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New for October 2021. This content dates back to December 2017 and was split from our phased array page back in June 2019 but somehow got left aside... We have never really vetted this idea, perhaps some readers would like to weigh in on it. Designing a phased array system with over an octave of bandwidth would not be without its challenges!
This tip was contributed by Colin, thanks!
A 2x or 4x array isn’t particularly useful, especially in radar because its directivity isn’t great. Assume that you have a 2x array with approximately lambda/2 spacing: If you double the frequency, you’ll find that you get a decently directive beam at boresight but also obviously huge sidelobes at 90 degrees left and right. Not great, but if you go back down to the fundamental you note that there’s nulls there… so, if you do one pulse (or other signal) at the fundamental, and another pulse/signal at the 1st octave then multiply the two results (video/post processing) then you null out the sidelobes! Even while turning the array!
Turns out of course that this is not a coincidence, your most offensive lobes occur when the waveform ‘beats’ with the array, in any vector other than boresight, your nulls occur when they cancel. By doubling the frequency (and using lambda/2 spacing) you flip the nulls and lobes such that they are orthogonal in any direction other than boresight. You can do this with really any even numbered array with spacing of around 0.5 lambda. An odd numbered array doesn’t work as well because you leave some element as an awkward third wheel with no match. What you get is essentially the directivity of an array twice the size of the one you’re using, without having to actually build/buy that array.
But wait, there’s more: you're probably thinking about how much noise gets added to the system, it’s not as much as you would think though. By multiplying the two waveforms you square the power of the actual target as well as the noise so it sort of cancels. Another advantage here is that it’s really easy to build a multi octave radio in terms of impedance matching. You don’t need to actually span or process multiple octaves of bandwidth, you just need little bits of bandwidth at the fundamental and the octave. You can even use more than one octave, but that might be stretching it hardware-wise.