I have had some parts around for a while now that I intended to build a balun out of. I finally got around to working on one over the past week or so (I started last Sunday night and did all the rest of it this evening HI).
My idea was to make a 1:1 balun that fit right on the rig for using the internal tuner with a doublet, or any other balaned line fed antenna.
Below are links to pictures of what I came up with.
I used parallel runs of about 15-17" of 18 gauge magnet wire, two stacked FT-82-43 cores (Amidon), 3/4" stainless screws, two nuts, two flat washers, two lock washers, two wing nuts, about 1" of 18g stranded speaker wire (lead-in to the BNC connector), BNC connector for RG-58 coax, two small ring terminals minus the plastic sleeve, and a small enclosure box from Mouser.
The BNC connector is bolted to the enclosure. It is a crimp style. I soldered the center pin then used the rear nut/bolt part passed through the wall of the enclosure as the mount for the plug. It is a pretty slick idea and quite rigid. There are 10 wraps of the magnet wire around the cores. Wrapping the stacked cores was a chore. I did not use anything to bond the cores together first (no tape or anything, just the wire). Once I had about 3-4 wraps on there it stiffened up but it was a trick.
One addition I may make to the balun is a piece of plastic between the turns and the ring terminal crimps along the sides. I would imagine having the terminals that close (right against) the windings is not a good idea.
I have another idea for a balun that is identically designed with a chassis mount BNC connector (single hole, not the 2 or 4 hole flanges) for use as a dipole feed point. I have a T80-2 Amidon core wound up already, again 10 windings of the 18g magnet wire. This fit too tight inside the small square enclosure but I have some that are rectangular and will have about twice the vertical space. This will let me space out the ring terminals at the top as well as have plenty of space for wiring the bulkhead BNC connector on the bottom.
I have never used a BNC-binding post adapter with a balanced fed antenna, always 1:1 baluns. A BNC-binding post adapter is essentially taking the wires of your balanced line and putting a BNC plug on there. You have no transmission line transformer to convert between the balanced antenna and the unbalanced output of your rig.
Impedance matching is another story. I believe it is irrelevant what the impedance is of your antenna and what nominal impedance transmission line you use (300 ohm TV/ribbon wire or 450 ohm ladder line) in the case of a doublet, or similarly non-resonant antenna, because, well, its non-resonant. All the impedance matching is in the tuner. The magic of the balanced transmission line and balanced (albeit non-resonant) antenna is you don't get quite the attenuation that you would with coax, an unbalanced transmission line.
The one conversion I believe necessary in a balanced antenna configuration is converting between the unbalanced output of the rig to the balanced transmission line, without an impedance transformation.
The reason for the above is that tuners match higher impedances better than they do lower impedances. So, for example, if you start with a 200 ohm load and use a 4:1 balun you are left with 50 ohms. This is a great match. If you start with 1000 ohms and use a 4:1 balun you are left with 250 ohms. This is easy for a tuner to match. Yet, if you start with a 50 ohm load and use a 4:1 balun you are left with 12.5 ohms. Now, lets go a bit further. If you have a 25 ohm load and use a 4:1 balun you are left with 6.25 ohms. Yea, your tuner may tune it but it will have a hard time and you will risk burning it up. The lower impedances are always harder to match. In this instance, if you used a 1:1 balun you would see a range of 1000 to 25 ohms which your tuner should handle OK. If you have the option of a 4:1 balun then you have the high range covered, but if you have one balun its better a 1:1 than a 4:1.
I will use a BNC-binding post adapter with a random wire, because it is an unbalanced antenna. Nothing more.
I was intrigued by the use of the BNC connector on the balun enclosure. I had never thought of that. I was just going to use a short coax cable between the KX3 and my new home-brew balun.
I built a balun a couple weeks ago using a 1"x2"x3" box from Radio Shack ($3) and a T130-2 core and #18 gauge magnet wire off ebay or under $10. I wanted something to match a higher impedance of a W3EDP antenna, so I used a balun design by W2FMI using 4 wires (essentially two 4:1 baluns) on the core and tapped for 16:1, 9:1 and 4:1 (I also tapped off the half coil sides for 2:1, 6:1 and 12:1 (approx). I used a RadioShack 6 position rotary switch ($3). I then marked the switch positions as 100, 20, 300, 450, 650 and 800. Input is a BNC (female) and output is a pair of banana sockets. It was a bit of a tight fit, but seems to work out OK.
Testing with an MFJ259B and rf voltmeter shows a progression of voltage output as I switch through the positions.
I wanted to use the balun for a W3EDP antenna (http://www.zerobeat.net/g3ycc/w3edp.htm) so I need a higher impedance output. I have another version of the same balun that I built using an Amidon 2kw core, but it was too large to carry around for the KX3 in my portable case (I use an old video camera case that carries everything).
The larger version of the balun worked just fine when I used it with the KX3 and internal tuner. Just change impedance tap positions until I get a good match with the tuner. I haven't actually tried the new balun yet though. I may modify it to use the BNC connector like you have implemented.
I have some pictures, but not sure where to upload them to.