From 8211401cf376499a6d033d70020bd01af24a50a9 Mon Sep 17 00:00:00 2001 From: Xaseiresh Date: Wed, 8 May 2024 15:57:18 +0200 Subject: [PATCH] feat(tex): :sparkles: continue work on the Grundlagen-Chapter --- .vscode/settings.json | 2 +- TeX/Kapitel/Grundlagen.tex | 81 +++++++++++++++++- TeX/Literaturverzeichnis.bib | 41 ++++++++- TeX/config/hyphenation.tex | 4 +- .../grundlagen/IMS_Schematic.drawio.png | Bin 354779 -> 354568 bytes TeX/grafiken/grundlagen/OpAmp.drawio.png | Bin 0 -> 25785 bytes TeX/grafiken/grundlagen/OpAmp_10x.drawio.png | Bin 0 -> 33654 bytes .../grundlagen/OpAmp_Noise.drawio.png | Bin 0 -> 60228 bytes 8 files changed, 120 insertions(+), 8 deletions(-) create mode 100644 TeX/grafiken/grundlagen/OpAmp.drawio.png create mode 100644 TeX/grafiken/grundlagen/OpAmp_10x.drawio.png create mode 100644 TeX/grafiken/grundlagen/OpAmp_Noise.drawio.png diff --git a/.vscode/settings.json b/.vscode/settings.json index 52cc0a6..b5b45ff 100644 --- a/.vscode/settings.json +++ b/.vscode/settings.json @@ -2,7 +2,7 @@ "latex-workshop.intellisense.update.delay": 5000, "latex-workshop.latex.autoBuild.interval": 10000, "latex-workshop.latex.autoBuild.run": "never", - "latex-workshop.latex.outDir": "build/%DIR%", + "latex-workshop.latex.outDir": "%DIR%/build", "latex-workshop.latex.search.rootFiles.include": [ "TeX/*.tex", "**/*.rnw", diff --git a/TeX/Kapitel/Grundlagen.tex b/TeX/Kapitel/Grundlagen.tex index 6e02c1f..a421349 100644 --- a/TeX/Kapitel/Grundlagen.tex +++ b/TeX/Kapitel/Grundlagen.tex @@ -47,7 +47,7 @@ Ein typischer Aufbau eines IMS ist in Abbildung \ref{fig:IMS_Schematic} dargeste \begin{figure}[h] \centering - \includegraphics[width=0.9\textwidth]{grundlagen/IMS_Schematic.drawio.png} + \includegraphics[scale=0.15]{grundlagen/IMS_Schematic.drawio.png} \caption{\label{fig:IMS_Schematic}Schematischer Aufbau einer IMS-Röhre nach \cite[Seite 3, Abb. 1.2.b]{Eiceman2013Oct}} \end{figure} @@ -61,7 +61,7 @@ Das Messergebnis eines IMS-Laufes wird as Spektrum bezeichnet, und wird meist al \subsubsection{Aufgabe eines TIV im IMS} -Wie in Kapitel \ref{chap:function_description_ims} beschrieben, beruht ein IMS auf der Messung der diskreten Ionenpakete, deren zeitlicher Versatz und Größe. Um die kleinen Ströme der Ionen, welche sich im Bereich von $\SI{100}{\pico\ampere}$ bis $\SI{10}{\nano\ampere}$ befinden, messen zu können, ist ein Verstärker notwendig. Dieser Verstärker wird als sog. Transimpedanzverstärker bezeichnet, da er als Eingangsgröße einen Strom hat, und eine Spannung als Ausgang gibt. Die Verstärkung wird somit in Ohm angegeben. Der TIV stellt hiermit ein zentrales Bauteil eines IMS dar, dessen Parameter maßgeblich die Qualität der Messungen beeinflusst. +Wie in Kapitel \ref{chap:function_description_ims} beschrieben, beruht ein IMS auf der Messung der diskreten Ionenpakete, deren zeitlicher Versatz und Größe. Um die kleinen Ströme der Ione im Bereich von $\SI{100}{\pico\ampere}$ bis $\SI{10}{\nano\ampere}$ messen zu können, ist ein Verstärker notwendig. Dieser Verstärker wird als sog. Transimpedanzverstärker bezeichnet, da er als Eingangsgröße einen Strom hat, und eine Spannung als Ausgang gibt. Die Verstärkung wird somit in Ohm angegeben. Der TIV stellt hiermit ein zentrales