Resistor

For DC and AC simulation an ideal resistor with resistance $ R$ yields:

$\displaystyle Y = \dfrac{1}{R} \cdot \begin{pmatrix}1 & -1 \\ -1 & 1 \\ \end{pmatrix}$ (9.3)

The noise correlation matrix at temperature $ T$ yields:

$\displaystyle (\underline{C}_Y) = \frac{4\cdot k\cdot T}{R} \cdot \begin{pmatrix}1 & -1 \\ -1 & 1 \\ \end{pmatrix}$ (9.4)

The scattering parameters normalized to impedance $ Z_0$ writes as follows.

$\displaystyle S_{11} = S_{22} = \frac{R}{2\cdot Z_0+R} \\ $ (9.5)

$\displaystyle S_{12} = S_{21} = 1-S_{11} = \frac{2\cdot Z_0}{2\cdot Z_0+R}$ (9.6)

Being on temperature $ T$, the noise wave correlation matrix writes as follows.

$\displaystyle (\underline{C}) = k\cdot T\cdot\frac{4\cdot R\cdot Z_0}{(2\cdot Z_0+R)^2}\cdot \begin{pmatrix}1 & -1\\ -1 & 1\\ \end{pmatrix}$ (9.7)

The noise wave correlation matrix of a parallel resistor with resistance $ R$ writes as follows.

$\displaystyle (\underline{C}) = k\cdot T\cdot\frac{4\cdot R\cdot Z_0}{(2\cdot R+Z_0)^2}\cdot \begin{pmatrix}1 & 1\\ 1 & 1\\ \end{pmatrix}$ (9.8)

The noise wave correlation matrix of a grounded resistor with resistance $ R$ is a matrix consisting of one element and writes as follows.

$\displaystyle (\underline{C}) = k\cdot T\cdot\frac{4\cdot R\cdot Z_0}{(R+Z_0)^2}$ (9.9)


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