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%\documentclass[12pt,a4paper,openany,bibliography=totoc,captions=tableheading,numbers=noenddot]{scrreprt} %Book - Druckversion (doppelseitig) -\documentclass[12pt, a4paper, openany, DIV=16, BCOR=20mm, bibliography=totoc, captions=tableheading, numbers=noenddot]{scrbook} +%\documentclass[12pt, a4paper, openany, DIV=16, BCOR=20mm, bibliography=totoc, captions=tableheading, numbers=noenddot]{scrbook} %Book - Digitalversion (doppelseitig) -%\documentclass[12pt,a4paper,openany,bibliography=totoc,,captions=tableheading,numbers=noenddot]{scrbook} +\documentclass[12pt, a4paper, openany, bibliography=totoc,,captions=tableheading, numbers=noenddot]{scrbook} @@ -115,7 +115,7 @@ \include{Kapitel/Vermessung} \include{Kapitel/RevisionV11} -% \chapter{(Optional) Erstellung eines vollintegrierten TIV-Frontends} +\include{Kapitel/Zusammenfassung} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %Literaturverzeichnis diff --git a/TeX/Deckblatt.tex b/TeX/Deckblatt.tex index f2089a7..cdec5e4 100644 --- a/TeX/Deckblatt.tex +++ b/TeX/Deckblatt.tex @@ -1,35 +1,38 @@ \begin{titlepage} \enlargethispage{2.0cm} - \begin{center} -\vspace*{-2cm} + \vspace*{-1cm} + \begin{figure}[H] + \centering + \includegraphics[width=0.95\textwidth]{grafiken/title_header.png} + \end{figure} - \begin{figure}[h] - \centering - \includegraphics[height=4cm]{grafiken/welfenschloss_vektor.pdf} - \end{figure} + \vspace{2cm} -\vspace{1cm} + {\Large \textsc{Masterarbeit}} \\[0.2cm] + \rule{0.95\textwidth}{0.4pt}\\[3.5cm] - {\LARGE \textsc{Leibniz Universität Hannover}}\\[1.0cm] + {\LARGE \textbf{Entwicklung und Charakterisierung}} \\[0.2cm] + {\LARGE \textbf{eines rauscharmen Transimpedanzverstärkers}} \\ [0.2cm] + {\LARGE \textbf{für die Ionenmobilitätsspektrometrie}} \\ [2cm] + + {\large von} \\[0.2cm] + {\Large David Bailey} \\[0.2cm] + {\large Matrikelnummer: 10011830}\\[0.2cm] - {\Large \textsc{Fachpraktikum des Studienganges}} \\[0.2cm] - {\Large \textsc{M.Sc. Energietechnik}} \\ [2cm] + \vfill - {\Large \textbf{Implementation einer\\ - Arc-Detection der ECRH\\ - am Wendelstein W7-x\\ - Fusionsexperiment }} \\ [4cm] + {\large Betreuer:}\\[0.1cm] + {\large M. Hitzemann}\\[0.1cm] + {\large J. Winkelholz}\\[1cm] - {\Large Praktikumsbericht} \\ [1.5cm] + {\large Prüfer:}\\[0.1cm] + {\large 1. Prof. Dr.-Ing. Stefan Zimmermann}\\[0.1cm] + {\large 2. Prof. Dr.-Ing. Julia Körner}\\[1cm] - \vfil - - {\large David Bailey} \\ - {Matrikelnummer: 10011830 } \\ [1.5cm] + {September 2024}\\[2cm] \end{center} - \end{titlepage} diff --git a/TeX/Kapitel/Auslegung.tex b/TeX/Kapitel/Auslegung.tex index 6a2470b..f89b3b7 100644 --- a/TeX/Kapitel/Auslegung.tex +++ b/TeX/Kapitel/Auslegung.tex @@ -12,15 +12,24 @@ Eine Auswahl der Bauteile wird mit Hinsicht auf die Zielparameter des Designs du Wie in Abschnitt \ref{chap:tia_in_ims} dargestellt, ist die Aufgabe eines TIVs im IMS, die Stromflüsse der Ionenpakete auf eine messbare Spannung zu verstärken. Hierbei soll der TIV die Form eines solchen Paketes möglichst akkurat darstellen. -Für das in dieser Arbeit ausgewählte IMS-Verfahren ist bereits die Größe der Ionen-Pakete bekannt\todo{Insert ref here}. -Somit können aus diesen Messwerten die Zielwerte des Verstärkers abgeleitet werden. +Für das in dieser Arbeit ausgewählte IMS-Verfahren ist bereits die Größe der Ionen-Pakete bekannt. -Für eine erste Auslegung wird das folgende IMS-System angestrebt: \todo[inline]{Describe IMS}. -Dieses System generiert Ionenpakete mit einer Gausschen Verteilung \todo{verify this} mit einer Standardabweichung von circa $\SI{1.5}{\micro\second}$. +Der Verstärker wird so ausgelegt, dass er +für ein IMS nutzbar ist, welches am +Institut für Grundlagen der Elektrotechnik und Messtechnik +der Leibniz Universität Hannover genutzt wird. +Der Aufbau dieses IMS ist vergleichbar zu dem in +\cite{Reinecke2018Oct} dargestelltem System. + + +Dieses System generiert Ionenpakete mit einer +annähernd gausschen Verteilung, +mit einer Breite von circa $\SI{1.5}{\micro\second}$ +für die kleinsten Pakete. Eine beispielhafte Messung eines IMS-Systemes ist in Abbildung \ref{fig:example_ims_peak} dargestellt. Um diese Pakete abbilden zu können ist eine Bandbreite von mindestens $\SI{30}{\kilo\hertz}$ notwendig. -Die größte Peak-Amplitude, die hierbei zu erwarten ist, ist circa \todo{Insert peak amplitude}. -Somit reicht ein Eingangsbereich des TIV von $\pm\SI{1}{\nano\ampere}$. +Die größte Peak-Amplitude, die hierbei abgebildet werden soll, +befindet sich im Bereich von circa $\SI{1}{\nano\ampere}$. \begin{figure} \centering @@ -30,14 +39,17 @@ Somit reicht ein Eingangsbereich des TIV von $\pm\SI{1}{\nano\ampere}$. Der Ausgang des TIV wird einen Analog-Digital-Wandler (im folgenden ADC) antreiben. Diese Bauteile wandeln ein Spannungssignal in ein digitales Signal um, welches vom Rest des Systems ausgewertet werden kann. Der im Ziel-IMS ausgewählte ADC, -der \todo{insert ADC name}, hat einen Eingangsbereich von circa $\pm\SI{2}{\volt}$\todo{verify}. +der {\em LTC2274}, hat einen +differentiellen Eingangsbereich von $\pm\SI{2.25}{\volt}$. Bei gewünschtem nominalem Eingangsbereich von $\SI{1}{\nano\ampere}$ -und maximaler ADC-Eingangsspannung von $\pm\SI{2}{\volt}$ ist eine Verstärkung +und maximaler Ausgangsspannung von $\pm\SI{2}{\volt}$ ist eine Verstärkung von $\SI{1}{\giga\ohm}$ sinnvoll, um den ADC nicht zu saturieren. Somit kann die Gesamtverstärkung des TIVs festgelegt werden als: -$A_\mathrm{TIV} = V_\mathrm{out}/I_\mathrm{in} = \SI{1}{\volt} / \SI{1}{\nano\ampere} = \SI{1}{\giga\ohm}$ +\begin{equation*} + A_\mathrm{TIV} = V_\mathrm{out}/I_\mathrm{in} = \SI{1}{\volt} / \SI{1}{\nano\ampere} = \SI{1}{\giga\ohm} +\end{equation*} \cleardoublepage @@ -67,8 +79,14 @@ In einem TIV-Schaltkreis gibt es ein Bauteil mit hohem Widerstand: Der Rückkopp Somit wird vermutet, dass dieser Widerstand eine dominierende Quelle des thermischen Rauschens ist. Laut Gleichung \ref{eqn:thermal_voltage_noise} wächst die Amplitude des Spannungsrauschens mit der Wurzel des Widerstandswertes, wodurch eine erste Vermutung ist, dass ein kleinerer Widerstand besser wäre. -Für einen TIV ist der Eingang jedoch ein strombasierter Eingang. Somit muss das Stromrauschen betrachtet werden. -Dies lässt sich wie folgt berechnen:\todo{Cite or explain this} +Für einen TIV ist der Eingang jedoch ein strombasierter Eingang, und die +Verstärkung des TIV nimmt proportional zur Widerstandsgröße zu. + +Das Spannungsrauschen über dem Widerstand kann +nach Ersatzschaltbild \ref{fig:example_r_noise} +in einen äquivalenten Strom durch den Widerstand umgerechnet +werden, welcher in den Eingang des TIVs fließt. Dieser kann +wie folgt berechnet werden: \begin{eqnarray} I_\mathrm{n,rms} & = & \frac{V_\mathrm{n,rms}}{R} \\ @@ -111,6 +129,9 @@ Hierbei wird die Metallisierung nur auf einer Seite der Keramik, neben dem Wider Dies soll Streueffekte und Kapazitäten verringern. Das für diese Widerstandsart erstellte Modell ist in Abbildung \ref{fig:cst_model_1206_flipchip} dargestellt. +Bei der Modellierung wurde sich für beide Widerstandvarianten +auf \cite{VishayRFreq} bezogen. + \begin{figure}[hb] \begin{subfigure}[t]{.5\linewidth} \centering @@ -124,7 +145,7 @@ in Abbildung \ref{fig:cst_model_1206_flipchip} dargestellt. \end{subfigure} \caption[Simulationsmodelle der Widerstände in CST]{Die in CST Studio Suite 2021 erstellten Widerstandsmodelle. Zu sehen ist die Keramik in weiß, die Metallkontakte in Braun, und der Kohlefilm in Dunkellila. - Eigene Modellierung.