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When you are transmitting through an antenna, all you're really doing is making current go back and forth at your transmitting frequency. This creates radio waves. The waves bounce at the end of the wire, and you can exploit this by choosing the the length of the antenna in relation to your desired frequency to get a resonance.

EDIT: I've now tried this setup with a borrowed antenna analyser! Though it didn't result in any data about directionality, I can now at least onfirm that I can get descent SWR (better than 1:1.5) feeding a full wave antenna in the middle. It seems to be resonant on a frequency slightly lower than you get when feeding at the end, but I suppose this is natural as you double the end effects both at the feedpoint and at the ends.

When you are transmitting through an antenna, all you're really doing is making current go back and forth at your transmitting frequency. The current will form a wave that creates radio waves. The current waves bounce at the end of the wire, and you can exploit this by choosing the the length of the antenna in relation to your desired frequency to get a resonance.

EDIT: I've now tried this setup with a borrowed antenna analyser! Though it didn't result in any data about directionality, I can now at least confirm that I can get descent SWR (better than 1:1.5) feeding a full wave antenna in the middle. It seems to be resonant on a frequency slightly lower than you get when feeding at the end, but I suppose this is natural as you double the end effects both at the feed point and at the ends.

¹) In the second case, you could also say that the waves pass through one another, cancelling each other out in the middle. You could argue which description is more accurate, but the two really look the same so I will not go into that.

EDIT: I've now tried this setup with a borrowed antenna analyser! Though it didn't result in any data about directionality, I can now at least onfirm that I can get descent SWR (better than 1:1.5) feeding a full wave antenna in the middle. It seems to be resonant on a frequency slightly lower than you get when feeding at the end, but I suppose this is natural as you double the end effects both at the feedpoint and at the ends.

¹) In the second case, you could also say that the waves pass through one another, cancelling each other out in the middle. You could argue which description is more accurate, but the two really look the same so I will not go into that.

I've been doing simulations, i.e. wetware simulations, i.e. drawing things on a paper and grunting at them. I believe I've solved the pussel.

When you are transmitting through an antenna, all you're really doing is making current go back and forth at your transmitting frequency. This creates radio waves. The waves bounce at the end of the wire, and you can exploit this by choosing the the length of the antenna in relation to your desired frequency to get a resonance.

Up to high school physics, a length of wire is resonant if its length is an integer multiple of a half wavelength. In such an antenna, a standing wave can form, where the current is constantly zero at the boundary between each half wavelength segment of the antenna, and moves back and forth between these nodes. The direction of the current is reversed at each segment, in the sense that, at any given time, the segments will have currents (+, -, +, -, ...) or (-, +, -, +, ...).

For a more "visual" description, focus on any fixed segment $s$, and let's say current is flowing to the right. It moves happily along until it reaches the end of the segment, where one of two things happen. Either, it will find the right end of the antenna, or it will slam into another wave of current moving to the left; recall that the direction is flipped at every section. In any case, the current will bounce back¹ and start moving to the left until it reaches the other end of the segment ant the same thing happens again.

As is hinted by the name "end-fed antenna", the feed-point is designed to sit at the end of the antenna. It makes sure that the waves of current bounce, and provides large voltages in phase with the current waves to push them even higher, a bit like pushing a swing every time it reaches the end. An end-fed half wave has only one half-wave segment. "Using the harmonics of an end-fed antenna" simply means that we divide it up into more than one half-wave segments, and make sure our feed-point pushes and pulls at the right moments to get them resonating with the corresponding frequency.

Now we're ready to get to the antenna at hand: a wire one full wavelength long!

It has two of the half-wave segments I mentioned above. If we don't worry about any feeding points, but just imagine it resonating in free space, the current will move back and forth between the centre and the ends; the waves both go outwards, bounce at the ends, move inwards, bounce at each other and the cycle repeats.

Now the main question can be phrased as: What happens if we move the feed-point of a full-wavelength end-fed antenna from the end to the middle?

Formulating the theory from the point of view I've chosen to do in the previous paragraphs, the answer should be rather clear: Nothing happens! In a resonating wire, the current and voltages behave in the same way between segments as it does at the end points, so a feed line that manages to excite the antenna from the end should be able to perform the same function at any of the nodes along the antenna where the current is 0 and the voltage is maximised.

Answer: The radiation pattern obtained obtained from feeding the full wavelength antenna in the middle is thus the same as that obtained from feeding it at the end!

¹) In the second case, you could also say that the waves pass through one another, cancelling each other out in the middle. You could argue which description is more accurate, but the two really look the same so I will not go into that.

I've been doing simulations, i.e. wetware simulations, i.e. drawing things on a paper and grunting at them. I believe I've solved the puzzle.

When you are transmitting through an antenna, all you're really doing is making current go back and forth at your transmitting frequency. This creates radio waves. The waves bounce at the end of the wire, and you can exploit this by choosing the the length of the antenna in relation to your desired frequency to get a resonance.

Up to high school physics, a length of wire is resonant if its length is an integer multiple of a half wavelength. In such an antenna, a standing wave can form, where the current is constantly zero at the boundary between each half wavelength segment of the antenna, and moves back and forth between these nodes. The direction of the current is reversed at each segment, in the sense that, at any given time, the segments will have currents (+, -, +, -, ...) or (-, +, -, +, ...).

For a more "visual" description, focus on any fixed segment $s$, and let's say current is flowing to the right. It moves happily along until it reaches the end of the segment, where one of two things happen. Either, it will find the right end of the antenna, or it will slam into another wave of current moving to the left; recall that the direction is flipped at every section. In any case, the current will bounce back¹ and start moving to the left until it reaches the other end of the segment ant the same thing happens again.

As is hinted by the name "end-fed antenna", the feed-point is designed to sit at the end of the antenna. It makes sure that the waves of current bounce, and provides large voltages in phase with the current waves to push them even higher, a bit like pushing a swing every time it reaches the end. An end-fed half wave has only one half-wave segment. "Using the harmonics of an end-fed antenna" simply means that we divide it up into more than one half-wave segments, and make sure our feed-point pushes and pulls at the right moments to get them resonating with the corresponding frequency.

Now we're ready to get to the antenna at hand: a wire one full wavelength long!

It has two of the half-wave segments I mentioned above. If we don't worry about any feeding points, but just imagine it resonating in free space, the current will move back and forth between the centre and the ends; the waves both go outwards, bounce at the ends, move inwards, bounce at each other and the cycle repeats.

Now the main question can be phrased as: What happens if we move the feed-point of a full-wavelength end-fed antenna from the end to the middle?

Formulating the theory from the point of view I've chosen to do in the previous paragraphs, the answer should be rather clear: Nothing happens! In a resonating wire, the current and voltages behave in the same way between segments as it does at the end points, so a feed line that manages to excite the antenna from the end should be able to perform the same function at any of the nodes along the antenna where the current is 0 and the voltage is maximised.

Answer: The radiation pattern obtained obtained from feeding the full wavelength antenna in the middle is thus the same as that obtained from feeding it at the end!

¹) In the second case, you could also say that the waves pass through one another, cancelling each other out in the middle. You could argue which description is more accurate, but the two really look the same so I will not go into that.