From 807334402311acb957be8fb4a82675dc00417998 Mon Sep 17 00:00:00 2001 From: m-giger <34764641+m-giger@users.noreply.github.com> Date: Fri, 27 Jul 2018 14:08:58 +0200 Subject: [PATCH] Filter angepasst --- Elo2.tex | 2 ++ pictures/filter.png | Bin 0 -> 60383 bytes sections/ADWandler.tex | 37 +++++++++++--------- sections/filter.tex | 63 ++++++++++++++++++++++++++++++++--- sections/opampsAC.tex | 26 +++++++-------- sections/rauschen.tex | 2 +- sections/spannungsregler.tex | 56 +++++++++---------------------- 7 files changed, 111 insertions(+), 75 deletions(-) create mode 100644 pictures/filter.png diff --git a/Elo2.tex b/Elo2.tex index 68575a2..1c5d97a 100644 --- a/Elo2.tex +++ b/Elo2.tex @@ -24,7 +24,9 @@ \input{sections/DAWandler} \input{sections/ADWandler} +\newpage \input{sections/opampsAC} +\newpage \input{sections/filter} %\newpage diff --git a/pictures/filter.png b/pictures/filter.png new file mode 100644 index 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zh}EFX&3ymC_W!R=XJ9mh=it*}j$#wl%E?KXOD6psF-~!0#MOjqNus#89K0X?lc|2+ zp+k3xzoyfp+Vuaht4#XSxgz46x!}Qs)0%pF17RkFXNMoj)kJTKv?;u=2~CFz4?3Qm zD0ZND6%tB8Er5MW{M`7reyw=MP*rHl^XV950HVYL1bv-@i^z3En%MqrMFFXl z4U-It_{*d?iIsOC{!7Xvt(-aHjl+$oD}NNx7c0lPa$yjEMnpt>1f`M-Jt|E2!r`DNZy&rDZ$#WvI7XRm=NsX)&u{\bfseries}p{3cm}|c|p{10cm}|} \hline @@ -55,18 +54,74 @@ \subsection{Tiefpass-Filter\hartl{514}} Güte werden Spulen oder Verstärker benötigt. Für Systeme 2.Ordnung ist eine Polgüte von 0.7 optimal. } \\ \hline - \textbf{Kaskadierter Spannungsteiler} + + \end{longtable} + +\begin{minipage}{0.49\textwidth} +\includegraphics[width = 0.99\textwidth]{pictures/filter.png} +\end{minipage} +\begin{minipage}{0.49\textwidth} +$ +G1i = V_{OUT1}(V_{IN})\quad G1f = V_{OUT1}(V_{OUT3}) +$\\ +$ +G2 = V_{OUT2}(V_{OUT1}) \quad G3 = V_{OUT3}(V_{OUT2}) +$\\[1em] +\begin{minipage}[t]{0.49\textwidth} +$ +G1i = \dfrac{-R_1}{R_0\cdot(C_1\cdot R_1\cdot s+1)} +$\\ +$ +G2 = \dfrac{-1}{C_2\cdot R_2\cdot s} +$ +\end{minipage} +\begin{minipage}[t]{0.49\textwidth} +$ +G1f = \dfrac{-R_1\cdot V_{OUT3}}{R_5\cdot(C_1\cdot R_1\cdot s+1)} +$\\ +$ +G3 = \dfrac{-R_4}{R_3} +$ +\end{minipage} + +\begin{minipage}[t]{0.39\textwidth} +Gesamtgain bestimmen mit Mason: +\end{minipage}\hfill +\begin{minipage}[t]{0.49\textwidth} +$ +G_{13} = \dfrac{G1i\cdot G_2\cdot G_3}{1-G_{1f}\cdot G_2\cdot G_3} +$ +\end{minipage}\\ +\[ +G = \dfrac{\frac{-R_1}{R_0\cdot(C_1\cdot R_1\cdot s+1)}\cdot \frac{-1}{C_2\cdot R_2\cdot s}\cdot \frac{-R_4}{R_3}}{1-\left(\frac{-R_1}{R_5\cdot(C_1\cdot R_1\cdot s+1)}\cdot \frac{-1}{C_2\cdot R_2\cdot s}\cdot \frac{-R_4}{R_3}\right)} +\] +\[ +G = \frac{R_1\cdot R_4\cdot R_5}{R_0\cdot \left(C_1C_2R_1R_2R_3R_5 s^2 + C_2R_2R_3R_5 s + R_1R_4\right)} +\] +\end{minipage} + +Vorgehen: +\begin{enumerate} +\itemsep0em +\item Einzelne Übertragungsfunktionen aufstellen +\item Gesammtgain mittels Mason bestimmen +\item Kürzen +\item