I've wound a few air core baluns in my time, and yes, they work, but nothing excites the boards more than balun talk.
This is a VOLTAGE balun, which requires that the antenna be for the most part balanced, ie a dipole.
Problem is, in the real world, a dipole is usually not very well balanced due to the surroundings, and the voltage balun doesn't work as well as it should on paper.
That is why most these days opt for a "current" balun, which made out of broadband ferrite usually, does a better job - although in extremes, or the wrong choice of ferrite material, burns up.
Still, I have a place in my heart for air-wound baluns as long as you are aware of their possible deficiencies. In many cases, mine worked fine until I got into an extremely unbalanced situation, or where I *wanted* there to be common-mode current depending on the design of the antenna.
