On 8 December 2023 I built a proper centre: a balun on a ferrite toroid inside a sealed box. And, more to the point of this note, I checked it with an analyser — and then worked out that I had checked something other than what I thought.

Why a dipole needs a balun​

A dipole is balanced: two identical legs about the feed point. Coax is unbalanced: the centre conductor and the braid are not equals. Join one straight to the other, and part of the current that should have gone into the second leg flows instead down the outside of the braid towards the rig.

The cable becomes a third leg of the antenna. On transmit that means a distorted pattern and an SWR that changes when you move the cable. On receive — and a receiver is what I had then — the consequence is nastier: the braid picks up whatever it passes. Switch-mode power supplies, LED lamps, chargers — everything that makes noise in the house lands on the cable and walks into the receiver alongside the wanted signal.

In my case that was not marginal theory. The wire hangs six metres up — not “well away from the house” but directly above it, in the same field of noise. There was nowhere to move the antenna to, so the least I could do was stop the noise taking a second route in, along the cable.

A 1:1 balun breaks that path: it passes the differential current, which is what the whole thing was built for, and opposes the common-mode current, the one that flows on the braid.

What that toroid turned out to be​

The markings on the toroid itself cannot be read: it is wrapped first in white tape and then, all together, in black. Unwrapping proved unnecessary — the markings turned up somewhere else, in a purchase history: an M2000NM K32×20×9 ferrite toroid and PETD2-200 enamelled copper wire, 1.0 mm.

Size. K32×20×9 reads straightforwardly: 32 mm outside, 20 inside, 9 high. My estimate from the ruler in the photograph — “about 35–36 mm” — was three or four millimetres too generous: the winding and the tape add more to the overall size than the eye credits. In Western terms the core sits between an FT-114 (29.0 mm) and an FT-140 (35.6 mm).

Material. M2000NM is a manganese-zinc ferrite with an initial permeability of 2000. The closest Western equivalent is Fair-Rite 77: the same MnZn, the same μ_i = 2000. The guess — “a high-permeability ferrite, not powdered iron” — turned out right, and the core is exactly the class you would choose for this job deliberately.

The winding: 14 bifilar turns. Each turn is two wires laid side by side — the classic Guanella arrangement, where the two conductors form a length of transmission line on a shared core. The numbers agree with the photograph: 14 turns of a pair means 28 passes through the window, a millimetre and a bit each with the enamel, about 30 mm in all against an inner perimeter under the tape of roughly 56 mm. One layer with gaps — exactly what the close-up shows.

The white tape under the winding is not decoration, and it now has two reasons. The first is obvious: a ferrite toroid has sharp edges, and they cut the enamel where the wire bends over the rim. The second arrived with the markings: manganese-zinc ferrite is electrically conductive, its resistivity orders of magnitude lower than nickel-zinc. Laying bare wire straight onto a core like that is not a good idea, even with the enamel intact.

What that gives. The core constant comes from the geometry: mean magnetic path length l_e = π·(32 + 20)/2 ≈ 81.7 mm, cross-section A_e = 9·(32 − 20)/2 = 54 mm², hence A_L = μ₀·μ_i·A_e/l_e ≈ 1.66 µH/turn². On 14 turns that is 0.33 mH — but only if the permeability held at 2000. It does not: in MnZn ferrite μ′ starts falling above a megahertz while the losses rise. For a choke that is no misfortune but the working regime: the impedance simply stops being inductive and becomes resistive. Substituting the complex permeability of mix 77 — which is how the common-mode choke calculator works it out — 14 turns on this core give:

So from 160 down to 10 metres it is three or four kilohms, and from forty metres upwards almost purely resistive. The “few kilohms” benchmark mentioned below is met — though without much margin. And this is a calculation from an equivalent material's data, not a measurement; why that wording stands as final will become clear.

Will it take transmit power. The very losses that make M2000NM a good choke turn into heat on transmit: common-mode current warms this core, and high-permeability MnZn is more vulnerable in that respect than nickel-zinc mixes 43 or 31. In December 2023 the question did not arise — a receiver was connected to the box. But later my first digital contacts went out through this same assembly, so the core did work on transmit, and in a mode where the carrier is held for the whole transmission. It survived. I would still not repeat that blind at a hundred watts: a core for that kind of power gets calculated afresh.

The box​

The enclosure is an ordinary junction box. Through-bolts with washers and wing nuts pass through opposite walls: the antenna legs fasten to them, and they can be tightened in winter wearing gloves, with no soldering iron up the mast. The toroid lies flat, wrapped in black tape. One joint is made with a blue crimp terminal, the rest are under heatshrink.

That is the standard of work one need not be ashamed of, and at the same time the standard that can be reached in an evening out of what is in the drawer.

The measurement​

A NanoVNA, sweeping from 1 MHz, S11 from the cable side. On the output terminals, in place of the antenna legs, a 50 Ω resistor. That matters: what was measured was the assembly itself, not the antenna along with it.

At 3.660 MHz: 51.5 Ω with 198 nH in series, SWR 1.097. Four and a half ohms of reactance against fifty of resistance.

At 14.300 MHz: 50.19 Ω, SWR 1.040. Practically a perfect fifty ohms.

So from 80 to 20 metres the assembly stays transparent: it introduces neither loss nor a shift in impedance that would show at this scale.

And here is the point​

This measurement is not a test of the balun as a balun.

I fed a signal into the cable side and looked at what the instrument saw. It saw fifty ohms. But it would have shown the same fifty ohms had I connected that same resistor through a length of cable — no ferrite required. S11 into 50 Ω measures the differential path: whether the transformer has eaten the match, whether it has losses or stray resonances in the working range. That question has been answered, and the answer is good.

The question a balun is fitted for in the first place — how much impedance it presents to common-mode current — this measurement does not touch at all. Common-mode current flows on the outside of the braid, that is, on the very conductor that does not exist in the S11 setup.

This is not an error of the instrument, nor of the method. It is an error of interpretation, and I made it: I saw an SWR of 1.04 and decided the assembly had been checked. Half of it had.

How to measure it properly​

The common-mode impedance of a choke is measured differently: the two leads on one side are shorted together, the two on the other side likewise, and the impedance between those two points is measured. That is what common-mode current sees on its way. On HF the benchmark is a few kilohms across the working range; less means the braid is still acting as an antenna, just slightly worse at it.

