# Is there a way to explain antenna radiation patterns on receive without reciprocity?

I don't consider myself an expert, but I have a fairly decent understanding of radio. I belong to a club that includes a number of people who have less theoretical background.

I understand that reciprocity for an antenna means that we can calculate properties for an antenna when transmitting, when it is more intuitive and then we "hand wave" and say that reciprocity exists and because of that, we can apply the same parameters to an antenna being used in receive mode.

Is there a way to explain this to someone with less experience without having to invoke reciprocity?

Edit: the following is a secondary part of this question and is of lesser importance.

If not, is there a way to explain it to someone with more experience at a higher level than Maxwell's equations or the like?

Also I am not questioning Reciprocity, but it may not be intuitive to some. The comment by Brian K1LI may imply the best answer. "Don't try to explain without Reciprocity, but explain Reciprocity, if necessary.

Clarification by a simple example: If I want to explain why a Yagi has a null on receive, I can invoke reciprocity and say there is a null in various places or gain in various places because that is what it looks like when it is transmitting. Some people may be fine with that, especially if I explain why the principle holds, but It may not be an obvious answer.

Added April 17: I'm not sure what answer to accept. Most of them have some useful or interesting pieces, but none of them really provide a good answer to my question. What is the proper protocol on this site? I'm happy to write up an answer that is a combination of what was said by everyone, but I also want to give credit to those who have provided answers.

• Reciprocity is simply a statement of fact; it doesn't "explain" anything. The key is to recognize that the currents induced in the conductors of an antenna exposed to incoming electromagnetic wavefronts from various directions is is completely analogous to the process of generating electromagnetic wavefronts by driving currents onto those conductors. – Brian K1LI Apr 10 '19 at 19:58
• On accepting — it's not required to accept an answer. But it's also OK to accept any answer that particularly stood out and upvote the others and perhaps explain in a comment what was good about particular ones. But do put that in comments; keep your question text to be the actual question. (It's also good to avoid "Edit:" and explicit followup sections and instead reorganize your text so it makes the most sense to someone reading it for the first time now.) – Kevin Reid AG6YO Apr 17 '19 at 16:57

If I want to explain why a Yagi has a null on receive, I can invoke reciprocity and say there is a null in various places or gain in various places because that is what it looks like when it is transmitting.

You could take that approach, but it isn't the only approach you could take. As with any antenna, the explanation begins with the nature of the (transverse) electromagnetic wave that arrives at the antenna:

This linearly- and vertically-polarized wave - so called because of the orientation of the electric field vectors - will induce the largest currents in a conductor that is perfectly aligned with the $$E$$ field: a "vertical," in ham parlance.

At a great distance from the transmitting antenna, each of the $$E$$ field vectors extends to form an $$xy$$ plane; this plane is a wavefront, a plane on which the amplitude and phase of the $$E$$ field is everywhere the same. Depending on the relative orientation of the transmitting and receiving antennas, the wavefront will arrive at an angle, $$\theta$$, to the receiving antenna conductor:

At each point where the wavefront intersects the antenna, the $$E$$ field will have a component along the direction of the antenna conductor which can induce a current in the antenna. As the wavefront proceeds to cut across the antenna conductor, the arrival time of the wavefront will be delayed from the earlier points of intersection, introducing a phase difference between the currents induced at the successive points of intersection. Summing the amplitudes and phases of the individual interactions determines the total current on the conductor. Finding this response for all arrival angles establishes the pattern of the antenna.

In the case of a dipole - which, we should remember, may be an element of a yagi - the maximum induced current occurs when $$\theta$$=0 because all of the $$E$$ field vectors align perfectly with the antenna conductor and arrive at the same time (i.e., no phase differences). Conversely, when $$\theta$$=90$$^\circ$$ - that is, when the wave arrives "off the side" of the antenna - there is no component of the $$E$$ field along the direction of the antenna, so no current is induced.

Sure, you "just" have to calculate the electromagnetic waves generated by the transmitter, how these will interact with the receiving antenna and the mobile charges in them, and how this will result in transmitting electromagnetic forces through the antenna, ultimately to the feedline, and then the receiver.

