What is the phase of the impedance at each point on a resonant center fed half wave dipole?

Everyone knows that for an ideal center fed half wave dipole operated at resonance, the impedance at the center is 73 + j0 ohms.

The impedance at any point on the antenna is determined by the ratio of the amplitude of standing wave of voltage to the amplitude of the standing wave of current at each point.

The graph below is very common and shows how the impedance Z at any point on the antenna is E / I at each point. Notice how Z is between 73 ohms and 2500 ohms with no mention of the value of reactance in the impedance, even though AC impedance has a real part and an imaginary part.

The graph is very simple and easy to understand even for beginners. Especially the part about how the impedance in the center is (E / I) = (0 / I) = 73 + j0 ohms.

What's the value of the reactance in the impedance at all the other points on the antenna ?

The answer that i'm not looking for is that the reactance is zero everywhere on the antenna because it's resonant, but if this is true someone please explain why before i die of brain damage :(

After all this time no one has provided a sensible answer to this question so after some investigation i've answered it myself.

The animation in my question is related to the graph shown below. This graph which appears in numerous text books is confusing and misleading, as is the animation in my question.

The graph appears to show a snapshot in an instant of time of the voltage and current of the standing wave on a 1/2 wave dipole when the current is at a maximum, along with the resultant impedance Z.

The graphs confuses the reader in the following three ways.

1. Any normal person who looks at this graph would assume that the impedance Z at each point on the antenna is the voltage of the standing wave divided by the current of the standing wave at each point according to ohm's law. Then the astute reader asks : how can Z at the center be 73 Ω when the voltage at the center is 0 ? ... Z = E/I so Z = 0/I = 73 Ω ?

2. The impedance Z is shown as a single number so you get the impression that this impedance Z is a real number which doesn't have any reactance and so no relationship in phase with anything.

3. The graph shows that the dipole is all one piece and not split in the middle.

To clarify, voltage means the single ended AC RF voltage potential in volts present on the antenna element with respect to earth or zero volts, and current means AC RF current flowing through the antenna elements in amps. Voltage and current could be specified in peak, peak to peak, average or RMS, so long as the same units are used in the one context.

In truth the graph is showing the correct distribution of the voltage and current of the standing wave on a 1/2 wave dipole, however the impedance Z it depicts is actually the real part of the feed point impedance which would be present across two feed points terminals positioned along the various points along the length of the dipole elements.

The feed point impedance isn't the voltage of the standing wave divided by the current of the standing wave, but rather is a complex quantity equivalent to the differential voltage of the applied source across the two feed points divided by the resultant current of the standing wave at the feed points, the real part being equal to the radiation resistance of the antenna. For a series current fed center feed point the real part of the impedance is as everyone knows about 73 ohms and for a resonant dipole the current of the standing wave is in phase with the voltage of the applied source at the feed points.

The voltage of the standing wave divided by the current of the standing wave at any point along the antenna is actually called the Wave Impedance, and is a complex quantity which changes along the length of the antenna according to ohm's law. The wave impedance present at each point along the antenna isn't the same thing as the feed point impedance present across two feed point terminals.

The graph confuses feed point impedance with wave impedance and gives the reader the impression that the wave impedance is the feed point impedance by plotting standing wave voltage and current along the dipole with the real part of the feed point impedance. The impedance of free space you read about everywhere is actually the wave impedance of free space.

The animation in my question was taken from the Wikipedia article for a Half Wave Dipole. The text in the article does a very bad job at explaining what the animation is. The voltage and current in the animation are that of the standing wave on the antenna, which is circulating reactive stored energy present due to the fact that the antenna is a resonant system. The voltage and current of the standing wave are close to 90° out of phase with each other. The departure of phase difference away from 90 ° is the in-phase component of the standing wave which is responsible for radiation, the out of phase energy of the standing wave remains in the antenna. The animation erroneously shows that the voltage of the standing wave exists in the gap between the two feed points and so the voltage of the standing wave at the feed points is not always zero during each cycle of applied RF. This is not the case for a resonant antenna where the voltage of the standing wave which is about 90° out of phase with the applied RF at the feed points is always zero at the feed points.

I contacted the author of the animation in Wikipedia and managed to convince him to update the image, although the text in the article still doesn't explain the relationship between feed point impedance, and phase of the source and standing wave of a dipole antenna.

Everyone knows that for an ideal center fed half wave dipole operated at resonance, the impedance at the center is 73 + j0 ohms.

That's certainly not true.

From Wikipedia - dipole: -

Note that I've added on the vertical red lines and the horizontal blue and black lines that show the resistive and reactive parts of the impedance at exactly 0.5$$\\lambda\$$.

A true half-wave dipole is one half of the wavelength λ in length, where λ = c/f in free space. Such a dipole has a feedpoint impedance consisting of 73 Ω resistance and +43 Ω reactance, thus presenting a slightly inductive reactance.

At slightly below the half-wavelength length of the input signal, the impedance will be truly resistive but at the ideal 0.5$$\\lambda\$$ point it's got significant reactance.

The answer that i'm not looking for is that the reactance is zero everywhere on the antenna because it's resonant

The reactance IS NOT zero everywhere because at the feed-point it's not-zero AND, the feed-point is one point inside "everywhere".

• Hi Andy thanks for your reply. Your comment that "for an ideal center fed half wave dipole operated at resonance, the impedance at the center is 73 + j0 ohms" is ""certainly not true" is incorrect. You have shown a graph of resistance and reactance plotted against dipole wavelengths which is not relevant at all to the question. The question asks about complex impedance at different points along the length of a resonant half wave dipole, not impedance graphs for dipoles of various wavelengths. Commented Jun 25, 2020 at 8:04
• It is correct - the impedance is 73 ohms + j43 ohms. You said it was 73 ohms + j0 ohms and that is incorrect. Commented Jun 25, 2020 at 8:10
• Sorry Andy you don't understand the question so i'm not going to comment further. Commented Jun 25, 2020 at 9:46