It is done with the same NanoVNA and the same pair of hands. The only difference is where the leads go — and whether you have asked yourself the right question.

What can no longer be found out​

The right measurement — common-mode impedance between the shorted pairs — was never made, and can no longer be made: the assembly is not available for it. The three or four kilohms in the table above remain a calculation from an equivalent material's data. A well-founded calculation, but not a measurement.

The box with its toroid did its job honestly: first quiet reception, later the first digital contacts. The one thing left undone was a single measurement — precisely the one the instrument had been taken out for.

And that is probably the thing worth taking from this note. The instrument was in hand, the assembly on the bench, time was unlimited. Only one thing was missing: the right question. Next time the list of what to measure gets written before the leads touch the terminals.

What exactly I was building​

“JUNIOR” is a kit by Serhii Belenetskyi, US5MSQ: a beginner's HF receiver for two bands, 80 and 20 metres. A receiver only: there is no transmit path in it at all — an antenna at the input, headphones at the output, and nothing going back on the air. I read his article about building it and bought the kit directly from him.

Choosing a kit rather than my own design from scratch was deliberate. A first receiver has one trap: it stays silent, and it is not clear why. The circuit? The assembly? The components? The antenna? Propagation? A ready kit crosses the circuit and the components off that list. What remains is my soldering and my antenna — exactly what I wanted to learn.

The circuit in one paragraph​

A single-conversion superheterodyne. The antenna signal passes through an adjustable attenuator and a two-pole bandpass filter into the first SA612 mixer. The local oscillator is a VFO at 8.5–8.8 MHz for 80 metres or 9–9.35 MHz for 20; a relay switches the bands. The 5 MHz intermediate frequency goes through a four-crystal filter 2.4 kHz wide, is amplified by a single transistor stage, and reaches a second SA612 working here as a product detector with a 4998 kHz carrier oscillator. Then an LM386 and the headphones. Tuning is by varicap from a potentiometer — the knob turns a voltage, not a capacitor.

These are the author's figures from the description, not my measurements. I did not yet know how to make my own.

Three evenings with a soldering iron​

12 November 2023, the bare version 2.5 board. Double-sided glass-epoxy with mask and full silkscreen: every position is labelled, nothing has to be hunted for. Both mixers, in SOIC packages, were already on the board — the author solders the SMD parts himself, and for a beginner's kit that is the right decision: the finest work is already done, and everything left can be soldered with an ordinary tip.

The author's order: resistors and capacitors first, then the chokes L1–L4 standing 1–1.5 mm above the board, L6 vertically, then connectors, the relay, the transistors, and the integrated circuits last.

The 1–1.5 mm requirement looks like pedantry one is tempted to ignore. Do not: L1–L4 are not “supply-rail chokes” but the inductors of the input bandpass filter. How high they stand above the solid ground plane goes into the tuned circuit along with them.

By 14 November the board was assembled. The four filter crystals ZQ1–ZQ4 lie flat in a row down the middle; the fifth, the carrier crystal, sits apart beside coil L6. The only chip in a socket is the LM386, and that too makes sense: if a beginner burns something out, it will be the audio amplifier.

17 November, the connectors. All external wiring goes to screw terminals, with no wire soldered straight into a hole: the board can be lifted out of the case without switching the iron on. At a stage when you do not yet know what will need checking, that saves you.

Alignment: four steps and a screwdriver​

Here is where a kit from its designer differs from “built from a magazine article”. The whole procedure is written as a sequence in which each step is verified before the next.

1. Operating points. Voltages at the test points, tolerance ±10 %. If one is wrong, you cannot go on, because the remaining steps measure its consequences.
2. Carrier frequency. Set trimmer C37 to 4998.00 kHz. This is the adjustment that decides how people sound: the crystal filter stands still, and where the audio zero lands within its passband is set by the carrier oscillator. An error of a couple of hundred hertz does not break reception — it makes voices either nasal or thin.
3. Setting the band edges. On 20 metres the top edge with the core of L5 and the bottom with resistor R9; on 80, the bottom edge with trimmer C15.
4. Input circuits. On 80 metres, trimmers C6 and C14 for maximum signal around 3650 kHz; on 20, C4 and C13 at 14150 kHz.

No instruments beyond the digital display were needed: it is also the frequency counter.

The case​

28 November, into the case. The board stands on pillars in the far corner, with the A16-PLL digital display in front of it. The panel holes are marked out from a template supplied with the kit, and a self-adhesive fascia goes over the top. It looks incomparably better than my metalwork deserves — which is exactly why the template is in the kit.

The green PLL TUNING lamp is the display's automatic frequency control. The VFO here runs on a coil and a varicap, and it drifts: for the first few minutes after switch-on the frequency moves noticeably. The display not only shows the frequency but also pulls the oscillator back, and with it the set stays on a station for as long as the station is talking.

What it draws​

12.8 V, 0.06 A. Sixty milliamps including the display — which fits the specification: the author quotes 30 mA on 80 metres without the display, plus up to 40 mA for the display itself.

The figure matters not in itself. A receiver with that appetite runs a day from a power bank and does not care whether the mains is on.

The antenna: forty metres of twisted pair​

The most interesting thing in this story cost less than the connectors on the back panel.

Two legs of twenty metres each, ordinary twisted pair, six metres up. Forty metres of wire in all.

Now let us work out what came of it. At 3.605 MHz a wavelength is 83.2 m and a half wave 41.6 m; with the shortening factor applied, a real resonant dipole comes out at about 39–40 m. So “just the wire that happened to be there” turned out to be almost exactly a half-wave dipole for 80 metres. The resonance happened by itself, with no intention on my part.

Six metres of height is 0.07 of a wavelength. By any textbook that is “low”, and by any textbook that is bad. For what I wanted to hear it is exactly right. An antenna's pattern does not care which way the signal is travelling: a dipole that at this height would radiate almost straight up equally hears mostly from above. And what comes from above on 80 metres is whatever bounced off the ionosphere close to vertically — stations thirty to a hundred kilometres away. That is precisely the distance at which the regional roundtable's members sit.

The angle is easy to work out. In the morning on 3.6 MHz the signal is turned back by a layer two to three hundred kilometres up; for a correspondent a hundred kilometres away that is an arrival angle of about eighty degrees above the horizon, and for one thirty kilometres away, practically vertical. The closest are also audible by ground wave, which on 80 metres reaches a few tens of kilometres, but the rest arrives from exactly there — from above.

