Does a standard, normal, bare-bones TV set up have any amplification/buffering/silicon up by the antenna? I can't find any reference to such doing Google searches, but I feel like Dave mentioned something about this in a recent video (the one with an amplifier chip with only 3 pins), and I've also seen tiny little sparks and even got a little jolt once off an antenna jack on the back of a TV (two separate TVs, so I doubt it's a fault), making me think that TVs provide a fair bit of phantom voltage to the antenna by default. I should probably just get a voltmeter and stick in the antenna jack, but I don't have a TV anymore...
Also, a more fundamental question: a TV splitter takes a signal off a 75 ohm cable, and splits it into two 75 ohm cables. Now, my impression is that a properly terminated cable with a 75 ohm impedance behaves likes a perfect 75 ohm resistor. If you connect two of those in parallel, you've got 37.5 ohms. Is the input cable from the antenna therefore improperly terminated, leading to reflections, or do splitters include resistance to match the parallel outputs to the input? Or is there some other clever option?