diff --git a/ELK2_FS/formelsammlung.tex b/ELK2_FS/formelsammlung.tex index 8e4a45b..38b414e 100644 --- a/ELK2_FS/formelsammlung.tex +++ b/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} diff --git a/ELK2_FS/img/img_02_00_modell_opv.png b/ELK2_FS/img/img_02_00_modell_opv.png new file mode 100644 index 0000000..4e78b51 Binary files /dev/null and b/ELK2_FS/img/img_02_00_modell_opv.png differ diff --git a/ELK2_FS/img/img_02_12_testschaltung_schleifenverstaerkung.png b/ELK2_FS/img/img_02_12_testschaltung_schleifenverstaerkung.png new file mode 100644 index 0000000..28469bd Binary files /dev/null and b/ELK2_FS/img/img_02_12_testschaltung_schleifenverstaerkung.png differ diff --git a/ELK2_FS/img/img_02_13_mitkopplung.png b/ELK2_FS/img/img_02_13_mitkopplung.png new file mode 100644 index 0000000..d6cf69d Binary files /dev/null and b/ELK2_FS/img/img_02_13_mitkopplung.png differ diff --git a/ELK2_FS/img/img_02_13_ruhestromkompensation.png b/ELK2_FS/img/img_02_13_ruhestromkompensation.png new file mode 100644 index 0000000..4448839 Binary files /dev/null and b/ELK2_FS/img/img_02_13_ruhestromkompensation.png differ diff --git a/ELK2_FS/img/img_02_14_uio_kompensation.png b/ELK2_FS/img/img_02_14_uio_kompensation.png new file mode 100644 index 0000000..27d540d Binary files /dev/null and b/ELK2_FS/img/img_02_14_uio_kompensation.png differ diff --git a/ELK2_FS/img/img_06_01_gegentaktverstaerker.png b/ELK2_FS/img/img_06_01_gegentaktverstaerker.png new file mode 100644 index 0000000..4f57233 Binary files /dev/null and b/ELK2_FS/img/img_06_01_gegentaktverstaerker.png differ diff --git a/ELK2_FS/img/img_06_02_gegentakt_verbessert.png b/ELK2_FS/img/img_06_02_gegentakt_verbessert.png new file mode 100644 index 0000000..9d05b56 Binary files /dev/null and b/ELK2_FS/img/img_06_02_gegentakt_verbessert.png differ diff --git a/ELK2_FS/img/img_07_MOS_dynamisch.png b/ELK2_FS/img/img_07_MOS_dynamisch.png new file mode 100644 index 0000000..4778743 Binary files /dev/null and b/ELK2_FS/img/img_07_MOS_dynamisch.png differ diff --git a/ELK2_FS/img/img_07_MOS_ohmsch.png b/ELK2_FS/img/img_07_MOS_ohmsch.png new file mode 100644 index 0000000..99df8d3 Binary files /dev/null and b/ELK2_FS/img/img_07_MOS_ohmsch.png differ diff --git a/ELK2_FS/img/img_07_Millerplateau.png b/ELK2_FS/img/img_07_Millerplateau.png new file mode 100644 index 0000000..d85aef5 Binary files /dev/null and b/ELK2_FS/img/img_07_Millerplateau.png differ diff --git a/ELK2_FS/latex4ei/latex4ei_sheet.cls b/ELK2_FS/latex4ei/latex4ei_sheet.cls index 057bd43..d7816cd 100644 --- a/ELK2_FS/latex4ei/latex4ei_sheet.cls +++ b/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}} diff --git a/ELK2_FS/thema4_linearer_OPV.tex b/ELK2_FS/thema4_linearer_OPV.tex index 26b6a5a..352b9f3 100644 --- a/ELK2_FS/thema4_linearer_OPV.tex +++ b/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} \end{sectionbox} - \begin{sectionbox} - % Standard lineare OPV-Schaltungen TODO + % 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}{ + $\underline{g} = - \frac{\underline{v}(g\_out)}{\underline{v}(g\_in)}$ + } + + % 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}} + + + % 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 + % ---------------------------------------------------------------------- \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} + + \end{sectionbox} + %Force column break + \begin{sectionbox} + \subsubsection{Summierer (Invertierend)} - \pbox{4cm}{\includegraphics[width = 3cm]{img_02_07_summierer}} - \parbox{3.5cm}{} + \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{Differenzverstärker (aktiver Subtrahierer, einfache Struktur)} - \pbox{4cm}{\includegraphics[width = 3cm]{img_02_08_differenzverstaerker}} - \parbox{3.5cm}{} + \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{Instrumentenverstärker (verbesserter Differenzverstärker)} - \pbox{4cm}{\includegraphics[width = 3cm]{img_02_09_instrumentenverstaerker}} - \parbox{3.5cm}{} + \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}