And here is where the advice “hang it higher” hides its catch. That advice is about DX, that is, about low angles, and to get them on 80 metres a dipole has to go up half a wavelength — forty metres. At exactly that height a null appears at the zenith, and such an antenna hears a neighbour thirty kilometres away worse than mine at six. All I lost by hanging it low is not direction but efficiency. In English this mode is called NVIS, and my antenna is a textbook case of it, arrived at with no intention whatever.

Ground losses under a wire that low are appreciable. On receive that barely matters: on 80 metres the floor is set not by the receiver but by atmospheric noise, and that arrives through the same antenna. The losses attenuate signal and noise alike — the ratio between them does not change.

On 20 metres the same wire is 1.9 wavelengths: a multi-lobed antenna, sensitive to low angles. So 14 MHz comes in as well, except that the antenna chooses the directions for itself rather than for me.

The roundtable​

The Volyn Radio Amateurs League meets every Sunday at eight in the morning on 3.605 MHz.

24 December 2023, 8:43, a Sunday. The display reads 3.605.00, and beside it an open notebook in which I wrote down the callsigns as they were spoken: UR3PD, UR4PWL, UT1PA, UR3PF, UT1PQ, UR3PBW. Lower on the same page, a line reading “750th anniversary”: the roundtable does not talk only about equipment.

That was the moment the whole thing was for. Not “the receiver works” — it worked on empty hiss too. But when voices came out of the headphones calling each other by name and arranging the next Sunday, it became clear that the wire outside and the box on the table were connected to something alive.

What I took from it​

Selectivity is made of hardware. The 2.4 kHz bandwidth is set by the crystal filter, and it cannot be “adjusted”. Narrow or wide was decided when I laid four crystals in a row.

The carrier frequency decides how people sound. One trimmer, two hundred hertz, and the timbre of the whole band is different. Before JUNIOR I thought sidebands were a matter of theory.

The attenuator is not decoration. In the evening on 80 metres a strong neighbour overloads the front end, and the RF knob is needed not “just in case” but every evening.

Stability is an engineering problem of its own. A VFO on a coil and a varicap drifts, and no quality of soldering fixes it. What fixes it is automatic frequency control — digital laid over analogue.

The antenna is half the receiver. Forty metres of twisted pair six metres up gave more than any amount of trimmer-turning inside the box. That is the cheapest lesson of the lot, and the most important.

What it does not do​

To be honest, so that nobody buys the kit with the wrong expectations:

• it does not transmit — it is a receiver, full stop;
• one bandwidth for every occasion: no narrower filter for Morse, and no wider one;
• no S-meter, so a correspondent's strength is judged by ear;
• two bands, 80 and 20, and nothing else.

These are not complaints. They are the boundaries at which the next set begins — and that is exactly why the next one on my bench is a direct-conversion receiver, built from scratch, with no kit and no one else's board.

Sources​

• Radio kit: the JUNIOR receiver for the beginning short-wave listener — description, circuit design, assembly order and alignment by the author, US5MSQ.
• Volyn Radio Amateurs League — the frequency, day and time of the regional roundtable.

In short: the first two say how much the Sun is giving out (and therefore how dense the ionosphere is), and the last two say how quiet the Earth's magnetic field is (and therefore whether a storm is choking that ionosphere).

Below is a full account of each index: what it means physically, how to read it, what it affects and when it is worth getting on the air. Beside each section there is a live gauge that pulls the current value from NOAA and shows where we stand.

Note that the colours run in opposite directions: SFI and SSN turn green upwards (more light, better conditions), while K and A turn green downwards (quiet is better for the low bands). That is not a whim but physics, and it is explained below.

Two pairs of indices​

It helps to hold all four in your head as two pairs, because they answer two different questions.

Solar (what the Sun is giving):

• SFI — the Sun's radio flux at a wavelength of 10.7 cm;
• SSN — the number of spots on the solar disc.

These decide how dense the F layer of the ionosphere is, and therefore whether the high bands (10–20 m) will open.

Geomagnetic (what is happening at the Earth):

• K index — the highest geomagnetic activity over 3 hours;
• A index — the average geomagnetic activity over a day.

These decide whether a magnetic storm will blow that ionosphere away, and therefore whether the low bands (40–160 m) hold up.

The ideal condition for HF is a high SFI and a low K. Now each index in turn.

SFI — the solar flux index​

What it is. The solar flux index is the power of the Sun's radio emission at 2800 MHz (a wavelength of 10.7 cm), measured by the observatory at Penticton, Canada, and published by NOAA. The unit is the sfu (10⁻²² W·m⁻²·Hz⁻¹). It is a convenient proxy for ionising ultraviolet: the brighter the Sun shines at 10.7 cm, the more it ionises the F layer.

Hence the main rule: the higher the SFI, the denser the ionosphere and the higher the ceiling (the MUF — the highest frequency the ionosphere will still reflect).

The current SFI, right now:

How to read it:

• 60–80 (red, “poor”) — solar minimum. The high bands (10–15 m) are dead; 20–40 m work, and even then unreliably.
• 80–100 (yellow, “middling”) — moderate activity. 20 m works decently, 15 m opens from time to time.
• 100–250 (green, “good”) — a high SFI. 10, 12 and 15 m open, and long DX paths on HF come alive.

What it affects. Chiefly the high bands (10–20 m). There the SFI decides whether there will be a contact at all. On the low bands (40–160 m) the SFI matters little — there it is geomagnetic quiet that rules.

In practice: once the SFI reaches about 100 it is worth trying 10 and 15 m; at 150–200 you can count on transcontinental paths on the high HF bands all day long.

SSN — the sunspot number​

What it is. The sunspot number (the Wolf number) counts the groups and the individual spots on the solar disc, weighted by size. Spots are regions of heightened magnetic activity, and they radiate more ionising energy.

Why it tracks the SFI. Spots and the 10.7 cm emission are both products of solar activity, and they are related almost linearly (a correlation above 90 %). So reading the SSN largely repeats the SFI, but it states the number of spots on the Sun directly, which many people find more vivid.

The current SSN, right now:

How to read it:

• 0–30 (red, “minimum”) — solar minimum. The high bands barely work.
• 30–60 (yellow, “moderate”) — activity rising; 15–20 m are steady.
• 60–250 (green, “high”) — an active Sun, good HF conditions, frequent flares and storms.

