Linear devices

As the MNA matrix is the y-parameter matrix of the whole circuit, components that are defined by y-parameters can be easily inserted by adding these parameters to the MNA matrix elements (so-called 'stamping').

Components that cannot be defined by y-parameters need to add additional columns and rows to the MNA matrix. Components defined by z-parameters can be added in the following way (example for a 2-port). It is easily extendable for any port number.

$$\begin{bmatrix}. & . & 1 & 0\\ . & . & 0 & 1\\ -1 & 0 & Z_{11} & ... ...n}\\ I_{out} \end{bmatrix} = \begin{bmatrix}I_{1}\\ I_{2}\\ 0\\ 0 \end{bmatrix}$$ (9.1)

Components that are characterized by S-parameters (normalized to $Z_0$) can be put into the MNA matrix by the following scheme (example for a 3-port). It is easily extendable for any port number.

$$\begin{bmatrix}. & . & . & 1 & 0 & 0\\ . & . & . & 0 & 1 & 0\\ . ... ... \end{bmatrix} = \begin{bmatrix}I_{1}\\ I_{2}\\ I_{3}\\ 0\\ 0\\ 0 \end{bmatrix}$$ (9.2)