Every reputable antenna book that I've read says that dipole antennas are resonant at integer multiples of a half wave length.

Wikipedia describes resonance as:

the phenomenon of increased amplitude that occurs when the frequency of a periodically applied force is equal or close to a natural frequency of the system on which it acts. When an oscillating force is applied at a resonant frequency of a dynamic system, the system will oscillate at a higher amplitude than when the same force is applied at other, non-resonant frequencies.

For a dipole to me this means that resonance occurs when an AC source is applied with frequency that has a wavelength which allows an increase in the amplitude of the standing wave on the antenna to occur, because the applied source "tops up" the circulating energy at exactly the right moments, due to the resonant length.

Everyone knows that a center fed resonant 1/2 wave dipole has a feed point impedance of about 70 ohms with no reactance.

My understanding is that there is no reactance because the length of the elements results in the current of the standing wave at the center feed point being in phase with the applied source, and the voltage of the standing wave at the feed point (which is always about 90 deg out of phase with the current of the standing wave everywhere on the antenna), is at the zero cross over point and so contributes no reactance to the feed point impedance.

So the impedance is low with no reactance.

My understanding is that only for a resonant dipole does there exist any points where if split at those points and used as the feed point there will be no reactance.

For dipoles which are odd multiples of a 1/2 wave of the frequency of the applied source in length, the points where there is no reactance are at the current maximums or current loops, because it is at those points that the current is in phase with the applied votage source and the out of phase voltage is at the zero crossing point.

For a full wave dipole with feed point at the center, the voltage of the standing wave at the feed point is in phase with the applied source and at a maximum value, whereas the current is 180 deg out of phase with the source but at the zero crossing point.

This means the feed point impedance is high with no reactance.

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So to me it seems that a full wave dipole is a resonant antenna, and if the feed point is in the center it has a high non-reactive impedance.

There is of course an under-current in between the lines of this question, and that is the idea that reactance in the feed point impedance does not always mean not resonant, or in other words, an antenna of resonant length can have reactance in the feed point impedance, it just depends on where along the antenna length the feed point is. In fact it seems that resonance together with no reactance in the feed point impedance is the exception rather than the rule.

What am I missing ?

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    $\begingroup$ Probably just a lot of people calling it the wrong thing because it no worky when set up wrong. Set up correctly, a (almost) center-fed full wave antenna is actually quite popular, and used by tons of people, often for portable ops. Feed a full wave not exactly at the center, but slightly off-center with a 49:1 transformer, and then call it an end-fed with a tuned length counterpoise. Up in the air, a full wave has more lobes (and nulls!) than a half-wave, but laying half of the full wave on or near the ground likely lessens that pattern distortion. $\endgroup$
    – hotpaw2
    Aug 29 '21 at 4:27
  • $\begingroup$ @hotpaw2 Thanks for the comment, so this antenna has no reactance in the feed point impedance ? $\endgroup$
    – Andrew
    Aug 29 '21 at 4:59
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    $\begingroup$ You missed a word. Resonance is not at multiples of a half wavelength. The word you missed is odd. It occurs at odd multiples of a half wavelength. A full wavelength is an even multiple. $\endgroup$
    – user10489
    Aug 29 '21 at 14:41

Let's consider a simpler case by bringing the tips of a half-wave resonant dipole together so the two wires of the dipole are parallel, making a quarter-wave section of of balanced transmission line. Let's also assume the line is lossless. We might also need to adjust the length a little bit to ensure it's still electrically a quarter-wave, because the velocity factor of a dipole and a balanced transmission line are not be the same.

Now if you apply a wave to this transmission line stub, there must be a reflected wave. 100% of the power must be reflected because the line is lossless and there's nowhere for it to go. What's the phase of the reflected wave, relative to the forward wave?

  • There's a 90 degree delay traveling from one end to the other end.
  • The open circuit at the end has a reflection coefficient of -1, so that's a 180 degree shift.
  • There's another 90 degree delay traveling from the open end back to the "feedpoint".

90 + 180 + 90 = 360, so the reflected wave is in phase with the forward wave. Let's say the characteristic impedance of this transmission line is 200 ohms and it's being driven by a 1V (RMS) voltage source. The current at first will be 5 mA. After half a cycle the first reflected wave has arrived which is in phase, so the 5 mA of current from the reflected wave adds to the forward wave and now the current is 10 mA. Another half wave later another reflection has come back, and now the current is 15 mA. Every half wave the current increases another 5 mA, approaching infinity.

So 1 volt can move infinite current: that's zero impedance.

Now if you make the transmission line an additional quarter wavelength long it would make a full-wave dipole if you pulled the tips apart. An additional 180 degrees (90 there, and 90 back) of delay has been added, so now the reflected wave is out of phase with the forward wave. That initial 5 mA of current is cancelled, rather than reinforced by the reflection.