What it affects. The same as the SFI: the density of the F layer and the high bands. The SSN swings through the eleven-year solar cycle: at the peak it can run into the hundreds, at the minimum it falls almost to zero.

In practice: watching the SSN tells you where in the eleven-year cycle we are — whether activity is rising or falling.

The K index — geomagnetic activity over 3 hours​

What it is. The K index measures the disturbance of the Earth's magnetic field as seen by individual observatories. The planetary Kp averages them worldwide. The scale is logarithmic, from 0 (completely quiet) to 9 (an extreme storm), in thirds of a point.

Every 3 hours NOAA issues a new Kp — the fastest pulse of the geomagnetic state you get.

Why it matters on HF. A magnetic storm disturbs the lower ionosphere (the D layer) and chokes propagation on the low bands. The higher the K, the worse conditions get, especially on 40–160 m and on polar paths.

The current K index, right now:

How to read it:

• 1–3 (green, “quiet”) — ideal. The low bands are at their best.
• 3–6 (yellow, “unsettled”) — moderate disturbance. 40 and 80 m are somewhat worse; on the high HF bands it is barely noticeable.
• 6–9 (red, “storm”) — a magnetic storm. 40–160 m are heavily suppressed, aurora is possible, and polar paths collapse entirely.

In practice: Kp ≥ 5 is a signal that the low bands will be poor; Kp ≤ 2 is the best time for 40, 80 and 160 m.

The A index — geomagnetic activity over a day​

What it is. The A index is a daily roll-up of the K index. Each three-hourly K is converted into an “equivalent amplitude” (a), and the eight intervals of the day are then averaged. The result is a linear scale from 0 to a few hundred, which compares one day with another more conveniently than the logarithmic K.

How to read it:

• 0–40 (green, “quiet”) — the magnetosphere is in good shape, HF is normal.
• 40–100 (yellow, “unsettled”) — disturbed; the low bands are noticeably worse.
• 100–400 (red, “storm”) — a strong storm; 40–160 m are effectively closed.

The current A index, right now:

What it affects. The same as the K index, but on a daily scale. The difference is speed: K catches the short shove of a storm, A shows what the day was like as a whole.

In practice: the A index is useful when going back over logs — it makes it easy to see which day was geomagnetically quiet.

Two kinds of index, two directions of colour​

Look at the zone scales once more and remember the central symmetry:

The practical conclusion: the best conditions come when the SFI is high and the K is low. That combination is what gives you open high bands and working low ones at the same time.

Where the data comes from​

The live gauges and all the zone thresholds take their data from NOAA's open sources:

• SFI and SSN — the daily table daily-solar-indices.txt;
• K index and A index — the series noaa-planetary-k-index.json (updated every 3 hours).

The zone boundaries for the SFI (green begins at 100) and for the K index (quiet from 1 to 3) follow the way these indices are usually shown on DX clusters.

What to watch next​

Once these four numbers make sense, so does a propagation forecast:

1. Look at the SFI: if it is 100 or more, try the high bands (10–20 m).
2. Look at Kp: if it is 2 or less, take on 40–160 m without hesitation.
3. Compare the A index with the day before: if it has doubled or tripled, the magnetic background is deteriorating — wait.
4. When going through a log, remember: the number of contacts depends more on the calendar (weekends) than on the Sun, whereas the high bands depend on the SFI exactly as described.

The interesting part is not that it works. The interesting part is how many ways there are to get it wrong, none of which announce themselves with an error.

The signal path​

sound card (48 kHz)
   → AudioWorklet → ring buffer
   → resample to 3200 Hz with a filter
   → FFT 256, periodic Hann window, reflect padding
   → spectrogram, 65 bins over 400–1200 Hz, log1p
   → squelch: is there a tone or not
   → ONNX: 8 seconds of audio → per-frame distributions
   → greedy CTC decoding
   → stitching onto the previous window

An eight-second window is taken every two seconds, so neighbouring passes share six seconds of audio. That is the main difficulty, but more on it below.

The browser spoils the audio by default​

A microphone input arrives with three “improvements”: echo cancellation, noise suppression and automatic gain. For a weak Morse signal each of them is fatal, and the worst is noise suppression: a steady tone is literally the thing it knows how to remove.

audio: {
  echoCancellation: false,
  noiseSuppression: false,
  autoGainControl: false,
}

The second problem from the same family: capture lives in an AudioWorklet, not on a timer. In a background tab timers are throttled to roughly one firing a minute, while a real-time audio stream is not throttled at all. On a timer, the decoder would work only while somebody was looking at it.

The preprocessing is not a matter of choice​

The network learned one particular input, and every constant here is taken from its metadata rather than chosen: a periodic Hann window (hanning(N+1)[:-1], not hanning(N)), reflect padding of 128 samples, bins 32…96 at 12.5 Hz per bin, log1p.

A spectrogram that differs from the trained one by a window or half a bin does not degrade gracefully — it produces confident nonsense. The most treacherous part is the padding: numpy's reflect does not repeat the edge sample, so [1,2,3] becomes [3,2,1,2,3,2,1]. Getting that wrong shifts every frame by half a window and costs you the first letter of every decode.

That is why the project has scripts/check-dsp.ts: it synthesises Morse with known text, runs it through the real sample rate, the real resampler and the real spectrogram, and then asks the model what it heard. Unit tests of the transform alone are not enough for this.

Resampling that must not be done naively​

The model author's example changes the rate by linear interpolation alone — and says so plainly: it is an example with minimal dependencies, and the documented way to prepare audio there is ffmpeg, which filters first.

Copying the interpolation alone would fold everything above 1600 Hz back into the band the model looks at, and a card delivering 48 kHz has plenty up there. So the filter ffmpeg would have applied is applied here: a 255-tap windowed sinc, Blackman window, cutoff 1400 Hz — below the Nyquist of the target rate and above the 1200 Hz the network reads.

The kernel is evaluated only at the positions actually needed, so the cost scales with the output rate rather than the input: about 1.6 million multiply-accumulates per second of audio.

Why CTC, and why greedy decoding​

The model is trained with CTC, so the output is one distribution per 15 ms frame over 41 symbols plus a blank. The best path is read greedily: take the most likely class in each frame, drop the blanks, collapse runs of identical symbols.

This is not the best decoder available — a beam search with a language model would read better. But a Morse decoder that quietly invents plausible words is worse than one that prints what it heard. Predictable behaviour is worth more here than a few percent of accuracy.

