When a broadband distributed transmission line has a standing wave due to the electrical length being a multiple of 1/4 wavelength, the impedance reaches a "resonant" characteristic in terms of impedance matching with a ground plane.

However this is not related to a resonant antennae which using the Q of reactive and resistive ratio to amplify either current (series LC) at centre frequency or voltage ( shunt LC ).

There are several versions of definitions of resonance.

• lumped elements store energy and maximimize this behavior at resonance.
• Transmission lines at resonance just look like resistance,
  • either matched (half wave) or reflected to ground reference ( quarter wave) and their respective multiples of wavelength.
  • or conjugate mismatched such as a 1/4 wave notch filter by impedance inversion.

So the conflict of assumptions is that non-resonant antennae do not store energy and yet energy storage elements can radiate through non-resonant wires.

But in effect all standing wave antenna have perfect resonance and those that reflect some back to the source are imperfect resonators.

The assumptions require context to resonance with a reactive gain above unity or a passive amplifier with the ideal being conjugate reactance cancelling to result in a resistive load.

Viz. A non-resonant antenna is made resonant with the conjugate matched impedance. this is the case for AM coil antennae with very high Q for voltage amplification.