> I bought an expensive 10m (30ft) active HDMI cable
I think what I was referring to are repeaters you put between cables, that amplifies the signal. You connect that device between two HDMI cables (say 5m) + connect it to power for it to actually extend the distance the signal can travel.
I'm not sure what an active HDMI cable would be, maybe circuitry inside the cable that draws power from the HDMI port?