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Demian Arancibia edited untitled.tex
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This section aims to include all relevant design parameters that might influence the selected performance objectives in \S~\ref{sec:obj}.
\subsection{Antenna Aspects}
\subsubsection{Collecting Area}
We will use $A$ in this document as each array element collecting area (thus we could also write $\pi \cdot D^2$, with $D$ being the dish diameter).
\subsubsection{Efficiency}
We will use $\eta_a$ in this document as the antenna efficiency with $\eta_a = \eta_{\text{surface efficiency}} \cdot \eta_{\text{aperture blockage}} \cdot \eta_{\text{feed spillover efficiency}} \cdot \eta_{\text{illumination taper efficiency}}$ (as defined in \cite{antenna}).
\subsection{Pad Aspects}
\subsubsection{Quantity}
In case re-configuration of the array is envisioned, there might be a bigger number of pads ready for aperture connection to the system.
\subsubsection{Position}
The
challengue challenge of positions has been addressed in x, y and z.
\subsection{Receiver Aspects}
\subsubsection{Bandwidth}
\subsubsection{Temperature}
...
\subsection{Correlator Aspects}
\subsubsection{Position}
\subsubsection{Efficiency}
We will use $\eta_c$ as correlator efficiency in this document, with $\eta_c(t_{int}) = \frac{\text{correlator sensitivity}}{\text{sesitivity of a perfect analog correlator having the same } t_{int}}$ (see \cite{sensitivity}).
\section{Objectives}\label{sec:obj}
This section aims to include array performance objectives that might be influenced by design variables in \S~\ref{sec:var}.
\subsection{Brightness Sensitivity Limit}
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\begin{equation}\label{eq:system_equivalent_flux_density}
SEFD = {\frac{T_{sys}}{\frac{\eta_a A}{2k_B}}}
\end{equation}
in units of Janskys where $T_{sys}$ is the system temperature including contributions from receiver noise, feed losses, spillover, atmospheric emission, galactic background and cosmic background,
and $k_B = 1.380 \times 10^{-23}$ Joule $K^{-1}$ is the Boltzmann
constant, $A$ is the antenna collecting area (thus we could also write $\pi \cdot D^2$), and $\eta_a$ is the antenna efficiency with $\eta_a = \eta_{\text{surface efficiency}} \cdot \eta_{\text{aperture blockage}} \cdot \eta_{\text{feed spillover efficiency}} \cdot \eta_{\text{illumination taper efficiency}}$ constant (see
\cite{antenna}). \cite{sensitivity}).
If we assume N apertures with the same $SEFD$, observing the same bandwidth $\Delta\nu$, during the same integration time $t_{int}$, then the weak-source limit in the sensitivity of a synthesis image of a single polarization is
\begin{equation}\label{eq:sens}
\Delta I_m = {\frac{1}{\eta_s }}{\frac{SEFD}{\sqrt{(N(N-1) \Delta \nu t_{int}}}}
\end{equation}
in units of Janskys per synthesized beam
area area, with $\eta_s$ most important factor being
correlator efficiency $\eta_c = \frac{\text{correlator sensitivity}}{\text{sesitivity of a perfect analog correlator having the same } t_{int}}$ $\eta_c$ (see \cite{sensitivity}).
\subsection{}
\subsection{Operations Costs}
\subsubsection{Components reliability}
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