# Destructive interference between two close antennas

let's consider this two planar biconical dipoles of total length and width each one 10mm, at a distance D = 25.6mm.

They are excited with the discrete ports in the picture, which corresponds in this case to a voltage source with 150$$\Omega$$ of source impedance. The two voltage sources, as indicated by the ports arrows in figure, are with opposite polarities. In other words, there is a 180° phase shift.

In this condition, I'm expecting that the radiation pattern of this system (for instance in terms of directivity) falls at the wavelength equal to R = 25.6mm (11.72GHz), because there will be destructive interference between the waves emitted by each antenna. And, in fact, that's what I've got by a simulation in CST MWS:

This graph represents the Directivity on Theta = 90° plane (XY plane) averaged with respect to Phi. There is a directivity drop at 12GHz because of destructive interference.

Nice, it's well predictable.

Why have I thought it's a destructive interference? Because the single elements patterns are, at 12GHz, on XY plane ($$\theta = 90°$$):

So, each element irradiates with peaks of 1.99dBi along y-axis. But, if we look at the radiation pattern of the total system, we have an hole along y-axis.

Since this happens at the frequency whose wavelength is equal to the y-axis distance between the two elements, I'd say it's caused by a field cancellation.

Now let's consider a more complex case with more elements in a circular array:

In this case, the simulation has shown me that the destructive interference frequency is shifted from about 12GHz to 14GHz:

Question: Can you help me on understanding (also qualitatively) how can the presence of other elements shift this frequency (and why it has been increased)?

• Look at the radiation patterns in all cases, and do that before you start plotting over frequency. What looks like "destructive interference" is actually just a hole in the radiation pattern - the power is going somewhere else. As the frequency changes, the blob that is your radiation pattern will change shape. The graphs of Directivity @ Theta-90 (phi=?) are a very narrow view of the antenna's behaviour and hard to interpret alone. – tomnexus Jan 5 at 14:51
• Sounds like an answer to me @tomnexus. – rclocher3 Jan 5 at 16:35
• @tomnexus The graphs with Directivity vs Frequency represent the Directivity on Theta = 90° plane (XY plane) averaged with respect to Phi. So there is a decrease of mean directivity at 12GHz when there are two antennas, and at 14GHz when there are 8 antennas. I've updated the question with the single - element radiation pattern on XY plane. – Kinka-Byo Jan 5 at 17:15
• @tomnexus I fully agree with rclocher3. Respectfully, comments are not for answering questions, although there seems to be a trend on this site to do that. :-) – Mike Waters Jan 5 at 17:47
• I don't think it's an answer... I meant by the comment, kindly, that this was an unanswerable question so far, and needed more information. OP will probably discover the answer while trying to explain it fully, which is great :) The frequency slices of one point on a strange radiation pattern of a large structure will probably never make sense or be explained in isolation. – tomnexus Jan 5 at 18:57

Look at the radiation patterns in all cases, and do that before you start plotting over frequency. What looks like "destructive interference" only happens in a certain direction, where the spacing and phasing of the elements result in a smaller far field strength. This is just a hole in the radiation pattern - the power is going somewhere else. As the frequency changes, the blob that is your radiation pattern will change shape.

The graphs of Directivity @ Theta-90 (phi=?) are a very narrow view of the antenna's behaviour and hard to interpret alone.

Since you're plotting directivity, the power must have gone somewhere on the sphere (losses and mismatch are ignored). The average directivity of an antenna is always 1.0, the antenna will be doing something to concentrate it in certain directions and not others.

Here are a few 3D pattern animations I found on the web: from OpenEMS:

and from JEM engineering (just rotating, not changing frequency):

So I'd suggest starting with some 3D patterns, see if they make any sense at all, and if they almost do what you want, then only start making cuts through the pattern, and/or plotting the gain at some point over frequency.

There is no single "destructive interference frequency". There is maybe a frequency where destructive interference occurs in a useful direction. It can be shown that for any array, at any frequency, for any given polarization, there exists at least one (and often more) nulls in the radiation pattern, which must occur due to destructive interference between the elements.

Furthermore, directivity alone is not necessarily a figure of merit. Remember that the radiation pattern is a 3-dimensional function, and directivity is a measure of just one point on that function. Some array may have at some frequency a high directivity, but the radiation pattern may look like a sea urchin. This wouldn't be of much practical use: usually we want one lobe, not 50. So if you want to understand your arrays, look at the whole pattern, not just directivity.