What is a Rat-Race Coupler?

A Rat-Race Coupler is a type of RF coupler that is manufactured using microstrips in the shape of a ring/circle. It is a four-port coupler, with each port placed at a distance of one-quarter wavelength (λ) away from the other around the top half of the ring. The bottom half of the ring is three-quarter wavelengths (λ) in length. As seen in the figure below it has three branches which are 90 degree phase shifted from each other and one branch that provides a 270 degree phase shift.

This coupler is quite versitile and can be used as a power combiner by combining two in-phase signals. Or can be used as a power divider to provide two equally split signals that are 180 degrees out of phase of two equally split in-phase output.

Case 1: As seen in the diagram, when an input signal is fed from port A, we get two equal amplitude in-phase output signals at ports B & C. Port D is isolated in this case.

Case 2: If an input signal is fed from port D, we receive two equal amplitude output signals at ports B & C with 180 degree phase difference. Port A will be isolated in this case.

Case 3: When operating as a power combiner, the in-phase input signals are fed into ports B and C, and we get the sum of the inputs at port A, while the difference of the inputs at port D. This is why port A is referred to as the 'sum port' and port D is referred to as the 'delta port'.

The S-Matrix of a Rat-Race Coupler Can be seen below:

Since rat-race couplers are manufactured using microstrips, they are developed to operate at a specific frequency. The rat-race coupler has a characteristic impedance of √2 compared to the port impedance.