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For a resonant half wave dipole, the voltage and current of the standing waves on the antenna are 90 degrees out of phase with each other. At resonance, is the phase of the current reflected back from the ends of the antenna when it arrives back at the feed point the same as the phase of the voltage of the applied RF at the feed point ? And if so is this why there is no reactance seen in the impedance at the feed point at resonance ?

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  • $\begingroup$ Doesn't anyone know the answer to this question ? $\endgroup$ – Andrew Jun 8 at 12:12
  • $\begingroup$ I'm actually doing some equations every evening after work, I will be in touch with you If I have something! $\endgroup$ – Arnaud Jun 9 at 17:00
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the voltage and current of the standing waves on the antenna are 90 degrees out of phase with each other

What do you mean by "voltage" here? Voltage is just something measured in volts. Many things are measured in volts. Do you mean electric potential difference? If so, between what two points? Or do you mean electric potential?

If you mean electric potential, this is statement is (very nearly) true. The phase difference between the electric and magnetic potential is related to the argument of the complex power of the antenna. As the Q of the antenna approaches infinity, the argument approaches 90 degrees. Practical transmitting antennas have a sufficiently high Q that the argument is very nearly 90 degrees.

If you mean electric potential difference, this statement is not true. Although the electric field strength (measured in volts per meter) may be out of phase with current, the two feed terminals are not very many meters apart, and so the electric potential difference between them due to the reactive power in the dipole is small.

At resonance, is the phase of the current reflected back from the ends of the antenna when it arrives back at the feed point the same as the phase of the voltage of the applied RF at the feed point ?

If here by voltage you mean electric potential difference, then yes. As for why this can be, again it's because the feedpoint terminals are not physically far apart, so the electric field strength can't make much of an electric potential difference between them.

And if so is this why there is no reactance seen in the impedance at the feed point at resonance ?

Because the electric potential difference and current are in phase, and this is no reactance by definition.

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  • $\begingroup$ Hi Phil thanks for the reply, i mean electric potential, and i'm talking about an ideal dipole with an infinite Q. The part about Q and how this affects the phase difference between the voltage and current of the standing wave is something i don't understand very well yet. $\endgroup$ – Andrew 6 hours ago
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No one knows the answer to this question so i had a go at figuring it out for myself.

If there are mistakes please tell me so that i can update the answer and at least there will one place on the internet that has the truth about this subject.

Standing Waves and Phase.

An understanding of phase and standing waves makes it much easier to comprehend antenna resonance and impedance.

Consider a transmission line with a source which is a pure sine wave at one end and a matched resistive load at the other. Let's assume that the voltage and current of the source are in phase. There will be a traveling wave of RF energy which is moving away from the source and down the line. There is no mismatch at the load, and so there are no standing waves anywhere along the line.

Since the source voltage and current are in phase, it makes sense that the voltage and current of the traveling wave are also in phase. Because a traveling wave is moving, the phase of it with respect to the source is a function of the position along the line as well as of time. For a single point, there is no distance involved and so phase is only a function of time and not distance.

At 1/4 the wavelength of the frequency of the applied source along the line away from the source, the phase of the RF at that point with respect to the source is -90° or it lags the source by 90°. If you move to a point another 1/4 wavelength along the line the phase is now different, and is -180° with respect to the source.

So the phase of the traveling wave with respect to the source at any point on the line is dependent on the distance from the source, because the traveling wave along the line is moving and as it does so it's phase changes with respect to some other point on the line. The phase change in degrees of one complete cycle of the traveling wave compared to the phase of the source matches exactly the distance it travels in wavelength expressed as degrees along the length of the line.

Phase Relationship Between Source and Standing Wave.

If the load is removed from the above mentioned transmission line, now there is an open circuit at the end, and a Standing Wave appears along the transmission line. The standing wave is caused by the vector addition of the original or forward wave sent from the source and the wave reflected back from the open circuited end.

This is all explained in the awesome antenna theory books i've read.

