diff --git a/Final.tex b/Final.tex index c05887a..476303a 100644 --- a/Final.tex +++ b/Final.tex @@ -169,7 +169,30 @@ $V_{CC} = \pm \SI{15}{V}$. \includegraphics[width=0.4\textwidth]{lm741_oclsg} \end{figure} -\section{Ease of Use} +\section{A Combined Description of the Filter} + +Using the more complete model of the op-amp makes analysis more +complex. The following observations simplify the task: +\begin{itemize} +\item $v_p$ remains at ground potential, so the dependent voltage + source has voltage $A(-v_n)$ +\item $R_i \to \infty$ is, in effect, an open circuit, so the $R_i$ + branch need not be considered +\item $R_o = 0$ is a wire, and $R_o$ can be ignored. +\end{itemize} + +The simplified circuit can be depicted as such: + +\begin{figure}[h] + \caption{A simplification of the combined model} + \begin{circuitikz}[american voltages] + \draw (0,0) node[left=0cm]{$v_{in}$} to [short, o-] [R, l_=$R_1$, i=$i$] (1.5,0); + \draw (1.5,0) to [C, l_=$\frac{1}{j\omega C_1}$] (2.75,0); + \draw (2.75,0) node [above=0.1cm]{$v_n$} to [short, o-] [R, l_=$R_2$] (5,0); + \draw (5,0) node [above=0.1cm]{$v_{out}$} to [short, o-] [american controlled voltage source, label=$A(-v_n)$] (7,0); + \draw (7,0) node[ground]{}; +\end{circuitikz} +\end{figure} \subsection{Maintaining the Integrity of the Specifications}