deletions | additions       diff --git a/untitled.tex b/untitled.tex  index a41d9eb..06f98fa 100644  --- a/untitled.tex  +++ b/untitled.tex 
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\end{equation}  where $k_B = 1.380 x 10^{-23}$ Joule $K^{-1}$ is the Boltzmann constant, $A$ is the antenna collecting area, and $\eta_a$ is the antenna efficiency.   \begin{equation}\label{eq:antenna_efficiency}  \eta_a = \eta_{surface} * \eta_{'aperture blockage'} * \eta_{'feed spillover'} \eta_{"feed spillover"}  * \eta_{'illumination taper'} \eta_{"illumination taper"}  \end{equation}  \subsubsection{Maximize System Efficiency}  \begin{equation}\label{eq:system_efficiency} 
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