Hybrid (3 dB) couplers

Updated January 2, 2010

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Hybrid couplers are the special case of a four-port directional coupler that is designed for a 3-dB (equal) power split. Hybrids come in two types, 90 degree or quadrature hybrids, and 180 degree hybrids. Why isn't there a "45 degree hybrid" you ask? Maybe it wouldn't isolate the fourth port! Anyone that can submit a proof of this statement will win a gift!

Hybrid couplers are often used in creating reflection phase shifters.

All of the couplers discussed on this page have separate pages that go into detail on their operation. This page will help tie the entire mess together.

180 degree hybrid couplers

These include rat-race couplers and waveguide magic tees. Here we will look at the rat-race and introduce the vector and shorthand notation that is often used when referring to 180 degree hybrid couplers.

Here's a plot that shows the ideal, "classic" rat-race response (equal split at center frequency).

The rat-race gives about 32% bandwidth for a phase error of +/-10 degrees from the ideal 180 degree split.

90 degree hybrid couplers

These are often called quadrature couplers, and include Lange couplers, the branchline coupler, overlay couplers, edge couplers, and short-slot hybrid couplers. Here we will just look at a branchline, and show you some of the "short hand" notation that is often used when referring to hybrids.

Below the branchline is used as a combiner. The input signals are vectors of magnitude A and B, then the outputs are as shown. Note that because we are dealing with voltages, the outputs have a square-root-of-two factor. Power is split exactly in half (-3 dB), equal to the square of the voltages.

Now let's look at it as a divider. Here only an input signal is present at port A. It splits by 3 dB at the two outputs, and is isolated from Port B (ideally zero energy comes out this port).

Converting a branchline coupler to a 180 degree hybrid

In some applications like a monopulse comparator, available 180 degree hybrids complicate the layout because the "sum" port is between the split ports. But it is as easy as adding a 90 degree section to one of the ports of a branchline. Below we've lengthened "Input A" by a quarter-wavelength (impedance is Z₀). Now we've got a sum and a difference output, just like a rat-race.

This image was corrected on March 28, 2008, previously the short-hand notation was wrong (our apologies for the error). Thanks to Lyn and Bernhard who both pointed this out!

Now let's look at the response of this component, and compare it to the "classic" rat-race:

The bandwidth is less. If we just look at the frequency where the 180 degree split is within +/- 10 degrees, it is about 20% (0.9 to 1.1 GHz). Referring to the classic rat-race above, it has 32 percent bandwidth for the same phase error.

Using back-to-back hybrids to achieve an RF-RF crossover

By cascading two hybrid couplers, you can create a four-port network that provides isolation between two RF paths that cross each other (as opposed to an airbridge or wirebond crossover). This should only be attempted where there is plenty of room for it, and it is probably useful over only 10% bandwidth.

Here's a schematic:

And here's the response. S41 is the path that is coupled, S21 and S31 are isolated, at least at the center frequency (in this case 1 GHz). This structure has a severe bandwidth limitation. In most cases you should consider a 3-dimensional RF crossover first, like an airbridge or a wirebond, before you resort to this!