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add formulae for regulation principle

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acereca 2018-08-03 21:23:14 +02:00
parent f9f2184e3e
commit 4ea048d8a2
2 changed files with 27 additions and 5 deletions
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2
parts/experiments.tex
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@ -171,7 +171,7 @@ Wanting to observe and characterize the voltage drop, happening between the Powe
\centering \centering
\hspace*{-.16\columnwidth} \hspace*{-.16\columnwidth}
\includegraphics[width=1.3\columnwidth]{../pitstop/20180727/ret_vdip.pdf} \includegraphics[width=1.3\columnwidth]{../pitstop/20180727/ret_vdip.pdf}
\caption{Voltage dip observed between PowerIt and HICANN, each point represents the state after enabling additional Reticles on the PowerWafer (\pyval{0})} \caption{Voltage dip observed between PowerIt and HICANN, each point represents the state after enabling additional Reticles on the PowerWafer ()}
\label{1v8dip} \label{1v8dip}
\end{figure} \end{figure}

30
parts/theory.tex
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@ -74,9 +74,10 @@ Our calculation is based on:
\subsection{1.8V Output Voltage} \subsection{1.8V Output Voltage}
\begin{align} \begin{align}
R_{SET} =& 1 / \left(\frac{1}{R_{potentiometer}} + \frac{1}{R_{parallel}}\right) + R_{series}\\ R_{potentiometer} = P_{val} \frac{10k\Omega}{256} \label{eq:rpot}\\
=& \frac{R_\text{potentiometer}\cdot R_\text{parallel}}{R_\text{potentiometer} + R_\text{parallel}} + R_\text{series}\\ R_{SET} =& 1 / \left(\frac{1}{R_{potentiometer}} + \frac{1}{R_{parallel}}\right) + R_{series}\nonumber\\
V_O =& \frac{30.1 k\Omega}{R_{SET} + 6.49 k\Omega} \cdot 0.7V + 0.7V =& \frac{R_\text{potentiometer}\cdot R_\text{parallel}}{R_\text{potentiometer} + R_\text{parallel}} + R_\text{series}\label{eq:rset}\\
V_O =& \frac{30.1 k\Omega}{R_{SET} + 6.49 k\Omega} \cdot 0.7V + 0.7V\label{eq:vout}
\end{align} \end{align}
\begin{figure}[H] \begin{figure}[H]
@ -135,10 +136,31 @@ This model allowes for two fixed resistance values and their respective currents
I_{ges} = n_{ret} \cdot I_{ret} I_{ges} = n_{ret} \cdot I_{ret}
\end{align} \end{align}
Therefore the voltage Differential as measured by a Voltmeter (\autoref{retmodel}) can be described as in \autoref{eq:vdip} Therefore the voltage Differential as measured by a Voltmeter (\autoref{retmodel}) can be described with \autoref{eq:vdip}
\begin{align} \label{eq:vdip} \begin{align} \label{eq:vdip}
V_{dip} =&\ V_{R_1} + V_{R_0} \nonumber\\ V_{dip} =&\ V_{R_1} + V_{R_0} \nonumber\\
=&\ R_1 \cdot I_{ret} + R_0 \cdot I_{ges}(n_{ret}) \nonumber\\ =&\ R_1 \cdot I_{ret} + R_0 \cdot I_{ges}(n_{ret}) \nonumber\\
=&\ I_{ret} \cdot \left( R_1 + R_0 \cdot n_{ret} \right) =&\ I_{ret} \cdot \left( R_1 + R_0 \cdot n_{ret} \right)
\end{align} \end{align}
Combining Equations \ref{eq:rset}, \ref{eq:vout} and %TODO
we gather \autoref{eq:fullreg}
\begin{align} \label{eq:fullreg}
P_{val} = \frac{
R_{par} \left[ \left( \frac{0.7V \cdot 30.1k\Omega}{V_{O}-0.7V} - 6.49k\Omega \right) - R_{ser}\right]
}{
R_{par} + \left( \frac{0.7V \cdot 30.1k\Omega}{V_{O}-0.7V} - 6.49k\Omega \right) - R_{ser}
}\cdot
\frac{256}{10k\Omega}
\end{align}
inside the code used for Regulation %TODO: reference
, \autoref{eq:fullreg} will be used to create a lookup table, while \autoref{eq:vout2} will be used at runtime, for which Equations \ref{eq:vdip} and \ref{eq:voff} are needed.
\begin{align} \label{eq:voff}
V_{dip} =& V_O - V_{off}\\
\Rightarrow V_O =& I_{ret} \cdot \left( R_1 + R_0 \cdot n_{ret} \right) + V{off}\label{eq:vout2}
\end{align}