# How can the impedance of a half wave dipole at its resonant frequency be purely resistive when the voltage and current are seemingly not in phase?

A half wave center-fed dipole has a resonant frequency where the input impedance appears to be purely resistive. How can this be, when the voltage and current distribution along the length of a half wave dipole when fed with an AC waveform of the resonant frequency are seemingly not in phase and in fact appear to be 90 degrees out of phase?

• I think the animation is not completely correct. 1. The voltage is not zero in the middle, but it is perhaps 10x smaller than the tips, so doesn't show. The current at the feedpoint is in phase, at resonance, by definition. This doesn't mean that the voltage at the tips is in phase with the current at the centre. Oct 27, 2018 at 0:30

Andrew, the typical graphics showing standing waves are showing voltage and current distribution along the wire, not phase shift from each other. Voltage and current are always in-phase at every point, they are syncronized in time, so there are no reactive components in the impedance. The instant of time when voltage is at its max peak also current is at the same value. The same is true at the zero crossing instant or at any other time. This happens at the center of the antenna, at its extremes, and at all the points in between. This fact is useful in the off-center feed dipole (aka OCF dipole), which is feed at a point where it has about 200 ohms with a 4:1 balun. This points have about the same impedance at several bands, making it a multi-band antenna.

• Hello, and welcome to ham.stackexchange.com! Thanks for a nice first answer. We look forward to seeing more of you here. :-) Please consider reading the tour and help pages to get the most from the site. Oct 16, 2019 at 18:20

Andrew, a dipole is a standing wave antenna. That means that the energy existing on the dipole that hasn't been radiated is in standing waves which do not change phase. The equation for a standing current wave is $$I(x,t) = I_{\max} \sin(kx) \cos(\omega t)$$. The distance $$x$$ determines the magnitude of the standing wave, not the phase. Only time determines the phase. At any instant in time, the phase of the standing wave is the same all up and down the length of the antenna. At resonance, the standing wave voltage and standing wave current are everywhere in phase. The forward current and reflected current are coherent phasors of close to equal magnitudes rotating in opposite directions. It's obvious that their sum would have constant phase. Same is true for the forward and reflected voltage phasors.

Phase has two different meanings for this context. The amplitudes of the voltage standing wave and current standing wave are out of phase in time but the phase of the voltage standing wave and current standing wave are in phase, i.e. equal in time.

The phase and current of the r-f energy along each half of a dipole are the result of natural laws, which show that current must be at/near zero at the far ends of the dipole while voltage there must be maximum.

The practical concern to the user of that dipole is its self-impedance at its feedpoint terminals.

A thin-wire, center-fed dipole that physically is 1/2-wavelength long has a feedpoint self-impedance of 73 +j43.5 Ω in free space (source: Kraus' Antennas, 3rd Edition, p. 446).

To achieve resonance (where the voltage and current at its feedpoint are in phase and the "j" term of its impedance is zero), that dipole must be shortened a few percent, which somewhat reduces that 73 Ω radiation resistance — as a function of the O.D. of the radiating conductors of that dipole.

• Hi Richard thanks for the reply. But the part I don't understand is that if the dipole is shortened, and the reactive component is then zero, the current is still maximum in the center and zero at the ends, and the voltage is zero in the center and maximum at the ends, and the two are not in phase. I think i'm getting phase in the time domain and voltage and current distribution along the length of the wire mixed up ... Oct 26, 2018 at 21:56
• I think the answer is this : The AC voltage and current in the time domain are actually in phase at resonance at the feed point, so if you drew a graph of time versus voltage and current amplitude when measured at the feed point you would see that they are in phase. However the voltage and current distribution along the wire are actually standing waves which are set up because the length of the antenna is such that the applied AC voltage reinforces that which is reflected from each end, and these have nothing to with the phase of the voltage and current.over time, Is that correct ? Oct 26, 2018 at 22:42
• One certainty is that as far as its characteristics as a dissipator of r-f power, a resonant antenna can be replaced by a pure, physical resistor of the same ohmic value, wherein current and voltage always are in phase (unity power factor). The mechanism whereby the e-m fields radiated by the antenna into space produce that radiation resistance is complex. I'll do some research on that, but maybe other readers here have a good, short explanation to post as to how/why that occurs. Oct 27, 2018 at 16:01

nice to get back to communicate with you.

In my file "Displacement of Resonance Frequency", I wrote that theoretical statement, but it was already corrected to avoid confusing readers.

Reality is how you explain it, when the physical length of the antenna is in resonance with the frequency, the current wave distributions in the antenna are in phase and the RF voltage waves are also in phase.

This condition in the antenna, determines its best radiation resistance and maximum efficiency of it.

To this answer, I added the updated link of the file "Displacement of Resonance Frequency.pdf", which unfortunately has not yet updated its complement file "Coaxial Cable Length and Node.pdf".

This file was written with the purpose of clarifying a reality, typically considered as an old myth and the scarce information that links themes of resonance lengths in optimization processes of antenna systems.

I know that should not include links, because they probably will not work, but if required in the future, it is possible to locate it from the web.

Greetings.

Displacement of Resonance Frequency.pd: https://files.acrobat.com/a/preview/7021823f-839c-4122-bdb7-c41eede5891d

Thanks to everyone who provided answers to this question, but none are completely correct, so after all this time I have answered the question myself.

This image appears in the Wikipedia article for Half Wave Dipole.

The voltage and current shown in the image is the actual voltage and current of the standing wave which exists along the elements of a resonant half wave dipole antenna. The standing wave on the antenna is circulating reactive energy present due to the fact that the antenna is a resonant system.

The voltage and current of the standing wave are always about 90 degrees out of phase with each other. The voltage of the standing wave always lags the current by a bit less than 90 deg, and for a given antenna and frequency of operation this phase difference is constant at each point along the length of the dipole elements.

The departure of phase difference away from 90 deg between the voltage and current of the standing wave is the non-reactive energy of the standing wave which results in radiation. Reactive energy stays in the antenna as circulating resonant energy and non-reactive energy leaves the antenna as radiation. For a high Q antenna the source tops up the much larger in amplitude energy of the standing wave as energy is radiated away.

The phase difference between voltage and current of the standing wave does not determine the reactance present in the center feed point impedance. Rather, it is the phase difference between that of standing wave and of the source which determines what the reactance in the impedance will be.

The voltage and current of the source at the center feed point are in phase. At resonance, the current of the standing wave is exactly in phase with that the voltage of the source, and the voltage of the standing wave, which is out of phase by almost 90 deg, is at the zero crossing point and so is zero all the time at the feed points and so contributes no reactance to the feed point impedance.

At resonance the current of the standing wave is in phase with the source because the ends of the dipole elements are an electrical 1/4 wavelength away from the feed points.

This presents a low impedance with no reactance between the two center feed points.

Hope that helps to clear up some of the confusion !