An isolator is a one-way two-port, transporting incoming waves lossless from the input (port 1) to the output (port 2), but dissipating all waves flowing into the output. The ideal isolator with reference impedances $ Z_1$ (input) and $ Z_2$ (output) is determined by the following Z parameters (for DC and AC simulation).

$\displaystyle Z_{11} = Z_1 \qquad Z_{12} = 0$ (9.88)

$\displaystyle Z_{21} = 2\cdot\sqrt{Z_1\cdot Z_2} \qquad Z_{22} = Z_2$ (9.89)

A more useful MNA representation is with Y parameters.

$\displaystyle (\underline{Y}) = \begin{pmatrix}\dfrac{1}{Z_1} & 0 \\ \dfrac{-2}{\sqrt{Z_1\cdot Z_2}} & \dfrac{1}{Z_2} \end{pmatrix}$ (9.90)

Isolator with reference impedance $ Z_1$ (input) and $ Z_2$ (output) and temperature $ T$:

$\displaystyle (\underline{C}_Y) = 4\cdot k\cdot T\cdot \begin{pmatrix}\dfrac{1}{Z_1} & 0 \\ \dfrac{-2}{\sqrt{Z_1\cdot Z_2}} & \dfrac{1}{Z_2} \\ \end{pmatrix}$ (9.91)

With the reference impedance of the input $ Z_1$ and the one of the output $ Z_2$, the scattering parameters of an ideal isolator writes as follows.

$\displaystyle S_{11} = \frac{Z_1-Z_0}{Z_1+Z_0}$ (9.92)

$\displaystyle S_{12} = 0$ (9.93)

$\displaystyle S_{22} = \frac{Z_2-Z_0}{Z_2+Z_0}$ (9.94)

$\displaystyle S_{21} = \sqrt{1-(S_{11})^2}\cdot\sqrt{1-(S_{22})^2}$ (9.95)

Being on temperature $ T$, the noise wave correlation matrix of an ideal isolator with reference impedance $ Z_1$ and $ Z_2$ (input and output) writes as follows.

$\displaystyle (\underline{C}) = \frac{4\cdot k\cdot T\cdot Z_0}{(Z_1+Z_0)^2}\cd...
...Z_1}{Z_0+Z_2} & Z_2\cdot\left(\dfrac{Z_1-Z_0}{Z_2+Z_0}\right)^2\\ \end{pmatrix}$ (9.96)

This document was generated by Stefan Jahn on 2007-12-30 using latex2html.