181 lines
8.9 KiB
TeX
181 lines
8.9 KiB
TeX
%! 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*} values 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*} values 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{31.7}{\milli\volt} (\(\approx\) \SI{.33}{\%}).
|
|
It is also possible to see a systematic error in \autoref{fig:postcalib10v}.
|
|
This error could be corrected, but requires further iterations of the calibration procedure.
|
|
Additional iterations would allow for a reduction of \(\Delta V\), up to a value of \SI{24.5}{\milli\volt} (\(\approx\) \SI{.25}{\%}).
|
|
|
|
In comparison to this, the \SI{1.8}{\volt} measurement should have a bit better accuracy because of the even simpler circuit.
|
|
|
|
\begin{align*}
|
|
\SI{.33}{\%} \cdot \SI{1.8}{\volt} \approx \SI{5.9}{\milli\volt}\\
|
|
\SI{.25}{\%} \cdot \SI{1.8}{\volt} \approx \SI{4.5}{\milli\volt}
|
|
\end{align*}
|
|
|
|
And also the accuracy of measuring \SI{48}{\volt} should be worse than \SI{24}{\milli\volt}, again because of the circuits complexity.
|
|
|
|
\begin{align*}
|
|
\SI{.33}{\%} \cdot \SI{48}{\volt} \approx \SI{158}{\milli\volt}\\
|
|
\SI{.25}{\%} \cdot \SI{48}{\volt} \approx \SI{120}{\milli\volt}
|
|
\end{align*}
|
|
|
|
\section{Regulation}\label{sec:withoutreg}
|
|
|
|
These are the obtained results from attempting to regulate the \SI{1.8}{\volt} terminals.
|
|
|
|
\subsection{Without Regulation}
|
|
|
|
Before the regulation could be attempted some parameters were needed to complete the SWRM, see equations~\ref{eq:iretmeancorr},~\ref{eq:r0} and~\ref{eq:r1}.
|
|
With these values and their respective (error) ranges the in \autoref{fig:reg} found plot could be created.
|
|
|
|
\begin{figure}[H]
|
|
\centering
|
|
\vspace{-.5cm}
|
|
\hspace*{-.16\columnwidth}
|
|
\includegraphics[width=1.3\columnwidth]{../pitstop/20180828/reticle_variance.pdf}
|
|
\vspace{-.5cm}
|
|
\caption{%
|
|
Plot of the expected range of V\(_\text{drop}\) for different current draw. This result is the expected spread without any regulation. Shown are the range for 98\% and 50\% of reticles, as well as the mean V\(_\text{drop}\) for all reticles.
|
|
}%
|
|
\label{fig:reg}
|
|
\end{figure}
|
|
|
|
In \autoref{fig:reg} the expected spread of V\(_\text{drop}\) can be found.
|
|
This spread is the worst case V\(_\text{drop}\) distribution.
|
|
The reason for that is that with a regulated voltage a constant V\(_\text{drop}\) is expected.
|
|
This applies to all currents up until \(\approx\) \SI{80}{\ampere}, becase from there the regulation would not work anymore and V\(_\text{drop}\) would behave like in the unregulated case.
|
|
|
|
\subsection{With Regulation}
|
|
|
|
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/20180828/ret_vdip.pdf}
|
|
\vspace{-1cm}
|
|
\caption{%
|
|
Observed reticle voltages V\(_\text{ret}\) before or 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 placed central.
|
|
}%
|
|
\label{fig:postreg}
|
|
\end{figure}
|
|
|
|
In \autoref{fig:postreg} 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 I\(_\text{thresh}=\SI{81.3}{\ampere}\).
|
|
There the minmal potentiometer setting is used.
|
|
From here V\(_\text{drop}\) behaves the same as without regulation.
|
|
|
|
Secondly V\(_\text{drop}\) for different reticles is different.
|
|
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.
|
|
|
|
The residuals observed are the result of the I\(_\text{ana}\) > I\(_\text{thresh}\) not regulated V\(_\text{drop}\).
|
|
|
|
Also, the expected behavior from \autoref{sec:withoutreg} can be observed.
|
|
|
|
Additionally if the range of I\(_\text{ana}\) > I\(_\text{thresh}\) is observed, V\(_\text{drop}\) does not increase by more than about \SI{30}{\milli\volt}.
|
|
|
|
|
|
\subsection{Distance Wafer Resistance Model (DWRM)}\label{sec:dwrm}
|
|
|
|
So far, the discussed measurements and SWRM have been enough to create a first iteration regulation mechanism.
|
|
Until now assumptions like a constant R\(_0\) over the complete wafer, have driven the creation of equations to satisfy this model.
|
|
They also led to observable inaccuracies, as seen in \autoref{eq:r0}.
|
|
Although the SWRM approximates the real world, it is not exact enough.
|
|
To further develop a model that could describe the real world setup in a better way, the next model would have to describe e.g. a different R\(_0\).
|
|
|
|
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=.45\columnwidth]{tikz/reticlepower_2}
|
|
\caption{Modified model of the to measure resistances and their currents.
|
|
Similar to SWRM \(R_0\) describes the resistance of the shortest 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 AnaB.}%
|
|
\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=1.1\columnwidth]{../pitstop/20180821/reticel_rtheo.pdf}
|
|
\vspace{-.5cm}
|
|
\caption{Distances of reticles to the nearest voltage supplying connection for DWRM, distance is normed to the reticle-side length}%
|
|
\label{fig:retmodelrdist}
|
|
\end{figure} |