From da5ff1995f5d4b4991451d83a70ec80d8e82387c Mon Sep 17 00:00:00 2001 From: fleischmannma75068 Date: Fri, 19 Jun 2020 13:36:31 +0200 Subject: [PATCH] OPV Schaltungen, parbox --- ELK2_FS/formelsammlung.tex | 46 +++-- ELK2_FS/img/.DS_Store | Bin 0 -> 6148 bytes .../img_02_02_invertierender_verstaerker.png | Bin 0 -> 139547 bytes ..._02_03_nichtinvertierender_verstaerker.png | Bin 0 -> 145310 bytes ELK2_FS/img/img_02_04_impedanzwandler.png | Bin 0 -> 118689 bytes ELK2_FS/img/img_02_05_integrierer.png | Bin 0 -> 137178 bytes ELK2_FS/img/img_02_06_differenzierer.png | Bin 0 -> 111824 bytes ELK2_FS/img/img_02_07_summierer.png | Bin 0 -> 167039 bytes .../img/img_02_08_differenzverstaerker.png | Bin 0 -> 101474 bytes .../img/img_02_09_instrumentenverstaerker.png | Bin 0 -> 135325 bytes ELK2_FS/img/img_02_10_stromquelle.png | Bin 0 -> 111779 bytes ELK2_FS/img/img_02_11_NIC.png | Bin 0 -> 94725 bytes ELK2_FS/thema3_transistor.tex | 38 ++++- ELK2_FS/thema4_linearer_OPV.tex | 161 ++++++++++++++++-- 14 files changed, 210 insertions(+), 35 deletions(-) create mode 100644 ELK2_FS/img/.DS_Store create mode 100644 ELK2_FS/img/img_02_02_invertierender_verstaerker.png create mode 100644 ELK2_FS/img/img_02_03_nichtinvertierender_verstaerker.png create mode 100644 ELK2_FS/img/img_02_04_impedanzwandler.png create mode 100644 ELK2_FS/img/img_02_05_integrierer.png create mode 100644 ELK2_FS/img/img_02_06_differenzierer.png create mode 100644 ELK2_FS/img/img_02_07_summierer.png create mode 100644 ELK2_FS/img/img_02_08_differenzverstaerker.png create mode 100644 ELK2_FS/img/img_02_09_instrumentenverstaerker.png create mode 100644 ELK2_FS/img/img_02_10_stromquelle.png create mode 100644 ELK2_FS/img/img_02_11_NIC.png diff --git a/ELK2_FS/formelsammlung.tex b/ELK2_FS/formelsammlung.tex index 73d7c29..8e4a45b 100644 --- a/ELK2_FS/formelsammlung.tex +++ b/ELK2_FS/formelsammlung.tex @@ -1,15 +1,15 @@ -% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % +% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % ELK2 Formelsammlung % % @encode: UTF-8, tabwidth = 4, newline = LF % @author: Mario Fleischmann % @source: http://www.latex4ei.de -% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % +% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % -% ====================================================================== +% ============================================================================================ % Document Settings -% ====================================================================== +% ============================================================================================ % possible options: color/nocolor, english/german, threecolumn % default: color, english @@ -17,32 +17,58 @@ \usepackage{gensymb} \usepackage{cancel} + +\usepackage{pbox} % Spaltenpaket + % set document information \title{Elektronik 2} \author{Mario Fleischmann} \myemail{fleischmannma75068@th-nuernberg.de} - \fancyfoot[L]{Keine Gewähr auf Vollständigkeit oder Richtigkeit!} -% DOCUMENT_BEGIN =============================================================== +% DOCUMENT_BEGIN ============================================================================= \begin{document} \IfFileExists{git.id}{\input{git.id}}{} \ifdefined\GitRevision\mydate{\GitNiceDate\ (git \GitRevision)}\fi -\maketitle % requires ./img/Logo.pdf +\maketitle % requires EFI Logo: ./img/Logo.pdf -% SECTION ==================================================================================== +% Thema 1: Grundlagen der Schaltungs-Analyse ================================================= +%TODO: \input{./thema1_grundlagen.tex} +% ============================================================================================ + +% Thema 2: SPICE Simulation, PSPICE Tutorial ================================================= +%TODO: \input{./thema2_pspice.tex} +% ============================================================================================ + +% Thema 3: Lineare Transistorschaltungen ===================================================== \input{./thema3_transistor.tex} % ============================================================================================ -% SECTION ==================================================================================== +% Thema 4: Lineare OPV-Schaltungen============================================================ \input{./thema4_linearer_OPV.tex} % ============================================================================================ -% SECTION ==================================================================================== +% Thema 5: Nichtlineare OPV-Schaltungen ====================================================== \input{./thema5_nichtlinearer_OPV.tex} % ============================================================================================ +% Thema 6: Gegentakt-, Leistungs-Verstärker ================================================== +%TODO :\input{./thema6_gegentakt_verstaerker.tex} +% ============================================================================================ + +% Thema 7: Leistungselektronische Schaltungen, Lastschalter ================================== +%\input{./thema7_leistungselektronik_schalter.tex} +% ============================================================================================ + +% Thema 8: Leistungselektronische Schaltungen, Schaltverhalten, Brücken und Treiber ========== +%\input{./thema8_leistungselektronik_schaltungen.tex} +% ============================================================================================ + +% Thema 9: Spannungsversorgung, DC-DC Wandler ================================================ +%\input{./thema9_spannungsversorgung.tex} +% ============================================================================================ + % DOCUMENT_END 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xZ9RQ3rTlkU_V=Ql6&o`U~dYiMRrq~{p%{{S;n-`)TK literal 0 HcmV?d00001 diff --git a/ELK2_FS/thema3_transistor.tex b/ELK2_FS/thema3_transistor.tex index 9bc1a69..ee24400 100644 --- a/ELK2_FS/thema3_transistor.tex +++ b/ELK2_FS/thema3_transistor.tex @@ -3,31 +3,38 @@ % ============================================================================================ \begin{sectionbox} + + % BJT Formeln + % ---------------------------------------------------------------------- \subsection{Bipolartransistor} % NF Modell % - \begin{bluebox} + \begin{emphbox} $g_m \approx \frac{{I_C}^{(A)}}{U_T}$ \quad\ $g_{ce} \approx \frac{{I_C}^{(A)}}{VAF}$ \quad\ $g_{be} \approx \frac{{g_m}^{(A)}}{BF(=β_0)}$ - \end{bluebox} + \end{emphbox} % HF Modell % - \begin{bluebox} + \begin{emphbox} \item$c_{bc} \approx {C_{JBC}}^{(A)} = \frac{CJC}{(1-\frac{{U_{BC}}^{(A)}}{VJC})^{^{MJC}}}$ \item$c_{be} \approx {C_{DBE}}^{(A)} = T_F \cdot g_m$ - \end{bluebox} + \end{emphbox} % Typische Größenrelationen % - \begin{bluebox} + \begin{emphbox} $g_m >> g_{be} >> g_{ce}$ \quad\ $g_m >> \omega \cdot c_{bc}$ \quad\ $c_{be} >> c_{bc}$ - \end{bluebox} + \end{emphbox} \end{sectionbox} \begin{sectionbox} - \subsection{Seriengegengekoppelte Emitterschaltung} % Ohne CE% - % Spannungsverstärkung % + + % Seriengegengekoppelte Emitterschaltung (ohne CE) + % ---------------------------------------------------------------------- + \subsection{Seriengegengekoppelte Emitterschaltung} + + % Spannungsverstärkung % $\underline{a}_V = \frac {-g_m \cdot {r_L}^*} {1+(g_m+g_{be}) \cdot