Wenn gefragt Gain bei DC und $\omega \rightarrow \infty$ bestimmen +\end{enumerate} +\pagebreak +\begin{longtable}{|>{\bfseries}p{3cm}|c|p{10cm}|} +\hline \textbf{Kaskadierter Spannungsteiler} & %TODO Bild einfügen & \[ H(s) = \frac{Y(s)}{X(s)} = \frac{Z_2 Z_4}{Z_1Z_2+Z_1Z_3+Z_1Z_4+Z_2Z_3+Z_2Z_4} \]\\ \hline -% ---------------------------------------------------------------------------------------------------- +%---------------------------------------------------------------------------------------------------- {Sallen Key\newline (Einfachmit-kopplung)\newline \hartl{517} } - & \includegraphics[width=4cm, valign=t]{./pictures/sallenkey.png} + & \includegraphics[width=6cm, angle = 270,valign=t]{./pictures/sallenkey.png} & {\textbf{ Standard Sallen Key}\newline Stromgleichungen:\newline $0 = (U_2-U_{in})\cdot \frac{1}{R_1}+(U_2-U_3)\cdot \frac{1}{R_2}+(U_2-U_{out})\cdot s C_1$ \newline diff --git a/sections/opampsAC.tex b/sections/opampsAC.tex index 817243a..145b011 100644 --- a/sections/opampsAC.tex +++ b/sections/opampsAC.tex @@ -34,33 +34,33 @@ \subsection{Open-Loop/Closed-Loop Verhalten} \large{$A_{ol}(s)=\frac{A_{ol_0}}{(1+\frac{s}{\omega_{p_{ol_1}}})(1+\frac{s}{\omega_{p_{ol_2}}})\dots}$} & $\begin{aligned} A_{cl}(s) &= \frac{A_{cl_0}}{(1+\frac{s}{\omega_{p_{cl_1}}})(1+\frac{s}{\omega_{p_{cl_2}}})\dots} = \frac{T_{in}(s)\cdot A_{ol}(s)}{1+\beta(s)\cdot A_{ol}(s)}\\ - \beta(s) &= \frac{V_{opn}}{V_{out}}\;\text{oder}\;\frac{V_{opp}}{V_{out}}\\ - T_{in}(s) &= \frac{V_{opn}}{V_{in}}\;\text{oder}\;\frac{V_{opp}}{V_{in}}\\ + \beta(s) &= \frac{V_{opn}}{V_{out}}\;\text{oder}\;\frac{V_{opp}}{V_{out}}\quad + T_{in}(s) = \frac{V_{opn}}{V_{in}}\;\text{oder}\;\frac{V_{opp}}{V_{in}}\\ V_{out} &= A_{cl}(s)\cdot V_{in} = \frac{T_{in}(s)\cdot A_{ol}(s)}{1 + \underbrace{A_{ol}(s)\cdot \beta(s)}_{T_s(s):Loop-Gain}} \cdot V_{in} \end{aligned}$\\ \hline \end{tabular} \\ \\ -\begin{minipage}{0.6\textwidth} +\begin{minipage}{0.49\textwidth} Durch das Schliessen des Loops wird die Bandbreite vergrössert, das gain-bandwidth-product(GBP) bleibt jedoch konstant. Die Verstärkung wird jedoch um $T_{s0}(s)$ (Linearer Loop Gain) reduziert. Der Phasengang wird durch das Verschieben des ersten Poles auch verändert, wie folgende Grafik zeigt. -\end{minipage} -\begin{minipage}{0.39\textwidth} \includegraphics[width=0.7\textwidth, valign=t]{./pictures/AolAcl.png} -\end{minipage} -\vspace{-7mm} +\end{minipage} +\begin{minipage}{0.49\textwidth} \subsection{Stabilität des Systems} -\begin{tabular}{m{0.45\linewidth}m{0.45\linewidth}} - Um die Stabilität des OpAmps zu betrachten, wird der Loop geöffnet. Damit das System stabil ist, darf das - Fehlersignal sich selbst nicht verstärken. Damit dies der Fall ist muss die Phase $>-180^\circ$ sein bei einem Loop Gain von $1$, da das Vergleichsglied die Phase noch um $180^\circ$ dreht. + + Um die Stabilität des OpAmps zu