# From its electromagnetic field, what makes a too short antenna capacitive, and a too long dipole antenna inductive?

I know that at a given frequency and therefore wavelength, a dipole antenna that is too (electrically) short looks capacitive, and one that is too long looks inductive. I can see it on the Smith Chart, and I can counteract it e.g. by "loading" a short antenna with an inductor. There are also some thought experiments out there, e.g. "0 length dipoles", that show why a short antenna must be capacitive to make sense.

But what I don't understand is what actually happens to the electromagnetic field to make the antenna look like an inductor or capacitor at the given wavelength.

I do (roughly, at least) know how current is distributed along a mismatched dipole: On a short dipole, the current is roughly triangularly distributed, because as you get closer to the extreme slope of the sine lobe the slope looks more and more linear. On a long dipole, you get larger and larger (and then more and more) opposite sign current lobes that cancel the electric field.

But how that makes the dipole effectively a capacitor or an inductor, I don't understand. I guess there must be some analogy on how the fields look and/or behave to how they do on either component. Is there some intuitive, maybe even visual explanation?

• Excuse me, but you cannot see it on Smith Chart. That chart presents the behaviour of a TEM waveform transmission line which radiates nothing. Antennas generate totally different waveforms to the space. It's a common trick to make calculations for antennas as lossy transmission lines where the radiation is taken as a loss, but using Smith Chart essentially assumes the behaviour that you said you found.
– user136077
Jul 15, 2022 at 21:25
• @user287001 I think that was my point. I can see the point on the Smith Chart move to be more inductive or more capacitive when adding or removing length (or am I wrong?), but it does not help understand nor explain. I was merely stating that I can't do that using the Smith Chart. Jul 15, 2022 at 21:38
• If you want to see "something", go to this site amanogawa.com linear antennas menu ... Jul 16, 2022 at 16:36
• If you think that a "short antenna" is an "open circuit", one can understand that it is a capacitor ... Jul 16, 2022 at 16:45
• n4djantennaramblings.blogspot.com/2010/02/… Oct 26, 2022 at 5:00

$$S = \frac{1}{2} \int \int{(\vec{E} \times \vec{H}^*) . d\vec{A}}$$ This is from the complex Poynting theory is: $$S = P_{rad} + 2j\omega(W_m-W_e)$$ In case of infinitesimal dipole, the imaginary part is negative, indicating more average electric energy than magnetic, exactly like a capacitive reactance.