Inductor

During DC simulation an inductor is a short circuit, thus, its MNA matrix entries need an additional row and column.

$$\begin{bmatrix}. & . & +1\\ . & . & -1\\ +1 & -1 & 0\\ \end{bmatr... ...in{bmatrix}I_1\\ I_2\\ 0 \end{bmatrix} = \begin{bmatrix}0\\ 0\\ 0 \end{bmatrix}$$ (9.13)

During AC simulation the Y-parameter matrix of an ideal inductor with the inductance $L$ writes as follows.

$$Y = \begin{pmatrix}+\dfrac{1}{j\omega L} & -\dfrac{1}{j\omega L}\\ -\dfrac{1}{j\omega L} & +\dfrac{1}{j\omega L}\\ \end{pmatrix}$$ (9.14)

The scattering parameters of an ideal inductor with inductance $L$ writes as follows.

$$S_{11} = S_{22} = \frac{j\omega L}{2\cdot Z_0 + j\omega L} \\$$ (9.15)

$$S_{12} = S_{21} = 1-S_{11}$$ (9.16)

An ideal inductor is noise free.