R_E}$ % Schnittstellenimpedanzen % @@ -35,7 +42,10 @@ $\underline{z}_{a,Tr} = r_{ce}\cdot(1+(R_E||(r_{be}+{r_G}^*))\cdot\frac{g_m\cdot r_{be}}{r_{be}+{r_G}^*})$ \newline $\underline{z}_{a,Tr}({r_G^*}=0) \approx r_{ce} \cdot (1 + g_m \cdot R_E))$ + % Emitterschaltung (mit CE) + % ---------------------------------------------------------------------- \subsection{Emitterschaltung} + % Spannungsverstärkung % $\underline{a}_V = -g_m \cdot {r_L}^*$ @@ -49,6 +59,8 @@ % Eckfrequenz Emitterkondensator $f_{3dB,CE} = \frac {g_m} {2\pi \cdot C_E}$ + % Kollektorschaltung + % ---------------------------------------------------------------------- \subsection{Kollektorschaltung} % Spannungsverstärkung % $\underline{a}_V = \frac{g_m \cdot {r_L}^*}{1+g_m \cdot {r_L}^*}$ @@ -69,6 +81,9 @@ \end{sectionbox} \begin{sectionbox} + + % Koppelkondensatoren + % ---------------------------------------------------------------------- \subsection{AC-, DC- Kopplung} $f_{3dB,Ck1} = \frac{1}{2\pi\cdot (R_G + r_{in})\cdot C_{k1}}$ \newline @@ -81,9 +96,16 @@ $HP_2$: $f_{3dB,Ck2} = f_{3dB,Ck1} = 0,644 \cdot f_{3dB,uB}$ \end{cookbox} +\end{sectionbox} + +\begin{sectionbox} + % Differenzstruktur + + % ---------------------------------------------------------------------- \subsection{Differenzverstärkung} $\underline{a}_{VD1} (=\frac{\underline{u}_{out1}}{\underline{u}_{id}}) = - \underline{a}_{VD2}(=\frac{-\underline{u}_{out2}}{\underline{u}_{id}}) $ \newline $= -\frac{g_m}{2}\cdot (r_L||r_{ce})=\frac{\underline{a}_{VD}}{2}$ \newline $\underline{z}_{inD} (=\underline{z}_{id}) =\frac{\underline{u}_{id}}{\underline{i}_{in1}} = 2\cdot r_{be}$ + \end{sectionbox} diff --git a/ELK2_FS/thema4_linearer_OPV.tex b/ELK2_FS/thema4_linearer_OPV.tex index 7f94ae3..26b6a5a 100644 --- a/ELK2_FS/thema4_linearer_OPV.tex +++ b/ELK2_FS/thema4_linearer_OPV.tex @@ -3,33 +3,160 @@ % ============================================================================================ \begin{sectionbox} + + % OPV Formeln + % ---------------------------------------------------------------------- \subsection{Operationsverstärker} - % Differenzverstärkung % - $A_{VD}(=V_{UD})=\frac{U_{OUT}}{U_{ID}}(typ.>100k)>>1$ \newline - % GLeichtaktverstärkung % - $A_{VC}=\frac{U_{OUT}}{U_{CM}} \approx 0$ \newline - % Common Mode Rejection Ratio % - $CMMR=\frac{A_{VD}}{A_{VC}}>>1$ \quad\ - $CMMR/dB=20\cdot log(\frac{A_{VD}}{A_{VC}})$ - % Frequenzgang % - $\underline{V}_{ud}(f)=\frac{V_{UD}}{\cancel{1}+\frac{j\cdot f}{f_1}}$ \newline - $f_1(=f_{1,3dB})=\frac{f_T(=GBW)}{V_{ud}}$ + % Differenzverstärkung % + $A_{VD}(=V_{UD})=\frac{U_{OUT}}{U_{ID}}(typ.>100k)>>1$ + % GLeichtaktverstärkung % + $A_{VC}=\frac{U_{OUT}}{U_{CM}} \approx 0$ + + % Common Mode Rejection Ratio % + $CMMR=\frac{A_{VD}}{A_{VC}}>>1$ \quad\ + $CMMR/dB=20\cdot log(\frac{A_{VD}}{A_{VC}})$ + + % Frequenzgang % + $\underline{V}_{ud}(f)=\frac{V_{UD}}{\cancel{1}+\frac{j\cdot f}{f_1}}$ + \begin{emphbox} + $f_1(=f_{1,3dB})=\frac{f_T(=GBW)}{V_{ud}}$ + \end{emphbox} + + % Standard-Rückkopplungsstruktur + % ---------------------------------------------------------------------- \subsection{Standardstruktur} + \begin{center} \includegraphics[width = 0.5\columnwidth]{img_02_01_Standardstruktur} \end{center} - $\underline{u}_2 = \underline{a}_V^+ \cdot \underline{u}_1^+ + \underline{a}_V^- \cdot \underline{u}_1^-$ \newline - $\underline{a}_V^+ = \frac{\underline{V}_{ud}}{1+\underline{k}\cdot\underline{V}_{ud}}$ \quad\ - $\underline{a}_V^- = -\frac{\underline{V}_{ud}\cdot(1-\underline{k})}{1+\underline{k}\cdot\underline{V}_{ud}}$\newline + % Schleifenverstärkung % + Schleifenverstärkung: $\underline{g} = \underline{V}_{ud} \cdot \underline{k}$ - % TODO: Nicht invertierender / invertierender Betrieb % - Betriebsfrequenzgrenze \emph{der Schaltung}: $f_g \approx \frac{GBW}{1/|\underline{k}(f_g)|}$ + % Ausgangsspannung % + $\underline{u}_2 = \underline{a}_V^+ \cdot \underline{u}_1^+ + \underline{a}_V^- \cdot \underline{u}_1^-$ - \subsection{Standard Linearverstärker} + % 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 + \end{emphbox} - \subsection{Stabilität} + \subsubsection{Betriebsmodi} + + % Nichtinvertierender Betrieb % + \underline{Nichtinvertierender Betrieb:} + \begin{bluebox} + \begin{center} + $\underline{u}_1^- = 0!$ \quad\ + $\underline{u}_1 = \underline{u}_1^+$ \quad\ + $\underline{g} = \underline{k} \cdot \underline{V}_{ud}$ + \end{center} + \end{bluebox} + + Normalbetrieb: $|\underline{k} \cdot \underline{V}_{ud}| >> 1$ + \begin{emphbox} + $\underline{a}_V = +\frac{1}{\underline{k}} = 1 + \frac{\underline{Z}_2}{\underline{Z}_1}$ + \end{emphbox} + + OPV-Vorwärtsbertrieb: $|\underline{k} \cdot \underline{V}_{ud}| << 1$ + \begin{emphbox} + $\underline{a}_V = \underline{V}_{ud}$ + \end{emphbox} + + % Invertierender Betrieb % + \underline{Invertierender Betrieb:} + \begin{bluebox} + \begin{center} + $\underline{u}_1^+ = 0!$ \quad\ + $\underline{u}_1 = \underline{u}_1^-$ \quad\ + $\underline{g} = \underline{k} \cdot \underline{V}_{ud}$ + \end{center} + \end{bluebox} + + Normalbetrieb: $|\underline{k} \cdot \underline{V}_{ud}| >> 1$ + \begin{emphbox} + $\underline{a}_V = -\frac{1-\underline{k}}{\underline{k}} = 1 - \frac{1}{\underline{k}} + = -\frac{\underline{Z}_2}{\underline{Z}_1}$ + \end{emphbox} + + OPV-Vorwärtsbertrieb: $|\underline{k} \cdot \underline{V}_{ud}| << 1$ + \begin{emphbox} + $\underline{a}_V = -\underline{V}_{ud} \cdot (1 - \underline{k})$ + \end{emphbox} + + \subsubsection{Betriebsfrequenzgrenze der Schaltung} + Betriebsfrequenzgrenze $f_g$ (= Durchtrittsfreq. $f_D$) + \begin{bluebox} + \begin{center} + $|\underline{g}(f_g (= f_D))| = |\underline{k}(f_g) \cdot \underline{V}_{ud}(f_g)| = 1$ + \end{center} + \end{bluebox} + + \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 + % ---------------------------------------------------------------------- + \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} } + + \subsubsection{Nichtinvertierender Standard Verstärker} + \pbox{4cm}{\includegraphics[width = 3cm]{img_02_03_nichtinvertierender_verstaerker}} + \parbox{3.5cm}{} + + \subsubsection{Spannungsfolger, Impedanzwandler} + \pbox{4cm}{\includegraphics[width = 3cm]{img_02_04_impedanzwandler}} + \parbox{3.5cm}{} + + \subsubsection{Integrierer} + \pbox{4cm}{\includegraphics[width = 3cm]{img_02_05_integrierer}} + \parbox{3.5cm}{} + + \subsubsection{Differentiator (Differenzierer)} + \pbox{4cm}{\includegraphics[width = 3cm]{img_02_06_differenzierer}} + \parbox{3.5cm}{} + + \subsubsection{Summierer (Invertierend)} + \pbox{4cm}{\includegraphics[width = 3cm]{img_02_07_summierer}} + \parbox{3.5cm}{} + + \subsubsection{Differenzverstärker (aktiver Subtrahierer, einfache Struktur)} + \pbox{4cm}{\includegraphics[width = 3cm]{img_02_08_differenzverstaerker}} + \parbox{3.5cm}{} + + + \subsubsection{Instrumentenverstärker (verbesserter Differenzverstärker)} + \pbox{4cm}{\includegraphics[width = 3cm]{img_02_09_instrumentenverstaerker}} + \parbox{3.5cm}{} + + \end{sectionbox} + %Force column break + \begin{sectionbox} + + \subsubsection{Spannungsgesteuerte Stromquelle ($G_m$)} + \pbox{4cm}{\includegraphics[width = 3cm]{img_02_10_stromquelle}} + \parbox{3.5cm}{} + + \subsubsection{Negativ-Impedanz-Konverter (NIC)} + \pbox{4cm}{\includegraphics[width = 3cm]{img_02_11_NIC}} + \parbox{3.5cm}{} + + \end{sectionbox}

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