} + Eigene Modellierung nach \cite{VishayRFreq}.} \end{figure} Mithilfe dieser Modelle werden die kapazitiven Kopplungen bestimmt. @@ -212,9 +233,10 @@ da sich die auf einer leitenden Fläche befindende Ladung wie folgt berechnen l \iint \mathbf{D} \cdot dS = \iiint \rho_f dV\label{eqn:integral_d} \end{equation} -Durch Bestimmung der Flussrichtungen des D-Feldes lassen sich somit die Quellen der -Ladungen bestimmen. Dies ist zum Verständnis der Kapazität und der späteren Verminderung dieser -nützlich.\todo{Rewrite this more understandably} +Die Quellen des D-Feldes geben so Hinweise auf die Ladungsverteilung +der Simulation, wobei diese Ladungen von den hier betrachteten +Kapazitäten verursacht werden. Die D-Felder zeigen somit auf, +welche Elemente der Simulation zur Kapazität beitragen. \begin{figure}[p] \centering @@ -347,9 +369,12 @@ trifft auf sowohl den Standard-Widerstand als auch den Flipchip zu. Um den parasitären Kapazitäten entgegen zu wirken soll nun erprobt werden, ob durch eine bestimmte Platzierung von Elektroden im PCB-Material -die Parallelkapazität verringert werden kann.\todo{Find a citation for this.} -Durch korrekte Platzierung von Elektroden mit festgelegtem Potential kann theoretisch das D-Feld auf diese umgeleitet -werden, wodurch das PCB-Material selbst eine kleinere Teilhabe an der parasitären Kapazität des Widerstandes haben sollte. +die Parallelkapazität verringert werden kann. +Durch korrekte Platzierung eines sog. Guard Rings bzw. +einer Abschirmungselektrode +kann theoretisch das D-Feld auf diese umgeleitet +werden, wodurch das PCB-Material selbst eine kleinere Teilhabe an der +parasitären Kapazität des Widerstandes haben sollte \cite{SierraReduceCapacitances}\cite{Yang:21}. Ein erster Versuch hierfür wird aus zwei symmetrischen Elektroden aufgebaut, welche unterhalb der Kontakte der Widerstände aufgebaut werden und auf dasselbe Potential wie die entsprechenden Kontakte gelegt werden. @@ -379,7 +404,10 @@ Abbidlung \ref{fig:r_shielding_capacitances} zeigt alle Kapazitäten, welche von \begin{figure}[h] \centering \includegraphics[width=0.6\linewidth]{entwicklung/cst_estatic_shld/shielding_capacitors.drawio.png} - \caption{\label{fig:r_shielding_capacitances}Schematische Darstellung der Kapazitäten, welche einer der Widerstandskontakte sieht.} + \caption[Schematische Darstellung der Kapazitäten, welche einer der Widerstandskontakte sieht]{ + \label{fig:r_shielding_capacitances} + Schematische Darstellung der Kapazitäten, welche einer der Widerstandskontakte sieht. + Eigene Darstellung.} \end{figure} Von Interesse sind die Parallelkapazität der Widerstandskontake, $C_\mathrm{r,p}$, @@ -455,7 +483,7 @@ Bandbreite zu vermeiden. Mit der verringerten Parallelkapazität lassen sich somit größere Widerstände verwenden. Die erneut berechneten Grenzwerte sind in Tabelle \ref{table:para_rshield_max} aufgelistet. -\begin{table}[hb] +\begin{table}[ht] \centering \caption{\label{table:para_rshield_max}Obere Grenzwerte der Widerstandsauswahl mit Abschrimung} \begin{tabular}{ |c|r| } @@ -468,6 +496,8 @@ Grenzwerte sind in Tabelle \ref{table:para_rshield_max} aufgelistet. \end{tabular} \end{table} +\FloatBarrier + Da die berechneten Werte noch nicht der in Kapitel \ref{chap:tia_design_goals} festgelegten Verstärkung entsprechen, werden zusätzlich noch andere Möglichkeiten zur Verringerung der Parallelkapazität hinzu gezogen. @@ -503,7 +533,7 @@ Abbildung \ref{fig:r_series_para_sim} zeigt die verwendete Schaltung auf; die Er in Abbildung \ref{fig:r_series_para_results} aufgezeigt. Varriert wird hierbei die Größe der einzelnen Kapazitäten zur Erde hin. -\begin{figure}[hb!] +\begin{figure}[htb!] \centering \includegraphics[width=0.8\textwidth]{entwicklung/r_series/series_noshield.png} \caption{\label{fig:r_series_para_sim}Aufbau der Simulation zur @@ -520,13 +550,13 @@ Kapazitäten zur Erde hin. Rückkoppelpfad.} \end{figure} +\FloatBarrier + Deutlich zu erkennen ist eine starke Überhöhung der Bandbreite der Schaltung bei steigenden parasitären Kapazitäten, welche auf eine Instabilität der Schaltung hinweisen. Eine Verringerung der Kapazität zur Erde ist somit notwendig zum Erhalt der Stabilität bei Nutzung einer Reihenschaltung von Widerständen. -\FloatBarrier - Hierfür können die im vorherigen Teil beschriebenen Abschirmungselektroden genutzt werden. Werden diese Elektroden über einen Widerstandsteiler auf die gleichen Potentiale wie die hochimpedanten Widerstandszweige gelegt, so fließt kein Strom durch die parasitären Kapazitäten zur Abschirmung und @@ -541,7 +571,7 @@ jedoch in einer Simulation schwer zu belegen, da die parasitären Rauscheffekte einer realen Schaltung nicht einfach zu simulieren sind. -\begin{figure}[hbt!] +\begin{figure}[htb!] \centering \includegraphics[width=0.8\textwidth]{entwicklung/r_series/series_shielded.png} \caption[Aufbau der Simulation zur @@ -549,7 +579,7 @@ einer realen Schaltung nicht einfach zu simulieren sind. Analyse des Effektes der Schirmungskapazitäten auf eine Widerstands-Serienschaltung.} \end{figure} -\begin{figure}[hbt!] +\begin{figure}[htb!] \centering \includegraphics[scale=0.8]{datavis/Parasitics/Rf_series_shielded.png} \caption[Ergebnisse der Simulation @@ -561,8 +591,7 @@ einer realen Schaltung nicht einfach zu simulieren sind. \end{figure} -\FloatBarrier -\newpage +\clearpage \subsection{Effekte des OpAmp} \label{chap:effects_opamp} @@ -604,8 +633,8 @@ der Schaltung gewählt. Die Stromquelle I1 wird als Stimulus-Eingang genutzt und gibt ein Signal von $\SI{1}{\nano\ampere}$ aus. Eine parasitäre Eingangskapazität -von $\SI{10}{\pico\farad}$ wird entsprechend Erfahrungswerten\todo{rewrite} -bestehender Schaltkreise gewählt. +von $\SI{10}{\pico\farad}$ wird als beispielhafter +Wert der Eingangskapazität von OpAmp, PCB und Eingangsbuchse gewählt. Die parasitäre Parallelkapazität C1 wird auf $\SI{3}{\femto\farad}$ als absolutes Minimum der in Kapitel \ref{chap:r_para_calculations} berechneten Kapazitäten gesetzt. Gemessen wird die Ausgangsspannung des Verstärkers U1. @@ -639,9 +668,9 @@ welche somit die Stabilität des Systems beeinflusst. Eine solche Überhöhung muss vermieden werden, um Oszillationen sowie übermäßiges Rauschen zu vermeiden. Ab dem $\SI{1}{\giga\hertz}$ GBWP-OpAmp ist keine solche Überhöhung zu sehen, die Bandbreite ist hier überwiegend durch den Rückkoppelwiderstand begrenzt und das System ist stabil. -Die Reduktion der -3dB-Bandbreite, welche in Tabelle \ref{table:opamp_gbwp_results} ab +Die Reduktion der -3~dB-Bandbreite, welche in Tabelle \ref{table:opamp_gbwp_results} ab $\SI{316.22}{\mega\hertz}$ zu sehen ist, ist durch die Resonanz zu erklären. -Diese zieht die Übertragungsfunktion nach oben und verschärft den Abfall, wodurch die -3dB-Frequenz +Diese zieht die Übertragungsfunktion nach oben und verschärft den Abfall, wodurch die -3~dB-Frequenz nach oben gezogen wird. \begin{table}[ht] @@ -649,7 +678,7 @@ nach oben gezogen wird. \caption{\label{table:opamp_gbwp_results}Aus der Simulation bestimmte Bandbreiten der OpAmps bei variiertem GBWP} \begin{tabular}{ |r|r|r| } \hline - GBWP & -3dB Punk & Überhöhung \\ + GBWP & -3~dB Punk & Überhöhung \\ \hline $\SI{1.00}{\mega\hertz}$ & $\SI{6.00}{\kilo\hertz}$ & $\SI{22.03}{\decibel}$ \\ $\SI{3.16}{\mega\hertz}$ & $\SI{10.96}{\kilo\hertz}$ & $\SI{17.01}{\decibel}$ \\ @@ -675,9 +704,9 @@ welche somit die Stabilität des Systems beeinflusst. Eine solche Überhöhung muss vermieden werden, um Oszillationen sowie übermäßiges Rauschen zu vermeiden. Ab dem $\SI{1}{\giga\hertz}$ GBWP-OpAmp ist keine solche Überhöhung zu sehen, die Bandbreite ist hier überwiegend durch den Rückkoppelwiderstand begrenzt, und das System ist stabil. -Die Reduktion der -3dB-Bandbreite, welche in Tabelle \ref{table:opamp_gbwp_results} ab +Die Reduktion der -3~dB-Bandbreite, welche in Tabelle \ref{table:opamp_gbwp_results} ab $\SI{316.22}{\mega\hertz}$ zu sehen ist, ist durch die Resonanz zu erklären. -Diese zieht die Transferfunktion nach oben und verschärft den Abfall, wodurch die -3dB-Frequenz +Diese zieht die Transferfunktion nach oben und verschärft den Abfall, wodurch die -3~dB-Frequenz nach oben gezogen wird. Zur Erfassung der benötigten offenen Verstärkung des OpAmp wird die LTSpice Simulation aus @@ -685,7 +714,7 @@ Abbildung \ref{fig:opamp_gbwp_circuit} erneut genutzt. Nun wird jedoch nicht das variiert, sondern die offene Verstärkung. Abbildung \ref{fig:opamp_aol_sweep_2} zeigt die Simulationsergebnisse auf. -\begin{figure}[hb] +\begin{figure}[ht] \centering \includegraphics[scale=0.8]{datavis/Parasitics/SingleStage_Aol_Sweep.png} \caption[Darstellung des Einflusses der offenen Verstärkung @@ -705,6 +734,8 @@ Ungleich des GBWP ist so eine Begrenzung der Bandbreite durch eine zu kleine off Verstärkung nicht detrimental für die Stabilität der Schaltung. Lediglich die Bandbreite selbst muss beachtet werden. +\FloatBarrier + Um sicher zu stellen dass die Stabilität der Schaltung auch bei variierenden parasitären Effekten gegeben ist, werden Simulationen mit variablem C1 und Cin (siehe Abbildung \ref{fig:opamp_gbwp_circuit}) durchgeführt. Die Ergebnisse hiervon sind in Abbildungen \ref{fig:opamp_gbwp_variation_result_1} und @@ -723,7 +754,7 @@ Die Ergebnisse hiervon sind in Abbildungen \ref{fig:opamp_gbwp_variation_result_ } \end{figure} -\begin{figure}[ht] +\begin{figure}[htb] \centering \includegraphics[scale=0.8]{datavis/Parasitics/SingleStage_Cfp_Sweep.png} \caption[Ergebnisse der Simulation eines idealen @@ -749,6 +780,8 @@ Aus den Simulationen wird geschlossen, dass ein Mindest-GBWP von $\SI{1}{\giga\h notwendig ist, um stabil zu bleiben und die Bandbreite zu erhalten, wobei ein größeres GBWP vorteilhaft erscheint. Eine minimale offene Verstärkung von circa 10 000 ist notwendig, um die Bandbreite nicht zu beeinflussen. +\FloatBarrier + \subsubsection{Verbesserung der OpAmp Bandbreite} Wie im vorherigen Kapitel beschrieben, ist eine höhere Bandbreite des OpAmp notwendig, @@ -778,9 +811,8 @@ Hierfür werden zwei Möglichkeiten erprobt: \item[b)] \textbf{Eine Komposit-Schaltung von OpAmps:} Anstelle einzelne Stufen hintereinander zu schalten ist es ebenso möglich, - mehrere OpAmps zu einem Gesamtverstärker mit insgesamt höherer Bandbreite zu verschalten.\todo{ - Find a citation for this? - } + mehrere OpAmps zu einem Gesamtverstärker mit insgesamt höherer Bandbreite zu verschalten + \cite[S.S. 332]{Horowitz:1981307}. Vorteilhaft ist die insgesamt höhere Präzision, da der Feedback-Pfad des gesamten Systems über alle OpAmps geschaltet ist. @@ -904,7 +936,7 @@ genügend GBWP und kleinen Eingangsleckströmen, um als TIV nutzbar zu sein. Bestimmung OpAmp-Rauschens]{ \label{fig:opamp_vin_noise_schematic}Schaltkreis der LTSpice-Simulation zur Bestimmung OpAmp-Rauschens.} -\end{figure} +\end{figure}\todo{Trim this image?} Variiert werden $C_\mathrm{in}$ sowie $R_\mathrm{f}$, um die Auswirkungen dieser Parameter betrachten zu können. Hierbei wird das Rauschen eingangsbezogen gemessen, d.h. die Ausgangsspannung @@ -914,7 +946,7 @@ und \ref{fig:opamp_vin_noise_cin} dargestellt. \FloatBarrier -\begin{figure}[ht] +\begin{figure}[hbt] \includegraphics[scale=0.8]{datavis/Parasitics/SingleStage_LTC_Rf_Sweep_Noise.png} \caption[Rauschen in Abhängigkeit von $R_\mathrm{f}$]{ \label{fig:opamp_vin_noise_rf}Rauschen in Abhängigkeit von $R_\mathrm{f}$. diff --git a/TeX/Kapitel/Auslegung/Schaltungsdesign.tex b/TeX/Kapitel/Auslegung/Schaltungsdesign.tex index 724186f..e3eed10 100644 --- a/TeX/Kapitel/Auslegung/Schaltungsdesign.tex +++ b/TeX/Kapitel/Auslegung/Schaltungsdesign.tex @@ -117,7 +117,7 @@ verringern. Aus dem gleichen Grund werden Kupferflächen reduziert und als Muster anstatt als ausgefüllte Flächen ausgeführt. Um einen Ladungsaufbau zu verhindern, muss der Isolations-Lack der Platine um den Rückkoppelpfad entfernt werden, während Leckströme durch -weitere Abschirmungspfade verringert werden. +weitere Abschirmungspfade verringert werden \cite[S.S. 42]{DatasheetADA4530}. Abbildung \ref{fig:tia_v1_pcb} zeigt das Design der Platine für den Teil des TIVs selbst. Der Messeingang ist hierbei der runde Kreis des inneren @@ -198,7 +198,7 @@ Komponentenreihen (E24), nicht trivial ist. Die erstellte Filter-Stufe ist in Abbildung \ref{fig:filter_stage_design} dargestellt. Die berechnete Übertragungsfunktion dieses Filters ist in Abbildung \ref{fig:filter_stage_bandwidth} aufgezeichnet. -Zu sehen ist eine glatte Übertragungsfunktion bis hin zum -3dB-Punkt bei $\SI{30}{\kilo\hertz}$, +Zu sehen ist eine glatte Übertragungsfunktion bis hin zum -3~dB-Punkt bei $\SI{30}{\kilo\hertz}$, nach welchem wie erhofft ein steiler Abfall von -80dB/Dekade vor liegt. Somit werden Rauschanteile sowie andere Störsignale bereits ab $\SI{50}{\kilo\hertz}$ um einen Faktor von 20dB gedämpft. diff --git a/TeX/Kapitel/Einleitung.tex b/TeX/Kapitel/Einleitung.tex index c64875f..31e6e00 100644 --- a/TeX/Kapitel/Einleitung.tex +++ b/TeX/Kapitel/Einleitung.tex @@ -1,20 +1,49 @@ \chapter{Einleitung} -\todo[inline]{Rework this *after* completing other chapters} +Die Analyse von Gasgemischen findet in vielen +Bereichen der Industrie- und Medizintechnik Anwendung. +Mitunter geht es um medizinisch wichtige Daten wie +die Überwachung des Metabolismus eines Patienten, +oder um sicherheitsrelevante Messungen wie die +Überprüfung einer Stoffprobe auf explosive Stoffe. -Die Analyse von Gasgemischen findet in vielen Bereichen der Industrie- und Medizintechnik Anwendung. Mitunter geht es um medizinisch wichtige Daten wie die Überwachung des Metabolismus eines Patienten, oder um sicherheitsrelevante Messungen wie die Überprüfung einer Stoffprobe auf explosive Stoffe. -Von Vorteil sind hierbei sowohl schnelle als auch sensitive Messungen, um Zuverlässig auf gegebene Zustandsänderungen reagieren zu können.