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\title{Amplitude Calibration \\
  IRAM Plateau de Bure Interferometer}
\author{S. Guilloteau$^{1}$}
\date{Document probably older than you think}
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\begin{displaymath}
Tcal = C_{eff} \frac{F_{eff} * (1+Gain\_i) * T_{atm}}
{B_s * ( 1 - F_{eff} * \frac{T_{cab}-T_{atm}}{T_{cab}-T_{emi}})}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline922}%
$T_{cab} = 290 K$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline924}%
$T_{atm} = 240 K$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline926}%
$T_{emi} = 50 K$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline928}%
$C_{eff} =
  1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath343}%
\begin{displaymath}  
Tcal = \frac{240 * (1+Gain\_i) * F_{eff}}{B_s * (1 - 0.2*F_{eff})}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmldisplayA{displaymath352}%
\begin{displaymath}
T_{emi} = (1.-F_{eff})*T_{cab} + F_{eff} * C^{te} * Water * Air\_mass
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmldisplayA{displaymath369}%
\begin{displaymath}
\frac{\partial Tcal}{\partial Trec} = 
\frac{\partial Tcal}{\partial T_{emi}} \frac{\partial T_{emi}}{\partial Trec} 
+ \frac{\partial Tcal}{\partial Tau} \frac{\partial Tau}{\partial Trec} 
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath381}%
\begin{displaymath}
\frac{\partial Tcal}{\partial T_{emi}} 
= \frac{Tcal}{T_{emi}-T_{load}} 
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath388}%
\begin{displaymath}
\frac{\partial T_{emi}}{\partial Trec} = -1 + \frac{T_{emi}+Trec}
{T_{load}+Trec}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath394}%
\begin{displaymath}
\frac{\partial Tcal}{\partial T_{emi}} \frac{\partial T_{emi}}{\partial Trec} 
= \frac{Tcal}{T_{load}+Trec}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath402}%
\begin{displaymath}
\frac{\partial Tcal}{\partial Tau} = Air\_mass * Tcal
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath406}%
\begin{displaymath}
\frac{\partial Tau}{\partial Trec} =
\frac{\partial Tau}{\partial T_{emi}} \frac{\partial T_{emi}}{\partial Trec} 
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath414}%
\begin{displaymath}
\frac{\partial Tau}{\partial Trec} =
\frac{1}{Air\_mass * T_{atm} * F_{eff}} \frac{\partial T_{emi}}{\partial Trec} 
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath423}%
\begin{displaymath}
\frac{\partial Tcal}{\partial Tau} \frac{\partial Tau}{\partial Trec} =
\frac{Tcal}{T_{atm} * F_{eff}} \frac{T_{emi}-T_{load}}{T_{load}+Trec}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath435}%
\begin{displaymath}
\frac{1}{Tcal} \frac{\partial Tcal}{\partial Trec} = 
\frac{T_{atm}*F_{eff} - T_{load} + T_{emi}}
{F_{eff}*T_{atm}*(T_{load} + Trec)}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline960}%
$T_{load} = T_{cab}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath450}%
\begin{displaymath}
\frac{1}{Tcal} \frac{\partial Tcal}{\partial Trec} = 
\frac{F_{eff}-1}{F_{eff}} \frac{1}{T_{load}+Trec}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline962}%
$3$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline964}%
$10^{-4}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline968}%
$Tcab$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath463}%
\begin{displaymath}
\frac{1}{Tcal} \frac{\partial Tcal}{\partial T_{cab}} = 
\frac{(T_{atm} - T_{emi}} 
{(T_{cab}-T_{emi})*(T_{cab}-T_{emi}-F_{eff}*(T_{cab}-T_{atm})}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline970}%
$3.6$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline972}%
$10^{-3}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmldisplayA{displaymath482}%
\begin{displaymath}
\frac{1}{Tcal} \frac{\partial Tcal}{\partial F_{eff}} = 
\frac{1}{F_{eff}} + \frac{1}{\frac{T_{cab}-T_{emi}}{T_{cab}-T_{atm}}-F_{eff}}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmldisplayA{displaymath498}%
\begin{displaymath}
\frac{\partial Tcal}{\partial C_{eff}} = 
\frac{Tcal}{C_{eff}} - \frac{Tcal}{T_{load}-T_{emi}}
\frac{\partial T_{emi}}{\partial C_{eff}} 
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath509}%
\begin{displaymath}
\frac{\partial T_{emi}}{\partial C_{eff}} =
\frac{(T_{emi}+Trec)^2}{T_{load}+Trec}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath515}%
\begin{displaymath}
\frac{1}{Tcal} \frac{\partial Tcal}{\partial C_{eff}} = 
\frac{1}{C_{eff}} -
\frac{(T_{emi}+Trec)^2}{C_{eff}^2 * (T_{load}+Trec) * (T_{load}-T_{emi}) }
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmldisplayA{displaymath529}%
\begin{displaymath}
\frac{\partial Tcal}{\partial \eta} = \frac{Tcal}{\eta} +
\frac{\partial Tau}{\partial \eta} \frac{\partial Tcal}{\partial Tau} +
\frac{\partial Trec}{\partial \eta} \frac{\partial Tcal}{\partial Trec}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath543}%
\begin{displaymath}
\frac{\partial Tau}{\partial \eta} =
\frac{1}{T_{atm} * F_{eff}}\frac{\partial Temi}{\partial \eta} 
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath552}%
\begin{displaymath}
\frac{\partial Temi}{\partial \eta} =
-\frac{T_{emi}+Trec}{\eta ^2} +
\frac{\partial Trec}{\partial \eta} \frac{T_{emi}-T_{load}}{T_{load}+Trec}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath563}%
\begin{displaymath}
\frac{1}{Tcal} \frac{\partial Tcal}{\partial \eta} = 
\frac{\eta * T_{atm} * F{eff} - T_{emi} - Trec}{\eta ^2}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath573}%
\begin{displaymath}
\frac{\partial Trec}{\partial \eta} =
Trec \frac{Trec-T_{cold}}{T_{load}- \eta * T_{cold} + (1-\eta) * Trec}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1030}%
$T_{cold}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
\stepcounter{subsection}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1046}%
$_{II}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}

\end{document}
