If that's the case, why do all TV antenna installations use 75ohm coax?

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Because it is much more convenient to install and easier to keep dry. And
TV receivers don't have 300-ohm antenna sockets.

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No-one uses 300ohm feeder at UHF!

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Except when engineering economics and the appreciably lower loss of 300-ohm
line is less expensive than providing and running a higher power
transmitting station.

" Bank Managers wielding the Almighty Dollar Rule ! ". Terman and radio
hams have to take backseats.
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Reg, G4FGQ