# What exactly makes an antenna resonant?

When an antenna is resonant, the impedance seen at the feed point is purely resistive and has no reactance.

What are the physical properties of an antenna that actually make it resonant and how do these properties relate to the frequency at which resonance occurs ?

A resonant antenna produces feedback that is in phase with the applied signal.

For a more intuitive example, consider a mechanically resonant structure, like a tuning fork. If the fork is struck, a mechanical wave travels through the fork's structure. Some of the energy in this wave is lost as sound to the air, but most of that kinetic energy eventually propagates back to the point where the fork was initially struck.

The time it takes for this to happen determines the resonant frequency of the tuning fork and the note you'll hear when its struck.

If you were to repeatedly strike the tuning fork at this frequency, you'd find it would be "softer" than it would be at other frequency because right at the instant you're striking it, the fork is vibrating away from the striker. That is, the feedback is in phase with the applied signal.

Resonant antennas are analogous for electromagnetic waves. Consider a resonant dipole: each leg is tuned to be electrically a quarter wavelength long. The time it takes for the wavefront to travel from the feedpoint to the end is a delay of 90 degrees, and back from the end to the feedback another 90 degrees for 180 degrees in total. The time it takes this to happen is the time it takes the phase of the driving signal to move 180 degrees.

Because the feedback from reflections within the antenna is in phase with the applied signal at the feedpoint, the antenna is resonant.

• i know i'm not supposed to say thanks in comments but thank you because i was pretty sure it was as simple as that, but i wanted to check. And following on from that that a dipole which is exactly 1/2 wave length has some inductive reactance because the electrical length is less than the free space wavelength. – Andrew Dec 13 '19 at 2:54

The antenna has inductance and capacitance, which is the same thing a tank circuit has. A current traveling along the antenna creates a magnetic field; the field and the current interact with each other, thus it will be subject to inductance. The charges that accumulate on the conductors creates an electrostatic field that causes them to interact with each other (or with conductive objects nearby). The conductors thus behave like the plates of a capacitor. The combination is resonant at the frequency where the inductive and capacitive reactances are equal.

• @Andrew could you try to phrase that as helpful feedback? For example, the current in the antenna definitely does induce a magnetic field, and the temporal change in the energy stored in that magnetic field and the current is what effects inductance. What's wrong about that? – Marcus Müller Dec 11 '19 at 9:19
• @gbarry Hi Gbarry thanks for your answer. When an antenna is resonant it doesn't have any reactance present in the impedance presented at the feed point because wave forms at the resonant frequency and present on the antenna are in phase. It is not the case that there is inductive and capacitve reactance present that are equal and cancel out at resonance. And the fact that there is no reactance is not the reason the antenna is resonant, but rather the other way around where a resonant antenna does not have any reactance. – Andrew Dec 15 '19 at 22:13
• As per another answer to this post, an antenna is resonant when it's length is an odd multiple of 1/2 wave length of an applied signal and such that he feedback from reflections within the antenna is in phase with the applied signal at the feed point. – Andrew Dec 15 '19 at 22:19
• I hope we can get more opinions about this. For a thought experiment, let's consider @Phil Frost's tuning fork. Can we say its resonance is only determined by the motion of the arms in relation to the applied stimulus? Can we say the tuning fork has no mass and no compliance (or however "springiness" is measured)? I believe it does, and ultimately we can transform this back to the antenna. Also, why does adding parallel capacitance or series inductance lower the antenna's resonant frequency if it had none to begin with? – gbarry Dec 16 '19 at 8:23
• @gbarry These are all very good questions, most of which i don't know the answers to. I think that a fork is different to an antenna because the applied stimulus is the equivalent of a very wide band pulse and it remains after a short amount of time 'ringing' at the frequency which matches it's natural mechanical resonant frequency where as with an antenna we are applying one fixed frequency to a thing which doesn't vibrate mechanically so the analogy doens't match up exactly. – Andrew Dec 18 '19 at 2:34