Everyone talks about the impedance but no one talks about the real issue: balanced vs unbalanced.
The mere fact is an impedance mismatch does make for some inefficiences; but on the Rx side you have a LOT more leeway than on Tx.
Anyway...the big thing between 300 ohm vs 75 ohm is the fact it's a balanced vs an unbalanced system. Twin-lead is actually a balanced transmission line...and a basic dipole antenna is actually a balanced antenna. You don't have a "Ground" connection like you do on coax; it's opposing currents on each line. In order to properly connect to an unbalanced medium...like coax, you have to transform from a balanced signal to an unbalanced signal.
This is what the balun does...it stands for "Balanced/unbalanced". Since it is just a transformer, you can use it to match impedance; but it's main goal is to properly transfer from the balanced nature of a dipole and twin-lead; to the unblanced connection of coax.
Antennas have natural impedances that manufacturers have standardized.
Basically any antenna can have any impedance...it just depends on the wavelength you're using and the rest of the system. It wasn't the antennas that was standardized, but rather the transmission line impedance. In terms of coax....television coax is 75 ohms because it provides a lower loss factor than another impedance at the expense of voltage. Transmitters typically use a higher-loss 50 ohm impedance due to the voltage handling.
matching transformer above is a 2:1 balun
It's actually a 4:1 balun. 300/75 is 4. Voltage and current are going to be a function of the impedance of the system.
Now here's the reason most people have bad luck with folded dipoles; they don't use them properly. Twin-lead takes special consideration when running; you have to keep the feedline perpendicular to the antenna elements for 1/8 a wavelength or more...otherwise you would completely throw off the balanced nature of the antenna. You also have to keep it away from metal that may run parallel as that will severely degrade the impedance of the feedline. Some of the best DX I've gotten on the FM band has been with a twin-lead folded dipole. The other thing to consider is that the impedance along twin-lead transforms as it runs down the line. So often times doing something like adding or removing a little bit of twin-lead knocks a system back in to the right impedance. That's why most of them are designed with so much lead on them...that's a known point where the impedance for that wavelength will be 300 ohms. Add 4 inches of wire at FM broadcast frequencies and suddenly it may appear as a 1200 ohm impedance.
Connecting a wire to the center of a 75 ohm F connector or one screw terminal of a 75ohm connection is actually a valid way of doing it. A monopole in free space provides about 73 ohms of impedance when resonant. Hell...what do you think most HT/walkie-talkie antennas are? It's a piece of wire with maybe an inductor connected to the center conductor of the connector using the rest of the unit as a ground plane.
