# How much transmission power increase is added by an undriven element identical to a simple dipole antenna 1/4 wavelength away?

These wonderful old videos helped me understand how antennas work.

The explanation for making antenna transmission unidirectional relies on using an undriven element 1/4 wavelength away from the driven dipole. The passive element absorbs and retransmits the EM energy in all directions.

Half the retransmitted energy is spent on destructive interference. So that leaves half the retransmitted energy to go towards constructive interference. But how much of the original transmitted energy is captured and retransmitted?

• Links to videos become degraded over time and, videos become removed so, can you phrase your question in a way that doesn't rely on external links. For these reasons, many folk won't watch the videos you have linked. Commented May 15, 2023 at 11:04
• The video is ancillary and for entertainment value. The core of the question is contained in the paragraph of text following it. Commented May 16, 2023 at 14:08

The linked video is made to help radar and radio users or the lowest level maintenance personnel students to get some confidence "I can understand how it works". Unfortunately the given knowledge is only qualitative and misleading for any calculations. The video says that out of phase waves cancel each other, so the radiation is directed to the direction where waves are in-phase.

Less vague image of radiowaves is possible to get only with hard math. That's = solving the wave equations with certain boundary conditions (=where's metal, what's the feeding signal) .

The antenna is concentrated generally to quite a small area. The elements are so near each other that they induce so strong currents to each other that every piece must be taken into the account when one tries to solve what kind wave is actually formed. Claiming that every antenna element radiates independently, one only calculates the resultant field in some distant point is useless. The waves cancelled by opposite phases are never even born.

The main question was how much energy a passive reflector element behind a dipole captures and re-radiates. There's no easy way to tell it because the electromagnetic field settles to the system which contains the main dipole and the reflector and that system radiates as a whole. By solving (numerically) the wave equations one can find how much current there flows on the surface of the reflector and become able to say "it's like a dipole which radiates amount XXX". PhD-level math skills are needed to do the calculations. That's beyond the capabilities of most of us, including me.

Antenna theorists have developed some crutches which help the mathematical handling of multi-element antennas. One of them is "the mutual impedance between the elements" but such quantities must be either measured from an existing antenna or one must calculate them with hard 3d vector field math including differential and integral calculus. Only to see what to expect if you are going to understand more of the math side see for ex. this writing of Yagi-Uda antenna: https://www.ripublication.com/irph/ijece/ijecev4n1__13.pdf Find more in university level antenna theory books. If you are one of those enlightened who can read and understand the linked text without difficulties you'll find there also the wanted answer (a guess only).

Not a asked, but maybe useful:

Independently radiating elements can be more useful approximation if the distance between them is so high that they do not induce substantial currents to each other. There's no strict limit how long distance is enough, but mathematicians have found some distance classes where the antenna part interactions and the dominant math classification properties of the electromagnetic field are different. They, of course, depend on the antenna geometry and the wavelength, but such classes can be found. They speak of reactive nearfield, radiative nearfield, far-field and transition zone. Read for ex. this qualitative description for a start: https://en.wikipedia.org/wiki/Near_and_far_field

If we happen to have 2 antennas so far away from each other that their interaction can be forgotten with no remarkable error and they radiate in sync the same signal we can still found directions where the radiation is weaker than in others, even zero. Nothing of the waves is cancelled. Both antennas radiate as they are designed to do. There are only areas where the currents induced to a receiving antenna cancel each other. Or so we can easily imagine. But that "radiate independently -thinking" leads to difficulties, as we can see soon.

Someone, a little more alert person may claim that in the low total field strength areas the energy density is lower - some energy is vanished. It's not. In the higher total field areas the doubled field strength means quadruple energy density. That looks extremely contradictory - we just said that the antennas are so far away from each other that they do not cause substantial currents to each other. How in the hell they can still together decide to stop transmission to some directions and direct more energy to others?

Unfortunately we still do not have any plausible explanation what the electromagnetic waves actually are - an explanation which is in accordance what we can see, smell, hear and touch. But this hopefully assures us that waves which radiate from multiple sources but contain the same signal must be seen as a whole.

OK, I think I understand your question now. It's basically about converting a unidirectional transmission (from a driven dipole) into a single direction by using a shorted dipole a quarter of a wavelength from the driven dipole.

how much of the original transmitted energy is captured and retransmitted?

Because the shorted dipole is within the so-called near-field, energy is preserved and, the original energy fed to the driven dipole is refocused in the single direction. Theoretically, no energy is lost.

NB the "near-field" extends to about 1 full wavelength of the transmitted signal.

• I understand your use of the word 'refocused' but in terms of how the undriven element is doing that, the word is not illuminating. EdHalfsunk's reply has many more words for me to contend with and although it provides some threads for me to follow, it also confuses the issue with " 2 antennas so far away from each other that their interaction can be forgotten". Commented May 16, 2023 at 14:01
• chatGPT said "The undriven element, often referred to as a reflector, can alter the radiation pattern of the driven dipole antenna by reflecting the radiated energy in a desired direction." and "However, it's important to note that directivity does not increase the actual transmission power of the antenna system. The total radiated power remains the same, but the energy is concentrated in a specific direction." But it also does not explain how. So far the analogy of interference is the most illuminating but does notbegin to suggest how much energy the undriven element is capturing. Commented May 16, 2023 at 14:04
• If the undriven element is simply a skinny wire 1 mm wide, then the cross section it presents to the radiated EM is a miniscule fraction of a parabolic dish covering pi/2 radians. Can I simply use the ratio of cross-sectional areas? Commented May 16, 2023 at 14:07
• Firstly, this is not a forum so, please stick with the question posted in your question. If you are not happy with the word refocussed then maybe I'm not the one to converse with. A skinny wire (as you call it) belies the fact that a skinny wires creates a good reflection. Commented May 16, 2023 at 16:59
• To begin to answer the question initially presented (how much power increase…) I would first need to know how much energy is captured. That is why I started talking about cross section of the driven element that intercepts the radiated energy. Commented May 17, 2023 at 12:56