\\ -Eine der Methoden dieser Analyse bietet das Ionenmobilitätsspektrometer (im Folgenden hier IMS) an. Das IMS nutzt die variablen Ionisierbarkeiten und Mobilitäten von Molekülen in einem Gas aus um diese zu trennen und zu vermessen. Durch diese Funktionsweise können Messungen innerhalb weniger Minuten bis Sekunden durchgeführt werden, wobei Stoffkonzentrationen von \todo[inline]{Add concentration here} festgestellt werden können. +Eine der Methoden dieser Analyse bietet +das Ionenmobilitätsspektrometer (IMS) an. +Das IMS nutzt die variable Ionisierbarkeit und +Mobilität von Molekülen in einem Gas aus um diese +zu trennen und zu vermessen. Durch diese Funktionsweise +können Messungen innerhalb weniger Minuten bis zehntel von +Sekunden durchgeführt werden, +und es können kleinste Stoffmengen festgestellt werden \cite{Eiceman2013Oct}. -Ein zentraler Bestandteil des Aufbaus eines IMS ist nun der Transimpedanzverstärker (im Folgenden hier TIV). Dieses Element befasst sich mit der Umwandlung der zu messenden Ionen in ein Spannungssignal, welche von der Ausleseleketronik verarbeitet werden können. Somit bestimmt die Qualität und Sensitivität des TIV maßgeblich die Datenerfassung des IMS insgesamt. -Von relevanz sind hier verschiedene Parameter wie z.B. Bandbreite, Rauschverhalten und Verstärkung, welche auf den jeweiligen Anwendungsbereich des IMS angepasst werden müssen. +Ein zentraler Bestandteil des Aufbaus eines +IMS ist nun der Transimpedanzverstärker (TIV) \cite{Reinecke2018Oct}. +Dieser ist ein zentrales Element der Messkette, +welche die Ionen detektiert und für die restliche +Auswertung messbar macht. +Somit bestimmt die Performance des TIV maßgeblich +z.~B. die Detektionsgrenze und das Auflösungsvermögen +des IMS. +Bestehende TIVs bieten akzeptable Messqualität, sind jedoch +entweder sehr teuer, oder benötigen manuelle Nachjustierungen +und Korrekturen. -In dieser Arbeit wird die Auslegung und Erstellung eines kompakten, sensitiven TIVs dargestellt, welcher auf die IMS-Geräte des Institut für Grundlagen der Elektrotechnik und Messtechnik (GEM) an der Leibniz Universität Hannover angepasst ist. -Der TIV wird auf zwei verschiedene IMS-Systeme mit unterschiedlichen Anforderungen angepasst.\\ -In Kapitel 2 wird die Funktionsweise eines IMS nähergehend erklärt. Hierbei werden die jeweiligen Größen- und Zeitskalen, für die der TIV ausgelegt werden soll, erläutert, und die Aufgabe des TIV im Bezug auf das Gesamtsystem wird genauer erklärt. Zudem werden notwendige Grundlagen vermittelt.\\ -In Kapitel 3 wird ein Modell des TIVs erstellt. Zuerst werden die Zielparameter beschrieben, welche vom TIV gewünscht sind. -Neben der Erläuterung der Funktionsweise eines TIVs werden die verschiedenen parasitären Effekte genauer charakterisiert, welche die Schaltung beeinträchtigen, und es wird auf Möglichkeiten eingegangen um diesen Effekten entgegen zu wirken. Hiernach wird eine reale Schaltung ausgelegt, und mithilfe von Simulationen charakterisiert.\\ -In Kapitel 4 wird ein Prototyp der TIV-Schaltung erbaut und vermessen. Es werden hierbei vergleiche mit den erstellten Simulationen gezogen, und es wird auf Diskrepanzen zu diesen eingegangen. Abschließend werden Messungen an einem realen IMS-System ausgeführt, um die Funktionstüchtigkeit des erbauten TIV zu bestätigen.\\ -Kapitel 5 befasst sich mit der Erstellung einer vollintegrierten Schaltung auf Basis des erstellten TIV, welcher die gesamte Analogkette der IMS-Messung beinhaltet. \todo{Did this happen?}\\ -Abschließend beschreibt Kapitel 6 einen Ausblick auf zukünftige Anwendungsgebiete des erstellten TIV, und fasst die erstellten Messungen zusammen. \ No newline at end of file +Es soll in dieser Arbeit ein neuer TIV ausgelegt werden, +welcher ohne Nachjustierungen und mit leicht verfügbaren +Bauteilen gebaut werden kann, um eine kostengünstige +und reproduzierbare Alternative anzubieten. +In dieser Arbeit wird die Entwicklung, Auslegung +und Vermessung des neuen TIV-Designs beschrieben. +Hierbei werden verschiedene störende Faktoren +wie z.~B. parasitären Effekte analytisch sowie mithilfe +von Simulationen untersucht, und basierend hierauf +werden Möglichkeiten zur Reduktion und Kompensation +der negativen Effekte ausgelegt. + +Der erstellte TIV wird vermessen und charakterisiert, +wobei die Messergebnisse mit den Simulationen verglichen +werden. Eventuelle Fehler und ungewünschtes Verhalten werden +genauer analysiert und korrigiert. +Schlussendlich werden einige Vergleichsmessungen des neu +erstellten TIVs mit den bestehenden Designs durchgeführt. \ No newline at end of file diff --git a/TeX/Kapitel/Grundlagen.tex b/TeX/Kapitel/Grundlagen.tex index f3bf792..0cc8445 100644 --- a/TeX/Kapitel/Grundlagen.tex +++ b/TeX/Kapitel/Grundlagen.tex @@ -20,7 +20,7 @@ stellen zu können, sowie um später die Betriebsparameter dessen festlegen zu k Im Folgenden soll auf die Relevanz und den Anwendungsbereich von Ionenmobilitätsspektrometern eingegangen werden, um dar zu legen dass die Technologie breite praktische Anwendungen findet. Ein IMS bietet im Vergleich zu anderen Gasanalyseverfahren wie z.B. einem Massenspektrometer folgende Vorteile \cite{Eiceman2013Oct}: \begin{itemize} - \item Kostengünstig. Ein IMS kann mitunter für wenige hundert Euro aufgebaut werden\cite{Reinecke2018Oct}, wodurch sie leichter in größeren Mengen aufgebaut werden können. + \item Kostengünstig. Ein IMS kann mitunter für wenige hundert Euro aufgebaut werden \cite{Reinecke2018Oct}, wodurch sie leichter in größeren Mengen aufgebaut werden können. \item Simpler, kompakter Aufbau. Ein IMS kann unter atmosphärischem Druck betrieben werden, und braucht somit kein Vakuum-Equipment. Hierdurch sind die Systeme wesentlich transportabler als z.B. Massenspektrometer. \item Schnelle Messungen. Messungen mit einem IMS können bis hinunter auf wenige zehntel von Sekunden dauern. Hierdurch lassen sich schnell wichtige Messwerte erfassen. \item Hohe Sensitivität. Ein IMS kann Stoffkonzentrationen im unteren ppb messen, wodurch auch kleinste Mengen eines Stoffes sicher bestimmt werden können. @@ -42,7 +42,7 @@ Der Author Eiceman beschreibt im Buch ``Ion Mobility Spectrometry'' die Ionenmob ``Der Term Ionen Mobilitäts Spektrometrie (IMS) beschreibt die Prinzipien, Methoden und Instrumente zur Charakterisierung von Substanzen anhand der Geschwindigkeit von Gruppen (definiert als Gruppen von gasförmigen Ionen) entnommen von einer Substanz, in einem elektrischen Feld und einem Driftgas.'' \cite[S.S. 1]{Eiceman2013Oct} \end{quote} -Ein IMS-System analysiert somit Gase, in dem eine Gasprobe ionisiert wird, und mithilfe verschiedener Methodiken in diskrete Gruppen aufgespalten wird. Der Ablauf dieses Vorganges ist grundsätzlich wie folgt \cite[Seite 4]{Eiceman2013Oct}: +Ein IMS-System analysiert somit Gase, in dem eine Gasprobe ionisiert wird, und mithilfe verschiedener Methodiken in diskrete Gruppen aufgespalten wird. Der Ablauf dieses Vorganges ist grundsätzlich wie folgt \cite[S.S. 4]{Eiceman2013Oct}: Ein IMS-System analysiert somit Gase, indem eine Gasprobe ionisiert wird und mithilfe eines Trägergases und eines elektrischen Feldes in diskrete Gruppen aufgespalten wird. Der Ablauf dieses Vorganges @@ -110,25 +110,23 @@ 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 der Bauteile -und des PCBs sowie durch durch Verunreinigungen. Diese erlauben +und des PCBs sowie durch durch Verunreinigungen \cite{AltiumLeakages}. Diese erlauben es kleinen Leckströmen zwischen Zweigen der Schaltung zu fließen, -und können bei Zweigen mit hoher Impedanz störend wirken. +und können bei Zweigen mit hoher Impedanz störend wirken +\cite[S.S. 33-34]{DatasheetADA4530}. Abbildung \ref{fig:example_leakages} zeigt beispielhaft einige der Leckströme auf -einer Platine. \todo{Find a citation for this} +einer Platine. \begin{figure}[hb] \centering - \includegraphics[scale=0.25]{grundlagen/Examples_Leakages.drawio.png} + \includegraphics[scale=0.18]{grundlagen/Examples_Leakages.drawio.png} \caption[Schematische Darstellung der Leckströme eines PCBs]{\label{fig:example_leakages} - Schematische Darstellung eines PCBs mit Anschlüssen zu Bauteilen (goldene Pads) - und Leiterbahnen (dunkelgrün) mit verschiedenen Leckstrompfaden entlang der Oberfläche - (schraffiert dargestellt). + Schematische Darstellung eines PCBs mit Anschlüssen zu Bauteilen + und Leiterbahnen, mit verschiedenen Leckstrompfaden entlang der Oberfläche. Leckströme fließen überwiegend zwischen freigelegten Kupferflächen, können zudem auch durch Oberflächenladungen in einem Isolator wie dem PCB-Lötstopplack entstehen. - Eigene Darstellung nach ???.