Rabbi Yehoshua says that a rod above a doorway conveys ritual impurity regardless of its size; this is true even if it’s 100 cubits higher than the doorway (i.e., 150+ feet). Rabbi Yochanan ben Nuri says that we shouldn’t treat this any more stringently than we do a projection (i.e., higher than 12 handbreadths, its measure is an opening of a handbreadth).
Regarding a projection that goes all the way around a house and extends into the doorway by three fingerbreadths, if there’s ritual impurity in the house, utensils under the projection are rendered unclean. If there’s ritual impurity under the projection, Rabbi Eliezer rules the house unclean while Rabbi Yehoshua rules it clean. The same parameters apply to a courtyard that’s surrounded by a portico.