How can a half wave dipole which has an impedance of 73 + j43 ohms ever be resonant?

Is it true that for a half wave dipole, cancelling out reactance using for example a gamma match does not make the antenna resonant at all, but rather just cancels out the reactance of what is actually a non-resonant antenna which has an impedance when fed from the center of 73 + j43 ohms ?

A physically half-wave dipole isn't resonant. As you say, it has an impedance around 73+j43 ohms. Since the reactance is non-zero, it is by definition not resonant.

Any manner of matching devices could be added to the antenna, and considered as a whole, they would make a resonant system. But that's not what people usually mean when they say "resonant antenna".

Instead, the antenna can be made just a little shorter. At slightly less than a half-wavelength the reactance drops to zero and the antenna becomes resonant, no matching device required.

In practice this is almost always done, so unless writing in a context where very strict language is required, a "half-wave dipole" really means "a dipole of approximately a half-wave, adjusted to achieve resonance." This means the dipole is electrically a half-wave long.

This is a convention that goes beyond dipoles. For example, a quarter-wave transformer is understood to be a length of transmission line not physically the length of a quarter-wavelength in free space, but whatever length is a quarter-wavelength at the propagation velocity within the transmission line.

• thanks now i understand that part, any chance of answering the other questions in this question ? – Andrew Dec 10 '19 at 5:44
• Maybe try asking fewer, more coherent questions now that the misconception has been cleared up? – Phil Frost - W8II Dec 10 '19 at 5:46
• RE: Instead, the antenna can be made just a little shorter. At slightly less than a half-wavelength the reactance drops to zero and the antenna becomes resonant, no matching device required. — However that shorter radiating length also has less radiation resistance. According to John Kraus in ANTENNAS... (3rd Ed), it drops to about 65 Ω, which, without a matching device would produce an SWR of about 1.15:1 to a 75 Ω transmission line connected across its feedpoint terminals., – Richard Fry Dec 10 '19 at 12:13
• @RichardFry Are you saying an SWR of 1.15 requires a matching device? In any amateur application, I think not... – Phil Frost - W8II Dec 10 '19 at 21:10

A half wave dipole which is physically half a wave length long is not resonant.

This is confusing because the term "half wave dipole" seems to inherently describe an antenna with a length which is the same as one half the wavelength of the applied RF energy, and so technically should always be exactly resonant because the two dipole element lengths are each exactly 1/4 of the wavelength of the applied RF.

The confusion arises because the actual length of a half wave length can be unclear.

For an EMF wave, the wavelength has one value when the wave travels in free space, and another lesser value (usually about 5 % less) when the wave travels along a piece of metal. This is because EMF energy travels slower in a medium which is more dense than air.

So often a half wave dipole is described with a length that is the value of the half wave length in free space. If the dipole was made of air then doing this would be correct. But a half wave dipole made of metal with a length of the half a wave length of the EMF in free space is not the length that makes the dipole resonant.

And so the impedance for this lie is about 73 + j73 ohms, and this antenna which is technically not a half wave dipole is not exactly resonant.

So there is the term "electrical half wave length" which is the actual length of the half wave length of the EMF wave when it travels inside the material that the antenna is made from, noting that the length / diameter ratio of the elements and the immediate surrounding also have an effect on this length.

The length of a half wave dipole which by definition is resonant is the electrical half wave length of the EMF wave in the actual antenna elements, and then the impedance has no reactance.

Also, adding reactance to a non-resonant antenna to cancel out antenna reactance of the opposite sign doesn't make the antenna resonant. It just cancels out the reactance, resulting in a non-resonant antenna with added reactance to give a combined system which makes the antenna appear resonant.

• And yet you copied its text wholesale into another answer, and reposted it in a new answer that didn't have the downvotes. So I have deleted the new one and reinstated this one – Scott Earle Jul 9 at 2:25
• @ScottEarle Hi Scott thanks for the reply. I saw all the down votes and then i just assumed that i said something horrible inaccurate, so i deleted the answer and made a new one with the same text, and i was going to update it with a correct answer, but then after more research it seems my answer is exactly correct, and referring to the length of a half wave dipole using the free space length and then saying that a half wave dipole is not resonant, which just confuses the hell out of everyone, is technically incorrect, so i just left the same text there. – Andrew 2 days ago
• Not sure why it got down voted, maybe i need to explain the answer in a simpler way that's easier to understand. – Andrew 2 days ago
• Andrew, do you understand why @ScottEarle said what he did? I respectfully ask that you familiarize yourself with the SE rules in Help. Heck, I have to occasionally re-read portions of them myself! :-) – Mike Waters yesterday