} + Eigene Darstellung nach \cite{AltiumLeakages}.} \end{figure} -\todo{Add labelling here, I guess?} -\todo{Find a citation} \paragraph*{Parasitäre Kapazitäten:} \label{chap:basics_parasitics_capacitances} @@ -136,7 +134,8 @@ 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 -im Bereich von einigen $\SI{}{\pico\farad}$. +im Bereich von einigen $\SI{}{\femto\farad}$, bei größeren Komponenten +sogar im Bereich von $\SI{}{\pico\farad}$. Abbildung \ref{fig:example_parasitic_c} zeigt einige dieser Kapazitäten auf. \begin{figure}[h] @@ -146,25 +145,28 @@ Abbildung \ref{fig:example_parasitic_c} zeigt einige dieser Kapazitäten auf. Schematische Darstellung einer Schnittfläche eines PCBs mit Leitungen und einem Bauteil, mit einigen parasitären Kapazitäten eingezeichnet. Diese Kapazitäten entstehen sowohl zwischen zwei Leitungen, Leitungen und Erdflächen, sowie den Anschlüssen eines Bauteiles. - Eigene Darstellung nach.} + Eigene Darstellung nach \cite{SierraReduceCapacitances} und \cite{AltiumReduceCapacitance}.} \end{figure} -\todo{find citation} -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 beeinflusst. +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 beeinflusst +\cite{Yang:21}\cite{JBellemann22}\cite{VishayRFreq}\cite[S.S. 39]{DatasheetADA4530}. Die Parallelkapazität ist stark von der Bauform des Widerstandes abhängig, -und liegt bei der Standardbaugröße ``1206'' im Bereich von ca. $\SI{30}{\femto\farad}$. +und liegt bei der Standardbaugröße ``1206'' im Bereich von ca. $\SI{50}{\femto\farad}$ \cite{JBellemann22}. So wird sich bei dem $\SI{100}{\mega\ohm}$ Widerstand ein RC-Pass-Filter mit einer Grenzfrequenz von $\SI{53.05}{\kilo\hertz}$ ausbilden. Abbildung \ref{fig:example_r_cp} zeigt einige in einer Simulation berechneten Verläufe verschiedener Widerstandsimpedanzen über die Frequenz, und wie diese durch die parasitäre Kapazität einbrechen. -\begin{figure} +\FloatBarrier + +\begin{figure}[ht] \centering \includegraphics[scale=0.8]{datavis/Parasitics/Examples_R_Cp_RSweep.png} \caption[Impedanzverläufe verschiedener Widerstandswerte]{\label{fig:example_r_cp} - Impedanzverläufe verschiedener Widerstandswerte bei gleicher parasitärer Kapazität $C_p = \SI{30}{\femto\farad}$, - dem typischen Wert für die ``1206''-Bauform. + Impedanzverläufe verschiedener Widerstandswerte bei gleicher parasitärer Kapazität $C_p = \SI{50}{\femto\farad}$, + dem typischen Wert für die ``1206''-Bauform \cite{JBellemann22}. } \end{figure} @@ -172,23 +174,29 @@ Widerstandsimpedanzen Johnson-Nyquist-Rauschen, betrifft resistive Komponenten. Es wird verursacht durch die thermische Bewegung von Ladungsträgern und bildet ein weißes Rauschen aus. -Der Effektivwert des Rauschen lässt sich über die folgende Formel berechnen: +Der Effektivwert des Rauschen lässt sich über die folgende Formel berechnen \cite[S.S. 474]{Horowitz:1981307}: \begin{equation} U_{\mathrm{n,rms}} = \sqrt{4k_BTR\Delta f}\label{eqn:thermal_voltage_noise} \end{equation} -Hierbei ist $U_{\mathrm{n,rms}}$ 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. Abbildung \ref{fig:example_r_noise} zeigt den schematischen Aufbau eines rauschenden Widerstandes. \todo{Insert citation} +Hierbei ist $U_{\mathrm{n,rms}}$ 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. + Abbildung \ref{fig:example_r_noise} zeigt den + schematischen Aufbau eines rauschenden Widerstandes. -\begin{figure}[hb] +\begin{figure}[ht] \centering \includegraphics[scale=0.15]{grundlagen/Schematic_Resistor.drawio.png} \caption[Ersatzschaltbild für die Modellierung eines rauschenden, hochohmigen Widerstandes]{ \label{fig:example_r_noise}Ersatzschaltbild für die Modellierung eines - rauschenden, hochohmigen Widerstandes nach \cite{WikipediaResistors2024May}. + rauschenden, hochohmigen Widerstandes nach \cite[S.S. 474]. Durch die niedrigen Frequenzen und hohen Impendanzen kann die parasitäre Induktivität des Widerstandes - in diesem Anwendungsfall ausgelassen werden.} + in diesem Anwendungsfall vernachlässigt werden.} \end{figure} \cleardoublepage @@ -206,10 +214,7 @@ Die Spannung am Ausgang ergibt sich idealerweise durch folgende Formel: \begin{equation} U_{\mathrm{out}} = A_\mathrm{ol} * \left(V_+ - V_-\right) \end{equation} - -Hierbei ist $A_{\mathrm{ol}}$ der sog. Open-Loop-Gain bzw. die offene Verstärkung. Für einen idealen OpAmp kann dieser Wert als quasi unendlich angenommen werden. Mithilfe eines Rückkoppelpfades wird das Ausgangssignal meist an den negativen Eingang zurück geführt. -Der OpAmp wird somit den Ausgang so treiben, dass es keine Differenzspannung zwischen den Eingangssignalen gibt. -Mit korrekter Auswahl der Rückkopplung können quasi-beliebige Übertragungsfunktionen eingestellt werden. Abbildung \ref{fig:example_opamp_amplifier} zeigt einen simplen Verstärker-Schaltkreis, welcher das Eingangssignal um den Faktor 10 skaliert. +Hierbei ist $A_{\mathrm{ol}}$ der sog. Open-Loop-Gain bzw. die offene Verstärkung. Für einen idealen OpAmp kann dieser Wert als quasi unendlich angenommen werden. \begin{figure}[ht] \centering @@ -217,6 +222,7 @@ Mit korrekter Auswahl der Rückkopplung können quasi-beliebige Übertragungsfun \caption{\label{fig:example_opamp}Schematisches Symbol eines idealen OpAmps, eigene Darstellung.} \end{figure} + Mithilfe eines Rückkoppelpfades wird das Ausgangssignal meist an den negativen Eingang zurück geführt. Der OpAmp wird somit den Ausgang so treiben, dass es keine Differenzspannung zwischen den Eingangssignalen gibt. Mit korrekter Auswahl der Rückkopplung können @@ -230,7 +236,6 @@ Verstärker-Schaltkreis, welcher das Eingangssignal um den Faktor 10 skaliert. \caption{\label{fig:example_opamp_amplifier}Beispielhafte Verstärkerschaltung mit einem OpAmp, eigene Darstellung, nach \cite{Cox2002}.} \end{figure} -\todo{Check Jonas' corrections for these graphics} \FloatBarrier @@ -242,7 +247,11 @@ Diese sind wie folgt: \paragraph*{Eingangs-Leckströme:} Ein idealier OpAmp besitzt Eingänge, durch welche kein Strom fließen kann, um das Eingangssignal möglichst wenig zu stören. - Reale OpAmps haben jedoch messbare Eingangsströme. Je nach OpAmp-Typ befinden sich diese im Bereich von $\SI{1}{\micro\ampere}$ bis hin zu $\SI{1}{\femto\ampere}$. Diese Leckströme können in der Anwedung als TIV den gemessenen Strom stark verzerren, und beeinflussen somit negativ das Messergebnis \cite{analogINBIAS2008}. + Reale OpAmps haben jedoch messbare Eingangsströme. + Je nach OpAmp-Typ befinden sich diese im Bereich von + $\SI{1}{\femto\ampere}$ bis hin zu $\SI{1}{\micro\ampere}$. + Diese Leckströme können in der Anwedung als TIV den gemessenen Strom stark verzerren, + und beeinflussen somit negativ das Messergebnis \cite[S.S. 302]{Horowitz:1981307}\cite{analogINBIAS2008}. \paragraph*{Parasitäre Kapazitäten:} Ein OpAmp hat, bedingt durch die physikalische Auslegung des Bauteils, verschiedene ungewollte Kapazitäten sowohl gegen Masse, als auch zwischen den Kanälen selbst. @@ -251,7 +260,7 @@ Diese sind wie folgt: \paragraph*{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 Produkt aus Verstärkung und Bandbreite angegeben \cite{Cox2002}. + Dies wird als Produkt aus Verstärkung und Bandbreite angegeben \cite[S.S. 247]{Horowitz:1981307}\cite{Cox2002}. Im folgenden wird dies als GBWP, aus dem Englischen ``Gain-Bandwidth-Product'', bezeichnet. Dies kann ebenfalls die Übertragungsfunktion beeinflussen, da ein zu niedriges GBWP die Übertragungsfunktion instabil werden lässt. @@ -268,22 +277,21 @@ Diese sind wie folgt: Zudem ensteht eine Instabilität, welche den Schaltkreis zum oszillieren bringen kann.