# For a half wave dipole antenna, what's the value of the reactances that cancel out when the antenna is resonant?

According to a few descriptions of antenna fundamentals i've read recently including that in Wikipedia and the ARRL handbook, when a half wave dipole is resonant, the inductive and capacitive reactances cancel out, and that's why there is no reactance in the impedance.

My understanding is that the amount of reactance seen at the feed point of a center fed half wave dipole is determined by the phase relationship in time between the applied AC electric potential at the feed point and the resultant AC current which arrives at the feed point after being reflected back from the ends of the antenna.

So keeping in mind that a half wave dipole appears to be a series RLC circuit, what are the values of reactance that cancel out at resonance ?

And why is an antenna resonant, because the voltage and current are in phase or because the reactances cancel out, or both ?

• It's important to note that a "disturbance" (wave) travels along the antenna, not charges (electrons). Just like an ideal wave in water, where individual water molecules are only displaced vertically, though the wave travels horizontally. The drift velocity of an electron in copper is orders of magnitude slower than the near-light-speed at which a wave (disturbance) travels along an antenna conductor. – Brian K1LI Jun 10 at 10:40
• Seems like what you're asking boils down to whether an antenna resonates in the same sense that an RLC circuit does — is that a correct understanding of your question? – natevw - AF7TB Jul 3 at 17:44
• @natevw-AF7TB Hi Nate yes that's correct. – Andrew Jul 7 at 0:32

An antenna is not a series RLC circuit, but it can be modeled with lumped circuit elements over a certain frequency range. See, for example, Tang et al, "Equivalent Circuit of a Dipole Antenna Using Frequency-Independent Lumped Elements."

A thought experiment shows why: we observe that the feedpoint impedance of a half-wave dipole exhibits periodic behavior at harmonics of its design frequency, but a simple lumped circuit does not. For example, using the formulas of Tang et al, we can model the "input impedance" of the equivalent circuit of a 20-m half-wave dipole:

It "resonates" at about 14.3-MHz. The same antenna modeled by NEC-2 shows the very different behavior to which we are accustomed:

The input impedance behavior of the half-wave dipole is more reminiscent of a transmission line, which can also be modeled with lumped elements. But, since the object of the lumped-element model is computational simplicity, the number of elements required to produce an accurate transmission line model would probably defeat the purpose.

The value of reactance varies both in magnitude and sign as functions of the operating frequency, the radiating length of the antenna, and the physical location of the feedpoint terminals along that length.

At resonance, jX = 0.

In my mind the difference is that:

• An RLC circuit "resonates" by bouncing energy back and forth within itself. And at a particular frequency this stored energy is retained for a particularly long time. (The Q of such a circuit represents the tradeoff between ringing for an extra long time at only one particular frequency, versus the energy bouncing around with still somewhat acceptable efficiency across a wider range of frequencies.)
• The "resonance" of an antenna usually has more to do with its radiation resistance at a particular frequency. Here's where I don't want to steer you wrong since maybe this is more conceptually related than I imagine, but the resistive energy loss in an RLC circuit is something of an inevitable "defect" whereas it's the entire point in a good antenna. You just want the energy to be lost as EMF radiation rather than thermally.

That said, a small loop antenna is decidedly both: it's an RLC circuit designed so that ideally all the R would be due to radiation rather than loss. This is again related to Q — and with resonance being at an exact "point" frequency means that any modulation sidebands need to be taken up by a lossy resistance somewhere but in practice with most antennas, and even many small loop antennas, the Q curve tends to be on the scale of e.g. the entire 80m "band" rather than anywhere near a concern for the bandwidth of a single CW/SSB transmission.

No one has actually answered this question, so i did some research and have answered it myself as follows.

The idea that for a half wave dipole there are inductive and capacitive reactances which cancel out at resonance is false.

Confusion seems to exist because a resonant half wave dipole has similarities to a series RLC circuit.

Even though a resonant half wave dipole is similar to a series RLC circuit in some respects, the frequency of resonance for a series RLC circuit is determined by the combination of the lumped constant values of inductance and capacitance which exist inside the components, whereas for a half wave dipole antenna the resonant frequency is determined by the electrical length of the antenna elements.

For a resonant half wave dipole, the electrical length of the antenna elements is exactly one quarter of the wavelength of the applied AC electric potential. This means that AC current reflected from the ends of the antenna arrives back at the feed point in phase in time with the applied wave form. Because the voltage and current at the feed point are then in phase, there is zero reactance and the impedance at the feed point is purely resistive.

In contrast, for a series RLC circuit, reactance exists inside the components regardless of the wave length of the applied AC electric potential, including at resonance, but at resonance the combined reactances of the inductor and capacitor in the RLC circuit are equal in magnitude but opposite in sign and so cancel to produce a net zero reactance.

So for a half wave dipole at resonance, there are no reactances to cancel out, and the resonance is caused by the fact that the electrical length of the antenna elements is 90 deg or one quarter the wave length of the applied AC electric potential, which in turn results in the voltage and current at the feed point being in phase, and then the feed point impedance is purely resistive.

See this question What is the impedance of an off-center fed resonant dipole? which also helps explain further.

I hope this clears up the confusion which exists for some regarding antenna resonance.

• Thanks for writing this up, it at least helps clarify what you are asking above. Your answer seems correct to me but I'm still learning this stuff too. – natevw - AF7TB Jul 3 at 17:41
• @natevw-AF7TB Thanks Nate. Whoever down voted my answer, how about explaining the reason for the down vote so we can all learn something ? – Andrew Jul 7 at 0:29