The original incident and the reflected traveling waves, while still present, are completely obscured by the addition of the each to the other. This is just like when you mix yellow and magenta together and you get red, yellow and magenta are still there but all you can see is red.

The phase of the original traveling wave sent from source can no longer be seen at all. The waveform seen everywhere along the transmission line now isn't moving along the line, but is stationary and has a fixed voltage profile along the length of the line. Luckily for us, the standing wave everywhere along the transmission line at once is oscillating in amplitude at the frequency of the applied source, and the phase at any point with respect to the phase of the source is now not a function of the position on the line, but is in fact the same everywhere.

At the end of the line where there is an open circuit the current must be zero and according to the laws of conservation of energy the voltage is forced to a maximum value. So the positions of the peaks and troughs and crossing points of the voltage and current of the standing wave are fixed with respect to the end of the line, and everywhere on the line there is a phase difference of precisely 90° between the voltage and the current of the standing wave. We said earlier that the voltage and current at the source are in phase, and now we just determined that the voltage and current of the standing wave are 90° apart.

If you think about it, it makes sense that the phase of the standing wave must be synchronized somehow to the phase of the voltage of the source, since the source is the thing that started the whole process off in the first place. It doesn't make sense for the standing wave to just have some arbitrary phase of its own.

Think about this.

When the source was first connected and the traveling wave was sent along the line toward the load for the first time, it took a specific amount of time for the wave to reach the load, and the time taken is directly related to how far it is from source to load.

It's the same as walking to the shops, the further away it is the longer it takes you to get there, and the longer it takes for you to start walking back home again.

When the wave reaches the load, then is when it starts to get reflected, and there is the relationship between the phase of the voltage of the source and the phase of the standing wave.

If the distance from the source to load is odd multiples of 1/4 wave length of the frequency of the source, then the standing wave current is in phase with the that of the voltage of the source, and the standing wave voltage is 90° out of phase with that of the voltage of the source.

Sound familiar ?

The thing is, who cares what the phase relationship is between that of a voltage source and that of some standing wave on a transmission line ? No one, including the authors of all of the antenna books i've ever read, and that's why I could never understand how a dipole works and i cried a lot !

Standing Wave Determines Impedance, Not Traveling Waves.

To recap at this point, if the end of a transmission line is open circuit, there is complete reflection of the incident wave sent from the source at the open circuit load, and the only waveform that exists on the line is a full standing wave. The original traveling wave sent from the source and its reflection are obscured, and so the phase of these traveling waves cannot be seen or measured.

In contrast, just like a great big mobile phone that's replaced the ideals and morals of every teenager in the world with internet propaganda, the difference in phase between the voltage and current of the standing wave everywhere on the line is right there in front our noses, and is fixed at 90°. Furthermore, the phase of the standing wave everywhere on the line with respect to the phase of the source is also constant and is determined by the distance between the source and load.

The standing wave is the actual condition on the antenna. The phase of the standing wave is fixed and its amplitude is oscillating at the frequency of the source. The original incident and reflected traveling waves while still present can no longer be seen and have been obscured by the addition of each to the other. Since the traveling waves can't be measured, they can't have an effect on the complex impedance at any point of the antenna. It's the standing wave which determines the complex voltage, current and impedance on the antenna. Saying that the traveling waves determine the impedance is the same as saying that the mid-life-crisis red Toyota coupe my friend bought recently is actually yellow and magenta.

Forgotten Characteristics of a Dipole.

To summarize, now we understand two new points, which just like Vegemite is refreshing, nutritious and character building.

  1. The standing wave is the actual condition on the antenna, and the complex voltage and complex current of the standing wave at each point on the antenna including at the feed points determine the complex impedance at those points according to ohm's law. The phase of the original incident and traveling waves have no bearing on the impedance anywhere on the antenna.

  2. In an open circuit transmission line, the phase of the resultant standing wave is directly related to the phase of the voltage source, and the exact phase difference between the two is determined by the distance from source to open circuit. In exactly the same way, in a dipole antenna, the phase of the standing wave present on the elements is related to the phase of the applied energy at the feed points, and is determined by the distance between the feed points and the ends of the antenna.

