diff --git a/D8/BB/4k1HzOsc.txt b/D8/BB/4k1HzOsc.txt new file mode 100644 index 0000000..824da41 --- /dev/null +++ b/D8/BB/4k1HzOsc.txt @@ -0,0 +1,28 @@ +$ 1 0.000005 0.14549914146182014 50 5 43 +c -64 128 -64 288 0 1.0000000000000001e-7 0.7237624443288374 +a 16 144 160 144 8 5 -5 1000000 0.7237624443288374 2.5000888138184743 100000 +w -64 128 16 128 0 +w 16 128 16 64 0 +r 16 64 160 64 0 1000 +w 160 64 160 144 0 +w 16 160 16 208 0 +r 16 208 16 288 0 1000 +w -64 288 16 288 0 +g 16 288 16 336 0 +r 16 208 160 208 0 1000 +w 160 208 160 144 0 +p 224 144 224 288 1 0 +w 224 288 16 288 0 +w 224 144 160 144 0 +R -192 128 -192 192 0 0 40 5 0 0 0.5 +s -208 64 -80 64 0 1 false +r 224 144 384 144 0 5100 +l 384 144 544 144 0 0.1 0.0011361541550910638 +c 544 144 544 288 0 1.5000000000000002e-8 -0.05351672070695961 +w 544 144 640 144 0 +p 640 144 640 288 1 0 +w 544 288 640 288 0 +w 544 288 224 288 0 +o 12 1 0 5122 10 0.1 0 1 +o 0 1 0 4099 5 0.025 1 2 0 3 +o 21 1 0 5122 10 0.1 2 1 diff --git a/D8/BB/D8_spesifikasjoner.pdf b/D8/BB/D8_spesifikasjoner.pdf new file mode 100644 index 0000000..ff712da Binary files /dev/null and b/D8/BB/D8_spesifikasjoner.pdf differ diff --git a/D8/BB/Design_8.pdf b/D8/BB/Design_8.pdf new file mode 100644 index 0000000..e7935e5 Binary files /dev/null and b/D8/BB/Design_8.pdf differ diff --git a/D8/D8.pdf b/D8/D8.pdf new file mode 100644 index 0000000..fc3ed6e Binary files /dev/null and b/D8/D8.pdf differ diff --git a/D8/D8.tex b/D8/D8.tex new file mode 100644 index 0000000..e55e485 --- /dev/null +++ b/D8/D8.tex @@ -0,0 +1,556 @@ +%Dokumentinnstillinger:--------------------------------- +\documentclass[11pt,norsk]{elsys-design} + + +\heading{Designnotat} +\title{Sinus-generator} +\author{Øyvind Skaaden} +\version{2.0} +\date{\today} + +\begin{document} + +\maketitle + +%Automatisk generert innholdsfortegnelse:------------------ +\toc + +%Selve rapporten:------------------------------------------ +\section{Problembeskrivelse} +\label{sec:innledning} + +I veldig mange sammenhenger er det å kunne generere et periodisk signal en veldig nyttig ting. I de fleste tilfeller ønsker vi at signalet skal ha en enkel tone, og da må vi bruke et sinussignal. +For å generere et sinussignal er det flere måter å gjøre det på, men her vil vi ta utganspunk i systemet i \autoref{fig:introsystem}. + +\begin{figure}[!htbp] + \centering + \includegraphics[width=0.4\textwidth]{figurer/D8_Innledning.pdf} + \caption{Blokkdiagram for sinus-generatoren. Spenningen $v_2$ er utgangen på sinus-generatoren.