vectron MD-011 GPSDO that Carlos Cabezas EB4FBZ has lent me to reference all my QO-100 groundstation (see more information about the Vectron GPSDO in this post).

The Vectron MD-011 has an Allan deviation of $$10^{-11}$$ at $$\tau = 1\,\mathrm{s}$$ and $$2\cdot10^{-11}$$ at $$\tau = 10\,\mathrm{s}$$ according to the datasheet, so it is an improvement of an order of magnitude compared to my DF9NP TCXO-based GPSDO. I have made more measurements with the Vectron MD-011 as in my previous experiments, measuring the phase of the BPSK beacon transmitted from Bochum and a CW tone transmitted with my station. This post summarizes my results and conclusions.

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## Measuring the Allan deviation of a GPSDO with an SDR

A few days ago I tried to measure the QO-100 NB transponder LO stability using my DF9NP 10MHz GPSDO. It turned out that my GPSDO was less stable than the LO, so my measurements showed nothing about the QO-100 LO. Carlos Cabezas EB4FBZ has been kind enough to lend me a Vectron MD-011 GPSDO, which is much better than my DF9NP GPSDO and should allow me to measure the QO-100 LO.

Before starting the measurements with QO-100, I have taken the time to use the Vectron GPSDO to measure the Allan deviation of my DF9NP GPSDO over several days. This post is an account of the methods and results.

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## Can my station measure the QO-100 NB transponder LO stability?

Following a long discussion with Bernd Zoelgert DL2BZ about the frequency stability of the local oscillator of the QO-100 narrowband transponder, I have decided to try to measure the Allan deviation of the transponder. The focus here is on short-term stability, so we are concerned with observation intervals around $$\tau = 1 \mathrm{s}$$.

Of course, as with any measurement problem, the performance of the measurement equipment should be better than the “device under test”. In this case, to measure the QO-100 LO it is necessary to compare it against a reference clock which is more stable (ideally an order of magnitude better).

My whole station is locked to a DF9NP GPSDO, which is a 10MHz VCTCXO disciplined by a uBlox LEA-4S GPS receiver. That’s great to measure long-term stability, but for short-term measurements you are essentially relying on the stability of the VCTCXO, which is not so great. Therefore, the whole purpose of this experiment is first to determine whether my station is actually able to measure the QO-100 LO or not. Spoiler: it turns out the answer is “no”, as in most articles whose title is phrased as a question.

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## Using an external reference with the LimeSDR Mini

A while ago I spoke about feeding an external reference to the LimeSDR USB. Now I wanted to use an external reference with the LimeSDR Mini that I have in my QO-100 groundstation to lock all the system to GPS. Preferably I wanted to use 27MHz as the reference, since this is what I am using in my LNB, so this would save me from having to run 10MHz or another frequency to the groundstation.

I wasn’t so sure how well this would work, since there are a few threads with questions in the MiriadRF forums, but I haven’t seen any explaining things in a clear way. There are different anecdotes of things that worked or didn’t work for several people, but not that many definitive answers. Among all the threads, this one seems mostly helpful.

Somewhat surprisingly, everything has worked well on the first try. I am now using a 27MHz external reference with my LimeSDR Mini. Hopefully this post will be of help to other people.

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## Measuring QO-100 beacons frequency

Continuing with my frequency measurements of Es’hail 2, I have now been measuring the frequency of the beacons of the QO-100 narrowband transponder for several days. The main goal of these frequency measurements is to use Doppler to study the orbit of Es’hail 2. Previously, I had been doing frequency measurements on the engineering beacons at 10706MHz and 11205MHz. However, these beacons are currently being transmitted on a MENA beam, so I’m quite lucky to be in Spain, as they can’t be received in many other parts of Europe.

During the in-orbit tests of Es’hail 2, the engineering beacons were transmitted on a global beam, and I performed some differential Doppler studies with Jean Marc Momple 3B8DU, in Mauritius. The engineering beacons are no longer any good for these kind of studies, since their area of coverage is small. Thus, I have started to measure the beacons in the narrowband transponder, which covers all the satellite footprint.

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## LimeSDR external reference quick HOWTO

To do accurate frequency measurements of Andrés EB4FJV‘s 2.3GHz beacon, I have needed to setup my LimeSDR to use my DF9NP 10MHz GPSDO as an external reference. This is a quick HOWTO with the steps to make the LimeSDR use an external reference.