} \end{figure} -\FloatBarrier - \paragraph*{Endliche Verstärkung:} Ein realer OpAmp kann ein Signal nur um einen gewissen, endlichen Faktor verstärken. Dieser Faktor wird als ``offene'' Verstärkung bezeichnet, da er ohne Rückkopplung gemessen wird. Diese Begrenzung führt zu einer Limitierung der absoluten - Verstärkung einer OpAmp-Stufe. Zusammen mit einer Eingangskapazität bildet + Verstärkung einer OpAmp-Stufe \cite[S.S. 249]{Horowitz:1981307}. + Zusammen mit einer Eingangskapazität bildet sich im Falle eines TIVs hieraus ebenfalls eine Grenze der Bandbreite, da die Eingangskapazität den Anstieg der Eingangsspannung, und durch die endliche Verstärkung auch den - Anstieg der Ausgangsspannung, begrenzt. + Anstieg der Ausgangsspannung, begrenzt \cite[S.S.541]{Horowitz:1981307}. Dieser Effekt ist in Abbildung \ref{fig:opamp_aol_sweep} dargestellt, welche einen klaren Einbruch der Bandbreite bei zu geringer offener Verstärkung zeigt. \label{chap:opamp_aol_limit_explained} -\begin{figure}[H] +\begin{figure}[ht] \centering \includegraphics[scale=0.8]{datavis/Parasitics/SingleStage_Aol_Sweep.png} \caption[Einfluss der offenen Verstärkung auf einen TIV]{\label{fig:opamp_aol_sweep} @@ -311,12 +319,14 @@ Diese sind wie folgt: \caption[Schematisches Ersatzschaltbild der Rauschquellen eines OpAmp]{\label{fig:example_opamp_noise}Schematisches, vereinfachtes Ersatzschaltbild der zusammengefassten Rauschquellen eines OpAmp nach \cite{tiNoise2007}. Hierbei sind die Rauschquellen eingangsbezogen dargestellt.} -\end{figure}\todo{Gotta edit this for the correct connectors too :P} +\end{figure} \begin{figure}[ht] \centering \includegraphics[scale=0.8]{datavis/Parasitics/SingleStage_noise_example.png} - \caption{\label{fig:example_opamp_noise_plot}Darstellung des Rauschens eines beispielhaft gewählten OpAmps. + \caption[ + Darstellung des Rauschens eines beispielhaft gewählten OpAmps + ]{\label{fig:example_opamp_noise_plot}Darstellung des Rauschens eines beispielhaft gewählten OpAmps. Deutlich zu erkennen ist das Spannungsrauschen in den unteren Frequenzen, welches bis ca. $\SI{1}{\kilo\hertz}$ dominiert, sowie das Stromrauschen in den oberen Frequenzen, welches ab $\SI{100}{\kilo\hertz}$ stark ansteigt.} @@ -325,10 +335,11 @@ Diese sind wie folgt: \cleardoublepage \section{Aufbau eines Transimpedanzverstärkers} -\todo[inline]{Add more sources} \label{chap:basics_tia} -Im Folgenden wird auf den grundlegenden Aufbau und die Funktionalität eines TIVs eingegangen. +Im Folgenden wird auf den grundlegenden Aufbau +und die Funktionalität eines TIVs eingegangen, +basierend auf \cite{Reinecke2018Oct} und \cite[S.S. 233]{Horowitz:1981307}. Ein TIV ist eine variante einer OpAmp-Verschaltung, dessen Aufgabe es ist, einen Strom in eine Spannung um zu wandeln. Somit wird die Verstärkung der Schaltung in $\Omega$ angegeben. Die grundlegende Schaltung ist hierbei in Abbildung \ref{fig:example_tia_circuit} aufgeführt. @@ -337,11 +348,10 @@ Somit wird die Verstärkung der Schaltung in $\Omega$ angegeben. Die grundlegend \centering \includegraphics[scale=0.2]{grundlagen/OpAmp_TIA.drawio.png} \caption[Grundlegender Schaltkreis eines Transimpedanzverstärkers, - eigene Darstellung nach \cite{Reinecke2018Oct}]{ + eigene Darstellung nach \cite{Reinecke2018Oct} und \cite[S.S. 233]{Horowitz:1981307}]{ \label{fig:example_tia_circuit}Grundlegender Schaltkreis eines Transimpedanzverstärkers, - eigene Darstellung nach \cite{Reinecke2018Oct}.} + eigene Darstellung nach \cite{Reinecke2018Oct} und \cite[S.S. 233]{Horowitz:1981307}.} \end{figure} -\todo{Find a citation for this?} Die Funktionsweise ist wie folgt: \begin{itemize} diff --git a/TeX/Kapitel/RevisionV11.tex b/TeX/Kapitel/RevisionV11.tex index 27b3675..9aa6edf 100644 --- a/TeX/Kapitel/RevisionV11.tex +++ b/TeX/Kapitel/RevisionV11.tex @@ -241,16 +241,16 @@ stärkere Abfall der Verstärkung sogar vorteilhaft. Eine Vermutung der Ursache dieser Resonanz ist der kaskadierte Aufbau des Verstärkers selbst, wobei das GBWP der ersten oder zweiten Stufe zu einer leichten Überhöhung der Bandbreite führen kann. -Aus der Messung der Übertragungsfunktionen können nun die -3dB-Punkte der Platinen +Aus der Messung der Übertragungsfunktionen können nun die -3~dB-Punkte der Platinen entnommen werden. Diese sind in Tabelle \ref{table:v11_bandwidths} dargestellt. \begin{table}[hb] \centering - \caption{\label{table:v11_bandwidths}-3dB-Frequenzen des ungefilterten + \caption{\label{table:v11_bandwidths}-3~dB-Frequenzen des ungefilterten TIV-Ausgangs der Revision} \begin{tabular}{ |r|r|r| } \hline - Widerstand & -3dB Punk \\ + Widerstand & -3~dB Punk \\ \hline $\SI{20}{\mega\ohm}$ & $\SI{97.556}{\kilo\hertz}$ \\ $\SI{47}{\mega\ohm}$ & $\SI{54.747}{\kilo\hertz}$ \\ @@ -270,7 +270,7 @@ und ist erneut im Falle der $\SI{47}{\mega\ohm}$ Variante von Vorteil. Abbildung \ref{fig:v11_comparison_bandwidth} zeigt einen direkten Vergleich der Bandbreiten der TIV-Stufen der vorherigen und neuen Revison für die $\SI{47}{\mega\ohm}$ Variante. Der steilere Abfall sowie die -leicht höhere -3dB-Frequenz der Revision +leicht höhere -3~dB-Frequenz der Revision ist hierbei deutlich zu erkennen. \begin{figure}[ht] @@ -390,6 +390,8 @@ Zwar ist das Rauschen im Vergleich zur ursprünglichen Version geringfügig erh bieten alle Versionen der Schaltung mit Ausnahme des $\SI{20}{\mega\ohm}$ TIVs ein akzeptabel geringes Rauschen. +\FloatBarrier + \subsection{Konsistenz des Schaltkreises} In diesem Abschnitt wird darauf eingegangen, wie wiederholbar @@ -423,6 +425,8 @@ Das Verhalten der TIVs scheint somit eine gute Konsistenz aufzuweisen. Es ist somit nicht notwendig, die Platinen nach der Anfertigung noch weiter abzustimmen. +\FloatBarrier + \subsection{Einfluss der Kaskadenschaltung} In diesem Abschnitt wird die Kaskadenschaltung der zwei ADA4817 genauer @@ -480,7 +484,7 @@ in der zweiten Stufe von Vorteil. \FloatBarrier -\subsubsection{Verstärkungsverteilung} +\subsubsection{Einfluss der Verstärkungsverteilung} In diesem Kapitel soll nun untersucht werden, welche Verteilung der Verstärkungen zwischen erster und zweiter Stufe am besten ist. @@ -519,7 +523,7 @@ und nicht durch das GBWP oder die Rückkoppelwiderstände. Dies ist von Vorteil, hierdurch die Bandbreite der Schaltung durch Umverteilung der Verstärkung beliebig einstellen lässt, ohne hierbei die Stabilität des Schaltkreises zu gefährden. -Generell ist nur die Einhaltung der Zielparameter von -3dB bei $\SI{30}{\kilo\hertz}$ +Generell ist nur die Einhaltung der Zielparameter von -3~dB bei $\SI{30}{\kilo\hertz}$ wichtig. Höhere Bandbreiten werden durch die Filterstufe entfernt. @@ -548,12 +552,77 @@ Somit ist bestätigt, dass die Verteilung der Verstärkungen der TIV-Stufen ein Paramter ist. Generell soll die Verstärkung der ersten Stufe so groß wie möglich gehalten werden, d.h. die zweite Stufe so klein wie möglich, um das Rauschen zu vermindern. +\section{Messung an einem IMS} + +Mit der Funktionalität des erstellten TIVs bestätigt, wird nun eine +Messung an einem aktivem IMS durchgeführt. +Hierbei soll das Auflösungsvermögen sowie das Rauschniveau des neu +erstellten TIVs mit dem Verhalten des vorherig genutzten Verstärkers +verglichen werden. + +Anhand der bereits durchgeführten Messungen wird der $\SI{47}{\mega\ohm}$ +TIV als Verstärker für dieses Experiment genutzt. Dieser besitzt +das niedrigste Rauschen bei der gewollten Bandbreite von $\SI{30}{\kilo\hertz}$, +und ist somit die beste Auswahl. +Das genutzte IMS-System ist vom Typ ???