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Why does a single-feed truncated square patch radiate CP

 
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somewhatconfused
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Joined: 01 May 2014
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PostPosted: Thu May 01, 2014 2:35 am    Post subject: Why does a single-feed truncated square patch radiate CP Reply with quote

If you have a square patch and truncate the edges along one of the diagonals you can get circular polarisation with a single feed.
So you have a 90 degree phase shift between the TM10 and TM01 modes, but where does this phase shift come from? Is it just due to a path difference between the feed point and the resonant paths for the different modes?
Does what I'm saying make any sense?
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bigSteve
Antenna Wizard


Joined: 14 Mar 2009
Posts: 265

PostPosted: Sat May 03, 2014 6:26 pm    Post subject: Reply with quote

Honestly, it is not super clear why cutting the edges creates circular polarization.

You are right on this:
you need 2 orthogonal components for circular polarization, and this can be created with a square patch fed anywhere on the patch antenna (obviously the impedance changes depending on where it is fed).

Then we just need to figure out how to get the modes 90 degrees out of phase. Since we can vary the impedance (which is in essence the phase) depending on where we feed it, we can move the feed off the diagonal on a square patch (where the two modes would be fed symmetrically) to disturb the relative phase of the two modes. The goal then is to get them 90 degrees out of phase.

From here I believe it is optimization, where it is found that cutting the corners helps to achieve balance on the modes and hte 90 degree phase shift.

Unfortunately, I don't have a simple answer on why this cut enables 90 degree phase shift. But that is the basic idea.
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somewhatconfused
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PostPosted: Mon Jul 07, 2014 8:45 pm    Post subject: Reply with quote

Ok thanks Steve
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helix
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Joined: 29 Jan 2015
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PostPosted: Fri Jan 30, 2015 5:50 am    Post subject: Reply with quote

Here's a more detailed explanation...

FIRST, with a square patch (aligned with x and y axes), you have two modes which are basically microstrip currents in the x and y directions. You can feed a square patch on a diagonal, but it will not produce CP (only a linear polarization that is now diagonal!); the patch MUST be made slightly rectangular AND fed close to the diagonal to get CP.

The reasoning goes something like this... A patch mode can be modeled as a parallel LCR resonator, and two modes in a probe fed configuration can be modeled as two such LCR resonators in series.

The impedance of a parallel LCR circuit (resonant at w0) operating at a frequency w near w0 is something like:

Z ~ R/(1+ j2Q(dw/w0)) where dw = w - w0

if you have two modes, they are in series, so the input impedance of the patch is:

Z = Z1 + Z2 = R/(1+ j2Q(dw/w01)) + R/(1+ j2Q(dw/w02))

If w01 and w02 are spaced correctly, there will be a frequency w between them such that

Z ~ R/(1+j) + R/(1-j) = R(1-j)/2 + R(1+j)/2

So at this frequency, the impedance of one mode is -45 degrees and the other +45 degrees... when put in series, the net effect is that the input impedance of the patch is real. But the impedance of the two modes differs by 90 degrees. So that's basically how you can get CP in a diagonally fed slightly RECTANGULAR patch. There are more complicated explanations (involving poles of complex functions) but I like this one because it's pretty heuristic.


NOW for the cropped corner patch. I red about this in Bancroft's book a few years ago and didn't believe it. So I did some work with the eigensolver in HFSS and I'll be darned, it certainly does appear to be true.

Take a square patch as before and probe feed it along a center line. There are two modes, whose microstrip currents are aligned with the x and y axes. But in this case only one is excited because the probe feed is along the center line. The two modes are called "degenerate" because they are resonant at the same frequency. NOW, when you start cutting two of the opposite corners, it does something very interesting to those two degenerate modes. The modal distributions actually switch to something different! Instead of the microstrip currents of the two modes being aligned along the x and y axes, the currents actually align along the diagonals. One current goes from one cropped corner to the other cropped corner, the other goes from the non-cropped corner to the other non-cropped corner. So the modes are still orthogonal spatially, but each mode excites two edges of the patch instead of one as before. NOW, essentially because one mode is "working off of" the two cropped corners and the other is not, their resonant frequencies are now slightly different (the frequency of the cropped-corner one is slightly higher). Sound familiar?! Same situation as before. But look! Because the modes have changed to be diagonal, the probe now excites both. You now have the same situation as before, effectively. And this is more or less why a cropped corner patch can generate CP.
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