Circulators#
Theoretical Model#
Theorem: Explicit Representations
If a circulator has characteristic admittance \(G\), then it has the following admittance representation:
\[ \boldsymbol{i} = \boldsymbol{Y}\boldsymbol{v} \qquad \boldsymbol{Y} = \begin{bmatrix} 0 & G & -G \\ -G & 0 & G \\ G & -G & 0\end{bmatrix} \]
If a circulator has characteristic impedance \(R\), then it has the following impedance representation:
\[ \boldsymbol{v} = \boldsymbol{Z}\boldsymbol{i} \qquad \boldsymbol{Z} = \begin{bmatrix} 0 & R & -R \\ -R & 0 & R \\ R & -R & 0\end{bmatrix} \]
Proof
TODO
