Idea: Optimizing simple Yagi antennas?

[LM21]

Has anyone studied what happens to the radiated power if you just add reflector or director elements to an unmatched dipole. Gain goes up but antenna impedance goes down. Do you always need impedance matching to get more power to a receiver. Is there already info about optimum design.
A job for a VNA, I  think.

[A.Z.]

http://on5au.be/content/a10/ant36.html