Circulator S-Matrix: 3-Port and 4-Port Configurations

This page dives into the S-Matrix (Scattering Matrix) representation of both 3-port and 4-port circulators. We’ll cover the basics of these components and how their S-matrices are defined.

What are 3-Port and 4-Port Circulators?

A circulator is a multi-port device that directs an RF signal from one port to the next in a specific direction – either clockwise or counter-clockwise. Think of it as a one-way traffic controller for RF signals.

The number of ports determines the type of circulator: we have 3-port circulators and 4-port circulators.

Figure 1: 3-Port RF Circulator Application Note

Figure 1 illustrates a typical application of a 3-port RF circulator. The signal to be transmitted flows from port 1 to port 2, and the signal received by the antenna travels from port 2 to port 3.

3 Port Circulator S-Matrix

Figure 2: 3-Port Circulator S-Matrix

A 3-port circulator can be implemented using a 120-degree H-plane waveguide or a strip line symmetrical Y-junction with a central ferrite disc.

The S-matrix for an ideal, perfectly matched, lossless, and non-reciprocal 3-port circulator is represented as follows:

[S] = | 0 0 S13 |
| S21 0 0 |
| 0 S32 0 |

Figure 2 shows the S-matrix for a perfectly matched, lossless, non-reciprocal 3-port circulator.

4 Port Circulator S-Matrix

Figure 3: 4-Port Circulator S-Matrix

A 4-port circulator can be constructed using two magic-T junctions and a non-reciprocal 180-degree phase shifter. Another method involves combining two 3-dB side-hole directional couplers with two non-reciprocal phase shifters.

Figure 3 illustrates the S-matrix of an ideal, perfectly matched, lossless, and non-reciprocal 4-port circulator.