Now I wonder how that all ties in with changing that 100 Ohm impedance
to 50 Ohms?

See chapter 26-6 of the ARRL handbook (19th ed., 2000) "Coupling the
Line to the Antenna".

.. . . 26-6 of the ARRL Antenna Book (19th ed., 2000) "Coupling the
Line to the Antenna".

Nutz.

Spank.

w3rv