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For LF/MF (2200m/630m), I am interested in the situation of a vertical antenna with capacitance hat top-loading, where the vertical antenna is VERY short compared to wavelength, and the antenna is brought to resonance across operational frequencies via suitable base inductive loading (i.e. variometer).

Given this situation, using antenna modeling I always end up with a resistance value significantly less then 50 ohm. When I calculate the necessary values for an LC impedance matching circuit, I end up with extremely high values necessary for capacitance (e.g. 50-60nF), which means variable capacitors are not a viable option.

What other options are available for matching a resistive component of less than 50 ohms? E.g. matching in the range of 5-10 ohms, to 50 ohm coax?

Could a "reverse" ferrite unun transformer work? E.g. 1:2, 1:4, 1:6? If so, suggestions for best approaches? What would be the implications for efficiency and limits on input power?

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The gold standard books on baluns are by Jerry Sevick. They all seem to be out of print and expensive on ebay, but you may find one, or someone willing to summarise the relevant pages of their copy. Latest edition here?.

A few points I still carry with me 20 years after last reading the book:

  • Number of turns is important, skews the best performance up and down in frequency
  • Transmission line transformers don't get warm if they're made right, even at 2 kW
  • 50:450 is different to 5.6:50 - the line impedance is different (less important at low frequencies) and you need more turns on the core (you need more blocking impedance, also the stray effects matter less).

Converting my comment and totally not answering your question directly:

This is how a parallel Capacitor works:

  • Guessing the antenna is 5-j1000 Ohms (1/10 wavelength ?)
  • Frequency 1 MHz, with a span of 1 kHz
  • Series inductor of 161.5 uH which is +j1020 ohms slightly too big for resonance
  • Parallel capacitor of 9.5 nF raises the impedance to exactly 50.

Using the amazing smith chart at https://www.will-kelsey.com/smith_chart/

Circuit

This is the result:
enter image description here

Of course it's quite narrow band, but this is mainly because of the antenna+inductor circuit Q, not the matching network. Here is the Smith chart when I use the perfect +j1000 inductor in series, plotted at 5 ohms (equivalent to using a perfect 5:50 impedance transformer). See the bandwidth is about the same (~2 kHz at 2:1 SWR, but this is a lossless inductor).

enter image description here

Play with the Smith chart online to see the impact of different solutions. For small changes in frequency I think you'll find a fixed C and variable L will be good enough. For large changes like going from 500 kHz to 1.8 MHz you'll need different C too.

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I think I just found part of the answer to my own question: https://www.balundesigns.com/model-1435-1-4-unun-12-5-to-50-ohms-5kw/

If anyone can elaborate on the theoretical and practical aspects of constructing such ununs (especially how to make low ohm coax, and what ferrite cores to use for 2200m and 630m), please chime in.

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  • $\begingroup$ Coax impedance is not important at these frequencies, because it's such a small fraction of a wavelength long. But in designs I've seen, they use two wire lines, two copper strips maybe 4 mm wide, 0.5 mm thick, with a thin layer of kapton separating them, then taped tightly, to make a transmission line under 25 ohms. $\endgroup$
    – tomnexus
    Dec 2, 2021 at 0:23
  • $\begingroup$ Or just use twisted pair... $\endgroup$
    – user10489
    Dec 2, 2021 at 3:20
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What type of shortened vertical are you trying to design? 1/4λ counterpoised? A 1/2λ end-fed? Because if you're electrically in the 1/4λ region and not using a ground plane, you will have a very hard time even when you load the base or any other part of the antenna.

But that being said, you will likely need a transformer to match the input impedance, but not before you get the antenna resonant with enough inductance. Remember that by definition, a shortened antenna is capacitive and you need to add inductance; (you may have to add capacitance too, but one problem at a time.) The problem with shortened antennas, is adding L or C can severely narrow the bandwidth as far transmitting impedances are concerned. Also, keep in mind that getting a feed-point impedance that your SWR meter likes, doesn't mean your antenna is resonant and you've created an efficient antenna.

Yes, you can use an unun in either direction eg. 1:4 or 4:1 (50>200 ohms or 50>12.5 ohms)

Please let us know what type of vertical you are going for.

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  • $\begingroup$ At wavelengths that long, the only practical antenna that I know of for someone who doesn't have access to a very tall broadcasting transmission tower is a severely-shortened ground-mounted vertical (or an L). Vertical polarization is the goal to take advantage of ground-wave propagation, and elevated radials aren't practical. That's almost certainly what the OP is talking about. $\endgroup$
    – rclocher3
    Dec 3, 2021 at 0:34

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