Rat Race Coupler S-Matrix Explained

This page describes the Rat Race Coupler S-Matrix (scattering matrix). It also covers the basics of the Rat Race Coupler along with its S-matrix. The advantages of the Rat Race coupler and its applications are also mentioned.

What is a Rat Race Coupler?

It is a 180° hybrid having 4 ports, as shown in the figure below. It is also called a hybrid ring coupler. It is used as a 3 dB coupler and in various RF and microwave systems as an alternative to a magic tee device. Unlike the magic tee, it doesn’t require any matching structure to obtain similar functionalities.

It’s available in various designs such as microstrip, stripline, and waveguide structures and is used in a wide variety of applications such as balanced mixers, balanced amplifiers, antenna feeding networks, power multipliers, or power dividers, etc.

Figure 1 depicts the working of a Rat Race Coupler. As shown, it has four ports which are $\lambda/4$ away from each other in the top half of the hybrid ring (i.e., between P1 and P2, P2 and P3, P3 and P4). In the bottom half of the hybrid ring, P1 and P4 ports are $3\lambda/4$ wavelengths away from each other. The power fed at port-1 is split across port-2 and port-4, whereas port-3 is completely isolated.

Rat Race Coupler S-Matrix and Applications

The Rat Race Coupler S-matrix is as follows. It can be used in the following applications or configurations:

• It can sum two in-phase combined input signals with very minimal or no loss.
• It can equally split an input signal and deliver outputs at two ports with no phase difference between them. Example: Input power at P3 and Outputs at P2 and P4 and no output at P1.
• It can also be used as a 180° phase-shifted power divider.
• It can also be used as a power combiner to sum two signals with a 180° phase-shift with minimal loss or absolutely no loss.

Advantages of Rat Race Coupler

Following are the benefits or advantages of a Rat Race Coupler:

• It offers a wider bandwidth.
• It offers acceptable return loss at its ports.
• It offers good isolation between its ports.
• It offers excellent amplitude/phase imbalance in the whole D-band frequency range, i.e., 2.20 to 3.30 GHz.