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I'm intending to make a sleeve balun (aka bazooka) for 2m, but rather than keep the lossy coax jacket as a dielectric (I have some RG58), was considering to remove it and replace it with heat shrink tubing.
I haven't been able to find anything here or via google, and am hopeful that some folks here might have some experience, insight, or resource pointers.
Otherwise I'm just going to try it both ways and measure.
The spies from CIA had this problem solved long ago. See https://www.cryptomuseum.com/covert/bugs/ec/sleevex/index.htm You need to have the relative dielectric constant between the coax shield and the sleeve equal to the dielectric of the cable. By this you maintain same velocity. Also you want to keep the impedance same, which requires quite a thick layer of polyethylene tube in place of the PVC on the outside of the shield. There is a fine calculator at https://www.pasternack.com/t-calculator-coax-cutoff.aspx Take 2.3 as relative dielectric constant of PE.
There is an article covering every aspect of sleeve baluns at http://www.w8ji.com/sleeve_baluns.htm
If you do not need flexibility, try this http://www.w6nbc.com/articles/2009-07QSTcoaxialdipole.pdf which uses air as dielectric.
For a bazooka balun, you want the $Z_0$ of the transmission line to be as high as possible. A thin layer of heat shrink is not ideal.
If you must use a sleeve balun for mechanical reasons, rather use a 30 mm diameter pipe with the coax inside it.
The impedance of a short circuited transmission line is
$Z_{SC} =jZ_0\tan(\beta x)$ where $\beta=2\pi/\lambda$
At a quarter wave this is an open circuit, but at any frequency away from a quarter wave, the impedance drops quickly and the line $Z_0$ matters a lot.
If the frequency changes by 10%, (or you get the velocity factor of the line wrong by 10%, very likely if you don't know the dielectric well, or measure it), then the impedance is $j6Z_0$. If your line $Z_0$ is $25\space\Omega$, that's only $150\space\Omega$, not a very good choking impedance. If you make a $120\space\Omega$ two wire line with a second piece of coax taped against the feed, it could be almost $1000\space\Omega$ at the same frequency offset.
So I suggest a kind of pitch fork of two parallel wires, a quarter wave long, one each side for symmetry, spaced about one coax diameter apart. Braids soldered together at the short circuit side, don't worry about the inners. No need to remove the jackets.
Like this, if you're using the outside of the bazooka as a dipole element (diameters and widths exaggerated a lot):
Or like this if you need a balun for a balanced antenna like a dipole:
Finally, you don't know the RF properties of the plastic and glue in the heat shrink. You can compare it to the coax jacket by putting a piece of both in a microwave oven, with a small glass of water on the far side. Cook them for a bit and see which plastic gets hot first. A good dielectric like PTFE or PE won't get hot at all.
It's a great idea to build and measure these things. The way to test for unbalanced currents is to mount the antenna say 2 or 3 metres high on a wooden pole, and watch the VSWR display while you run your hand down coax. If the graph jumps around then there are currents on the coax. Be sure to evaluate the whole frequency range you're interested in. At slightly higher frequencies, I remember seeing the trace dancing around in most of the graph, and being stable in the middle where the balun was working.
