%! TEX root = ../thesis.tex
\chapter{Experiments}
Now that the theoretical model exists, it can be checked with experiments.

\section{Characterization}

Now the Experiments to run, are those characterizing the behavior of the used hardware. These values can then later used for calibrating a PowerIt.

\subsection{sampling time}
First up was selecting an optimal number of cycles for which the adc will probe the to it at that moment connected pin, like described in \autoref{sec:adc}

In this case the uncalibrated measurement of input voltage was taken as example, and repeated with each of the possible 8 settings.

To be able to compare a reference voltage was measured with an external Voltmeter.
The resulting errors, from the set Voltage, can be seen in figures \ref{sampleticks1} and \ref{sampleticks2}

\begin{figure}[H]
    \centering
    \hspace*{-.175\columnwidth}
    \includegraphics[width=1.3\columnwidth]{./data/m04_cycledepends/cycledepends_20180529.pdf}
    \caption{plotted difference from set input voltage, and fitted linearly, May 29th 2018, $\approx$32\si\degree C}
    \label{sampleticks1}
\end{figure}

Both figures \ref{sampleticks1} and \ref{sampleticks2} contain the relative error of the measured voltage compared to the theoretical ,set input voltages. therefore the reference measurements (yellow), taken with an external multimeter, are not at 0.
Also shown are the calculated gain erors, which would need to be corrected for, in case of all 8 settings.

Important to note is the relative error in only the 0th case (both Figures), here the cycleTime-Setting was set to 0 and therefore the smallest available sampletimeof 3 Ticks. This excludes 0 a possible value to use. All other measurements are within errormargin of each other, and therefore the best candidate is a value of 1 resulting in a measuretime of 15 Ticks. 
\begin{figure}[H]
    \centering
    \hspace*{-.175\columnwidth}
    \includegraphics[width=1.3\columnwidth]{./data/m04_cycledepends/cycledepends_20180530.pdf}
    \caption{plotted difference from set input voltage, and fitted linearly, May 30th 2018, $\approx$25\si\degree C}
    \label{sampleticks2}
\end{figure}

Lastly the difference in disribution of measured values in both Figures, shows a Temperature dependency of the noisy data measured by the ADC.

\subsection{Voltages}

    These Measuremts are expected to be less accurate, the more components are contained in their respective measurement circuit. Because small errors will accumulate and in the case of 48V's be amplified.

    \subsubsection{48V Input}

    \begin{figure}[H]
        \centering
        \vspace{-1cm}
        \hspace*{-.16\columnwidth}
        \includegraphics[width=1.3\columnwidth]{../pitstop/20180815/calib_v48.pdf}
        \caption{Calibration of input voltage, plotted are a external measurement and internal values, vs the recalculated pin voltage based on the internal value and used default function (coefficients see \autoref{pitdb-example})}%
        \label{v48_precalib}
    \end{figure}

    When looking at calibrating the input voltage (fig. \ref{v48_precalib}), we can clearly see a relatively constand offset of $\approx$1V which can be the influence of an inaccurate resistor inside the voltage division and later amplification. The resulting calibrated polnomial coefficients (see \autoref{pitdb}, line 8) not only show an offset, but also some deviation in the incline and curve of our polynomial fit of 2nd degree (A Fit of second degree will be used in the complete calibration process).

    \subsubsection{9.6V Output}
    \begin{figure}[H]
        \centering
        \vspace{-1cm}
        \hspace*{-.16\columnwidth}
        \includegraphics[width=1.3\columnwidth]{../pitstop/20180815/calib_v10.pdf}
        \caption{TODOF}
        \label{v10_precalib}
    \end{figure}

    The 9.6V Calibration shows only a slight deviation of the internal values and the reference measurement, which results in a list of coefficients (fig. \ref{pitdb}, line 7), very similar to those set in the theoretical defaults.

    \begin{align}
        \sigma_{9.6V} \approx 5.3\%
    \end{align}

    this difference is explained by the simple voltage division used for our circuitry, and no amplification, as seen in the circuit for input voltage.

    \subsubsection{1.8V Output}

    \begin{figure}[H]
        \centering
        \vspace{-1cm}
        \hspace*{-.15\columnwidth}
        \includegraphics[width=1.3\columnwidth]{./data/m03_poticalib/adccalib_02.pdf}
        \caption{TODOF}%
        \label{fig:v18_precalib}
    \end{figure}


\subsection{Currents}

    \subsubsection{48V Input}
        \begin{figure}[H]
            \centering
            \hspace*{-.16\columnwidth}
            %TODO: transparent
            \includegraphics[width=1.3\columnwidth]{./pitstop/20180809/calib_i48.pdf}
            \caption{Calibration of input current adcs 21.06.2018}
            \label{}
        \end{figure}

