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Three-way planar rat-race coupler or is it a Gysel? (new for October 2017
We got the idea for this page from Richard, thanks! On this page we will unify the analysis of these two splitters, which are really quite similar (both are based on a ring that is 1.5 wavelengths, with taps at various quarterwave spacings).
Below is the most basic rat-race schematic, the "ring impedance" is set to SQRT(2)*Z0.
Note that we've set up two "matching" equations. IN this sense, we are talking about matching two signals to each other, not the other sense, where we would be looking at their impedance match. Does everyone know the difference between signal matching and signal tracking? A subject for anotheer day...
As a 180 degree, 3 dB splitter, port 1 woul;d be the input, and ports 2 and 3 are the outputs. Port 4 is terminated. But you can also feed Port 4, and an in-phase split occurs at ports 2 and 3.
Let's first look at the return loss and isolations, by symmetry, there are only three different plots to look at.
Now we will compare the transmission parameters, based on feeding port 1 (180 split) or port 2 (in-phase split), side by side. Click images to zoom in.
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Transmission to ports 2 and 3
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Transmission to ports 2 and 3
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Matching between ports 2 and 3
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Matching between ports 3 and 2
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Relative phases, ports 2 and 3
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Relative phases, ports 2 and 3
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These results are when Port 1 is fed
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These results are when Port 4 is fed
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Next we note that if you can have a single termination of 50 ohms at port 1, you could add a second termination at a new location, port 5 (lower right corner of schematic, but you must increase the impedance of the terminated ports to 100 ohms. Now the coupler behaves better! By the way, Gysel pointed out in his 1975 paper that the terminations don't have to be 50 ohms, but he made them 50 ohms for convenience (where's that 100 ohm load when you need it?)
Below are the transmission coefficient and isolation and return losses. Note that in the present example, Port 4 is still the input. Also note that the reflection coefficient that the termination sees at Port 1 is not a match, this is a don't care situation! We have achieved perfect balance in the two transmission coefficients S24 and S34, what more could you ask for?
More to come!