thema4a fertig.

ELK2_FS/formelsammlung.tex

@@ -26,6 +26,9 @@
 \myemail{fleischmannma75068@th-nuernberg.de}
 \fancyfoot[L]{Keine Gewähr auf Vollständigkeit oder Richtigkeit!}
 
+% document variables
+\newlength{\imagewidth}
+
 % DOCUMENT_BEGIN =============================================================================
 \begin{document}
 

ELK2_FS/latex4ei/latex4ei_sheet.cls

@@ -27,7 +27,7 @@
 % make three column design possible
 % ----------------------------------------------------------------------
 	\newcounter{columnnumber}
-	\setcounter{columnnumber}{4}
+	\setcounter{columnnumber}{3}
 	\DeclareOption{threecolumn}{\setcounter{columnnumber}{3}}
 
 

ELK2_FS/thema4_linearer_OPV.tex

@@ -1,9 +1,18 @@
+\setlength{\imagewidth}{6cm}
+
 % ============================================================================================
 \section{Lineare OPV-Schaltungen, Gegengekoppelte Strukturen}
 % ============================================================================================
 
 \begin{sectionbox}
 
+	% OPV Modelle
+	% ----------------------------------------------------------------------
+	\subsection{Allgemines Modell}
+  \begin{center}
+    \includegraphics[width = 0.5\columnwidth]{img_02_00_modell_opv}
+  \end{center}
+
 	% OPV Formeln
 	% ----------------------------------------------------------------------
 	\subsection{Operationsverstärker}
@@ -28,23 +37,27 @@
 	% ----------------------------------------------------------------------
   \subsection{Standardstruktur}
 
-  \begin{center}
-    \includegraphics[width = 0.5\columnwidth]{img_02_01_Standardstruktur}
-  \end{center}
+	\pbox{5cm}{\includegraphics[width = 5cm - 1cm]{img_02_01_Standardstruktur}}
+	\parbox{\textwidth - 5cm + 1cm}{
+		% Rückkopplungsfaktor %
+		\begin{bluebox}
+		$\underline{k} = \frac{\underline{u}_k}{\underline{u}_2}\vert_{u_1 = 0} = \frac{-\underline{u}_{id}}{\underline{u}_2}\vert_{u_1 = 0}$
+		\end{bluebox}
 
-	 	% Schleifenverstärkung %
+		% Schleifenverstärkung %
 		Schleifenverstärkung: $\underline{g} = \underline{V}_{ud} \cdot \underline{k}$
 
 		% Ausgangsspannung %
-	  $\underline{u}_2 = \underline{a}_V^+ \cdot \underline{u}_1^+ + \underline{a}_V^- \cdot \underline{u}_1^-$
+		$\underline{u}_2 = \underline{a}_V^+ \cdot \underline{u}_1^+ + \underline{a}_V^- \cdot \underline{u}_1^-$
 
 		% Spannungsverstärkung %
 		\begin{emphbox}
-		  $\underline{a}_V^+ = \frac{\underline{V}_{ud}}{1+\underline{k}\cdot\underline{V}_{ud}}$ \quad \quad\
-		  $\underline{a}_V^- = -\frac{\underline{V}_{ud}\cdot(1-\underline{k})}{1+\underline{k}\cdot\underline{V}_{ud}}$\newline
+			$\underline{a}_V^+ = \frac{\underline{V}_{ud}}{1+\underline{k}\cdot\underline{V}_{ud}}$ \newline
+			$\underline{a}_V^- = -\frac{\underline{V}_{ud}\cdot(1-\underline{k})}{1+\underline{k}\cdot\underline{V}_{ud}}$\newline
 		\end{emphbox}
+	}
 
-		\subsubsection{Betriebsmodi}
+	\subsubsection{Betriebsmodi}
 
 			% Nichtinvertierender Betrieb %
 	  	\underline{Nichtinvertierender Betrieb:}
@@ -98,65 +111,169 @@
 			\begin{emphbox}
 	  		$f_g \approx \frac{GBW}{1/|\underline{k}(f_g)|}$
 			\end{emphbox}
+
 \end{sectionbox}
+\begin{sectionbox}
 