The most expensive mistake: stitching the windows​

Neighbouring windows share six seconds of audio, so they share text as well. But not the same text: the shared seconds get decoded afresh and come back a letter or two different. So comparing for equality does not work — one discrepancy inside the overlap and the whole window is appended a second time.

That is exactly what turned the first live decode into EN35UKR PSE K, repeated fifteen times over.

The working solution is to find the overlap by agreement rather than equality: the longest tail of what has already been printed that matches the head of the new window on at least 75 % of its characters.

And the other half of the same problem: the search width has to be bounded by time, not by a round number of characters. An operator calling CQ repeats the same text every fifteen seconds, and a search wide enough to span two calls will happily merge them into one and lose a transmission.

Silence that reads as text​

Left to itself, the model reads noise as a stream of E, I, T and S — the shortest patterns in the alphabet. Something has to be the most likely class in every frame, and noise looks more like a short element than a long one.

This decoder behaves that way, and so do the commercial phone apps. The only difference is whether the result is shown to the operator.

Telling one from the other takes a single number: how far the strongest spectral bin rises above the typical one, averaged over the window. A carrier is narrow and steady; noise is neither. There is no dependence on absolute level anywhere in this, which is why it works equally well from a cable off the rig and from a microphone held to a speaker.

The threshold was not chosen but measured: noise sits around 1.5, even a deeply buried signal does not drop below 3, so the line is drawn at 2.5 — deliberately low. Losing a real transmission is worse than printing a little rubbish.

Two stations at once​

The model has one output and cannot follow two senders: given both, it produces text belonging to neither.

But its entire view of the world is the spectrogram. So zeroing the bins away from the wanted tone is exactly the same as filtering the audio, and it costs one pass over an array.

With two synthesised stations 350 Hz apart, together they decoded as C?Y06IXA3PKI K; with everything outside ±100 Hz zeroed, as CQ CQ DE UR3PKI K and TEST DE DL6LD K, both word for word.

Shifting the analysis window instead does not work: it spans 812 Hz, and a neighbour a few hundred hertz away stays inside it.

A line not to cross​

The decoder never writes to the log by itself.

In FT8 automatic logging is justified: there is a checksum, and a false decode is practically impossible. Morse has no checksum at all — the software cannot tell UR3PKI from UR3PKJ if the last dot drowned in a fade.

The most that is allowed is to drop a callsign into a field visibly marked as the decoder's guess. The reason is not technical but substantive: a log is a record of what happened on the air, and one invented callsign in it costs more than all the convenience of autofill.

Why this is a separate project​

The model comes from e04/deepcw-engine under AGPL-3.0. That licence extends to software provided over a network, so the source has to be available to everyone who opens the page.

That is why the decoder lives in its own repository, PetroOstapuk/cw-decoder, rather than as a page inside the platform: the licence condition is then met in full, and the platform's own code remains separate work.

To see how the alphabet itself is built, look at the code tree; to work out how long a dot lasts and how much bandwidth the signal takes, use the timing calculator.

It is in fact a binary tree, and in that form you can see the engineering decision taken in the 1840s: the frequency of a letter sets its depth. E is one dot, T one dash, because those are the commonest letters in English. Q, J and Z sit all the way down on the fourth level. Alfred Vail arrived at this not by theory but by counting: he counted the letters in the type cases of a local newspaper.

A variable-length code, allocated by symbol frequency. A hundred-odd years before Shannon and Huffman explained why that works.

The tree​

Left is a dot, right is a dash. The four letter levels are completely filled — there are no free nodes. The digits are longer than any letter and sit a level below.

Two things are immediately visible here that the table hides.

Frequent letters sit close to the root. Not roughly but systematically: the diameter of a pad here is the letter's frequency, and the largest ones have gathered at the top.

A dash costs three times a dot. So the depth of a node and the cost of a letter are different things: O (---) sits on the third level, as does S (...), but it takes more than twice as long to send — eleven units of time against five. The timing diagram under the tree shows this directly.

How well Vail aimed​

The correlation between a letter's frequency and the duration of its code — Spearman's rank correlation — comes out strong and negative. For work done by counting letters in type cases, that is almost indecently good.

The exceptions stand out on the chart. The loudest is O: the fourth commonest letter in English has the longest code the third level can offer.

Why this is not a Huffman code after all​

Here it gets interesting, because the analogy “Morse is Huffman” is pleasing and wrong, for two separate reasons.

Morse is not a prefix code. E is . and I is .. — the code for one letter is the start of the code for another. A prefix code forbids that, and it is precisely the prohibition that lets a stream be decoded without separators. Huffman always produces a code where symbols sit only at the leaves; in Morse a symbol sits at every node, internal ones included.

That is why Morse cannot be sent as a continuous stream: between letters there must be a gap three units long. So the alphabet is not binary at all but ternary — dot, dash and gap — and it is the gap that carries what the shape of the tree carries in Huffman.

And optimality is not measured the same way. Huffman minimises the number of symbols, on the assumption that every symbol costs the same. In telegraphy a dash costs three times a dot, so what has to be minimised is time, not the count of marks. That is a different problem — coding with unequal symbol costs — and it was not solved until 1961 (Karp, via integer linear programming), with workable approximations later still.

In short: Morse is not Huffman and was never meant to be. But the question “how close is it?” remains a fair one, and it can be answered exactly.

What the allocation error costs​

Let us compare fairly: take the same twenty-six codes and hand them out to the letters in the best possible way — the cheapest code to the commonest letter, and so on down. That this really is the optimum follows from the rearrangement inequality: no other allocation gives a shorter mean time.

Seven percent. So an allocation made in the 1840s by eye and by ear loses to the exact optimum for the same set of codes by less than a tenth.

The table shows where the time goes, and O heads it by a wide margin: eleven units where there should have been five.

But Vail cannot be blamed for it. The code we have just taken apart is not his. American Morse had different codes for a good dozen letters and used gaps inside symbols (O was sent there as two dots with a wide space between them). In 1848 Friedrich Gerke reworked it for the Hamburg telegraph line — he removed the internal gaps and evened out the lengths. In 1851 the German-Austrian Telegraph Union adopted that revision, and the international alphabet grew out of it.

So the frequency optimisation was Vail's, while the particular allocation we are measuring is Gerke's — and his aim was regularity, not the shortest time. Seven percent is what that regularity costs.

And a practical conclusion, the opposite of what you would expect​

The tree explains why the alphabet is the way it is. But you must not learn Morse from it.

