%! TEX root = ../thesis.tex
\chapter{Results}

In this chapter all results from the experiments, as well as reasons will be discussed.

\section{Calibration\label{calib}}

This calibration process yielded some workflows for use inside the system as well as calibration values for the used PowerIt. 

\subsection{Calibration-Database}

The obtained calibration values for the in these experiments used PowerIt, are combined in \autoref{pitdb}.

\begin{listing}[H]
    \centering
    \minty[%
        minted options={lastline=10}%
    ]{yaml}{pitstop/pitdb.yaml}
    \codecaption{
        PITDB entry for B05 PowerIt.
        \mintinline{cpp}{id} is obtained by the firmware and unique to each STM32Chip.
        The \mintinline{cpp}{name} corresponds to the label on each PowerIt.
        All \mintinline{cpp}{poly*} are all polynomial coefficients in order of 0th degree to 2nd degree. 
    }%
    \label{pitdb}
\end{listing}

And to compare, the values in \autoref{lst:pitdb-example} are theoretical values, obtained from all equations in \autoref{ch:theory}.


\begin{listing}[H]
    \begin{mintyfig}[]{yaml}
        ---
        uuid: 'default'
        name: 'Bxx'
        poly18i: [-3.0, 25.0, 0.0]
        poly48i: [0.0, 227.27, 0.0]
        poly10v: [0.0, 4.0, 0.0]
        poly18v: [0.0, 1.0, 0.0]
        poly48v: [0.0, 27.386, 0.0]

    \end{mintyfig}
    \codecaption{%
        Default PITDB entry for any PowerIt.
        All \mintinline{cpp}{poly*} are all polynomial coefficients in order of 0th degree to 2nd degree. 
    }%
    \label{lst:pitdb-example}
\end{listing}

\subsection{Accuracy}

To obtain an accuracy for the internal measurements, the experimental sweeps can be repeated after calibration.
One example of a calibrated measurement can be seen in \autoref{fig:postcalib10v}.

\begin{figure}[H]
    \centering
    \vspace{-1.5cm}
    \hspace*{-.15\columnwidth}
    \includegraphics[width=1.3\columnwidth]{../pitstop/20180825/postcalib_10v.pdf}
    \vspace{-1cm}
    \caption{%
        Voltages after calibration.
        Sweep from \SIrange{43.2}{52.8}{\volt} input voltage resulting in a range from \SIrange{8.64}{10.56}{\volt}.
        The errors in the bottom diagram show the differences between reference and PIT values.
    }%
    \label{fig:postcalib10v}
\end{figure}

This repeats the calibration measurement for \SI{9.6}{\volt}.
Here quite similar values can be observed, with a maximum \(\Delta V\) of around \SI{31.676}{\milli\volt}. 
It is also possible to see a systematic error in \autoref{fig:postcalib10v}.
This error could be corrected, but requires quite some time investment.
It would allow for a reduction of \(\Delta V\), up to a value of \SI{24.456}{\milli\volt}.

This result is similar to others, and for all it would be possible to achieve a bit better fits.


\section{Regulation}

    \subsection{Resulting Observation}

        To verify the regulation is working and to see if the prediction in \autoref{fig:regswrm} is correct new values were measured.
        These Values are the voltages with regulation enabled at different Reticles (see \autoref{fig:postreg}).

        \begin{figure}[H]
            \centering
            \vspace{-1cm}
            \hspace*{-.15\columnwidth}
            \includegraphics[width=1.3\columnwidth]{../pitstop/20180825/ret_vdip.pdf}
            \vspace{-1cm}
            \caption{%
                Observed AnaB voltages after regulation at multiple reticles.
                Reticle \#40 shows the best-case scenario with the least amount of V\(_\text{drop}\).
                Reticle \#5 is a worst-case scenario, with the highest V\(_\text{drop}\) while still being a usable reticle.
            }%
            \label{fig:postreg}
        \end{figure}

        In this figure three different reticles (\#5, \#29 and \#40) were measured.
        Observable is, that firstly the regulation, which was set to achieve \SI{1.8}{\volt} is working until I\(_{ana}\) is at about \SI{80}{\ampere}.
        There the minmal potentiometer setting is used.
        From here further regulation, with the same hardware, is impossible.

        Secondly the voltages for different reticles is different and not equal.
        This was one of the assumptions in the SWRM.
        To describe that behavior a distance based model (\autoref{sec:dwrm}: DWRM) could be the solution.

        And third, under the assumption of a constant fit (up to I\(_{ana} \approx \SI{80}{\ampere}\)) a systematic error can be observed.

        \begin{figure}[H]
            \centering
            \includegraphics[width=\columnwidth]{../pitstop/20180821/reticle_variance.pdf}
            \caption{%
            }%
            \label{fig:reg}
        \end{figure}

    \subsection{Distance Wafer Resistance Model (DWRM)}\label{sec:dwrm}

        Although the through SWRM gained functions approximate the real world, it is not exact enough.
        In a wafer, the distance between reticles and voltage connector (see \autoref{fig:mainpcb}) are resulting in additional resistance.

        Therefore the DWRM could be adapted.
        Circuit~\ref{fig:retmodelshell} visualizes a model, in which each different distance from the voltage connector, is classified with an additional resistance.

        \begin{figure}[H]
            \centering
            \includegraphics[width=.5\columnwidth]{tikz/reticlepower_2}
            \caption{Modified model of the to measure resistances and their currents.
            Similar to SWRM \(R_0\) describes the resistance of a connection between the PowerIt Output, up to the FET (depicted as switch), while \(R_1\) is a Resistance between FET and Reticles. But additionally \(R_{0+}\) described a Resistance, that depends on the distance between reticle and voltage connector. 
            The measurement is done between output terminals on the PowerIt and pins on a Analog readout board}%
            \label{fig:retmodelshell}
        \end{figure}

        With this model the voltage is now expected to change depending on the reticles distance instead of being the same. The distances inside a wafer are visualized in \autoref{fig:retmodelrdist}

        \begin{figure}[H]
            \centering
            \hspace*{-.14\columnwidth}
            \includegraphics[width=1.2\columnwidth]{../pitstop/20180821/reticel_rtheo.pdf}
            \vspace{-1cm}
            \caption{Distances of reticles to the nearest voltage supplying connection for DWRM, distance is in reticle-side length}%
            \label{fig:retmodelrdist}
        \end{figure}

        Additionally this model is a better fit to the already observed voltage distribution in \autoref{fig:wrdist}.