Calibration formulas

doc/Makefile

 TEX=tdc.tex
 
+PDF=$(TEX:.tex=.pdf)
 AUX=$(TEX:.tex=.aux)
 LOG=$(TEX:.tex=.log)
 

doc/tdc.tex

@@ -18,6 +18,31 @@
 \setlength{\parskip}{5pt}
 \maketitle{}
 \section{Specifications}
-TODO
+
+\section{Calibration mechanism}
+In the formulas below:
+\begin{itemize}
+\item $T_{sys}$ is the system clock period.
+\item $H(n)$ is the number of hits in the histogram for bin $n$.
+\item $W(n)$ is the width of bin $n$.
+\item $C = \displaystyle\sum\limits_{n} H(n)$ is the total number of hits in the histogram.
+\item $R(n)$ is the time stamp of an event whose signal propagated up to bin $n$. The LUT contains the function $R$.
+\item $f$ (respectively $f_{0}$) is the current (respectively reference) frequency of the online calibration ring oscillator.
+\end{itemize}
+
+\subsection{Offline calibration}
+\begin{equation}
+W_{0}(n) = \frac{H(n)}{C} \cdot T_{sys}
+\end{equation}
+
+\begin{equation}
+R_{0}(n) = \displaystyle\sum\limits_{i=0}^{n}{W_{0}(i)} = \frac{T_{sys}}{C} \cdot \displaystyle\sum\limits_{i=0}^{n}{H(i)}
+\end{equation}
+
+\subsection{Online calibration}
+
+\begin{equation}
+R(n) = \frac{f_{0}}{f} \cdot R_{0}(n)
+\end{equation}
 
 \end{document}