} + \label{fig:introsystem} +\end{figure} + +Vi ønsker å ikke være veldig langt unna frekvensen som velges, så vi ønsker å være innenfor $10 000$ ppm av frekvensen $f_0 $ til sisnussignalet. + +Siden vi lager sinusen fra en firkantpuls ønsker vi også at signalet ikke er veldig ødelagt av de overharmoniske svingningene. Derfor velger vi at harmonisk forvrengning, $D$, ikke skal være større enn $D_{max} = 2\% $. + +\section{Prinsipiell løsning} +\label{sec:prinsipielllosning} + +For å generere et firkantsignal er det flere måter å gjøre det på. Her vil det bli tatt utganspunkt i en type generator som heter relaksasjonsgenerator, som i \autoref{circ:relaksasjonStart}. Den genererer et firkantsignal basert på opp- og utladning av en kondensator i et $RC$-ledd. Vi kan da styrefrekvensen ved å velge riktig tidskonstant. + +Vi vil deretter filtrere ut alle overtonene til firkantsignalet med et lavpassfilter, fordi et firkantsignal er bygget opp av uendelig mange sinussignaler. Det totale systemet vil se ut som i \autoref{fig:prinsippSinus}. + +\begin{figure}[!htbp] + \centering + \includegraphics[width=0.7\textwidth]{figurer/D8_Prinsipp.pdf} + \caption{Blokkdiagram for delene i sinus-generatoren. Spenningen $v_1$ og $v_2$ er henholdsvis utgangen på firkantgeneratoren og utgangen på lavpassfilteret eller selve sinus-generatoren.} + \label{fig:prinsippSinus} +\end{figure} + +\subsection{Relasasjonsgenerator} + +\begin{figure}[!htpb] + \centering + \begin{circuitikz}[scale=0.92, every node/.style={transform shape}] + \draw + (0,0) node[op amp,yscale=1](opamp){} + + (opamp.up) ++ (0,.5) node[opampuplbl] {$+V$} -- (opamp.up) + (opamp.down) ++ (0,-.5) node[opampdownlbl] {$-V$} -- (opamp.down) + + (opamp.-) to [short] ++(0,1.5) coordinate(C) + to [R, l=$R_1 $, *-] (C-|opamp.out) + to (opamp.out) + (C) to [C, l_=$C$,] ++(-2,0) node[ground] {} + + (opamp.+) to [short] ++(0,-1.5) coordinate(R_b) + to [R, l_=$R_3 $, *-] (R_b-|opamp.out) + to (opamp.out) + (R_b) to [R, l=$R_2$] ++(-2,0) node[ground] {} + + (opamp.out) to [short, -o] ++(1,0) node[right] {$v_1$} + +; + \end{circuitikz} + \caption{Relaksjonsgenerator. Genererer et firkantsignal basert på tidskonstanten $\tau = R_1 \cdot C$.} + \label{circ:relaksasjonStart} +\end{figure} + +Vi antar forsyningsspenningen til operasjonsforsterkeren som brukes som en komparator i generatoren er like positiv og negativ, $ +V = - (-V) $. Da er perioden $T$ til signalet som blir generert som i \eqref{eq:periodeGenerator}. + +\begin{align} + T = 2 \cdot R_1 \cdot C \cdot \ln\left(1 + 2\frac{R_2}{R_3}\right) \label{eq:periodeGenerator} +\end{align} + +Vi kan også anta at $R_2 = R_3$, og skriver om fra periode $T$ til frekvens $f = \frac{1}{T}$ i \eqref{eq:frekvensGenerator}. + +\begin{align} + f = \frac{1}{2 \cdot R_1 \cdot C \cdot \ln\left(3\right)} \label{eq:frekvensGenerator} +\end{align} + +\subsection{Lavpass-filter} + +Siden en firkantpuls består av en grunnfrekvens og mange overtoner av grunnfrekvensen, kan vi hente ut et sinussignal fra firkantsignalgeneratoren ved å fjerne overtonene. Dette kan gjøres med et lavpass-filter. + +Igjen så finnes det mange varianter av et lavpassfilter, men her tas det utganspunkt i en Sallan-Key-topologi \cite{sallan-key} med en Butterworth-form\cite{butterworth} på