Branchline coupler port definition

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New for November 2024.

This is kind of an esoteric topic, but we think it is interesting.  It came about from discussions with Hadrien F4INX, Microwaves101's "French connection". Not the kind of French Connection that Popeye Doyle tries to capture in one of the greatest movies ever made, but a true friend and microwave subject matter expert.

The French Connection, 1971, starring Gene Hackman

On this page we hope to answer this question for all time: on a branchline coupler, which is the "through" port and which is the "coupled" port?  This question is never answered in any of the popular microwave textbooks, such as Pozar and Collin. They had bigger and better things on their minds!

As a baseline, let's first look at a coupled-line coupler; here it is easy to see which is the through and which is the coupled port.  We arranged the ports so that Port 1 is the input, Port 2 is the through port (the schematic symbol gives you a hint) and Port 3 is the coupled port (you already knew that it is a backwards wave coupler, right?)  Let's agree on a convention: on a four-port coupler, at least for this page, Port 4 is always the isolated port.

Here are the amplitudes of the coupled line 3dB coupler.  Note that the through port propagates more energy than the coupled port, outside of the center frequency.  Let's call that characteristic of a through port "Condition 1" that must be satisfied when labeling the through and coupled ports of a branchine coupler.

Here is a comparison of the coupled line's transmission phases for through and coupled arms.  The through arm has an additional 90 degrees of phase length (negative phase is positive length in weird world of microwaves). Let's call this Condition 2, that must be satisfied when assigning the through and coupled ports to the branchline coupler.

And here is a model of a simple branchline coupler.  You will recognize that it is a box (or circular) structure, with ports separated by four transmission lines of 90 degree (quarter-wave) length.  Two of the sides are fifty ohms (in our fifty ohm system) and two of them are ~35 ohms, which means they appear "fat" on a microstrip or stripline layout.  Again, we numbered the ports so that Port 1 is the input, Port 2 is the through port and Port 3 is the coupled port. Yes, we cheated, we first analyzed it, then moved the ports around.  If you want to be the smart guy at a design review you should memorize this... once Port 1 is assigned, the port that is connected via the fat line is the coupled port, the port that is connected via the 50 ohm line is isolated, and the diagonally opposite port is the through port.  Physically, this is way different from where the ports are on the coupled line coupler.  Bet you didn't see that coming!

Our port numbering here, is inconsistent with the numbering we have on this page. Whoops!

Here are the branchline amplitudes.  See how Port 2 has wider bandwidth than Port 3?  That obeys Condition 1 we established above.

Now let's look at branchline transmission phases.   Once again, the through line is 90 degrees longer (more negative) that the coupled line.  That satisfies Condition 2.  Voila, we have determined for all time how to label the through and coupled ports on a branchline coupler correctly!

Note that as you cruise around the world-wide web, you are likely to see different port definitions for the branchline coupler.  Professor Ricketts has ports 2 and 3 swapped compared to how we just defined it.  The port numbers are not important, what we are trying to do is nail down which is the coupled and which is the through port, which in the grand scheme of things is not all that important anyway.  So don't try to call out your college professor by saying "but I saw it on Microwaves101!"

Interestingly, Hadrien F4INX also tackled this topic, and afer some discussions we all seem to be on the same page. But remember, the coupler port is in the eye of the beholder!