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Rat Race Coupler S-Matrix | Rat Race Coupler scattering matrix

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

What is Rat Race Coupler?

It is 180o hybrid having 4 ports as shown in the figure. It is also called as hybrid ring coupler.

It is used as 3 dB coupler. It is used in various RF and microwave systems as alternative to magic tee device. But unlike magic tee, it does not require any matching structure in order to obtain similar functionalities. It is available in various designs such as microstrip, stripline and waveguide structures.

It is used in wide variety of applications such as balanced mixers, balanced amplifiers, antenna feeding networks, power multipliers or power dividers etc.

Rat Race Coupler

The figure-1 depicts working of Rat Race Coupler. As shown it has four ports which are λ/4 away from the 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*λ/4 wavelengths away from each other. The power fed at the port-1 is splitted across port-2 and port-4 where as port-3 is completely isolated.

Rat Race Coupler S-Matrix | Rat Race Coupler Applications

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

Rat Race Coupler S-Matrix

➨It can sum two in-phase combined input signals with very minimal or no loss.
➨It can equally split input signal and delivers 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 180o phase shifted power divider.
➨It can also be used as as power combiner to sum two signals with 180o phase-shift with minimal loss or absolutely no loss.

Advantages of Rat Race Coupler

Following are the benefits or advantages of Rat Race Coupler:
➨It offers wider bandwidth.
➨It offers acceptable return loss at its ports.
➨It offers good isolation between its ports.
➨It offers excellent amplitude/phase imbalance in whole D band frequency range i.e. 2.20 to 3.30 GHz.

S-Matrix of other RF devices

3-port and 4-port circulator S-matrix
RF Isolator S-matrix
Magic Tee S-matrix
Rat Race Coupler S-matrix
Branch Line Coupler S-matrix
Directional Coupler S-matrix
Fixed Attenuator S-matrix
Hybrid Ring S-matrix

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