So the 1 V source drives zero current. That's infinite impedance.

Now the only difference between a dipole and a transmission line like this is the dipole has been zippered apart. This makes it radiate, which is like a "loss". So the impedance isn't zero or infinite, it's just low or high because the reflected waves don't quite reinforce or cancel the forward wave completely. In any case the reactance is zero.

Now, which of these are "resonant"? Let's review the generic definition:

When an oscillating force is applied at a resonant frequency of a dynamic system, the system will oscillate at a higher amplitude than when the same force is applied at other, non-resonant frequencies.

OK, "higher amplitude" of what, voltage or current? Or maybe we care about maximum radiated power? If you feed a zero impedance with a voltage source you get infinite power, but if you feed an infinite impedance with a current source you also get infinite power. So it seems dipoles have two kinds of resonance.

You might also notice the source impedance of an ideal voltage source is zero, whereas for an ideal current source is infinite. So if we can feed our antenna with an ideal voltage or current source, we get infinite power when the load is matched to the source. You might be seeing some parallels to the maximum power transfer theorem.

So maybe if you want to be pragmatic, you say of the two kinds of resonance, the more practical one is "resonant", and the other kind of resonance is something else, like "antiresonance". Of the two choices, the low impedance resonances seem more practical since they are a good match for typical feedlines and available transmitters.

Or if you want to be theoretical, you say dipoles shouldn't be concerned with what kinds of feedlines and transmitters people use in practice, and you consider both kinds of resonance as "resonant". Figuring out which kind of resonance to use is a job for engineers.

Realistically, you'll encounter both definitions, and often you have to figure out what's intended from context.

  • $\begingroup$ Hi Phil thanks for that answer, i gave it an up-vote, the point i was asking in the question is that a full wave dipole can be resonant with no reactance in the feed point impedance ?, and as you say, what use is this if the antenna has theoretically an infinite feed point impedance and so the oscillating force can't be applied to the resonant system, so such an antenna is referred to as anti-resonant ... and yes i agree the context needs to be considered. I'm just trying to be pedantically technically accurate, otherwise it's too easy to get confused. $\endgroup$
    – Andrew
    Aug 29 '21 at 22:41
  • $\begingroup$ Isn't it it true to say that a current fed 1/2 wave dipole is series resonant and a voltage fed full wave dipole is parallel resonant ? and 1/4 wave in from the end of an open circuit transmission line there is a short circuit, and 1/2 wave in from the end it's an open circuit, the same with a dipole antenna ? $\endgroup$
    – Andrew
    Aug 29 '21 at 22:55
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    $\begingroup$ @Andrew a half-wave lossless open transmission line stub presents an infinite impedance. The corresponding full-wave dipole does not present an infinite impedance, even theoretically, because it has "loss" due to radiation. The impedance is merely high, in the neighborhood of 4000+0j to 6000+0j ohms, depending on how thick the wire is. $\endgroup$ Aug 29 '21 at 23:58
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    $\begingroup$ @Andrew You could say a half-wave dipole is like a series resonant RLC circuit in that it has a low impedance, and a full wave dipole is like a parallel resonant RLC circuit in that it has a high impedance. But a dipole doesn't have any series or parallel circuit in it, so I would not say it is series or parallel resonant. But yes, by some definitions you can say all integer multiples of a half-wavelength are resonant. By other definitions only the odd multiples are resonant. Like most words in natural language, meaning is subject to interpretation. $\endgroup$ Aug 30 '21 at 0:07
  • $\begingroup$ I agree with you, and I think the distinction is worth noting. That brings up another point for another day, that being the fact that dipole resonance isn't the same as that seen in a lumped constant RLC circuit where wave theory doesn't apply (as much), and a dipole isn't an RLC circuit, as you just alluded to, it just behaves in a similar way in some respects near resonance. $\endgroup$
    – Andrew
    Aug 30 '21 at 2:16

All HAMS? I think not. To be resonant, a dipole must be electrically half a wave length of the frequency being transmitted. So, it follows that resonance relates to frequency. Not necessarily length.

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    $\begingroup$ Thanks for the comment, if you do some research you will find that resonance depends mostly on the electrical length of the antenna which is directly related to the frequency of the source at the feed point for transmit or for the frequency of the received signal for receive, and that dipoles for example which are multiples of 1/2 wave length are resonant, not just one 1/2 wave length. $\endgroup$
    – Andrew
    Aug 29 '21 at 4:56
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    $\begingroup$ Hello and welcome to ham.stackexchange.com! $\endgroup$
    – rclocher3
    Aug 29 '21 at 20:11
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    $\begingroup$ I don't think it's in the best interests of this site to give new comers a minus point for their first answer. $\endgroup$
    – Andrew
    Aug 30 '21 at 2:36

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