A.Z. thank you for your detailed and informative posts, they are very helpful.
You're welcome, just trying to help
I'd pretty much decided to go the way you suggest, but one question: Isn't the 1:1 choke supposed to go as near to the transceiver as possible?
I have seen that suggested in various places: i.e long wire > 9:1 unun > coax > choke >coax > radio
It may be put near the rig too, but my suggestion if possible, is to place one choke near the antenna and a second one near the transceiver, then adding more chokes will NOT hurt
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the point is that, even with a good counterpoise, an endfed antenna will still "try" to use the coax as part of the radiating system, and sincerely, I'd try avoiding that, so, placing the choke near the antenna AND connecting a decent counterpoise will help, then, if you want adding more chokes along the feedline and near the rig, won't hurt; but now that I think at it... didn't you get your license ? Once upon a time that meant passing an exam, and the latter involved some basic stuff. including CM currents... but maybe nowadays things changed and I'm just an old fart ...
I may or may not wind my own (I've wound small ones for Rx only) but the commercial ones are not too expensive and by the time you get your toroids, boxes, connectors the savings are not huge.
two or three FT240-43, the winding wire (for the UnUn) and RG-174 coax (for the chokes), plus the box and the other stuff won't cost so much, commercial decent/good UnUns and chokes would cost much more, assuming you aren't going to buy CRAPPY chinese stuff which will cause problems instead of solving them, that is
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and then, willing to go for "buy" (SIGH ... where is the ham spite today ?) the unun and choke from "palomar" (again, NOT promoting them, just. an example) won't cost you more than the ATU, and then connecting the ATU to a poor piece of wire brought directly INSIDE the shack won't offer you the same results of a properly set up antenna, even if it's a humble "random" wire
I'll try the 7300's own ATU first, and see how it goes. 80m - 10m would be fine for me.
With the current antenna, w/o a good setup ? Well, good luck with that ! But remember, the "problem" is not the 7300, it's the ANTENNA and adding an external ATU to the combo will still resuilt in a CRAPPY antenna and a waste of money (to buy the external ATU), again, skip the idea and start by setting up the antenna as needed, that's the ANTENNA which radiates and receives, if it's crap then adding tuners, preamps or linears will just mean wasting money without solving the problem
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Forgot, the antenna is an "end fed" one, but don't call it "long wire"; a long wire antenna is at least one full wavelength long (or multiple of a wavelength), an EFHW is an endfed with a length of 1/2 wave at the lower desired frequency, a "random" is an endfed calculated so that it will NOT be a multiple of 1/2 wave on any of the desired frequencies and that it will be near/above 1/4 wave at the lower desired operating frequency, so please, avoid calling it "long wire", it's a mistake