Browse Source

thema4a fertig.

master
fleischmannma75068 2 years ago
parent
commit
734cc3c50f

+ 3
- 0
ELK2_FS/formelsammlung.tex View File

@@ -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}


BIN
ELK2_FS/img/img_02_00_modell_opv.png View File


BIN
ELK2_FS/img/img_02_12_testschaltung_schleifenverstaerkung.png View File


BIN
ELK2_FS/img/img_02_13_mitkopplung.png View File


BIN
ELK2_FS/img/img_02_13_ruhestromkompensation.png View File


BIN
ELK2_FS/img/img_02_14_uio_kompensation.png View File


BIN
ELK2_FS/img/img_06_01_gegentaktverstaerker.png View File


BIN
ELK2_FS/img/img_06_02_gegentakt_verbessert.png View File


BIN
ELK2_FS/img/img_07_MOS_dynamisch.png View File


BIN
ELK2_FS/img/img_07_MOS_ohmsch.png View File


BIN
ELK2_FS/img/img_07_Millerplateau.png View File


+ 1
- 1
ELK2_FS/latex4ei/latex4ei_sheet.cls View File

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



+ 161
- 44
ELK2_FS/thema4_linearer_OPV.tex View File

@@ -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}

Loading…
Cancel
Save