Your SWM8 sees the King Dome as an 18" round antenna. It doesn't know or care what else the antenna is. Obviously, the control cable to your King Dome is a separate cable from the coax that carries the programming.
Like I posted in an earlier response, my Vuqube Flex 2100 would NOT work with SWM8. It has a controller that sends signals over the coax cable to the antenna. the SWM8 would block that.
Unless, that is, I ran two coax cables from the antenna into the RV, then hooked the controller to one of them, THEN hooked the SWM8 in. Hmmm, I may test that sometime when I am at home and bored. I can take the SWM8 out of my attic to play.
