Demian Arancibia edited untitled.tex  almost 9 years ago

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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} 

\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}