I'm looking at a horn antenna and why its a good addition to a waveguide. I've read that the horn can operate at a wide range of frequencies since it has no resonant element. But I can't find a good description of what a resonant element is in this application.
In this context, a resonant element would be a chunk of the system that possesses a substantial quantity of impedance (either capacitance or inductance), different from that of the system as a whole. So if the horn had a local swelling or constriction somewhere along its length, the impedance of that segment would not match that of the horn inlet or outlet, and reflections would occur.
By the way it is not strictly true that a horn has no resonant elements in it. It has both inductance and capacitance contained in each little element of its length- however, by smoothly tapering the horn the impedance change from the throat to the exit of the horn is made gradual and the horn thereby becomes a transformer which matches the impedance of the waveguide to that of free space.