From 4ea048d8a2f3d0138cf9b651bfdff970d2696d1b Mon Sep 17 00:00:00 2001
From: acereca <acereca@outlook.de>
Date: Fri, 3 Aug 2018 21:23:14 +0200
Subject: [PATCH] add formulae for regulation principle

---
 parts/experiments.tex |  2 +-
 parts/theory.tex      | 30 ++++++++++++++++++++++++++----
 2 files changed, 27 insertions(+), 5 deletions(-)

diff --git a/parts/experiments.tex b/parts/experiments.tex
index 7e719f8..7382cab 100644
--- a/parts/experiments.tex
+++ b/parts/experiments.tex
@@ -171,7 +171,7 @@ Wanting to observe and characterize the voltage drop, happening between the Powe
     \centering
     \hspace*{-.16\columnwidth}
     \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}
 \end{figure}
 
diff --git a/parts/theory.tex b/parts/theory.tex
index 1297a33..40f82c4 100644
--- a/parts/theory.tex
+++ b/parts/theory.tex
@@ -74,9 +74,10 @@ Our calculation is based on:
 \subsection{1.8V Output Voltage}
 
 \begin{align}
-    R_{SET} =& 1 / \left(\frac{1}{R_{potentiometer}} + \frac{1}{R_{parallel}}\right) + R_{series}\\
-    =& \frac{R_\text{potentiometer}\cdot R_\text{parallel}}{R_\text{potentiometer} + R_\text{parallel}} + R_\text{series}\\
-    V_O =& \frac{30.1 k\Omega}{R_{SET} + 6.49 k\Omega} \cdot 0.7V + 0.7V
+    R_{potentiometer} = P_{val} \frac{10k\Omega}{256} \label{eq:rpot}\\
+    R_{SET} =& 1 / \left(\frac{1}{R_{potentiometer}} + \frac{1}{R_{parallel}}\right) + R_{series}\nonumber\\
+    =& \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}
 
 \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}
 \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}
     V_{dip} =&\ V_{R_1} + V_{R_0} \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)
 \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}
+