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\section{Overview}  This document presents a parametric model to help design an Interferometric Array. It Array providing a total cost estimate for the resulting solution.  In particular, this document  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{Variables}  This section aims to include all relevant design parameters that might influence the selected performance objectives. cost of the array.  \subsection{Antenna Aspects}  \subsubsection{Collecting Area}  \subsubsection{Temperature} 
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\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{Operations Costs}  \subsubsection{Components reliability}  \subsubsection{Maintenance complexity}  \subsubsection{Calibration Software Costs}  \subsubsection{Calibration Hardware Costs}  \subsubsection{Power Consumption Cost}  \subsubsection{Re-configuration Systems Operation Cost}  \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}). For $N$ antennas of diameter $D$ meters with accuracy $\frac{\lambda}{16}$, where $\lambda$ is in millimeters we could use \cite{mmadesign} as an upper limit for Antenna construction cost. 
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\text{Correlator cost} = 2N^2 + 112N +1360  \end{equation}  \subsubsection{Cost of Re-configuration Systems Construction}  \subsection{Operations Costs}  \subsubsection{Components reliability}  \subsubsection{Maintenance complexity}  \subsubsection{Calibration Software Costs}  \subsubsection{Calibration Hardware Costs}  \subsubsection{Power Consumption Cost}  \subsubsection{Re-configuration Systems Operation Cost}  \section{Mathematical Formulation}  Thus if we are using vector $x = {\text{antenna diameter}, \text{antenna efficiency}, \}$, the antenna diameter, as the optimization variable the problem we would like to solve is:  \begin{equation*}  \begin{aligned}  & \underset{x}{\text{minimize}}  & & f(x) = {\frac{2k_B}{\eta_s \eta_a}}{\frac{T_{sys}}{\pi x^2 \sqrt{2 \Delta \nu \tau_{acc}}}}\\  & \text{subject to}  & & X_{ij} = M_{ij}, \; (i,j) \in \Omega, \\  &&& X \succeq 0.  \end{aligned}  \end{equation*}  \section{Array Performance Data Generation - Python Implementation}  \section{Visualization Tool Notes}  \section{Conversation notes} 
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