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\hyphenation{op-tical net-works semi-conduc-tor}% correct bad hyphenation here

\font\myfont=cmr12 at 15pt 
\title{\myfont VLSI Labs 1\&2 \\ Simple MOSFET \& CMOS Inverter Trends}
\author{Aidan Sharpe}

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\begin{document}
\maketitle

\section{Introduction}

\section{Modelling a MOSFET}

\section{The Noise Margin}
The noise margin is the amount of noise that a CMOS circuit can withstand without compromising the operation of the circuit\cite{VLSI_System_Design}. This region is necessary to create a buffer that prevents small amounts of noise from switching the logic. There are two noise margins: noise margin high (NM\textsubscript{H}) and noise margin low (NM\textsubscript{L}). 

The two noise margins are defined in terms of four key voltages on the voltage transfer curve (VTC) seen in figure \ref{fig:inv_vtc}: $V_\text{IL}$, $V_\text{IH}$, $V_\text{OL}$, and $V_\text{OH}$. $V_\text{IL}$ is defined as the lower input voltage where the slope of the VTC is -1, and $V_\text{IH}$ is defined as the upper input voltage meeting the same requirement. $V_\text{OL}$ is defined as the output voltage when the input voltage is equal to $V_\text{IH}$, and similarly, $V_\text{OH}$ is defined as the output voltage when the input voltage is equal to $V_\text{IL}$.

\begin{figure}[H]
	\center
	\includegraphics[width=0.4\textwidth]{graphics/inverter-noise-margin.png}
	\caption{The VTC and its derivative for a CMOS inverter with $w_p=240$[nm] and $w_n=120$[nm]}
	\label{fig:inv_vtc}.
\end{figure}

\begin{table}[H]
\center
\caption{Important VTC voltages}
\begin{tabular}{c | c}
	$V_\text{IL}$ & 2.357 \\
	\hline
	$V_\text{IH}$ & 3.531 \\
	\hline
	$V_\text{OL}$ & 0.683 \\
	\hline
	$V_\text{OH}$ & 4.118 \\
\end{tabular}
\end{table}

With these voltages now defined, the noise margin high was calculated using
\begin{equation}
	\text{NM}_\text{H} = V_\text{OH} - V_\text{IH},
\end{equation}
and noise margin low was calculated with
\begin{equation}
	\text{NM}_\text{L} = V_\text{IL} - V_\text{OL}.
\end{equation}

\section{Discussion}

\section{Conclusion}

\end{document}