Bauteil eines IMS dar, dessen Parameter maßgeblich die Qualität der Messungen beeinflusst. Folgende Aufgaben werden an den TIV eines IMS gestellt: \begin{itemize} @@ -72,4 +72,79 @@ Folgende Aufgaben werden an den TIV eines IMS gestellt: \end{itemize} \section{Grundlagen des Operationsverstärkers} -\section{Grundlegende Parasitäreffekte} \ No newline at end of file + +Im folgenden werden die Grundlagen eines Operationsverstärkers (auch genannt OpAmp) dargelegt. Hierbei wird nicht auf den exakten internen Aufbau eingegangen, sondern das relevante Verhalten sowie einige Parasitäreffekte beschrieben. + +Ein klassischer Operationsverstärker ist ein elektronisches Bauteil, welches vielseitige Anwendungen in einer Schaltung findet. Er kann als verstärkendes oder filterndes Bauteil aufgebaut werden, sowie differenzierend oder integrierend wirken. Die grundlegende Operation eines OpAmps ist bei jeder Verschaltung jedoch äquivalent:\\ +Er besitzt zwei Eingänge, positiv und negativ, und einen Ausgang (siehe Abbildung \ref{fig:example_opamp}). +Dieser Ausgang wird so getrieben, dass die Spannung der Eingänge gleich ist. Mithilfe eines Rückkoppelpfades kann so die Transferfunktion des OpAmp angepasst werden. Abbildung \ref{fig:example_opamp_amplifier} zeigt einen simplen Verstärker-Schaltkreis, welcher das Eingangssignal um den Faktor 10 skaliert. + +\begin{figure} + \centering + \includegraphics[scale=0.25]{grundlagen/OpAmp.drawio.png} + \caption{\label{fig:example_opamp}Schematisches Symbol eines beispielhaften OpAmps} +\end{figure} + +\begin{figure} + \centering + \includegraphics[scale=0.25]{grundlagen/OpAmp_10x.drawio.png} + \caption{\label{fig:example_opamp_amplifier}Beispielhafte Verstärkerschaltung mit einem OpAmp} +\end{figure} + +Ein realer OpAmp kann für viele Anwendungen als nahezu ideal angesehen werden. Da in dieser Arbeit jedoch mit hohen Verstärkungen und kleinen Strömen gearbeitet wird, müssen die parasitären Effekte des OpAmps mit beachtet werden. Diese sind wie folgt: + +\begin{itemize} + \item Eingangs-Leckströme. Die Eingänge eines realen OpAmp können kleine Ströme führen. Je nach Verstärker befinden sich diese im Bereich von $\SI{1}{\micro\ampere}$ bis hin zu $\SI{1}{\femto\ampere}$. Diese Leckströme können die Spannungen an den Eingängen, und somit das Messergebis, beeinflussen\cite{analogINBIAS2008}. + \item Parasitäre Kapazitäten. Ein OpAmp hat, bedingt durch die physikalische Auslegung des Bauteils, verschiedene ungewollte Kapazitäten sowohl gegen Masse, als auch zwischen den Kanälen selbst. Diese können die Transferfunktion beeinflussen\cite{tiOpAmpCap2000}. + \item Endliche Geschwindigkeit. Ein realer OpAmp kann auf Signaländerungen nur in endlicher Zeit reagieren. Hierdurch ergibt sich eine Grenze der Bandbreite in Relation zur Verstärkung. Dies wird als Verstärkungs-Bandpreitenprodukt\todo{Spelling OK?