dempningen. + +Sallan-key-filteret er et andreordens-filter og disse kan seriekobles for å legge til flere ordener. Dersom det er to i serie vil vi kunne ha opp til et fjerdeordens-filter, tre så får vi sjetteordens osv.. I designnotat om hvordan lage et Anti-alias-filter \cite{anti-alias} gåes det mer i dybden i hvordan designe et n-ordens filter med Sallan-Key-topologi. Men kort oppsummert i dette avsnittet. + +\begin{figure}[!htpb] + \centering + \begin{circuitikz} + \draw + (0,0) node[op amp,yscale=-1](opamp){} + + (opamp.+) to [short] ++(-1,0) coordinate(C2) + to [C, l_=$C_2$, *-] ++(0,-2) + to ++(0,0) node[ground]{} + + (C2) to [R, l_=$R$] ++(-2,0) coordinate(R2) + to [short, *-] ++(0,1) coordinate(C1) + to [C, l=$C_1 $] (C1-|opamp.out) + to [short, -*] (opamp.out) + + (R2) to [R, l_=$R$, -o] ++(-2,0) node[left] {$v_i$} + + (opamp.-) to [short] ++(0,-1) coordinate(fb) + to [short] (fb-|opamp.out) + to [short] (opamp.out) + to [short, -o] ++(1,0) node[right] {$v_o$} + + ; + \end{circuitikz} + \caption{Kretstopologi for et andregrads lavpass-filter i Sallen-Key topologi.} + \label{circ:sallen-key-start} +\end{figure} + + +For å regne ut de forskjellige komponentverdiene har vi noen formler. Siden vi bruker operasjonsforsterkere (opamp) er det ganske standard å bruke motstandsverdier mellom $1k\Omega$ og $100k\Omega$. Motstandene kan da velges fritt innenfor disse grenser. + +$\omega_0 $ er knekkfrekvensen i radianer og gitt i (\ref{eq:knekkfreq}). +\begin{align} + \omega_0 = 2\pi \cdot f_0 \label{eq:knekkfreq} +\end{align} + +To tidskonstanter $\tau_1$ og $\tau_2$ i (\ref{eq:tidskonstanter}). + +\begin{align} + \tau_1 = \frac{1}{\omega_0 \zeta} \quad \text{og} \quad \tau_2 = \frac{1}{\omega_0^2\tau_1} \label{eq:tidskonstanter} +\end{align} + +Da er kondensatorverdiene gitt som i (\ref{eq:kondiser}). + +\begin{align} + C_1 = \frac{\tau_1}{R} \quad \text{og} \quad C_2 = \frac{\tau_2}{R} \label{eq:kondiser} +\end{align} + +Verdiene for $\zeta$ kan regnes ut eller så er de gitt for et normal Butterworth-filter for orden 1 til 6 i \autoref{tab:sallenKeyLosning}. Her kommer $\zeta$-verdiene i par som gjelder for et sett med et Sallen-Key-filter. + + +\begin{table}[!htpb] +\centering +\caption{$\zeta$-verdier for forskjellige ordener $n$ for et butterwurth-filter med et Allan-Key-filter topologi.} +\label{tab:sallenKeyLosning} +\begin{tabular}{|l|l|l|l|} +\hline \hline + & \multicolumn{3}{l|}{Polpar \textit{i}} \\ \hline +$n$ & $1$ & $2$ & $3$ \\ \hline +\hline +$1$ & $1$ & & \\ \hline +$2$ & $0.70711$ & & \\ \hline +$3$ & $1$ & $0.5$ & \\ \hline +$4$ & $0.92388$ & $0.38268$ & \\ \hline +$5$ & $1$ & $0.80902$ & $0.30902$ \\ \hline +$6$ & $0.96593$ & $0.70711$ & $0.25882$ \\ \hline +\hline +\end{tabular}% +\end{table} + +Hele sinusgeneratoren vil da være firkantgeneratoren og deretter filteret/ene i serie som vist i \autoref{circ:sinusTeori}. Dersom det seriekobles flere filtere gøres dette ved å koble $v_i$ på filteret på utgangen $v_2$. + +\begin{figure}[!htpb] + \centering + \begin{circuitikz}[scale=0.92, every node/.style={transform shape}] + \draw + (0,0) node[op amp,yscale=1](opamp){} + + (opamp.