+	% Standard-Rückkopplungsstruktur
+	% ----------------------------------------------------------------------
+	\subsection{Stabilität von gegengekoppelten OPV-Schaltungen}
+		$\varphi_R = \varphi(\underline{g}(f_D)) - (-180\degree)$
+		\begin{bluebox}
+			\item Bei negativer Schleifenverstärkung (= Mitkopplung): $\underline{g} < 1$
+			\item Robust stabile Schaltung: $\varphi_R > 45 \degree$
+		\end{bluebox}
+
+	% Testschaltung zur Ermittlung der Schleifenverstärkung
+	% ----------------------------------------------------------------------
+	\subsection{Testschaltung zur Ermittlung der Schleifenverstärkung}
+		\pbox{\imagewidth}{\includegraphics[width = \imagewidth - 1cm]{img_02_12_testschaltung_schleifenverstaerkung}}
+		\parbox{\textwidth - \imagewidth}{
+			$\underline{g} = - \frac{\underline{v}(g\_out)}{\underline{v}(g\_in)}$
+		}
 
-\begin{sectionbox}
+	% Kompensation der Ausgangs-Offset-Spannung
+	% ----------------------------------------------------------------------
+	\subsection{Kompensation der Ausgangs-Offset-Spannung}
+		\pbox{5cm}{\includegraphics[width = 4cm]{img_02_13_ruhestromkompensation}}
+		\pbox{6cm}{\includegraphics[width = 5cm]{img_02_14_uio_kompensation}}
+		\newline
+		\parbox{4cm}{\begin{emphbox} $R^+ = R^-$ \end{emphbox}} \quad\quad\quad
+		\parbox{4cm}{\begin{emphbox} $U_{ID} = U_{IO}$ \end{emphbox}}
 
-% Standard-Rückkopplungsstruktur
-% ----------------------------------------------------------------------
-\subsection{Stabilität von gegengekoppelten OPV-Schaltungen}
 
-\end{sectionbox}
+		% Gegenkopplung und Mitkopplung
+		% ----------------------------------------------------------------------
+		\subsection{Kompensation der Ausgangs-Offset-Spannung}
+		\pbox{\imagewidth}{\includegraphics[width = \imagewidth - 1cm]{img_02_13_mitkopplung}}
+		\parbox{\textwidth - \imagewidth}{
+			% Rückkopplungsfaktor %
+			\begin{bluebox}
+			$\underline{k}
+				= \frac{-\underline{u}_{id}\vert_{u_1 = 0}}{\underline{u}_2} \newline
+				= \frac{\underline{u}(-)-\underline{u}(+)}{\underline{u}_2}\vert_{u_1 = 0} \newline
+				= \underline{k}^{(-)} - \underline{k}^{(+)}$
+			\end{bluebox}
 
+			\begin{emphbox}
+			$\underline{k} = \frac{\underline{Z}_1}{\underline{Z}_1 + \underline{Z}_2} - \frac{\underline{Z}_3}{\underline{Z}_3 + \underline{Z}_4}$
+			\end{emphbox}
+		}
+
+\end{sectionbox}
+\newpage
 \begin{sectionbox}
 
-		% Standard lineare OPV-Schaltungen TODO
-		% ----------------------------------------------------------------------
+	% Standard lineare OPV-Schaltungen
+	% ----------------------------------------------------------------------
   \subsection{Standard Linearverstärker mit OPV}
 		\subsubsection{Invertierender Standard Verstärker}
-			\pbox{4cm}{\includegraphics[width = 3cm]{img_02_02_invertierender_verstaerker}}
-			\parbox{3.5cm}{\begin{emphbox} $f_g \approx \frac{GBW}{1/|\underline{k}(f_g)|}$ \end{emphbox} }
+			\pbox{\imagewidth}{\includegraphics[width = \imagewidth - 1cm]{img_02_02_invertierender_verstaerker}}
+			\parbox{\textwidth - \imagewidth}{
+				$\underline{a}_V = - \frac{R_2}{R_1}$ \newline
+				$\underline{z}_{in} = R_1$ \newline
+				$\underline{z}_a = (R_1+R_2)||\frac{\underline{z}_{a,OPV}}{1+\underline{k} \cdot \underline{V}_{ud}}$
+			}
 
 		\subsubsection{Nichtinvertierender Standard Verstärker}
-			\pbox{4cm}{\includegraphics[width = 3cm]{img_02_03_nichtinvertierender_verstaerker}}
-			\parbox{3.5cm}{}
+			\pbox{\imagewidth}{\includegraphics[width = \imagewidth - 1cm]{img_02_03_nichtinvertierender_verstaerker}}
+			\parbox{\textwidth - \imagewidth}{
+				$\underline{a}_V = 1 + \frac{R_2}{R_1}$ \newline
+				$\underline{z}_{in} = \underline{z}_{id} \cdot (1+\underline{k} \cdot \underline{V}_{ud})$ \newline
+				$\underline{z}_a = (R_1+R_2)||\frac{\underline{z}_{a,OPV}}{1+\underline{k} \cdot \underline{V}_{ud}}$
+			}
+
 