Now we are ready to begin to understand why there is no reactance present in the impedance of a resonant dipole !

Reactive Circulating Energy in a Dipole.

If we think about a dipole as a spread out extension of the end of an open circuit transmission line, one difference between the transmission line with no standing waves on it, and the dipole antenna, is that the length of the transmission line has no effect on impedance anywhere on the line, and the impedance is always the characteristic impedance which is a real number, whereas the dipole has open circuit ends, and as a result there is a standing wave present on the antenna, and so the real and imaginary parts of the complex impedance seen at each point on the antenna is different.

The voltage and current of the standing wave are 90° out of phase with each other everywhere on the antenna. The standing wave is reactive circulating energy in the antenna, and as such does no work.

An ideal dipole antenna has an infinite Q, since there is no loss. Real dipoles do in fact have a relatively hi Q because they are very efficient with a low ohmic resistance compared to the radiation resistance. For this discussion however, we are ignoring the fact most of the energy supplied by the source is radiated away into space, and how that has an effect on the conditions on the antenna.

That's another discussion for another time (ie: i haven't figured out that part yet).

What Happens When the Traveling Wave Goes Past the Feed Points.

For a matched system, the traveling wave sent by the source along the transmission line has voltage and current in phase. When the wave hits the series feed points of the antenna, which is a single point in it's journey in terms of distance, voltage and current are in phase.

When the wave moves past the feed points for the first time, before standing waves on the antenna have had a chance to appear, the voltage and current of the wave traveling from the feed points to the ends of the antenna again are still in phase.

How can it be any different ?

In the world of resonance where resistance is our friend and reactance is Darth Vader, life is good for the traveling wave. But as soon as it hits the open circuited end of the antenna, life crashes in a heap. The voltage of the standing wave instantly doubles and the current is slashed to zero.

The traveling wave feels like its having a nervous breakdown as its false sense of security evaporates in an instant.

Precisely when the leading edge of the standing wave reaches the end of the antenna, reflection of the standing wave begins, and as already mentioned, this is when the standing wave cycle starts.

For a 1/4 wave dipole element, in the time it takes for the wave to reach the end of the element, the voltage source at the feed points has progressed through 90° of it's 360° cycle. At that 90° point the cycle of the standing wave is just starting. The phase of the standing wave with respect to that of the RF at the source is -90° and remains so after the standing wave is established, so long as the original source continues to supply uninterrupted RF energy.

The open circuit ends of the antenna along with their loyal subject Reflection, boldly establish a new relationship between voltage and current of the standing wave. The old phase difference was zero, the New and Improved phase of the voltage of the standing wave with respect to the current is fixed, and the voltage lags the current by 90° at every point on the antenna. Everywhere on the antenna the phase difference between standing wave current and voltage is 90°.

Let's point out something else now while we are hopefully still a bit sane.

Traveling waves and standing waves in a transmission line operate in differential mode, where the desired effect is considered across the two wires of the line, and there is no common mode voltage or current.

In a matched system where there are no standing waves on the transmission line, as soon as the wave traveling along the transmission line goes past the feed points of the antenna, and the two differential waves with opposite polarity no longer cancel out, the effect of interest immediately becomes a common mode wave where at any one instant in time the same current flows through both antenna elements in the same direction. At the feed points, the differential mode current is instantly converted to a common mode current because the two conductor are no longer close to each other and so cancellation no longer occurs.

For this reason, the standing waves on the antenna can't travel back down the transmission line as the common mode current on the antenna is immediately cancelled out starting at the junction between antenna feed points and transmission line.

Reactance in the Impedance and Resonance.

In just the same way that people it seems are sometimes put in our paths to show us how not to behave, i'm going to explain why a resonant half wave dipole has no reactance in the impedance at the feed points by first describing what happens in a dipole that isn't being operated in it's resonant state.