\todo{Ask Moritz which IMS it was}, +welches bereits durch vorherige Messungen im Labor charakterisiert wurde +und somit eine gut verstandene Platform dar stellt. + +Es werden insgesamt vier Messungen durchgeführt, zwei als +Referenz mit dem bestehendem Verstärker und zwei mit dem neu +erstellten TIV. Für jeden Verstärker wird eine Messung +mit zehnfacher Mittlung zur Reduktion des Rauschens und eine +Messung ohne Mittlung durchgeführt. Die aufgenommenen +Spektren sind in Abbildungen \ref{fig:v11_real_meas_noavg} +und \ref{fig:v11_real_meas_avg} dargestellt. + +\begin{figure}[htb] + \centering + \missingfigure{Measurement of the averaged signal} + \caption[Ergebnisse der gemittelten Messung am IMS]{ + \label{fig:v11_real_meas_avg} + Ergebnisse der gemittelten Messungen der zwei Verstärker + im Vergleich, normalisiert auf die gleiche Peak-Höhe. + + Zu erkennen ist eine sehr gute Übereinstimmung der + Messergebnisse und vergleichbares Rauschen. + } +\end{figure} + +\begin{figure}[htb] + \centering + \missingfigure{Measurement of the noaveraged signal} + \caption[Ergebnisse der ungemittelten Messung am IMS]{ + \label{fig:v11_real_meas_noavg} + Ergebnisse der ungemittelten Messungen der zwei Verstärker + im Vergleich, normalisiert auf die gleiche Peak-Höhe. + + In dieser Messung lässt sich das rauschen besser vergleichen, + und zu erkennen ist ??? + } +\end{figure} + +Zu erkennen ist die gute Übereinstimmung der Messungen. +Die für die Datenauswertung relevanten Formen der +Gauss-Peaks werden vom neuen TIV gut dargestellt, es +sind keine Verzerrungen im Vergleich zum bestehenden +Verstärker zu erkennen, und das Rauschen liegt auf +gleichem Niveau. + +Somit ist bewiesen, dass der hier erstellte +TIV erfolgreich in einem echten IMS-System genutzt werden kann, +und hierbei vergleichbar gute Messergebnisse liefert +wie die bestehenden Systeme. + \section{Fazit} -Die Revision korrigiert erfolgreich die Instabilität, welche in der ursprünglichen Version -festgestellt wurde. -In den restlichen Parametern schneidet sie vergleichbar gut wie die ursprüngliche Version ab. +Die Revision korrigiert erfolgreich die Instabilität, welche in der ersten Version +des in dieser Arbeit erstellten TIVs festgestellt wurde. +In den restlichen Parametern schneidet sie vergleichbar gut wie die erste Version ab. Zudem lässt sich durch die korrekte Einstellung der Verstärkungsverteilung der kaskadierten Stufe die Bandbreite des Schaltkreises arbiträr limitieren, was eine zusätzliche Rauschreduktion -ermöglicht. -Somit wurde ein erfolgreicher und für ein IMS nutzbarer TIV entwickelt. \ No newline at end of file +ermöglicht. In der Messung am echten IMS konnte bestätigt werden, dass der TIV +Messwerte mit gleicher Qualität wie bestehende Systeme liefern kann. + +Zusammengefasst wurde somit bestätigt, dass erfolgreich ein TIV für die IMS entwickelt +wurde. \ No newline at end of file diff --git a/TeX/Kapitel/Vermessung.tex b/TeX/Kapitel/Vermessung.tex index 49a2da1..4d27777 100644 --- a/TeX/Kapitel/Vermessung.tex +++ b/TeX/Kapitel/Vermessung.tex @@ -147,14 +147,14 @@ aus Kapitel \ref{chap:r_para_mitigations}, da sich vermutlich nicht alle parasitären Eigenschaften akkurat modellieren ließen. Dennoch ist eine klare Verbindung zwischen Widerstandsgröße und Bandbreite erkennbar. Die gemessenen --3dB Grenzfrequenzen sind in Tabelle \ref{table:v10_bandwidths} aufgelistet. +-3~dB Grenzfrequenzen sind in Tabelle \ref{table:v10_bandwidths} aufgelistet. \begin{table}[H] \centering - \caption{\label{table:v10_bandwidths}-3dB-Frequenzen des ungefilterten TIV-Ausgangs} + \caption{\label{table:v10_bandwidths}-3~dB-Frequenzen des ungefilterten TIV-Ausgangs} \begin{tabular}{ |r|r|r| } \hline - Widerstand & -3dB Punk \\ + Widerstand & -3~dB Punk \\ \hline $\SI{20}{\mega\ohm}$ & $\SI{58.484}{\kilo\hertz}$ \\ $\SI{47}{\mega\ohm}$ & $\SI{49.355}{\kilo\hertz}$ \\ @@ -187,7 +187,7 @@ dargestellt. Die Auslegung der Filterstufe soll erst ab der Grenzfrequenz von $\SI{30}{\kilo\hertz}$ einen Abfall von -40dB/Dekate einbringen, wobei Frequenzen unterhalb der Grenzfrequenz nicht beeinflusst werden sollten. -Dieses Verhalten ist auch deutlich in der Messung zu erkennen. Die -3dB-Frequenzen +Dieses Verhalten ist auch deutlich in der Messung zu erkennen. Die -3~dB-Frequenzen der gefilterten Ausgänge sind in Tabelle \ref{table:v10_bandwidth_filters} aufgelistet. Wie bereits theorisiert, ist die Bandbreite der $\SI{120}{\mega\ohm}$-Variante zu gering für die vollen $\SI{30}{\kilo\hertz}$. Die anderen beiden Varianten besitzen @@ -195,10 +195,10 @@ genug Bandbreite. \begin{table}[H] \centering - \caption{\label{table:v10_bandwidth_filters}-3dB-Frequenzen der gefilterten Ausgänge des TIVs} + \caption{\label{table:v10_bandwidth_filters}-3~dB-Frequenzen der gefilterten Ausgänge des TIVs} \begin{tabular}{ |r|r|r| } \hline - Widerstand & -3dB Punk \\ + Widerstand & -3~dB Punk \\ \hline $\SI{20}{\mega\ohm}$ & $\SI{30.220}{\kilo\hertz}$ \\ $\SI{47}{\mega\ohm}$ & $\SI{30.199}{\kilo\hertz}$ \\ @@ -267,7 +267,7 @@ Hieraus kann geschlossen werden, dass die Abschirmungen einen merklichen und wic die Stabilität des Frequenzganges haben. Die korrekte Abstimmung der Abschirmung ist somit notwendig für die Funktionalität des TIVs. -\clearpage +\FloatBarrier \subsubsection{Messung ohne Abschirmung} @@ -283,7 +283,7 @@ nie korrekt übertragen wird. Die Messung dieses instabilen Ausgangssignals ist in Abbildung \ref{fig:v10_unshielded_waveform} dargestellt. -\begin{figure}[hb] +\begin{figure}[ht] \centering \includegraphics[scale=0.8]{datavis/V1_Measurements/unshielded_47M.png} \caption[Ausgangsspannung des TIV-Schaltkreises ohne Abschirmung]{\label{fig:v10_unshielded_waveform} @@ -302,7 +302,7 @@ Die Instabilität bei keiner Abschirmung ist somit erwartet und weißt zusätzli dass die bestehende Abschirmungsgeometrie ausreichend ist um diese Instabilität zu vermeiden. Eine Operation gänzlich ohne Abschirmungselektroden ist nicht möglich. -\clearpage +\FloatBarrier \subsection{Rauschen} \label{chap:v10_measurement_noise} @@ -369,7 +369,7 @@ Filterung gemessen, und ist in Tabelle \ref{table:v10_noise_table} aufgelistet. Das niedrigere Rauschniveau der Varianten mit größeren Widerständen, sowie die Effektivität der Filterung des Ausganges, sind deutlich zu erkennen. -\begin{table}[hb] +\begin{table}[htb] \centering \caption{\label{table:v10_noise_table}AC-RMS-Spannungen des Rauschens der Platinen} \begin{tabular}{ |r|r|r|r| } @@ -390,7 +390,6 @@ für die Messungen, mit einem breit verteiltem Rauschen ohne spezifische Töne u einem niedrigen Rauschlevel. \FloatBarrier -\newpage \subsection{Stabilität am