Anyone who traces a finger down the tree while a transmission runs in the headphones is putting counting where hearing should be: heard → counted → recalled. That intermediate step hits a ceiling around ten words a minute, and unlearning it afterwards is harder than learning properly from scratch. The method that works is Koch with Farnsworth: characters at 20–25 WPM from the very start, only the gaps stretched, and no table in front of you.

The tree is a good answer to “how does this work” and a poor answer to “how do I learn it”. They are different questions, and confusing them costs six months.

An open question I am leaving for later: everything counted above is for English letter frequencies. What a code optimised for someone else's language costs a Ukrainian operator, and what the same table looks like for the Cyrillic Morse alphabet, is a subject for another time — and one to begin by checking the Cyrillic table against a primary source rather than against memory.

On 6 March 2026 I showed it running for the first time — from my own laptop, through ngrok, with a link that lived until midnight. Even then it kept a shared log, accepted contacts from WSJT-X over UDP, imported ADIF with duplicate checking, and had separate dashboards for hunters and for organisers. The next evening the bridge for digital modes appeared — for Windows, Linux and macOS.

In April, seven weeks after that demonstration, the special callsign EN40CNP was on the air for the 40th anniversary of Chornobyl. Two weeks, 1565 contacts, several operators — and the whole log was merged by hand: the platform was not yet ready for real use. Vitalii, UT0UI, put the experience most precisely: “merging logs after the fact by hand is a right pain”.

By August it was ready. What follows is what came of it: the platform uahamaward.com, on which the “35th anniversary of Ukraine's independence” award made 17,387 contacts in 31 days, and not one of them was merged by hand — neither during the month nor after it.

The problem first​

Everyone keeps their own log. Then it all gets merged into one file. Then it turns out two people were working the same band and mode at the same time. Then somebody has lost their ADIF. Then LoTW refuses the duplicates.

At 1565 contacts that is a few evenings. At seventeen thousand it is no longer work but an impossibility.

Four requirements​

For the August activity I set myself not the task of “building a site” but four specific pains to remove.

1. Two people must not land on the same band and mode at once. Somebody has to see who is on the air and where — and see it now, not afterwards.
2. The log must be shared and live. Not a file at the end of the month but a table everyone sees in the same second.
3. The certificate must count itself. Conditions, points, number, PDF — with no human in the loop.
4. The ADIF that comes out must be accepted by LoTW and QRZ without edits. Not “almost the right format” but one that goes in first time.

What the platform does​

This is not a site with a table. It is several separate programs that work together — and each can be used on its own.

A shared log: everyone sees the same thing, now​

An operator opens the activator panel, presses “go on the air”, picks a band and a mode — and that slot is taken. The rest of the team sees it instantly, with no page reload: who is sitting where, on what frequency, in what mode.

• Every contact appears in the shared log within a second.
• Duplicates do not get through. The same correspondent, band, mode and minute will not be written twice — even if two tabs send them simultaneously. That is not rare: one program sends to two tabs, and both try to write.
• A session someone forgot to close shuts itself after an hour without contacts, so a band is not held by somebody who simply closed their laptop.
• A mistake in the log can be corrected or deleted; the edits are visible to everyone.
• The event page and the hunter page are public, with no registration: anyone can watch the activity and their own progress.

CAT: the radio straight from the browser​

Connect the radio over a COM port and the site fills the frequency and mode into the contact form by itself. Nothing has to be installed: it works in the browser.

• Frequency and mode are read from the radio rather than typed.
• VFO and band control from the same page.
• 172 models out of the box: Icom, Yaesu, Kenwood, Elecraft, Ten-Tec, Xiegu, FlexRadio, Alinco, JRC, AOR, Elad, Expert Electronics. The profiles come from the OmniRig format, so a radio not on the list is added with a description file rather than by rewriting code.
• If you do not need CAT, just pick the band and mode by hand; everything else works the same.

The bridge: WSJT-X writes to the log by itself​

A small program on your computer: it catches packets from WSJT-X and puts the contact straight into the award log. Make a QSO and it is already in the shared table, where the rest of the team can see it.

• Seven builds: Windows, Linux, macOS (x86 and ARM) — downloaded from the page and started with a double click.
• It updates itself, but only when you press the button: the bridge holds the port WSJT-X knows about, and an unexpected restart in the middle of an activation means lost contacts.
• Settings in a browser window, not on a command line.
• It forwards the packets on, so JTAlert, GridTracker or N1MM work alongside it. WSJT-X can only send to one address, which is why you previously had to choose just one.

Custom builds of WSJT-X and WSJT-Z with a country filter​

Two builds of the popular digital-mode programs, with what the originals lack.

• A country filter at the decoder level. You pick countries from the DXCC list: hidden stations do not appear in any window, and the program will not answer them even on a direct call. Unlike the existing filters it works by country rather than by text match — “Japan only” catches every prefix at once.
• A direct link to the platform. Log a QSO and it is on the award page immediately. No separate bridge needed.
• A Ukrainian interface: menus, settings, tooltips, errors. Mode and band names stayed in English — that is what people are used to.
• Callsign data from QRZ.com right in the program window.
• Along the way a bug in the inherited code was fixed: filtering out one signal made every subsequent signal in the same period disappear.

Spotting: announcements to the DX cluster​

From the log page, in two clicks — or automatically while you work.

• Manual spots and an automatic mode with a timer.
• The timer knows the node's rules, so you will not be refused for repeating. And it knows that after a frequency change you may spot immediately.
• A spot feed on the log page: other people's and your own, with the author's callsign.
• A cluster monitor of our own — like dxheat, but ours.

Certificates: counted, numbered and assembled automatically​

The organiser describes the conditions in the award settings, and the platform does the rest.

• Conditions: a minimum number of contacts or points, separate conditions per mode and band, several groups of conditions at once.
• Special days. A multiplier can be assigned to particular dates — for us those were 23 and 24 August. The multiplier applies to the score rather than to a log line, so the holiday rewards three bands rather than three hundred calls on one.
• The certificate number is your place in the log. The queue is worked out from contact dates, not from who pressed “download” first. And every condition has its own numbering.
• The PDF is generated in two languages — whichever one the hunter opened the site in.
• An ADIF that arrives a week later takes the place in the queue its dates have earned: the roll is recomputed from the log.

