A rat-race coupler, also known as a hybrid ring coupler, is a type of coupler used in RF and

microwave Microwave is a form of electromagnetic radiation with wavelengths shorter than other radio waves but longer than infrared waves. Its wavelength ranges from about one meter to one millimeter, corresponding to frequency, frequencies between 300&n ...

systems. In its simplest form, it is a 3 dB coupler and is thus an alternative to a

magic tee A magic T consisting of four rectangular waveguides meeting in a single three-dimensional junction A magic tee (or magic T or hybrid tee) is a hybrid or 3 dB coupler used in microwave systems. It is an alternative to the rat-race coupler. In co ...

. Compared to the magic tee, it has the advantage of being easy to realize in planar technologies such as

microstrip Microstrip is a type of electrical transmission line which can be fabricated with any technology where a conductor is separated from a ground plane by a dielectric layer known as ''substrate''. Microstrip lines are used to convey microwave-freq ...

and

stripline In electronics, stripline is a transverse electromagnetic (TEM) transmission line medium invented by Robert M. Barrett of the Air Force Cambridge Research Centre in the 1950s. Stripline is the earliest form of planar transmission line. De ...

, although

waveguide A waveguide is a structure that guides waves by restricting the transmission of energy to one direction. Common types of waveguides include acoustic waveguides which direct sound, optical waveguides which direct light, and radio-frequency w ...

rat races are also practical. Unlike magic tees, a rat-race needs no matching structure to achieve correct operation. The rat-race coupler has four ports, each placed one-quarter wavelength away from each other around the top half of the ring. The bottom half of the ring is three-quarter wavelengths in length. The ring has a characteristic impedance of factor

\sqrt

compared to port impedance. A signal input on port 1 will be split between ports 2 and 4, and port 3 will be isolated. The full

scattering matrix In physics, the ''S''-matrix or scattering matrix is a matrix that relates the initial state and the final state of a physical system undergoing a scattering process. It is used in quantum mechanics, scattering theory and quantum field theory ...

for an ideal 3 dB rat-race is :

S = \frac
\begin
 0 & 1 & 0 & -1 \\
 1 & 0 & 1 &  0 \\
 0 & 1 & 0 &  1 \\
-1 & 0 & 1 &  0
\end

Rat-race couplers are used to sum two in-phase combined signals with essentially no loss or to equally split an input signal with no resultant phase difference between its outputs. It is also possible to configure the coupler as a 180 degree phase-shifted output divider or to sum two 180 degree phase-shifted combined signals with almost no loss.

References

* David M Pozar "Microwave Engineering" * M L Sisodia, Vijay Laxmi Gupta (2001), "Microwaves : Introduction to Circuits,Devices and Antennas", New Age International * Kai Chang, Lung-Hwa Hsieh (2004), "Microwave Ring Circuits and Related Structures", Wiley-IEEE, {{ISBN, 0-471-44474-X, 9780471444749 Microwave technology