-) to [short] ++(0,1) coordinate(C) + to [R, l=$R_1 $, *-] (C-|opamp.out) + to (opamp.out) + (C) to [C, l_=$C$,] ++(-2,0) node[ground] {} + + (opamp.+) to [short] ++(0,-1) coordinate(R_b) + to [R, l_=$R_3 $, *-] (R_b-|opamp.out) + to (opamp.out) + (R_b) to [R, l=$R_2$] ++(-2,0) node[ground] {} + + (9,0) node[op amp,yscale=-1](opamp2){} + + (opamp2.+) to [short] ++(-1,0) coordinate(C2) + to [C, l_=$C_2$, *-] ++(0,-2) + to ++(0,0) node[ground]{} + + (C2) to [R, l_=$R$] ++(-2,0) coordinate(R2) + to [short, *-] ++(0,1) coordinate(C1) + to [C, l=$C_1 $] (C1-|opamp2.out) + to [short, -*] (opamp2.out) + + (R2) to [R, l_=$R$] ++(-2,0) coordinate(koblingInn) + + (opamp2.-) to [short] ++(0,-1) coordinate(fb) + to [short] (fb-|opamp2.out) + to [short] (opamp2.out) + to [short, -o] ++(1,0) node[right] {$v_2$} + + (opamp.out) to [short, *-o] (opamp.out-|koblingInn) node[below]{$v_1$} + to (koblingInn) + + ; + \end{circuitikz} + \caption{Relaksjonsgenerator med lavpass-filter. Genererer et sinussignal på utgangen $v_2$ basert på tidskonstanten $\tau = R_1 \cdot C$.} + \label{circ:sinusTeori} +\end{figure} + + +\section{Realisering og test} +\label{sec:realisering} +\subsection{Realisering} + +Frekvensen som sinusgeneratoren skal generere er gitt ved $f_0 = 4,1kHz$. + +Velger $R_1 = R_2 = R_3 = R = 1k\Omega$. Kondensatoren i generatoren er gitt i \eqref{eq:generatorKondis}. Operasjonsforsterkerene som blir brukt til generatoren er MC34082 \cite{opamp}, den har to opamper i samme pakke. + +\begin{align} + C = \frac{1}{2 \cdot R_1 \cdot f_0 \cdot \ln(3)} = 111\text{nF} \label{eq:generatorKondis} +\end{align} + +Vi trenger å lage et 4. ordens filter for å fjerne alle de uønskede frekvensene. Det blir da brukt en til MC34082P for filterene, da denne har 4 operasjonsforsterkere. + +Dermed blir hele kretsen som i \autoref{circ:prinsippKrets}. + +\begin{figure}[!htpb] + \centering + \begin{circuitikz}[scale=0.92, every node/.style={transform shape}] + \draw + (0,0) node[op amp,yscale=1](opamp){OP1} + + (opamp.-) to [short] ++(0,1) coordinate(C) + to [R, l=$R_1 $, *-] (C-|opamp.out) + to (opamp.out) + (C) to [C, l_=$C$,] ++(-2,0) node[ground] {} + + (opamp.+) to [short] ++(0,-1) coordinate(R_b) + to [R, l_=$R_3 $, *-] (R_b-|opamp.out) + to (opamp.out) + (R_b) to [R, l=$R_3 $] ++(-2,0) node[ground] {} + + + %% Filter 1 + (9,3) node[op amp,yscale=-1](opamp2){\raisebox{\depth}{\scalebox{1}[-1]{OP2}}} + + (opamp2.+) to [short] ++(-1,0) coordinate(C2) + to [C, l_=$C_2 $, *-] ++(0,-2) + to ++(0,0) node[ground]{} + + (C2) to [R, l_=$R$] ++(-2,0) coordinate(R2) + to [short, *-] ++(0,1) coordinate(C1) + to [C, l=$C_1 $] (C1-|opamp2.out) + to [short, -*] (opamp2.out) + + (R2) to [R, l_=$R$] ++(-2,0) coordinate(koblingInn) + + (opamp2.