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\section*{Lab 2}

The data gathered in this lab is listed in tables
1 and 2.

\begin{figure}[h]
    \centering
    \begin{tabular}{lcccccc}
        Node & $g_m$ (S) & $r_o$ ($\Omega$) & Gain & $I_\text{off} (A)$ & $I_\text{on} (A)$ & $I_\text{on}/I_\text{off}$ \\
        \hline
        longchannel pmos & 4.01E-04 & 1.36E+04 & 5.457 & 1.02E-11 & 1.36E-03 & 1.34E+08 \\
        longchannel nmos & 9.13E-04 & 1.31E+04 & 11.95 & 1.12E-11 & 3.22E-03 & 2.87E+08 \\
        50nm pmos & 2.11E-04 & 1.55E+04 & 3.259 & 8.84E-09 & 1.48E-04 & 1.68E+04 \\
        50nm nmos & 4.44E-04 & 1.31E+04 & 5.793 & 3.64E-09 & 3.12E-04 & 8.55E+04 \\
        16nmlp pmos & 1.62E-04 & 1.68E+04 & 2.72 & 2.30E-11 & 5.54E-05 & 2.40E+06 \\
        16nmlp nmos & 2.88E-04 & 1.33E+04 & 3.83 & 8.87E-12 & 9.13E-05 & 1.03E+07 \\
        16nmhp pmos & 3.33E-04 & 5.37E+03 & 1.787 & 9.22E-08 & 1.51E-04 & 1.64E+03 \\
        16nmhp nmos & 4.95E-04 & 5.56E+03 & 2.755 & 7.41E-08 & 2.17E-04 & 2.93E+03 \\
    \end{tabular}
    \label{fig:dc}
    \caption{Properties of various transistor sizes and types}
\end{figure}

\begin{figure}[h]
    \centering
    \begin{tabular}{lcccccc}
        Node & Oscillation Period (ps) & Oscillation Frequency (GHz) \\
        \hline
        longchannel & 1020 & 0.980 \\
        50nm & 222 & 4.49 \\
        16nmlp & 140 & 7.11 \\
        16nmhp & 32.2 & 31.0 \\
    \end{tabular}
    \label{fig:t}
    \caption{Switching frequency of 5-long inverter loop.}
\end{figure}

From these tables, we can see that smaller transistors have progressively smaller
gain, and progressively smaller ratios of on current $I_\text{on}$ and off current
$I_\text{off}$. We can explain the drop in gain with velocity saturation. At smaller
scales, short-channel effects make the relationship between current and gate voltage no longer
quadratic, but linear (and thus smaller in magnitude). This means that the transconductance
of a transistor decreases as it gets smaller, leading to lower gain. Furthermore,
due to short-channel effects such as impact ionization, current doesn't stop increasing
past the theoretical saturation point. This makes the transistor behave less like
a current source past saturation, and decreases gain.

Decreasing the size of the transistor does, however, significantly improve its timing characteristics.
While at 1$\mu m$ the 5-transistor loop we simulated has an oscillation frequency of 0.98GHz, the 16nm
high power loop can go as fast as 31GHz. This is likely due to the decreased capacitances at
this scale: it takes less time to charge up any part of the CMOS logic, including the outputs,
which makes it possible for subsequent transistors to respond faster, and so on.

For analog circuits, we care about gain, since we want to ensure that our signal is transmitted
properly through our circuit. Thus, bigger transistors are probably better suited for this application,
since they have higher (sometimes much higher) gains than smaller transistors. On the other hand,
from the digital side, the gain doesn't matter as much as the performance characteristics of the transistor,
which makes the smaller nodes (ones that we measured to have higher oscillation frequency) preferable. 

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