"Finding $g_{m}(c_{iss})$ and $f_{T}(c_{iss})$"

Finding $g_{m}(c_{iss})$ and $f_{T}(c_{iss})$

Noise Figure Budget

I can't use the entire noise budget for the input stage but I know this will be the bulk of the noise, so I will use the largest fraction of what is left of the noise budget:

\begin{equation} \alpha_{NF con}=0.25 \end{equation} \begin{equation} NF_{con}=0.4375\,\left[ \mathrm{dB}\right] \end{equation}

Design Equation Formulation:

\begin{equation} NF_{con}=NF \alpha_{NF con} \left(1 - \alpha_{NF fb}\right)\,\left[ \mathrm{dB}\right] \end{equation}

$g_m$ as a function of $c_{iss}$

\begin{equation} g_{m}=\frac{c_{iss XN} \left(- 3.886 \cdot 10^{92} c_{iss XN}^{2} - 2.389 \cdot 10^{70}\right)}{4.418 \cdot 10^{79} c_{iss XN}^{2} - 3.323 \cdot 10^{71} c_{iss XN} + 1.004 \cdot 10^{58}}\,\left[ \mathrm{\mathtt{\text{S}}}\right] \end{equation}

Finding $g_{m}$ and ranges for $c_{iss}$ which make $g_m>0$

From the roots of the denominator the minimum and maximum of $c_{iss}$ is found as:

\begin{equation} c_{iss min}=3.021 \cdot 10^{-14}\,\left[ \mathrm{F}\right] \end{equation} \begin{equation} c_{iss max}=7.521 \cdot 10^{-9}\,\left[ \mathrm{F}\right] \end{equation}

Finding $f_{T}$ as a function of $c_{iss}$

The transit frequency of my cmos model is:

\begin{equation} f_{T}=\frac{0.5 g_{m XN}}{\pi c_{iss XN}}\,\left[ \mathrm{Hz}\right] \end{equation}

For the required noise figure I have the following equation:

\begin{equation} f_{T}=\frac{- 1.943 \cdot 10^{92} c_{iss XN}^{2} - 1.195 \cdot 10^{70}}{\pi \left(4.418 \cdot 10^{79} c_{iss XN}^{2} - 3.323 \cdot 10^{71} c_{iss XN} + 1.004 \cdot 10^{58}\right)}\,\left[ \mathrm{Hz}\right] \end{equation}

Plots:

Go to Balanced-Cross-Coupled-MOSFET-Noisy-Nullor-Analysis_index

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Last project update: 2023-11-25 20:52:48