} charakterisiert\cite{Cox2002}. Im folgenden wird dies als GBWP aus dem Englischen ``Gain-Bandwidth-Product'' bezeichnet. Dies kann ebenfalls die Transferfunktion beeinflussen, siehe Abbildung \ref{fig:example_opamp_gbwp}. + Das GBWP gibt an, bei welcher Frequenz der OpAmp eine Verstärkung von 1 aufweist. Die effektive Bandbreite eines OpAmp kann somit durch Dividieren des GBWP mit der Verstärkung berechnet werden. + \item Rauschen. Ein realer OpAmp hat verschiedene Rauschquellen, welche in das Messsignal übergehen können. Dies sind Eingangsbezogenes Strom- und Spannungsrauschen \cite{tiNoise2007}, und sind in Abbildung \ref{fig:example_opamp_noise} dargestellt. Das Spannungsrauschen ist hierbei im unteren Frequenzbereich proportional zu $1/\omega$ und flacht ab einer Eckfrequenz zu einem konstanten Wert ab, während das Stromrauschen konstant anfängt und im höheren Frequenzbereich proportional zu $\omega$ zu nimmt. +\end{itemize} + +\begin{figure}[h] + \centering + \missingfigure{GBWP data here!} + \caption{\label{fig:example_opamp_gbwp}Darstellung des Limits der Bandbreite in Abhängigkeit des GBWP} +\end{figure} + +\begin{figure}[h] + \centering + \includegraphics[scale=0.25]{grundlagen/OpAmp_Noise.drawio.png} + \caption{\label{fig:example_opamp_noise}Schematische Darstellung der Rauschquellen eines OpAmp nach \cite{tiNoise2007}} +\end{figure} + +\section{Grundlegende Parasitäreffekte} + +In diesem Kapitel wird auf die parasitären Effekte weiterer Bauteile eingegangen, die im folgenden relevant sind und bei der Auslegung der Schaltung beachtet werden müssen. + +\paragraph*{Leckströme:} Diese treten bei fast allen Schaltungsaufbauten auf. Sie entstehen durch die hohen aber endlichen Oberflächenwiderstände des PCB-Materials sowie durch durch Verunreinigungen. Diese erlauben es kleinen Leckströmen zwischen Zweigen der Schaltung zu fließen, und können bei Zweigen mit hoher Impedanz störend wirken.\todo{Find a citation for this} + +\begin{figure} + \centering + \missingfigure{Include figure of leakage paths } + \caption{\label{fig:example_leakages}Schematische Darstellung verschiedener Leckstrompfade} +\end{figure} + +\paragraph*{Parasitäre Kapazitäten:} Diese entstehen ebenfalls durch den physikalischen Aufbau der Schaltung. Die Nähe von Leitungen oder Kontakten zueinander, oder zu einer Kupferebene wie z.B. der Erdungsebene, erstellt eine leichte kapazitive Kopplung hierzwischen. Dieser Effekt verursacht Kapazitäten von $\SI{10}{\femto\farad}$ bis hin zu einigen $\SI{}{\pico\farad}$. + +\begin{figure} + \centering + \missingfigure{Include figure of parasitics } + \caption{\label{fig:example_parasitic_c}Schematische Darstellung der parasitären Kapazität} +\end{figure} + +Wichtig ist dieser Effekt in Kombination mit hochohmigen Eingängen und Widerständen. So wird z.B. die Impedanz eines $\SI{100}{\mega\ohm}$ Widerstandes bereits ab wenigen zehn Kilohertz maßgeblich durch die eigene parasitäre Kapazität beeinflust. Diese liegt bei der Standardbaugröße ``1206'' im Bereich von ca. $\SI{30}{\femto\farad}$, und bildet einen RC-Pass-Filter mit einer Eckfrequenz von $\SI{53.05}{\kilo\hertz}$. Abbildung \ref{fig:example_r_cp} zeigt beispielhaft die Verläufe verschiedener Widerstandsimpedanzen über die Frequenz. + +\begin{figure} + \centering + \missingfigure{Include figure of clean resistance impedance calculation here!