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\begin{document}
\title{Symbolic Linear Circuit Analysis Program}
\maketitle
\section*{Just a filter }
\newpage
\subsection*{.symbolic gain matrix}
\[\left(\begin{array}{c}
0\\
0\\
0\\
\mathrm{V_{s}}\\
0\\
0\\
0
\end{array}\right)=\left(\begin{array}{ccccccc}
\mathrm{C_{a}}\, s & - \mathrm{C_{a}}\, s & 0 & 1 & 1 & 0 & 0\\
- \mathrm{C_{a}}\, s & \frac{1}{\mathrm{R_{L}}} + 3\, \mathrm{C_{a}}\, s &  - \frac{1}{\mathrm{R_{L}}} - 2\, \mathrm{C_{a}}\, s & 0 & 0 & 1 & 1\\
0 &  - \frac{1}{\mathrm{R_{L}}} - 2\, \mathrm{C_{a}}\, s & \frac{1}{\mathrm{R_{L}}} + 3\, \mathrm{C_{a}}\, s & 0 & -1 & 0 & -1\\
1 & 0 & 0 & 0 & 0 & 0 & 0\\
1 & 0 & -1 & 0 & - \mathrm{L_{a}}\, s & 0 & 0\\
0 & 1 & 0 & 0 & 0 & - \mathrm{L_{a}}\, s & 0\\
0 & 1 & -1 & 0 & 0 & 0 & - 2\, \mathrm{L_{a}}\, s
\end{array}\right)\left(\begin{array}{c}
\mathrm{V_{1}}\\
\mathrm{V_{2}}\\
\mathrm{V_{3}}\\
\mathrm{I_{V_{in}}}\\
\mathrm{I_{L_{1}}}\\
\mathrm{I_{L_{2}}}\\
\mathrm{I_{L_{3}}}
\end{array}\right) \] 

\newpage
\subsection*{.symbolic gain fourier}

\[\frac{\mathrm{V_{2}} - \mathrm{V_{3}}}{\mathrm{V_{in}}}=-\frac{1.0\, \left(4.0\, \mathrm{C_{a}}\, \mathrm{L_{a}}\, {\pi}^2\, \mathrm{R_{L}}\, f^2 + \mathrm{R_{L}}\right)}{ - 20.0\, \mathrm{C_{a}}\, \mathrm{L_{a}}\, {\pi}^2\, \mathrm{R_{L}}\, f^2 + \pi\, \mathrm{L_{a}}\, f\, 4.0\, \mathrm{i} + 2.0\, \mathrm{R_{L}}} \] 

\newpage
\subsection*{.numeric gain pz}

\begin{center}
The zero-frequency value of GAIN = -0.5 [-].
\end{center}


\begin{center}
Poles of GAIN; units HZ. 
\end{center}


\begin{center}
\begin{tabular}
[c]{|r|r|r|r|r|}\hline
\textbf{Poles} & \textbf{Real part} & \textbf{Imaginary part} & \textbf{Magnitude} & \textbf{Q} \\\hline
$1$ & $-31.83\times 10^{3}$ & $ 3.183\times 10^{6}$ & $ 3.183\times 10^{6}$ & $ 50.0 $\\
$2$ & $-31.83\times 10^{3}$ & $ -3.183\times 10^{6}$ & $ 3.183\times 10^{6}$ & $ 50.0 $\\
\hline
\end{tabular}
\end{center}


\begin{center}
Zeros of GAIN; units HZ. 
\end{center}


\begin{center}
\begin{tabular}
[c]{|r|r|r|r|r|}\hline
\textbf{Zeros} & \textbf{Real part} & \textbf{Imaginary part} & \textbf{Magnitude} & \textbf{Q} \\\hline
$1$ & $-5.033\times 10^{6}$ & $ 0$ & $ 5.033\times 10^{6}$ & $ - $\\
$2$ & $5.033\times 10^{6}$ & $ 0$ & $ 5.033\times 10^{6}$ & $ - $\\
\hline
\end{tabular}
\end{center}

\newpage
\subsection*{.plot gain pz}
\begin{figure}[htb]
\centering
\includegraphics{slicap-gain-pz.png}
\caption{slicap-gain-pz.png}
\end{figure}
\newpage
\subsection*{.plot gain step .t 0 1.5u}
\begin{figure}[htb]
\centering
\includegraphics{slicap-gain-step-_t-0-1_5u.png}
\caption{slicap-gain-step-\_t-0-1\_5u.png}
\end{figure}
\subsection*{About}

\begin{footnotesize}

 \LaTeX \hspace{1pt} generated by SLiCAP (Symbolic Linear Circuit Analysis Program): a MuPAD application. SLiCAP \copyright 2008-2009, Montagne Design \& Consultancy, Delft, The Netherlands. MuPAD Pro 4.0.6. 'The Open Computer Algebra System' \copyright 1997-2008, is a product of SciFace Software. \today, total SLiCAP  version 3.1 processing time: 4.35 seconds (limit=600 seconds).\end{footnotesize} 
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