Q: What is actual impedance of that type of antenna?
A: Probably a bit less than 50 ohms for most practical installations.  As much as 73 ohms in total isolation.  Standby for others' experience.

Q: How to match that type of dipole antenna to 50 Ohm?
A: Don't worry about it.  Perhaps decouple the feedline (ferrite or simple loops).

Q: Any software tools to simulate that type of antennas?
A: NEC or similar (not that it is really required)

Q: Any simplified formulas to calculate length and diameter of the arms of the dipole?
A: Length: 468 / MHz = total length in feet.  Diameter is not that critical for most applications, thicker might be slightly lower Z and slightly wider bandwidth.  YMMV.

Q: How far the pipe (lower arm of the dipole) should be from a connector and metal enclosure?
A: I've seen some less than 1/4 lambda from the connector, but that seems a bit too close.

Q: Can that type of antenna work from 100 MHz to 2.4 GHz?
A: Yes, and beyond.  Even 27 MHz CB.

In general, this sort of antenna doesn't normally require a great deal of analysis (unless you're using it on a space mission or something critical).  For most people, just build it and try it.  You can also use some of the coax shield for the lower element and enclose the whole thing in a plastic pipe.  Even commercial VHF or UHF antennas are made this way.

Clarifying the last question;  A single dipole antenna is usable over a very small part of that frequency band, maybe 10%. I wanted to note this just in case it was interpreted that you can make one antenna to cover the entire frequency band.

Only a bicone or monocone can easily make that 24:1 bandwith and cover the entire frequency band. It will be around 20" tall and 40" diameter though.

kchiggins

PS: I agree that complicated software isn't needed for this antenna. Material properties are not exactly known and their inaccuracies almost always make empirical development necessary.

Shakespeare used to make a CB (11 meter band) antenna called "The Big Stick" which was indeed a coaxial or sleeve dipole.  The antenna was an aluminum tube wrapped in the same color fiberglass as their 102" whip antenna.  it had a 3/8-24 threaded socket at one end and an so-239 (PL259 socket at the other.  The interconnection between the feed point and the connector was 18-2 zip cord (regular 18ga white insulated lamp cord) on the one I inspected after an iceing incident which broke the base section of the antenna.

I have built a few for VHF and tested them on a makeshift range with a Network analyzer.  They're ok, not much better than a 1/4 lambda monopole over a good ground plane.

The gain of the antenna is (guess what?) 0dBd (Who'd have guessed? )
I remain,

The Old Soldering Gunslinger

Hi,
Thanks to all, for your feedback on my question.

I think, the more complex coaxial dipole is built, instead of 1/4 wave one, to avoid large ground plane, as some RF modem enclosures are quite small, and not a plane at all.

The gain at 0 dBi is surprising. I will test may antennas soon, so I will let you know what my measurements are.

rfeng1

OSG wrote "0dBd" (note the trailing 'd', as in dipole).

  (it IS a dipole)

I've got one of those 'Big Stick" antennas, bought cheap for eventual conversion to 10m. For some inexplicable reason my example has reversed threads at the junction of the two halves. Weird.

The other advantage (besides slimness) of this type of antenna is that the feed point is elevated by another 1/4 lambda. That height increment can help for very low installations.

A halfwave at 915 MHz is 6.454".  The ground plane would be approx. 7" in diameter.  The quarer wave monopole would be 3.227" tall.

I remain,

The Old Soldering Gunslinger