# For a resonant 1/2 wave dipole, does the reflections being in phase with the applied signal cause the zero reactance seen in the feedpoint impedance?

For a resonant 1/2 wave dipole when used for transmitting, does the fact that the reflected waves on the antenna are in phase with the applied signal result in zero reactance at the feed point, or does zero reactance happen for some other reason ?

This question isn't answered in explanations found on Wikipedia, in the ARRL handbook and a in few other antenna books i've read.

• To explain a bit further, for a non-resonant antenna, the wrong length and subsequent applied and reflected waves being out of phase doesn't cause a phase change between voltage and current because this phase change is the same for both the V and the I, the reactance causes this phase difference. So what makes the antenna have reactance ? The answer is not because V and I are out of phase because it's the other way around, the reactance causes the V and I to be out of phase. – Andrew Dec 19 '19 at 21:33
• The entire comment i made above is false, because i missed the fact that the applied AC electric potential results in an AC current which is reflected from the ends of the antenna and arrives back at the feed point in phase with the applied signal, resulting in zero reactance, and that for an ideal dipole in free space the length of the antenna elements is the single factor which determines whether or not V and I are in phase at the feed point. – Andrew Jun 23 at 12:21

Basically yes. One of the ways to view reactance is in terms of the phase relationship between voltage and current at a given point. When there is an inductive reactance, voltage leads current. When there is a capacitive reactance, voltage lags current. When there is zero reactance, voltage and current are in phase.

The resonance condition means that a reflected wave comes back to the feedpoint with the same phase relationship as it had when it left, and therefore it doesn't contribute any reactance.

• When there is reactance present at the frequency being used, V and I aren't in phase, because there is reactance, and, at the same time the reflected waves are not in phase with the applied signal because the length is wrong, so there two things going on, 1. phase relationship between applied and reflected and 2. phase relationship between V and I. If the length is wrong this on it's own doesn't change V / I phase difference. So how does the reactance relate to the reflected waves being out of phase with the applied signal ? – Andrew Dec 19 '19 at 1:16
• It's like the reactance causes the V / I phase difference and the wrong length causes the applied / reflected difference, and these are two separate things which occur at the same time for different reasons and the reasons are what i don't understand. :( – Andrew Dec 19 '19 at 1:20
• The above comment "If the length is wrong this on it's own doesn't change V / I phase difference. " is incorrect. It is the length of the dipole elements which determines if the antenna is resonant and what the phase difference is between V and I. – Andrew Jun 20 at 11:24

"Does the fact that the reflected waves on the antenna are in phase with the applied signal result in zero reactance at the feed point, or does zero reactance happen for some other reason?"

The short answer to your question is, "Yes." It is helpful to think of the dipole antenna as an open-circuited two-wire transmission line whose conductors have been separated.

Owing to reflections from the open end of a transmission line, its input impedance vs. frequency is zero when the line's electrical length is an odd multiple of $$\frac{\lambda}{4}$$ at the operating frequency. For a lossless line that is $$\frac{\lambda}{4}$$ at 10MHz:

If the two $$\frac{\lambda}{4}$$ wires that comprise the transmission line are "unzipped" to form a $$\frac{\lambda}{2}$$ dipole, its input impedance repeats in a similar way:

• Thanks Brian, the units on the axes of the first graph are a bit confusing but once i worked out that it's a graph of reactance versus distance from the open circuited end of a transmission line when excited by a 10 Mhz waveform, i can see the correlation between the last 90 deg of length of the line and the 1/4 wave length of one dipole element. – Andrew Jun 20 at 2:20