What is the approximate feed point impedance at the center of a two-wire half-wave folded dipole antenna?
Why A folded dipole is two parallel conductors joined at the ends, so the driving current splits between them and the feed point sees an impedance stepped up by the square of the number of conductors. With two equal-diameter wires the step-up factor is 2^2 = 4, and 4 times the roughly 72 ohm impedance of a plain half-wave dipole gives about 288 ohms, conventionally rounded to 300 ohms. That is exactly why 300 ohm twinlead was the classic feed line and building material for folded dipoles.
Watch out The choice of 72 ohms is the feed point impedance of an ordinary single-wire half-wave dipole in free space, which is the starting value before the folded geometry multiplies it by four; 450 ohms is a common open-wire ladder line impedance, not a folded dipole feed point.
Fold a 72 ohm dipole in two and you multiply by 2 squared: 4 x 72 = about 300 ohms, the twinlead number.