I currently have an FM radio/alarm clock at my desk. It had a 12 inch antenna that stuck out of the top, which worked well enough, but wasn’t a winner for looks. Between that, and the fact I had some coax, I decided to improve it. The design is pretty simple, strip the insulation off 15 in of the coax, bend the two sides apart, and there was an FM antenna.
The pictures turned out a little hazy, but ought to give you the idea. I planned to use the stripped shielding as the ground side, but due to the difficulty of getting it in the right place, I cut it off and used a wire nut to hold the alternative piece of wire on.
I than ran it up the trim, out the door, an stuck it under the lip in the siding just above the door.
(The reason I love old FM radios compared to new ones) The radio had places to screw the + an – sides of the coax to!!!
I don’t know that you will ever find this on a new one, but back then they made these things to you could improve the antenna without taking it apart to find the hot and cold and so fourth. No connectors required, just screw and go!