# Circulator

A circulator is a passive non-reciprocal three- or four-port device, in which a microwave or radio frequency signal entering any port is transmitted to the next port in rotation (only). A port in this context is a point where an external waveguide or transmission line (such as a microstrip line or a coaxial cable), connects to the device. For a three-port circulator, a signal applied to port 1 only comes out of port 2; a signal applied to port 2 only comes out of port 3; a signal applied to port 3 only comes out of port 1, so to within a phase-factor, the scattering matrix for an ideal three-port circulator is

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