Have cable tv without a box connected to my one coax input. Tv has one coax and a few HDMI. Wanted to hang an HD antenna which has coax connection as well but already used up. Is there a simple coax to HDMI converter that can be used ? Or, do I need to use a external tuner that will take the HD in from the coax and convert to an HDMI output. In that case, would I put the TV HDMI input to channel 3 and switch channels via the external tuner ?