 		\subsubsection{Spannungsfolger, Impedanzwandler}
-			\pbox{4cm}{\includegraphics[width = 3cm]{img_02_04_impedanzwandler}}
-			\parbox{3.5cm}{}
+			\pbox{\imagewidth}{\includegraphics[width = {\imagewidth - 2cm}]{img_02_04_impedanzwandler}}
+			\parbox{\textwidth - \imagewidth}{
+				$\underline{a}_V = 1$ \newline
+				$\underline{z}_{in} = \underline{z}_{id} \cdot (1 + 1 \cdot \underline{V}_{ud})$ \newline
+				$\underline{z}_a = \frac{\underline{z}_{a,OPV}}{1 + 1 \cdot \underline{V}_{ud}}$
+			}
 
 		\subsubsection{Integrierer}
-			\pbox{4cm}{\includegraphics[width = 3cm]{img_02_05_integrierer}}
-			\parbox{3.5cm}{}
+			\pbox{\imagewidth}{\includegraphics[width = \imagewidth - 1cm]{img_02_05_integrierer}}
+			\parbox{\textwidth - \imagewidth + 1cm}{
+				$U_2(t)= -\frac{1}{R \cdot C} \cdot \int_0^t U_1(t) \cdot dt + U_2(0)$ \newline
+				$\frac{U_2(s)}{U_1(s)} = - \frac{1}{s \cdot R \cdot C}$ \newline
+				$\underline{a}_V = - \frac{1}{j\omega \cdot R \cdot C}$ \newline
+				$\underline{z}_{in} = R$ \newline
+				$\underline{z}_a = (\frac{1}{j\omega \cdot C}+R)||\frac{\underline{z}_{a,OPV}}{1+\underline{k} \cdot \underline{V}_{ud}}$
+			}
 
 		\subsubsection{Differentiator (Differenzierer)}
-			\pbox{4cm}{\includegraphics[width = 3cm]{img_02_06_differenzierer}}
-			\parbox{3.5cm}{}
+			\pbox{\imagewidth}{\includegraphics[width = \imagewidth - 1cm]{img_02_06_differenzierer}}
+			\parbox{\textwidth - \imagewidth}{
+				$U_2(t) \approx - R_2 \cdot C_1 \cdot \frac{U_1(t)}{dt}$ \newline
+				$\frac{U_2(s)}{U_1(s)} = - s \cdot R_2 \cdot C_1$ \newline
+				$\underline{a}_V \approx - j\omega \cdot R_2 \cdot C_1$ \newline
+				$\underline{z}_{in} \approx \frac{1}{j\omega \cdot C_1}$
+			}
+			\begin{emphbox}
+				für $\varphi_R = 45\degree$ : $R_1 = \frac{1}{f_D\cdot 2 \pi \cdot C_1} = \frac{1}{2\pi \cdot C_1 \cdot \sqrt{\frac{GBW}{2\pi \cdot R_2 \cdot C_1}}}$
+			\end{emphbox}
 
-		\subsubsection{Summierer (Invertierend)}
-			\pbox{4cm}{\includegraphics[width = 3cm]{img_02_07_summierer}}
-			\parbox{3.5cm}{}
+	\end{sectionbox}
+	%Force column break
+	\begin{sectionbox}
 
-		\subsubsection{Differenzverstärker (aktiver Subtrahierer, einfache Struktur)}
-			\pbox{4cm}{\includegraphics[width = 3cm]{img_02_08_differenzverstaerker}}
-			\parbox{3.5cm}{}
 
+		\subsubsection{Summierer (Invertierend)}
+			\pbox{\imagewidth}{\includegraphics[width = \imagewidth - 1cm]{img_02_07_summierer}}
+			\parbox{\textwidth - \imagewidth}{
+				$\underline{a}_{V,i} = \frac{R_2}{R_1}$ \newline
+				$\underline{z}_{in,i} = R_1$ \newline
+				$\underline{z}_a = (R_2+\frac{R_1}{n})||\frac{\underline{z}_{a,OPV}}{1 + \underline{k} \cdot \underline{V}_{ud}}$
+		}
 