Look at the figure below.

enter image description here

As mentioned earlier, because the phase change of the standing wave as time progresses can be directly correlated with phase change at points along the antenna, we can map out the change in phase of the standing wave in distance from the ends of the antenna in degrees.

The figure shows a dipole antenna which has elements which are 15° longer than 1/4 or 90° of the wave length of the applied sine wave at the feed points. This means the entire antenna is 30° longer than the half wave length of the applied sine wave.

The voltage and current distribution along the dipole is exactly the same as the section of an open circuit transmission line 105° of the wavelength before the open circuited end. The point at which the current maximum occurs is 15° either side of the feed points. The point at which the voltage crosses zero is also 15° either side of the feed points.

This antenna has 4 problems.

  1. The phase of the current of the standing wave at the feed points compared to the phase of the source voltage is -15°. The quotient of source voltage and standing wave current at the feed points contains reactance.

  2. The phase of the voltage of the standing wave, which lags the phase of the current of the standing wave by 90°, compared to the phase of the source voltage, is -105°. The quotient of the voltage and current of the standing wave at the feed points contains reactance.

  3. The standing wave voltage at the feed points which contributes reactance to the impedance seen at the feed points isn't always zero.

  4. The reactive circulating energy in the antenna isn't being topped up at the right moment and so antenna current isn't as high as it could be compared to when the antenna is operated at resonance. This is why some people don't like non-resonant antennas that much.

Now let's examine a half wave dipole which is by definition always exactly resonant.

enter image description here

As can be seen in the figure, the antenna elements are 90° in length.

This antenna has 4 reasons to be of interest to ham radio operators.

  1. The phase of the current of the standing wave at the feed points compared to the phase of the source voltage is 0°. The quotient of source voltage and standing wave current at the feed points contains no reactance.

  2. The phase of the voltage of the standing wave, which lags the phase of the current of the standing wave by 90°, compared to the phase of the source voltage, is -90°. The quotient of the voltage and current of the standing wave at the feed points contains the maximum reactance possible.

  3. The standing wave voltage at the feed points which could contribute reactance to the impedance seen at the feed points if it wasn't zero all the time, is always zero all the time, and so does not contribute any reactance to the impedance seen at the feed points

  4. The reactive circulating energy in the antenna is being topped up exactly at the right moment and so antenna current is at maximum value which is much larger than the energy supplied by the source. This is why everyone loves resonant antennas.

Misinformation Confuses Everyone.

The following statement is extremely daring and bold.

All of those diagrams that you see in text books and on the internet including what's in WikiLiar showing the voltage and current distribution on a half wave dipole are at best misleading and at worst incorrect.

Let's investigate why. Look at the below animation.

It gives the reader the impression that the voltage is zero in the middle of the space between the two inner ends of the dipole elements, and that there is current flowing across the gap.

‎‎‎‎‎‎########################enter image description here]3 enter image description here

It shows that for a resonant antenna the voltage of the standing wave at the feed points is not always zero.

And there is no indication or even a hint that there is a vector addition of voltage of the source and whatever the voltage is of the standing wave is at the feed points, a fact which is crucial to understanding the impedance presented across the two feed points.

There should also be a caption under the image which says "The amplitude of the standing wave is oscillating at the frequency of the source, the voltage and current everywhere on the antenna are 90° out of phase with each other, and when the antenna is operated at resonance, the voltage of the standing wave lags that of the source by 90°, and the resultant current of the standing wave is in phase with that of the source".

Even though the diagram is just trying to show a general idea of half wave dipole operation, it misinforms the reader in the worst way possible way by messing up what happens with the feed points which is the area of most confusion for everyone.

These diagrams are typical of the bullshit that's available on the internet, which helps to dumb everyone down by propagating misleading and inaccurate information.

Other sadly incorrect but vastly popular ideas especially amongst ham radio operators is that a dipole is a big capacitator and that at resonance the capacitive and inductive reactances cancel out. As you are no doubt gathering by now if you are still alive after having read this far, these facts are completely ridiculous.

