In microwave circuits described by scattering parameters, it is advantageous to regard noise as noise waves [5]. The noise characteristics of an n-port is then defined completely by one outgoing noise wave $ \underline{b}_{noise,n}$ at each port (see 2-port example in fig. 2.1) and the correlation between these noise sources. Therefore, mathematically, you can characterize a noisy n-port by its $ n\times n$ scattering matrix $ (\underline{S})$ and its $ n\times n$ noise wave correlation matrix $ (\underline{C})$.

\begin{displaymath}\begin{split}(\underline{C}) = \begin{pmatrix}\overline{\unde...
..._{n2} & \ldots & \underline{c}_{nn}\\ \end{pmatrix} \end{split}\end{displaymath} (2.1)

Where $ \overline{x}$ is the time average of $ x$ and $ \underline{x}^*$ is the conjugate complex of $ \underline{x}$. Noise correlation matrices are hermitian matrices because the following equations hold.

Im$\displaystyle \left(\underline{c}_{nn}\right) =$   Im$\displaystyle \left(\overline{\left\vert b_{noise,n}\right\vert^2}\right) = 0$ (2.2)

$\displaystyle \underline{c}_{nm} = \underline{c}_{mn}^*$ (2.3)

Where Im$ (\underline{x})$ is the imaginary part of $ \underline{x}$ and $ \vert\underline{x}\vert$ is the magnitude of $ \underline{x}$.

Figure 2.1: signal flow graph of a noisy 2-port

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