It's really a problem no different than transmitting, but in the other direction. Maxwell's equations already provide the mathematical basis for doing this, and software exists to numerically solve the problem. For example if you've ever modeled a Yagi in NEC, each of the parasitic elements is in a way a "receiving" the radiation from the other elements around it.

So in invoking reciprocity isn't necessary to explain radiation patterns, though it is often more practical. It's often easier, either in simulation or in a real test, to consider the antenna as transmitting then measure the field around the antenna, than it is to set up a transmitter and measure the received power, then move the transmitter and repeat the experiment dozens or hundreds of times until the antenna pattern is resolved with sufficient resolution.

• So to summarise, the answer is "no, not really", unless I want to simulate it and let the computer do the math behind the scenes. But it isn't really fair to call the reciprocity principal "Hand waving"? :-) (And the reciprocity principal works and is easy, so why would I want to?) – user3034958 Apr 10 '19 at 18:25
• @user3034958 Aren't you just letting the computer do the math behind the scenes in either case? – Phil Frost - W8II Apr 10 '19 at 18:41
• If you do anything useful with it, then you are probably doing it with a computer, but the main question was about a conceptual understanding for beginners that couldn't even name half the symbols in Maxwell's Equations and that didn't involve reciprocity. Note: I am not questioning the validity of either. – user3034958 Apr 10 '19 at 20:53
• @user3034958 A conceptual understanding of precisely what? How antennas receive? How they are directional? I don't see any particular need to invoke reciprocity to explain either of those things. – Phil Frost - W8II Apr 10 '19 at 21:04

According to Wikipedia, the Lorentz Reciprocity theorem loosely states that:

...the relationship between an oscillating current and the resulting electric field is unchanged if one interchanges the points where the current is placed and where the field is measured.

As shown in the citation, Maxwell's equations can be manipulated to show this is correct, but a simple experiment may help to understand it intuitively.

Place two, center-fed, vertically oriented, half-wave dipoles 10 wavelengths apart:

Using antenna simulation software, driving dipole 1 with a 1A RF current source induces a peak current of 26mA in dipole 2. Conversely, driving dipole 2 with a 1A RF current source induces a peak current of 26mA in dipole 1. This demonstrates the effect of reciprocity.

There is nothing special about the nature or disposition of the two antennas in the example. Repeating the experiment with the two antennas in any arrangement produces the same reciprocal result, as long as the antennas are in each other's far field. You can measure the pattern of antenna 1 by moving antenna 2 throughout the space surrounding antenna 1, while keeping antenna 2 "aimed at" antenna 1. Using a very short dipole for antenna 2 approximates the pattern of an isotropic radiator, making such "aiming" less critical.

• So to summarise, the answer is "no, not really", but it's easy to simulate it and let the computer do the math behind the scenes. :-) – user3034958 Apr 10 '19 at 18:28
• The point of this answer is the mental trick of considering another an actual transmitting antenna nearby not just thinking about the travelling waves. Reciprocity is difficult to explain i.t.o. waves and patterns, but once you imagine a pair of antennas, you can (more clearly) interchange transmitter and receiver). – tomnexus Apr 10 '19 at 19:36
• I see what you mean. Very good point. (actually a good reminder about teaching abstract concepts in general) – user3034958 Apr 10 '19 at 21:00

For simple antennas it's easy to imagine how they are more sensitive in some directions, than in others.

Imagine a short dipole, with a resistor at the feedpoint, and have a travelling wave impinge on it from some direction. It should be fairly obvious, even if the maths isn't simple, that the voltage developed at the feedpoint will be largest when the dipole is aligned with the E-field of the travelling wave. End-on, it won't develop any voltage.

The same for thinking about its polarisation - when it is oriented perpendicular to the E-field, no voltage will be induced.

This simplistic model works OK for a short dipole, which is basically a field probe. It seems to work for a half-wave dipole too, but the near fields are actually more complicated when significant current flows on the antenna, leading to scattered fields which add to the fields of the TEM wave. I think it's about as good as a transmitting model, when explaining the pattern of a dipole to a beginner. However it's not much use for explaining a yagi, or deriving input impedance etc.