I have an old tube tv. Big, black weighs about 60 pounds. Works fine still. The only connection on the back of the tv is a single coaxial. Bought an antenna so I can get all the local channels. Works great. Want to hook up a blu-ray dvd player to be able to watch Netflix and play dvds. Have a hdmi converter so the input from the dvd player is hdmi and output is coaxial to tv. Works fine with that one connection. When I attach a coaxial splitter to hook up the antenna and the hdmi, the tv starts to get fuzzy. Is there a splitter that can allow both the antenna and the hdmi hook ups without loosing the clarity of the picture?