    \subsubsection{9.6V Output}

    \subsubsection{1.8V Output}
        \begin{figure}[H]
            \centering
            \hspace*{-.15\columnwidth}
            %\vspace*{-.02\paperheight}
            %\includegraphics[width=\columnwidth]{pitstop/20180702/i18ana_nocalib.pdf}
            %\includegraphics[width=\columnwidth]{pitstop/20180702/i18digi_nocalib.pdf}
            \includegraphics[width=1.3\columnwidth]{./pitstop/20180809/calib_i18.pdf}
            \caption{Pre Calibration Measurement of Output Current at the 1.8V Analog and Digital Terminal (2.7.2018)}
            \label{precalib18iana}
        \end{figure}


\section{after Calibration}

\minty[minted options={lastline=10}, label={pitdb}]{yaml}{./pitstop/pitdb.yaml}

\subsection{Voltages}

    \subsubsection{48V Input}

    \subsubsection{9.6V Output}

    \subsubsection{1.8V Output}

\subsection{Currents}

    \subsubsection{48V Input}

    \subsubsection{9.6V Output}

    \subsubsection{1.8V Output}
        \begin{figure}[H]
            \centering
            \hspace*{-.16\columnwidth}
            \includegraphics[width=1.3\columnwidth]{./pitstop/20180702/i18ana_postcalib.pdf}
            \caption{Post Calibration Measurement of Output Current at the 1.8V Analog Terminal (29.06.2018}
            \label{postcalib18iana}
        \end{figure}

\section{1.8V Regulation}

\subsection{Characterization of Dropoff}

Wanting to observe and characterize the voltage drop, happening between the PowerIt output terminal and the HICANN Chips, first the in figure \ref{1v8dip} monitored behavior can be seen.

\begin{figure}[H]
    \centering
    \hspace*{-.16\columnwidth}
    \includegraphics[width=1.3\columnwidth]{./pitstop/20180807/ret_vdip.pdf}
    \caption{Voltage dip observed between PowerIt and HICANN, each point represents the state after enabling additional Reticles on the PowerWafer ()}
    \label{1v8dip}
\end{figure}

\subsection{after Numerical-Correction}

The initial approach is a numerical. Through derivation from figures \ref{1v8dip} and \ref{v18_precalib} we can plot a function which maps the measured output current to a corresponding potentiometer setting (fig. \ref{numericalreg}) for which the observed dropoff will be mitigated (or at least near that). Also important is that it is not possible to use non interger values for the potentiometer setting.

\begin{figure}[H]
    \centering
    \hspace*{-.16\columnwidth}
    \includegraphics[width=1.3\columnwidth]{./pitstop/20180807/ret_regulation.pdf}
    \caption{Potentiometer Setting (discrete integer), derived from ouput current (discrete floating point). }
    \label{numericalreg}
\end{figure}

Fitting these values, with a polynomial of 2nd degree, we obtain:
\begin{align}
    P_{val} =& \lfloor m_2 \cdot I_{ana}^2 + m_1 \cdot I_{ana} + m_0 \rceil\\
    m_2 =& 51.390262 \frac 1 A\\ 
    m_1 =& -0.263850\frac 1 A\nonumber\\
    m_0 =& 0.000258\frac 1 A\nonumber
\end{align}

Which is the numeraical solution if the only desired voltage on HICAN Chips is 1.8V. But if we want to change these, we need a more general solution.

Assuming the 2nd order Term to be small enough, we can assume a linear proportionality between the current and voltage:

\begin{align}
I_{ana, eff} = I_{ana} - \frac{V_{out}-1.8V}{c}
\end{align}

where c is obtained from the linear fit (incline) in figure \ref{1v8dip}

\begin{align}
    c = 71.6978\cdot 10^{-3} \frac V A
\end{align}

\begin{figure}[H]
    \centering
    \hspace*{-.1\columnwidth}
    \includegraphics[width=1.2\columnwidth]{./pitstop/20180807/reticle_pic}
    \caption{ret5wafer}
    \label{fig:wafer-ret5}
\end{figure}
\begin{figure}[H]
    \centering
    \hspace*{-.15\columnwidth}
    \includegraphics[width=1.3\columnwidth]{./pitstop/20180807/reticle_corr}
    \caption{ret5}
    \label{fig:ret5}
\end{figure}

\begin{align}
    \pyval{r0_from_neighbor}\\
    \pyval{r0_from_farthest}\\
    \pyval{r0mean}\\
    \pyval{r0meancorr}
\end{align}

\begin{align}
    \pyval{r1_from_neighbor}\\
    \pyval{r1_from_farthest}\\
    \pyval{r1mean}\\
    \pyval{r1meancorr}
\end{align}

\section{Pitfalls}