betrachten, wird der Loop geöffnet. Damit sich das Fehlersignal nicht selbst verstärkt muss die Phase $>-180^\circ$ sein bei einem Loop Gain von $1$, da das Vergleichsglied die Phase noch um $180^\circ$ dreht. Ein Mass für die Stabilität ist die Phasenmarge (Phase Margin) und die Verstärkungsmarge (Gain Margin). Optimal ist ein Phase Margin von $60^{\circ}$. Die UTF ist dann stabil, wenn sie nie $\infty$ wird d.h der Nenner darf nie 0 werden. - & \begin{center} - \includegraphics[width=5cm, valign=t]{pictures/margins.png} + \begin{center} + \includegraphics[width=4cm, valign=t]{pictures/margins.png} \end{center} -\end{tabular} + +\end{minipage} + + % ---------------------------------------------------------------------------------------------------- diff --git a/sections/rauschen.tex b/sections/rauschen.tex index 53456b6..0e89413 100644 --- a/sections/rauschen.tex +++ b/sections/rauschen.tex @@ -105,7 +105,7 @@ \section{Rauschen} \end{longtable} % ---------------------------------------------------------------------------------------------------- - +\pagebreak \begin{longtable}[t]{|p{4cm}|p{6.5cm}|p{7cm}|} \hline \multicolumn{3}{|l|}\textbf{ Rauschen von Widerständen} diff --git a/sections/spannungsregler.tex b/sections/spannungsregler.tex index 0e785af..000d509 100644 --- a/sections/spannungsregler.tex +++ b/sections/spannungsregler.tex @@ -278,45 +278,19 @@ \subsubsection{Skip-Mode} \end{itemize} \end{minipage} +\vspace{1cm} +\begin{Large} -%\begin{figure}[h!] -% -% \centering -% \begin{subfigure}[b]{0.45\textwidth} -% \centering -% \includegraphics[width=\textwidth]{pictures/ausgangsspannungsregelung} -% \caption{Voltage Mode} -% \end{subfigure} -% \qquad -% \begin{subfigure}[b]{0.45\textwidth} -% \centering -% \includegraphics[width=\textwidth]{pictures/currentmode} -% \caption{Current Mode} -% \end{subfigure} -% \caption{Vergleich Current Mode / Voltage Mode} -%\end{figure} -% -% -%\newpage -%\subsection{Effizienzsteigerung} -%\subsubsection{MOSFET statt Diode} -%\begin{figure}[htb] -%\includegraphics[scale=0.5]{pictures/effizient1} -%\end{figure} -%\begin{itemize} -% \item Diode hat Spannungsabfall -% \begin{itemize} -% \item Silizium-Diode: 0.7V -% \item Schottky-Diode: 0.3V -% \item MOSFET hat "`nur"' On-Widerstand $Rds_{on}$ -% \end{itemize} -% \item Umschalten vom Substratpotential beim Längstransistor nötig -% \begin{itemize} -% \item Synchronous rectifier -% \end{itemize} -%\end{itemize} -% -%\subsubsection{Skip-Mode} -%\begin{itemize} -% \item Lade- und Entladezyklen werden ausgelassen bei niedrigem Laststrom -%\end{itemize} +\begin{minipage}{0.49\textwidth} + +\[\boxed{ + u_L=\frac{di}{dt}\cdot L \quad = j\cdot\omega \cdot i\cdot L +}\] +\end{minipage} +\begin{minipage}{0.49\textwidth} +\[\boxed{ + i_c=\frac{du}{dt}\cdot C\quad = j\cdot\omega \cdot u\cdot C +}\] +\end{minipage} + +\end{Large} \ No newline at end of file