It is expected that larger copper pads have bigger capacitance. Comparing the two Figures \ref{hva} and \vref{hvp}, we may conjecture that the loss of efficiency in \textit{zone P} is due to the bigger pads capacitance, which could cause noise and channel coupling.\\

Being noise proportional to the electrode capacitance \cite{aspell-cmsw}, we decided to run a noise measurement for each channel. This way we could collect information about the capacitance of each readout pad.\\
\begin{figure}%[!htbp]
	\centering
	\includegraphics[width=12cm]{Images/calpulse-small}
	\caption{How a calibration pulse scan works}
	\label{calpulse}
\end{figure}

An off-beam analysis was thus performed, injecting calibration charge pulses of increasing amplitude to all of the pads via the VFAT2 chips, and fitting the \textit{S-Curve}s of each channel with an \texttt{erf} function.\\

The \texttt{erf} function, also known as \textbf{Gaussian error function}, is defined as:
$$
\mbox{erf}(x) = \dfrac{2}{\sqrt{\pi}} \int_0^x e^{-t^2}dt
$$
After we define a threshold for the VFAT2 chips, and we start injecting charge, as long as the injected potential ($Q=CV$) is under threshold ($\Delta V < th$) the output of the comparator is low. Then, like an \textbf{heaviside step function}, it should go high as soon as the pulse amplitude overcomes the threshold. Actually, if we take the contribution of the noise to the shapes of the calibration pulses into account (see \figurename~\vref{calpulse}), we can only predict that the output of the comparator goes high at a certain input charge value with a Gaussian probability, centered around the given threshold value.\\
%\begin{figure}%[!htbp]
%	\centering
%	\includegraphics[width=12cm]{Images/calpulse}
%	\caption{How a calibration pulse scan works}
%	\label{calpulse}
%\end{figure}

An \textbf{S-Curve} is a histogram of hits for a given threshold, counted while varying the injected charge \cite{vfat-man}; it corresponds to the shape of the \texttt{erf} function. Indeed, the same plot can be obtained by integrating the Gaussian distribution of the noise for any VFAT2 channel. Once an S-Curve is fitted with an \texttt{erf} function, the noise distribution \textit{sigma} is the same as that of the \texttt{erf} function, and the mean value corresponds to the threshold potential\footnote{ROOT stores the fit functions as objects, and makes their parameters (mean, RMS, \textit{sigma}, and so on) available via calls to the objects themselves. To compute the \textit{sigma}s of \figurename~\vref{s-allch}, we fitted the S-Curve of each channel with \texttt{erf} functions and plotted their \textit{sigma} parameters.}.\\
\begin{figure}%[!htbp]
	\centering
	\subfigure[S-Curve]	
	{\includegraphics[width=6.6cm]{Images/scurve-nocolors}\label{s-1ch}}
	\hspace{2mm}				% COLOURED IMAGES EXIST
	\subfigure[S-Curve \textit{sigma} vs pad largeness]
	{\includegraphics[width=6.6cm]{Images/scurve_width_ch-nocolors}\label{s-allch}}
	\caption{An S-Curve fitted by an \texttt{erf} function. On the right, the standard deviation (\textit{sigma}) of the pad's S-Curve is plotted as a function of the radial position of the pad in the detector, and thus as a function of its increasing largeness.}
	\label{scurve}
\end{figure}

\figurename~\vref{s-allch} allows us to state that the lack of efficiency of \textit{zone P} is not caused by parasitic capacitance of its pads: the larger pads (those at the right side of the plot) do not show a significant increase of noise.\\

According to VFAT2 specifications in \cite{aspell-cmsw}, each channel should have
$$
Q_{noise}^{EQ} = 400\mbox{e}^- + 50\dfrac{\mbox{e}^-}{pF}
$$
where $ Q_{noise}^{EQ} $ is the equivalent charge due to the noise, and the picofarads refer to the channel input capacitance. Assuming $300 \div 400 $ electrons per VFAT2 DAC step bin, with an S-Curve sigma $\sigma \simeq 7$ for all channels we can estimate an average input capacitance of about $48pF$.\\

Another reason for the difference in response between \textit{point P} and \textit{point A} is to be found. More tests will be performed as soon as possible.