Circulator:-

A circulator is a four port microwave device which has a specific property that each terminal is connected only to the text clockwise terminal. i.e. p[ort 1 is connected to port 2 only and not to port 3 and 4 and port 2 is connected to port 3 only etc.

Construction:-

• A four port Faraday rotation circulator is shown in figure,
• The power entering port 1 is TE10 mode and is converted to TE11 mode because of gradual rectangular to circular transition.
• This power passes port 3 unaffected since the electric field is not significantly cut and is rotated through 450 due to Ferrite passes port 4 unaffected and finally emerges out of port 2.

• Power from part 2 will have plane of polarization already titled by 450 with respect to port 1.

• This power passes port 4 unaffected because again the electric field is not significantly.

• This wave gets rotated by another 450 due to ferrite rod in clockwise direction.
• This power whose plane of polarization is tilled through 900 finds port 3 suitably aligned and emerges out of it.
• Similarly port 3 is coupled only to port 4 and port 4 to port 1.

$S=\begin{bmatrix}0 & S_{12} & S_{13} & S_{14} \\ S_{21} & 0 & S_{23} & S_{24} \\ S_{31} & S_{32} & 0 & S_{34} \\ S_{41} & S_{42} & S_{43} & 0 \end{bmatrix}$

Using properties of S matrix and properties of circular

$S=\begin{bmatrix}0&0&0&1 \\ 1&0&0&0 \\ 0&1&0&0 \\ 0&0&1&0 \end{bmatrix}$