IMS} \label{chap:v10_instability} @@ -413,7 +412,7 @@ Signals ausgegeben wird. Abbildung \ref{fig:measurement_v10_ims_instability} zeigt die Ausgangsspannung bei angeschlossener IMS-Röhre auf. -\begin{figure}[hb] +\begin{figure}[ht] \centering \includegraphics[scale=0.8]{datavis/V1_Measurements/V1.0-a1/Instability.png} \caption[Ausgangsspannung des diff --git a/TeX/Kapitel/Zusammenfassung.tex b/TeX/Kapitel/Zusammenfassung.tex new file mode 100644 index 0000000..bfcdd19 --- /dev/null +++ b/TeX/Kapitel/Zusammenfassung.tex @@ -0,0 +1,32 @@ +\cleardoublepage +\chapter{Zusammenfassung} + +In dieser Arbeit konnte erfolgreich ein neues +Design eines TIVs erstellt werden. +Hierbei wurden wichtige parasitären Effekte des Schaltkreises +dargestellt, und neuartige +Kompensationsmöglichkeiten zur Reduktion des Einflusses +dieser ausgelegt. + +Mithilfe des durch Simulation vertieften Verständisses +über die parasitären Effekte sowie der Arbeitsweise +der Operationsverstärker konnte ein erstes Design +ausgelegt werden, welches die Anforderungen +an Bandbreite und Rauschlevel erfüllte. +Lediglich die Stabilität des Schaltkreises führte +zu Problemen. + +Die Ursprünge der Instabilität wurde thematisiert, und es +konnte in einer Revision der Schaltung die Stabilität deutlich +verbessert werden. + +Der somit erstellte Schaltkreis konnte in einer Messung +an einem der IMS-Systeme des GEM an der Leibniz Universität +Hannover vermessen werden, und wurde mit den bestehenden +Systemen verglichen. Somit konnte bestätigt werden, dass +das neu erstellte System Messwerte mit guter Qualität liefert +und seine Zielanforderungen erfüllt. +Hierbei konnte der TIV so ausgelegt werden, dass keine manuellen +Nachjustierungen für eine korrekte Operation notwendig sind, +und der Preis sowie die Größe des Schaltkreises konnten im +Vergleich zur Vorgängerversion deutlich verringert werden. \ No newline at end of file diff --git a/TeX/Literaturverzeichnis.bib b/TeX/Literaturverzeichnis.bib index 4bcae5b..6bf8b14 100644 --- a/TeX/Literaturverzeichnis.bib +++ b/TeX/Literaturverzeichnis.bib @@ -1,3 +1,13 @@ +@book{Horowitz:1981307, + author = "Horowitz, Paul and Hill, Winfield", + title = "{The art of electronics; 3rd ed.}", + publisher = "Cambridge University Press", + address = "Cambridge", + year = "2015", + url = "https://cds.cern.ch/record/1981307", +} + + @article{Reinecke2018Oct, author = {Reinecke, Tobias and Clowers, Brian H.}, title = {{Implementation of a flexible, open-source platform for ion mobility spectrometry}}, @@ -58,20 +68,78 @@ eid = {MT-038} } -@misc{WikipediaResistors2024May, - author = {{Contributors to Wikimedia projects}}, - title = {{Johnson{\textendash}Nyquist noise - Wikipedia}}, - year = {2024}, - month = may, - note = {[Online; accessed 13. May 2024]}, - url = {https://en.wikipedia.org/w/index.php?title=Johnson-Nyquist_noise&oldid=1222085733} -} - @misc{ADFilterDesign, author = {{Analog Devices}}, title = {{Filter Design Tool}}, year = {2024}, - month = July, + month = jul, note = {[Online; accessed 05. July 2024]}, url = {https://tools.analog.com/en/filterwizard/} } + +@misc{JBellemann22, + author = {{Jeroen Belleman}}, + title = {{Shunt capacitance of 1206 SMD resistors}}, + year = {2010}, + month = dec, + note = {[Online; accessed 28th August 2024]}, + url = {http://jeroen.web.cern.ch/jeroen/resistor/shuntC.html} +} + +@misc{VishayRFreq, + title = {{Frequency Response of Thin Film Chip Resistors}}, + year = {2009}, + month = feb, + note = {[Online; accessed 28th August 2024]}, + url = {https://www.vishay.com/docs/60107/freqresp.pdf} +} + +@misc{DatasheetADA4530, + title = {{Datasheet ADA4530 - Femtoampere Input Bias Current Electrometer Amplifier}}, + year = {2024}, + month = jun, + note = {[Online; accessed 12th June 2024]}, + url = {https://www.analog.com/media/en/technical-documentation/data-sheets/ada4530-1.pdf} +} + +@misc{SierraReduceCapacitances, + title = {{How to reduce parasitic capacitance in PCB layout}}, + year = {2021}, + month = feb, + note = {[Online; accessed 10th June 2024]}, + url = {https://www.protoexpress.com/blog/how-to-reduce-parasitic-capacitance-pcb-layout/} +} + +@misc{AltiumReduceCapacitance, + title = {{How to Reduce Parasitic Capacitance in a PCB Layout}}, + author = {{Zachariah Peterson }}, + year = {2022}, + month = mar, + note = {[Online; accessed 10th June 2024]}, + url = {https://resources.altium.com/p/how-reduce-parasitic-capacitance-pcb-layout} +} + +@misc{AltiumLeakages, + title = {{PCB Leakage Current and Breakdown in High Voltage Design}}, + author = {{Zachariah Peterson}}, + year = {2020}, + month = jan, + note = {[Online; accessed 3rd June 2024]}, + url = {https://resources.altium.com/p/pcb-leakage-current-and-breakdown-in-high-voltage-design} +} + +@article{Yang:21, +author = {Jinqing Yang and Minjie Wan and Weixian Qian and Kan Ren and Dongming Lu and Jun Zhang and Guohua Gu and Qian Chen}, +journal = {Appl. Opt.}, +keywords = {Avalanche photodiodes; Fiber optic gyroscopes; Optical signals; Phase compensation; Photodetectors; Photodiodes}, +number = {31}, +pages = {9748--9756}, +publisher = {Optica Publishing Group}, +title = {Bandwidth extension method based on the field-shunting effect in a high-gain photoelectric receiver circuit}, +volume = {60}, +month = {Nov}, +year = {2021}, +url = {https://opg.optica.org/ao/abstract.cfm?URI=ao-60-31-9748}, +doi = {10.1364/AO.442413}, +abstract = {In the high-gain photoelectric receiver circuit, the method based on the field-shunting effect is applied to improve the bandwidth of the transimpedance amplifier. This method is implemented by adding a ground trace under the gain resistor, which reduces the parasitic capacitance of the gain resistor and thus increases the bandwidth. To obtain the specific impact of this method on bandwidth, a series of simulations are carried out, including electromagnetic simulations of a three-dimensional structure of circuit gain part and simulation program with integrated circuit emphasis (SPICE) simulations of the high-gain voltage-current feedback transimpedance amplifier. Finally, the optimal simulation result shows that selecting a 1206 size chip fixed resistor and setting the ground trace width to 1.1 mm can greatly reduce the influence of resistor parasitic effects on the circuit, thereby achieving the best performance of bandwidth extension. Further, the comparative experiment also verifies the effectiveness of the method for bandwidth enhancement.}, +} \ No newline at end of file diff --git a/TeX/grafiken/Auslegung/output_driver.png b/TeX/grafiken/Auslegung/output_driver.png index 687b679..56c5024 100644 Binary files a/TeX/grafiken/Auslegung/output_driver.png and b/TeX/grafiken/Auslegung/output_driver.png differ diff --git a/TeX/grafiken/Auslegung/power_dcdc.png b/TeX/grafiken/Auslegung/power_dcdc.png index 8d2f613..15f308f 100644 Binary files a/TeX/grafiken/Auslegung/power_dcdc.png and b/TeX/grafiken/Auslegung/power_dcdc.png differ diff --git a/TeX/grafiken/Auslegung/power_ldo.png b/TeX/grafiken/Auslegung/power_ldo.png index a3ff632..976766a 100644 Binary files a/TeX/grafiken/Auslegung/power_ldo.png and b/TeX/grafiken/Auslegung/power_ldo.png differ diff --git a/TeX/grafiken/Auslegung/v1.0/tia_stage.png b/TeX/grafiken/Auslegung/v1.0/tia_stage.png index f6901da..d16de86 100644 Binary files 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