QSL cards — electronic and for printing​

• An electronic QSL for each contact individually: the hunter opens their page, hovers over a “band × mode” cell, and downloads the card for exactly that contact.
• A 140 × 90 mm layout for printing, if paper cards are being ordered.
• Nothing has to be written out by hand — in August that produced 62 certificates and all the cards.

ADIF: import, export, and what LoTW accepts​

• Import of files up to 20,000 records with a progress bar — a full month's log goes in within 15–20 seconds.
• An export that QRZ.com and LoTW accept without edits: the right format version and correct submodes (ADIF does not know “FT4” as a mode — it is a submode of MFSK, and that is how it gets written).
• Frequency is in kilohertz everywhere — in the form, in the session, in the bridge. On output it is converted as it should be, so a contact does not end up 430 Hz away from where the other station logged it.
• A daily copy of the whole log emailed to the organisers — from once to eight times a day.

QRZ.com: contacts upload themselves​

If you have an XML Logbook Data subscription on QRZ, paste your logbook key into the settings and there is nothing more to do. The platform uploads every contact you make to your QRZ logbook by itself. No exports, no uploading ADIFs by hand.

• It works in two places: your personal log goes to your logbook, and the award log to the award's logbook.
• They are deliberately not the same: a QRZ logbook belongs to one callsign, and contacts made under an event callsign simply will not be accepted into your own. So the award has a key of its own.
• The state of each contact is visible separately: sent, duplicate, error — and exactly what QRZ replied if it did not go through.
• Contacts made before you pasted the key can be sent retrospectively.
• The key is stored encrypted and never shown back — the interface shows the last four characters.
• From the other side, QRZ is a directory: empty locators in the log are filled in automatically. Only the empty ones: a locator given on the air is worth more than a guess about where a station usually operates. Portable callsigns are skipped, because QRZ would return the home square and the contact was not made from there.

Statistics: what is visible about the event in real time​

• Each activator's output: how many contacts, on which bands, in which modes.
• Band coverage by hour — you can see where work has been done and where you are still awaited.
• A contact map: locator squares at their true boundaries, countries by QSO count, and a separate view by Ukrainian oblast.
• The hunter page: your own progress, how much is left to meet the conditions, and which activators are on the air now.
• A live PNG banner listing the active stations — for a QRZ.com page or your own site.

A personal logbook: not only for awards​

Every account has its own log, separate from any award: enter contacts by hand or from WSJT-X, upload ADIFs, download them back, switch on automatic syncing with your QRZ logbook. An award is one log and your personal one is another, and they do not mix: a contact made under an event callsign will not land in your own log, nor the other way round.

What the month produced​

Not one contact was merged by hand. Neither during the month nor after it.

How many people saw it​

Since the platform launched on 25 July.

The last line is the most important. 4,376 people used the platform and 123 created an account. That is not a registration failure — it is the design: a hunter does not need an account at all. They open the event page, type in their callsign, see their own progress and collect their certificate. Registration is only needed by someone who goes on the air themselves.

59 countries is no longer about us. Those are people who went looking for what they had been credited with and found a Ukrainian page.

Where this came from​

I built the platform myself — from the idea and the architecture through to production, the server and the domain. The first demonstration was on 6 March 2026 from a laptop; the first real event was on 1 August.

I say this not for applause but so it is clear what we are talking about: this is not a page with a table knocked up over a weekend.

What it costs you​

How to start​

If you are organising an activity​

1. Register at uahamaward.com — a minute, an email address and a callsign.
2. Write to me and I will set the award up for you. Name, callsign, dates, certificate conditions, artwork. After that you run it yourself.
3. Invite activators by callsign. They accept the invitation in their dashboard and can go on the air straight away.
4. Operate. The log, the certificates, the QSLs, the statistics and the QRZ upload take care of themselves.

If you are a hunter​

No registration at all is needed. The award log is public: type your callsign on the event page and you will see your own progress, how much is left to meet the conditions, and which activators are on the air. The certificate and the QSL download from the same place as soon as the conditions are met.

The platform will run any award — regional, club, national, a single day's activation or a whole month. Write to UR3PKI. I will help you set it up, configure the conditions and get to grips with the bridge, especially the first time.

And something interesting from the data​

When a log sits in a database rather than in thirty files, you can learn something from it. I went through August: how the daily volume depends on the solar indices (hardly at all — the calendar rules), while the high bands really do depend on them; why the median distance falls as the flux rises; how far radioteletype reaches and who worked through the geostationary satellite.

→ 17,387 contacts in August: an analysis of the log

73! Petro, UR3PKI

What follows is what can be seen in it. Not “the award was a success” but concrete numbers: when the bands opened, why Saturdays weigh more than the Sun, how far FT8 reaches compared with SSB, and why amateur radio remains a hobby of wealthy countries.

At a glance​

The map: the locator puts down a point, the callsign colours a country​

There are two different layers on the map, and they should not be confused. The squares are locators from the log, that is, the physical place a station worked from. The country colour comes from the callsign, that is, from where the operator was licensed. A German on holiday in Croatia puts a square in JN and colours Germany all the same — that is not an error, they are two different questions.

16,823 contacts (96.8 %) have a locator and appear on the map; 564 (3.2 %) do not, and those points are missing.

The leading locator fields confirm the geography without any statistics at all: Ukrainians sit in fields KN and KO, Germans in JO and JN, Poles in JO, Italians in JN, Britons in IO, Japanese in PM.

The small defects in the data are worth naming out loud as well: five callsigns — 489LGE, D01JAR/P, Y03FLP, Z50AF, Z62NS — match nothing in the prefix table and are assigned to no country. They are either mistypings made on the air or special callsigns absent from the reference.

Propagation: the bands day by day​

The award ran for 31 days (all times UTC) and gathered 17,387 contacts, of which 262 went through a geostationary satellite. Those are set aside in a section of their own and take no part in the propagation figures: the path to a geostationary satellite is the same by day and by night, in a storm and in quiet, so it says nothing about the ionosphere.

All correlations below are Spearman rank correlations.

Volume is governed by the calendar, not by the Sun​

The correlation between the daily number of contacts and the SFI (the solar flux at 10.7 cm) is only 0.12, and with the sunspot number it is actually negative. Meanwhile weekends average 615 contacts against 523 on weekdays, and three of the month's four biggest days are a Saturday or a Sunday: the 22nd (941), the 23rd (994) and the 16th (770). Sunday the 9th produced 736 contacts at an SFI of 94 — one of the lowest of the month.