-		\subsubsection{Instrumentenverstärker (verbesserter Differenzverstärker)}
-			\pbox{4cm}{\includegraphics[width = 3cm]{img_02_09_instrumentenverstaerker}}
-			\parbox{3.5cm}{}
+		\subsubsection{Differenzverstärker (aktiver Subtrahierer, einfache Struktur)}
+			\pbox{5cm}{\includegraphics[width = 5cm - 1cm]{img_02_08_differenzverstaerker}}
+			\parbox{\textwidth - 5cm + 1cm}{
+				$\underline{u}_2 = -\frac{R_2}{R_1}\cdot \underline{u}_{in2}$ \newline $+ \frac{R_1+R_2}{R1}\cdot\frac{R_4}{R_3+R_4}\cdot\underline{u}_{in1}$ \newline
+				$\underline{z}_{in1} = R_3 + R_4$ \newline
+				$\underline{z}_{in2} = R_1 \big \vert _{\underline{u}_{in1}=0} = R_1$ \newline
+				\begin{emphbox}
+					Für $R_3=R_1$ und $R_4=R_2$ : \newline
+					$\underline{u}_2 = \frac{R_2}{R_1}\cdot(\underline{u}_{in1} - \underline{u}_{in2})$
+				\end{emphbox}
+			}
+
+	\subsubsection{Instrumentenverstärker (verbesserter Differenzverstärker)}
+		\pbox{\imagewidth}{\includegraphics[width = \imagewidth - 1cm]{img_02_09_instrumentenverstaerker}}
+		\parbox{\textwidth - \imagewidth + 1cm}{
+			$\underline{u}_{out1} = (1+\frac{R_2}{R_1}) \cdot \underline{u}_{in1} - \frac{R_2}{R_1} \cdot \underline{u}_{in2}$ \newline
+			$\underline{u}_{out2} = (1+\frac{R_2}{R_1}) \cdot \underline{u}_{in2} - \frac{R_2}{R_1} \cdot \underline{u}_{in1}$ \newline
+			$\underline{u}_2 = \frac{R_4}{R_3} \cdot (1+2\cdot \frac{R_2}{R_1})\cdot (\underline{u}_{in1} - \underline{u}_{in2})$ \newline \newline
+			$\underline{z}_{in1,2} \to \infty$
+		}
+
+	\subsubsection{Spannungsgesteuerte Stromquelle ($G_m$)}
+		\pbox{\imagewidth}{\includegraphics[width = \imagewidth - 2cm]{img_02_10_stromquelle}}
+		\parbox{\textwidth - \imagewidth}{
+			$\underline{u}_1 = \underline{u}_2 \cdot (1-\frac{R_4 \cdot R_1}{R_3 \cdot R_2}+\frac{R_1}{R_L})$ \newline
+			\begin{emphbox}
+				Für $\frac{R_4}{R_3} = \frac{R_2}{R_1}$: \quad\
+				$i_2 = \frac{1}{R_1} \cdot u_1$
+			\end{emphbox}
+		}
 
-		\end{sectionbox}
-		%Force column break
-		\begin{sectionbox}
+	\subsubsection{Negativ-Impedanz-Konverter (NIC)}
+		\pbox{0.7\imagewidth}{\includegraphics[width = 0.7\imagewidth - 1cm]{img_02_11_NIC}}
+		\parbox{\textwidth - 0.7\imagewidth}{
+			$\underline{z}_1 = -\underline{Z} \cdot \frac{R_1}{R_2}$
+			\begin{emphbox}
+				Für $R_1 = R_2$: \quad\
+				$\underline{z}_1 = -\underline{Z}$
+			\end{emphbox}
+		}
 
-		\subsubsection{Spannungsgesteuerte Stromquelle ($G_m$)}
-			\pbox{4cm}{\includegraphics[width = 3cm]{img_02_10_stromquelle}}
-			\parbox{3.5cm}{}
+\end{sectionbox}
 
-		\subsubsection{Negativ-Impedanz-Konverter (NIC)}
-			\pbox{4cm}{\includegraphics[width = 3cm]{img_02_11_NIC}}
-			\parbox{3.5cm}{}
+\begin{sectionbox}
 
-		\end{sectionbox}
+	% Filter
+	% ----------------------------------------------------------------------
+	\subsection{Filter-Grundschaltungen mit OPV}
+	%TODO
+\end{sectionbox}