Digital_Communication_through_python/examp.tex at master · SaiManasaPappu/Digital_Communication_through_python · GitHub

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\documentclass{beamer}
\mode<presentation>
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\lstset{
%language=C,
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\numberwithin{equation}{section}

\title{\LARGE  {\bf POWER  ELECTRONICS}}
\author{{Sai Manasa Pappu   EE17BTECH11036}\\  { Sahir Bansal  EE17BTECH11035}}

\date{\today}

\begin{document}

\begin{frame}
\titlepage
\end{frame}


\begin{frame}
\frametitle{Problem Statement}
Python script to find the output of the 4th order low pass filter, with input as obtained from result of 3.1.
\bigbreak
\end{frame}

%\subsection{Literature}
\section{Solution}
\subsection{Centre}
\begin{frame}
\frametitle{Filter Response}
%\framesubtitle{Literature}
\bigbreak
\bigbreak
\bigbreak
Fourth order low pass filter cutoff frequency = 50 Hz. Note that this frequency is same as the input frequency.
\bigbreak
Hence input will be attenuated by 3dB.
\begin{align}
%\vec{x}^T\vec{x}-2\vec{O}^T\vec{x} +F = 0
V_{out} (peak) = \frac{1}{\sqrt{2}}V_{in} (peak)
\end{align}
%
Phase at f = 50 Hz is 4 x -45{\degree} = -180\degree

\begin{align}
\angle H(f) = -180 \degree
\end{align}
We can also verify the same by plotting magnitude and phase response of the filter in python.
\end{frame}


\begin{frame}
\begin{figure}
\frametitle{Magnitude Response}
\includegraphics[width=1\columnwidth ]{magnitude.png}
\label{magnitude.png}
\end{figure}
\end{frame}

\begin{frame}
\frametitle{Phase Response}
\begin{figure}
\centering
\includegraphics[width=1\columnwidth ]{phase.png}
\end{figure}
\end{frame}

\begin{frame}{}
\frametitle{Output}
    Hence output frequency will be same as input frequency, peak voltage reduces by a factor of ${\sqrt{2}}$ and is out of phase with input.
    \bigbreak

\begin{align}
V_{out} = \frac{1}{\sqrt{2}} V_{in} \angle 180 \degree
\end{align}

\begin{align}
V_{out} = -0.707V_{m}sin(wt)
\end{align}

\end{frame}


\begin{frame}
\frametitle{Output}
\begin{figure}
\centering
\includegraphics[width=1\columnwidth ]{out.png}
\end{figure}
\end{frame}


\begin{frame}{Github Link for Python Code }
\url{https://github.com/SaiManasaPappu/Digital-Communication/blob/master/3.5.py}

\end{frame}


\end{document}