I think the answer to the question, "How is it possible for a halfwave dipole antenna to be resonant?", could be answered more simply; it's because any radiator that is any multiple of 1/4 wavelength (minus the velocity factor of the antenna material), has the reflected voltage wave, in-phase with the incoming current and voltage signal at the feed-point.

A halfwave dipole is simply two 1/4 wave radiators with a differential voltage applied, per the first drawing. Furthermore, the parallel feedline, feeding that dipole, will not radiate since the fields on each wire are equal and opposite; the lower picture, showing a differential voltage being applied, is still just a parallel feed-line, which should not radiate.

However, if voltage were on only one of those parallel lines, and the other was a "ground", like a partially removed coax shield, the element with voltage on it would radiate, but there would be a lot of loss with the "ground" being so close and parallel to the radiator.

I think the answer to the question, "How is it possible for a halfwave dipole antenna to be resonant?", could be answered more simply; it's because any radiator that is any multiple of 1/4 wavelength (minus the velocity factor of the antenna material), has the reflected voltage wave, in-phase or 180 degrees out of phase with the incoming current and voltage signal at the feed-point, the only difference between in and out of phase would be the impedance at the antenna feed point; but as long as the antenna's radiating element is some multiple of a 1/4 wave length, the capacitive and inductive reactances are cancelled out leaving what looks like a pure resistive load to a particular radio frequency.

A halfwave dipole is simply two 1/4 wave radiators with a differential voltage applied, per the first drawing. Furthermore, the parallel feedline, feeding that dipole, will not radiate since the fields on each wire are equal and opposite; the lower picture, showing a differential voltage being applied, is still just a parallel feed-line, which should not radiate.

However, if voltage were on only one of those parallel lines, and the other was a "ground", like a partially removed coax shield, the element with voltage on it would radiate, but there would be a lot of loss with the "ground" being so close and parallel to the radiator.

I think the answer to the question, "How is it possible for a halfwave dipole antenna to be resonant?", could be answered more simply; it's because any radiator that is any multiple of 1/4 wavelength (minus the velocity factor of the antenna material), has the reflected voltage wave, in-phase with the incoming current and voltage signal at the feed-point.

A halfwave dipole is simply two 1/4 wave radiators with a differential voltage applied, per the first drawing. Furthermore, the parallel feedline, feeding the dipole, will not radiate since the fields on each wire are equal and opposite; the lower picture, showing a differential voltage being applied, is still just a parallel feed-line, which should not radiate.

However, if voltage were on only one of those parallel lines, and the other was a "ground", like a coax shield, the element with voltage on it would radiate, but there would be a lot of loss with the "ground" being so close and parallel to the radiator.

I think the answer to the question, "How is it possible for a halfwave dipole antenna to be resonant?", could be answered more simply; it's because any radiator that is any multiple of 1/4 wavelength (minus the velocity factor of the antenna material), has the reflected voltage wave, in-phase with the incoming current and voltage signal at the feed-point.

A halfwave dipole is simply two 1/4 wave radiators with a differential voltage applied, per the first drawing. Furthermore, the parallel feedline, feeding that dipole, will not radiate since the fields on each wire are equal and opposite; the lower picture, showing a differential voltage being applied, is still just a parallel feed-line, which should not radiate.

However, if voltage were on only one of those parallel lines, and the other was a "ground", like a partially removed coax shield, the element with voltage on it would radiate, but there would be a lot of loss with the "ground" being so close and parallel to the radiator.