For example, the formula for capacitance of a capacitor includes the surface areas of the plates. For a wire dipole, what's the surface area of the points at the inner ends of the elements which are the capacitor plates ? Not much. Not enough to be that of a capacitor which is half the determining factor for the resonance of the antenna !

And how does the formula for resonance 1/2π√LC which only has one solution for a fixed combination of L and C cater for the fact that a dipole is resonant on integer multiples of a half wave length ? Sorry, but it can't.

These ideas have come about due to confusion about where circuit theory and wave theory applies, and because of the fact that a dipole exhibits some similar characteristics to a resonant lumped constant circuit.

The Correct Half Wave Dipole Diagram.

Look again at the much better picture below.

This gives a correct indication of the voltage and current distribution for a half wave dipole.

Notice the vertical line at both of the feed points. These represent the in-phase voltage and current of the source at the feed points.

At any one instant in time, the voltage presented by the source adds vectorily to the voltage of the standing wave which is present at the feed points.

At any one instant in time, because the dipole is in essence a series circuit, the current flowing past the feed points from the source is the current of the standing wave, which is the same current that flows along the antenna and through the source.

enter image description here

The Reason a Half Wave Dipole Has No Reactance in The Impedance at the Feed Points.

Let's pretend that the voltage of the source is 100 Vpp, and since we are referencing everything to the phase of the source, we can say that at the left hand feed point it's +100∠0° Vpp and at the right hand feed point it's -100∠0° Vpp.

Let's also pretend that current flowing along the antenna and through the source is 5 App so that means the resistive part of the antenna impedance is 100/5 = 20 Ω, and let's pretend as well that the amplitude of voltage of the standing wave at the feed points is ±30V so that the complex value is ±30∠-105° Vpp

For a dipole with elements which are 105° in length.

  • The voltage at the left hand feed point is the vector sum of that provided by the source and the standing wave, so it's 100∠0° + 30∠-105° = 96.68∠−17.44°

  • The current flowing past the left hand feed point is 5∠-15° ie: the amplitude of the current of the standing wave.

  • The impedance seen between the two feed point terminals = 96.68∠−17.44° / 5∠-30° = 19.37∠-66.78° Ω : there is reactance, because the dipole is not being operated at resonance.

For a dipole with elements which are 90° in length ie: a half wave dipole :

  • The voltage at the left hand feed point is the vector sum of that provided by the source and that provided by the standing wave, so it's 100∠0° + 0∠-90° = 100∠0°.

  • The current flowing past the left hand feed point is 5∠0° ie: the amplitude of the current of the standing wave.

  • The impedance seen between the two feed point terminals = 100∠0° / 5∠0° = 20∠0° Ω : no reactance, because the dipole is being operated at resonance.

The above explanation clearly shows that for a dipole operated at resonance, the zero crossing point of the out of phase voltage of the standing wave on the antenna falls exactly in the same position as the feed points, and so the amplitude of this out of phase voltage at the feed points is always zero and so contributes no reactance to the impedance seen at the feed points.

Because the current of the standing wave at all points on the antenna including at the feed points is in phase with the source, because the length of the elements are exactly 1/4 λ, it doesn't add reactance to the impedance.

For a dipole not being operated at resonance, the out of phase standing wave voltage zero crossing point doesn't line up exactly with the feed points, and so at the feeds point there is a voltage which isn't always zero that is 90° out of phase with the standing wave current and source voltage, and it adds reactance to the impedance.

This is the reason why a half wave dipole has no reactance in the impedance presented across the feed point terminals.

References

  1. The Similarity of Waves by John Shives https://www.youtube.com/watch?v=DovunOxlY1k
  2. Transmission Lines by Alexander Shure.
  3. Antennas by Alexander Shure.
  4. Practical Antenna Handbook by Joseph Carr Vol 4, Chapter 5 only.
  5. https://www.ittc.ku.edu/~jstiles/723/eecs 723 handouts.htm
  6. https://en.wikipedia.org/wiki/Dipole_antenna
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