Demian Arancibia edited untitled.tex  almost 9 years ago

Commit id: dc43a020afb2af05748032303755a384592bf098

deletions | additions      

       

This document presents a parametric model to help design an Interferometric Array. It describes the relationship of design parameters in section 2 with performance objectives in section 3.   In particular, this document provides an explanation of the parameters and objectives selection. These explanations enable the reader to both assess completeness of the model, and accuracy of the mathematical relationships as well.  Section 4 provides the python code used to generate data in the format required for visual analysis of array design options performance. The python code is consistent with parameters and objectives selection in sections 2 and 3, and the mathematical relationships between them.  \section{Design Variables} \section{Variables}  This section aims to include all relevant design parameters that might influence the selected performance objectives.  \subsection{Antenna Aspects}  \subsubsection{Collecting Area} 

\subsection{Correlator Aspects}  \subsubsection{Position}  \subsubsection{Efficiency}  \section{Performance Objectives} \section{Objectives}  This section aims to include array performance objectives that might be influenced by design choices.  \subsection{Minimize Brightness Sensitivity Limit}  An overall antenna performance measure is the System Equivalent Flux Density, $SEFD$, defined as the flux density of a source that would deliver the same amount of power (see \cite{sensitivity2}):  

\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 with $\eta_s$ most important factor being correlator efficiency $\eta_c = \frac{\text{correlator sensitivity}}{\text{sesitivity of a perfect analog correlator having the same } t_{int}}$ (see \cite{sensitivity}).  \subsection{Minimize Operations \subsection{Operations  Costs} The operations cost is a complex problem divided in the sub-problems in this section.  \subsubsection{Maximize components \subsubsection{Components  reliability} \subsubsection{Minimize components \subsubsection{Maintenance  complexity} \subsubsection{Minimize Calibration \subsubsection{Calibration  Software Costs} \subsubsection{Minimize Calibration \subsubsection{Calibration  Hardware Costs} \subsubsection{Power Consumption Cost}  \subsubsection{Re-configuration Systems Operation Cost}  \subsection{Minimize Up-front \subsection{Up-front  Costs} \subsubsection{Cost of Antennas Construction}  A commonly used rule of thumb for the cost of an antenna is that it is proportional to $D^{\alpha}$, where $\alpha \approx 2.7$ for values of $D$ from a few meters to tens of meters. (see \cite{moran})  \subsubsection{Cost of Antenna Electronics}