This sounds banal until you notice how often, in amateur conversations about “a bad day”, the Sun is named as the culprit. On the scale of a month the deciding factor is when people have a free evening.

The high bands, though, do obey the Sun​

Move from the overall volume to individual bands and the Sun comes back into the picture. For 10–17 m against SFI, r = 0.35. When the SFI rose in the second half of the month from about 94 to a peak of 143 (on the 24th), 12 m gave more than 50 contacts in a day for the first time (55 on the 17th, 67 on the 25th), and 10 m reached 99 contacts on the 25th.

That said, 59 contacts on 10 m on the 10th at an SFI of 95 are a reminder that in summer 10 m is opened by sporadic E, which has no need of a high flux.

Magnetic storms pressed on the low bands​

2–3 August (A = 15 and 17, Kp up to 5.7) produced the month's minima — 223 and 420 contacts — and the correlation of 40/80 m with the A index is r = −0.20.

Signal quality in the digital modes, however, the storms barely touched: the median FT8/FT4 SNR stayed all month in a corridor of −12…−6 dB and is only weakly related to the SFI (r = 0.12). The best day by the share of strong signals (≥ −7 dB) was the 25th (55.7 %): a high SFI of 132 and a quiet magnetic background. The worst were the 27th and 29th (27.0 and 28.2 %), when the flux was already falling.

Distance runs against the Sun — and it is not an artefact​

The daily median activator-to-hunter distance correlates negatively with the SFI: r = −0.55.

A simple and wrong explanation suggests itself: when the SFI is high the upper bands open, and what changes is not the physics but the composition of the log. Checking rules that out. The same correlation computed within a single band does not fall apart: on 20 m r = −0.59, on 30 m −0.49, on 17 m −0.40.

So the effect is real within a band as well. A higher flux raises the MUF, a shorter hop opens on the same band, and nearby Europeans come into the log who at a low SFI simply would not have been there. The long paths do not go anywhere — they merely stop being visible behind the near ones.

The SNR is taken from the report sent to the correspondent: in digital modes a report is a signal-to-noise ratio in decibels, not the usual readability estimate. Distances are between the centres of locator squares (Maidenhead, 4 characters). The indices are NOAA SWPC daily tables; the A index for the 16th is missing from the source, and the table shows a dash there.

Through the satellite: QO-100​

262 QSOs in this log — 1.51 % — went not through the ionosphere but through the geostationary transponder QO-100 (Es'hail-2). In the log they are marked with the band 3cm and frequencies of 10,489,540–10,489,560 kHz — the satellite's narrowband downlink (10489.550–10489.800 MHz according to AMSAT-DL; a discrepancy of a few kilohertz comes from an uncalibrated LNB, an ordinary thing on this band).

Eight of them nearly went missing. Their frequency is recorded a thousand times too high — 10 489 540 000 instead of 10 489 540, the decimal point in the wrong place. That is the commonest hand-logging error, and on 3 cm it is visible: with the point moved, the number lands in the downlink to the nearest kilohertz, and there is nothing else on this band anywhere in the log. So they are counted — discarding them would have meant missing eight genuine contacts through the satellite.

One activator gathered 194 correspondents from 34 countries in 14 days. Half of Europe in the log from a single spot, with no dependence on propagation at all.

How far it reaches: distance by mode and band​

The question “how far does a mode reach” only makes sense when the locator is known for the great majority of contacts. Here it is known for 96.8 %, and evenly across the modes — so a difference between modes means a difference between modes, not a difference in who bothered to give a square.

These are the distances of this log, not a property of the modes as such. People work FT8 when the DX is already audible, and SSB when the other station can still be made out. What is being compared is not physics but habits along with physics. The telling line is FM: median 0 km, maximum 672. That is local operating, and there everything is as it should be.

Radioteletype deserves pulling out separately. 44 QSOs is a quarter of a percent of the log, and in any mode summary it drowns in “other”. But it is the only classic digital mode outside the FT family, and UR3QCC ran it single-handed: 34 correspondents, 14 countries, 10 days on the air, all on 20 m in the 14,087–14,095 kHz segment, above the FT4 slot and clear of it. Median 1545 km, maximum 8099 — further than CW and closer than FT8. For a mode that machines rather than ears receive nowadays, that is exactly in the middle. One RTTY contact went through QO-100: teletype, on 3 cm.

Who turned up: 8,226 callsigns​

Over 31 days, 8,226 different stations worked the award — 2.11 contacts per callsign. But the average says almost nothing here, because the distribution is very uneven:

• the top 10 % of hunters account for 44.1 % of all contacts;
• 67.8 % made contact exactly once;
• 70.5 % were on the air with the award on a single day;
• and 54 stations came back on ten days or more.

This is the portrait of a mass event with a small core: most participants looked in once, while the backbone of the log is held up by a few dozen who were on the air almost daily. Both halves are worth attention — the first says how many people the award reached, the second how many it held.

In pictures​

Four charts reduce 17,387 contacts to a picture: who worked whom, on which bands and in which modes.

Amateur radio is a privilege of wealthy countries​

The wealthier the country, the more of its operators appear in the log. Spearman rank correlation between a country's contact count and its development indicator:

These three figures are computed over all the countries in the log, and the tail of that series consists of countries with one or two contacts, where rank means almost nothing. So the same correlation was computed twice more: 0.31 among the 50 countries that produced ten contacts or more, and 0.55 with Ukraine excluded.

So the link with wealth is real but noticeably weaker than the full series suggests: to a large degree it is held up by countries that contribute a few lines to the log. Ukraine's home-field effect, on the contrary, was lowering the correlation rather than creating it.

At the same time, the 48 countries with a GDP per capita above $40,000 account for 75.9 % of all contacts, while the 16 countries below $15,000 account for just 0.5 %.

Short waves are an expensive hobby: transceivers, antennas, licences, education, free time. Among the twenty most active countries, most have a GDP per capita above $50,000.

There are counter-examples too. Ukraine accounts for 19.8 % of contacts at a GDP per capita of about $18,600: the award is a home one, and the home-field effect outweighs the economy. Poland holds a place in the top ten and Greece comes right behind it, despite a GDP below northern Europe's. Meanwhile the richest countries in the world are barely present: Luxembourg with 13 contacts at $156,000 per capita, Qatar with 4, Bahrain with 4, the UAE with 1. There are only a handful of radio amateurs there.

Top 20 countries​