Why do ham radio operators say that a full wave dipole isn't resonant?

Question

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.

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 ?

Answer 1

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.

Answer 2

I hope it's not bad form to reply at this late date, but there are a few issues I did not see directly addressed. First, any radiator of a capacitive type antenna (not just a dipole) is resonant at any integer multiple of a 1/4λ in length, not just integer multiples of a 1/2λ; and in the case of a 1/2λ dipole, it might be useful to think of it as 2 colinear, end-fed 1/4λ antennas with differential voltages at their feed-points; it's the fact that each element is 1/4λ in length that makes the element's feed-point impedance as low as 73 ohms. If each element were an even multiple of 1/4λ, i.e. 1/2λ, 1λ, 1-1/2λ, 2λ, etc. the antenna would still be reasonant, but the feed-point impedance would be very high (as in 2500-3000 Ohms) because a voltage applied at those even multiples is attempting to enter the radiator at a voltage node, and therefore has to overcome the reflected voltage of the previous cycle(s), which are in phase at 360 degrees; this is in contradistinction to any odd multiple of a 1/4λ element, i.e. 3/4λ, 1-1/4λ, etc., where the applied signal encounters one of the previous cycle's reflections at 180 degrees out of phase, which is a low impedance, current node. Think of it this way: when an AC signal has traveled out 1/4λ and then gets reflected back 1/4λ, it's traveled 1/2λ and meets the incoming signal 180 degrees out of phase, and when an AC signal has traveled 1/2λ out and gets reflected back for another 1/2λ, it has meets the signal entering the radiator at 360 degrees in the signal's cycle. And, because of resistive and radiation losses over the length of the radiator,in either even or odd multiples of a 1/4λ element, the higher the multiple, the more toward a mean impedance the antenna will have; in otherwords, the impedance of odd multiples of a 1/4λ will increase with lengthing, and the impedance of even multiples of a 1/4λ will decrease with lengthing, as the reflected voltages decrease, whether in-phase in the case of even multiple, or out-of-phase in odd multiples.

As far as a Full Wave Dipole, again, think of it as 2 colinear, end-fed 1/2λ antennas with differential voltages at their feed-points; and as such, as long as the feed-point voltages are differential, you can expect nearly double the gain of a 1/2λ dipole. As a side note, for those who don't feed their dipole with a differential voltage source, (as in someone using unbalanced line like coax cable with no BalUn) their antenna isn't a dipole, it's simply a 1/4λ antenna with a counterpoise. As a final note, a center-fed Full Wave Dipole would be the preferred way to co-phase 2-1/2λ antennas as bandwidth would be a little greater, and the radiation pattern would certainly be more omni-directional than two 1/2λ elements, end-fed at one end and phased with a delay segment into the next 1/2λ element, since the delay segment would also radiate/receive and create some distortion the antenna's pattern. A coil could be used as a delay element, but while that might contain some unwanted radiation and may be better for the pattern, it would narrow bandwidth a bit more than a normal folded phasing element. The only issues with a center-fed Full Wave Dipole would be making a 64:1 BalUn, and keeping the coax at 90 degrees to the antenna for at least 1/2 a wave length's distance. Everything's a trade-off!

Answer 3

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.