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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}
This section aims to include all relevant design parameters that might influence the selected performance objectives.
\subsection{System Efficiency}
\subsubsection{System \subsection{Antenna Aspects}
\subsubsection{Antenna Effective Collecting Area}
\subsubsection{Antenna Temperature}
It is often instructive to express the system temperature in terms of 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}):
\begin{equation}\label{eq:system_equivalent_flux_density}
SEFD = {\frac{T_{sys}}{\frac{\eta_a A}{2k_B}}}
\end{equation}
where $T_{sys}$ is the system temperature including contributions from receiver noise, feed losses, spillover, atmospheric emission, galactic background and cosmic background, $k_B = 1.380 \times 10^{-23}$ 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 $\eta_a = \eta_{\text{surface efficiency}} \cdot \eta_{\text{aperture blockage}} \cdot \eta_{\text{feed spillover efficiency}} \cdot \eta_{\text{illumination taper efficiency}}$ (see \cite{antenna}) \subsubsection{Antenna Pointing Accuracy}
\subsection{Pad Aspects}
\subsubsection{Quantity}
\subsubsection{Position}
\subsection{Receiver Aspects}
\subsubsection{Bandwidth}
\subsubsection{Bands Division} \subsubsection{Reciever Temperature}
\subsubsection{Calibration
Widgets} Cost}
\section{Performance Objectives}
This section aims to include all the array performance objectives that might be influenced by design choices.
\subsection{Minimize Brightness Sensitivity Limit}
...
in units of Janskys per synthesized beam area.
with $\eta_s$ most important factor being correlator efficiency $\eta_c = \frac{\text{correlator sensitivity}}{\text{sesitivity of a perfect analog correlator having the same } \tau_{acc}}$ (see \cite{sensitivity}).
\subsubsection{Minimize SEFD}
\subsubsection{Minimize System Temperature}
It is often instructive to express the system temperature in terms of 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}):
\begin{equation}\label{eq:system_equivalent_flux_density}
SEFD = {\frac{T_{sys}}{\frac{\eta_a A}{2k_B}}}
\end{equation}
where $T_{sys}$ is the system temperature including contributions from receiver noise, feed losses, spillover, atmospheric emission, galactic background and cosmic background, $k_B = 1.380 \times 10^{-23}$ 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 $\eta_a = \eta_{\text{surface efficiency}} \cdot \eta_{\text{aperture blockage}} \cdot \eta_{\text{feed spillover efficiency}} \cdot \eta_{\text{illumination taper efficiency}}$ (see
\cite{antenna}). \cite{antenna})
\subsection{Minimize Operations Costs}
The operations cost is a complex problem divided in the sub-problems in this section.
\subsubsection{Maximize components reliability}
...