# 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 :( 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. – Andrew Jun 25 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. – Andy aka Jun 25 at 8:10
• Sorry Andy you don't understand the question so i'm not going to comment further. – Andrew Jun 25 at 9:46