} + \caption{\label{fig:example_r_cp}Impedanzverläufe verschiedener Widerstandswerte bei gleicher parasitärer Kapazität $C_p = \SI{30}{\femto\farad}$} +\end{figure} + +\paragraph*{Thermisches Rauschen:} Dieses Rauschen, genannt Johnson-Nyquist-Rauschen, betrifft resistive Komponenten. Es wird verursacht durch die thermische Bewegung von Ladungsträgern, und bildet ein weißes Rauschen aus. Das Rauschen lässt sich über die Formel $V_{\mathrm{n,rms}} = \sqrt{4k_BTR\Delta f}$ berechnen. Hierbei ist $V_{\mathrm{n,rms}}$ der RMS-Wert des Rauschens, $k_B$ die Boltzmann-Konstante, $T$ die Temperatur, $R$ der Widerstand des betrachteten Bauteils und $\Delta f$ die Bandbreite, über welche gemessen wird. \todo{Insert citation} + +\begin{figure} + \centering + \missingfigure{Include figure of resistor noise } + \caption{\label{fig:example_r_noise}Schematische Darstellung einer Widerstands-Rauschquelle} +\end{figure} \ No newline at end of file diff --git a/TeX/Literaturverzeichnis.bib b/TeX/Literaturverzeichnis.bib index 3630702..0ee3857 100644 --- a/TeX/Literaturverzeichnis.bib +++ b/TeX/Literaturverzeichnis.bib @@ -11,6 +11,15 @@ doi = {10.1016/j.ohx.2018.e00030} } +@book{Cox2002, + author = {Cox, James F.}, + title = {{Fundamentals of Linear Electronics: Integrated and Discrete}}, + year = {2002}, + isbn = {978-0-76683018-9}, + publisher = {Delmar Thomson Learning}, + url = {https://books.google.de/books?vid=ISBN0766830187&redir_esc=y} +} + @book{Eiceman2013Oct, author = {G. A. Eiceman, Z.Karpas, Herbert H. Hill Jr.}, editor = {}, @@ -18,4 +27,34 @@ title = {{Ion Mobility Spectrometry}}, year = {2013}, isbn = {978-1-4398-5998-8} -} \ No newline at end of file +} + +@techreport{tiNoise2007, + author = {Texas Instruments}, + institution = {Texas Instruments}, + journal = {Digital Signal Processing Solutions}, + title = {{Noise Analysis in Operational Amplifier Circuits}}, + year = {2007}, + url = {{https://www.ti.com/lit/an/slva043b/slva043b.pdf}}, + eid = {SLVA043B} +} + +@techreport{tiOpAmpCap2000, + author = {Texas Instruments}, + institution = {Texas Instruments}, + title = {{Effect of Parasitic Capacitance in Op Amp Circuits}}, + year = {2007}, + month = sep, + url = {{https://www.ti.com/lit/an/sloa013a/sloa013a.pdf?ts=1715091777328}}, + eid = {SLOA013A} +} + +@techreport{analogINBIAS2008, + author = {Analog Devices}, + intitution = {Analog Devices}, + title = {Op Amp Input Bias Current}, + year = {2008}, + url = {{https://www.analog.com/media/en/training-seminars/tutorials/MT-038.pdf}}, + eid = {MT-038} +} + diff --git a/TeX/config/hyphenation.tex b/TeX/config/hyphenation.tex index 410dd0b..a7f612d 100644 --- a/TeX/config/hyphenation.tex +++ b/TeX/config/hyphenation.tex @@ -4,8 +4,6 @@ \hyphenation{IGBT-Durch-lass-span-nung} \hyphenation{Ei-gen-er-wär-mung} \hyphenation{STMCubeIDE} - - - +\hyphenation{Span-nungs-rau-schen} diff --git a/TeX/grafiken/grundlagen/IMS_Schematic.drawio.png b/TeX/grafiken/grundlagen/IMS_Schematic.drawio.png index 3310ebaf9477a8243690eab55ba145e7c9b3722c..1c4e16af1f904fd9b86c08eb7e04179aed5e7f30 100644 GIT binary patch delta 27543 zcmc%xcRZHw|38jrMI=fnTSz5TR<=k)RNLwUNJWB@blAGJeORM8eI&b&H1! z{NU!|xORi*op<0_8x?hSv+G8BP6}pLPS+&NuQ}d&oOv0GtTa>j#{+!a>AiW|7awX~ zeW<|#|FFS7oZJsJxWboDSuI$88cVDd!dR7i9Y2Hoxr9p#Nk})@;udO|hw^!1wd6Qx zDry@@i&>00w#7Dl(LyYY5q1)eH8 zS98Ov>hGjt$FOi$a0zP0G%9t*F3pelE9@$dlk%}IHm*+SwSKSQGB^Fm#Vu~j_{pH} ztnSh*t^LSlTjHwx=!r 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