-) to [short] ++(0,-1) coordinate(fb) + to [short] (fb-|opamp2.out) + to [short] (opamp2.out) + to [short] ++(1,0) coordinate(filter1ut) + + (opamp.out) to [short, *-o] (opamp.out-|koblingInn) node[below]{$v_1$} + to (koblingInn) + + % Filter 2 + (10,-3) node[op amp,yscale=-1](opamp3){\raisebox{\depth}{\scalebox{1}[-1]{OP3}}} + + (opamp3.+) to [short] ++(-1,0) coordinate(C4) + to [C, l_=$C_4$, *-] ++(0,-2) + to ++(0,0) node[ground]{} + + (C4) to [R, l_=$R$] ++(-2,0) coordinate(R4) + to [short, *-] ++(0,1) coordinate(C3) + to [C, l=$C_3$] (C3-|opamp3.out) + to [short, -*] (opamp3.out) + + (R4) to [R, l_=$R$] ++(-2,0) coordinate(koblingInn) + + (opamp3.-) to [short] ++(0,-1) coordinate(fb) + to [short] (fb-|opamp3.out) + to [short] (opamp3.out) + to [short, -o] ++(1,0) node[right] {$v_2$} + + (filter1ut) -- (filter1ut|-opamp.out) -- (opamp.out-|koblingInn) -- (koblingInn) + ; + \end{circuitikz} + \caption{Relaksjonsgenerator med 4. ordens lavpass-filter. Genererer et sinussignal på utgangen $v_2$ basert på tidskonstanten $\tau = R_1 \cdot C$ Uten komponentverdier.} + \label{circ:prinsippKrets} +\end{figure} + +Siden dette er et fjerde-ordens filter blir $\zeta_1 = 0.92388$ og $\zeta_2 = 0.38268$. Knekkfrekvensen $\omega_0 = 2\pi \cdot f_0 = 8,1\pi \cdot 10^3 $ rad/s. Da er tidskonstantene gitt i \eqref{eq:tid1} og \eqref{eq:tid2}. + +\begin{align} + \tau_1 = \frac{1}{\omega_0 \zeta_1} \approx 43\mu\text{s} \quad &\text{og} \quad \tau_2 = \frac{1}{\omega_0^2\tau_1} \approx 36\mu\text{s} \label{eq:tid1}\\ + \tau_3 = \frac{1}{\omega_0 \zeta_2} \approx 103\mu\text{s} \quad &\text{og} \quad \tau_4 = \frac{1}{\omega_0^2\tau_3} \approx 15\mu\text{s} \label{eq:tid2} +\end{align} + +Dermed blir kondensatorene gitt i \eqref{eq:kond1}, \eqref{eq:kond2}, \eqref{eq:kond3} og \eqref{eq:kond4}. + +\begin{align} + C_1 &= \frac{\tau_1}{R} \approx 43 \text{nF} \label{eq:kond1}\\ + C_2 &= \frac{\tau_2}{R} \approx 36 \text{nF} \label{eq:kond2} \\ + C_3 &= \frac{\tau_3}{R} \approx 103 \text{nF} \label{eq:kond3}\\ + C_4 &= \frac{\tau_4}{R} \approx 15 \text{nF} \label{eq:kond4} +\end{align} + +Alle koponentene justert for standardverdier er i \autoref{tab:komponenter}. + +\begin{table}[!htbp] + \centering + \caption{Tabell for alle komponeneter til kretsen, både utregnet og justert for standardverdier.} + \label{tab:komponenter} + \begin{tabular}{|l|c|c|} + \hline \hline + Komponent & Verdi & Justert for standardverdier \\ \hline + $R_1$ & $1k\Omega$ & $1k\Omega$ \\ \hline + $R_2$ & $1k\Omega$ & $1k\Omega$ \\ \hline + $R_3$ & $1k\Omega$ & $1k\Omega$ \\ \hline + $C$ & $111$nF & $100\text{nF}||10\text{nF}||1\text{nF}$ \\ \hline + $R$ & $1k\Omega$ & $1k\Omega$ \\ \hline + $C_1$ & $43$nF & $10\text{nF}||10\text{nF}||10\text{nF}||10\text{nF}||1\text{nF}||1\text{nF}||1\text{nF}$ \\ \hline + $C_2$ & $36$nF & $10\text{nF}||10\text{nF}||10\text{nF}||(10\text{nF}+10\text{nF})||1\text{nF}$ \\ \hline + $C_3$ & $103$nF & $100\text{nF}||1\text{nF}||1\text{nF}||1\text{nF}$ \\ \hline + $C_4$ & $15$nF & $10\text{nF}||(10\text{nF}+10\text{nF})$ \\ \hline + OP1 & \multicolumn{2}{c|}{LF353P} \\ \hline + OP2 & \multicolumn{2}{c|}{LM339N} \\ \hline + OP3 & \multicolumn{2}{c|}{LM339N} \\ \hline + \hline + \end{tabular} +\end{table} + +Den fullførte kretsen er som i \autoref{circ:sinusVerdier}. + +\begin{figure}[!htpb] + \centering + \begin{circuitikz}[scale=0.92, every node/.style={transform shape}] + \draw + (0,0) node[op amp,yscale=1](opamp){OP1} + + (opamp.-) to [short] ++(0,1) coordinate(C) + to [R, l=$1k\Omega$, *-] (C-|opamp.out) + to (opamp.out) + (C) to [C, l_=$111\text{nF}$,] ++(-2,0) node[ground] {} + + (opamp.+) to [short] ++(0,-1) coordinate(R_b) + to [R, l_=$1k\Omega$, *-] (R_b-|opamp.out) + to (opamp.out) + (R_b) to [R, l=$1k\Omega$] ++(-2,0) node[ground] {} + + + %% Filter 1 + (9,3) node[op amp,yscale=-1](opamp2){\raisebox{\depth}{\scalebox{1}[-1]{OP2}}} + + (opamp2.+) to [short] ++(-1,0) coordinate(C2) + to [C, l_=$36 \text{nF}$, *-] ++(0,-2) + to ++(0,0) node[ground]{} + + (C2) to [R, l_=$1k\Omega$] ++(-2,0) coordinate(R2) + to [short, *-] ++(0,1) coordinate(C1) + to [C, l=$43$nF] (C1-|opamp2.out) + to [short, -*] (opamp2.out) + + (R2) to [R, l_=$1k\Omega$] ++(-2,0) coordinate(koblingInn) + + (opamp2.-) to [short] ++(0,-1) coordinate(fb) + to [short] (fb-|opamp2.out) + to [short] (opamp2.out) + to [short] ++(1,0) coordinate(filter1ut) + + (opamp.out) to [short, *-o] (opamp.out-|koblingInn) node[below]{$v_1$} + to (koblingInn) + + % Filter 2 + (10,-3) node[op amp,yscale=-1](opamp3){\raisebox{\depth}{\scalebox{1}[-1]{OP3}}} + + (opamp3.+) to [short] ++(-1,0) coordinate(C4) + to [C, l_=$15 \text{nF}$, *-] ++(0,-2) + to ++(0,0) node[ground]{} + + (C4) to [R, l_=$1k\Omega$] ++(-2,0) coordinate(R4) + to [short, *-] ++(0,1) coordinate(C3) + to [C, l=$103 \text{nF}$] (C3-|opamp3.out) + to [short, -*] (opamp3.out) + + (R4) to [R, l_=$1k\Omega$] ++(-2,0) coordinate(koblingInn) + + (opamp3.-) to [short] ++(0,-1) coordinate(fb) + to [short] (fb-|opamp3.out) + to [short] (opamp3.out) + to [short, -o] ++(1,0) node[right] {$v_2$} + + (filter1ut) -- (filter1ut|-opamp.out) -- (opamp.out-|koblingInn) -- (koblingInn) + ; + \end{circuitikz} + \caption{Relaksjonsgenerator med lavpass-filter. Genererer et sinussignal på utgangen $v_2$ basert på tidskonstanten $\tau = R_1 \cdot C$.} + \label{circ:sinusVerdier} +\end{figure} + +\clearpage +\subsection{Test} + +Etter testing må motstandsverdien $R_1$ endres til $R_1 = 870\Omega$ og kondensatoren $C$ må endres til $C = 112$nF. Ellers helt lik krets. Endelige verdier kan sees i \autoref{tab:komponenterEndelig}. Den ferdige kretsen kan sees i \autoref{circ:ferdig} og \autoref{fig:irl}. + +\begin{table}[!htbp] + \centering + \caption{Tabell for alle komponeneter til kretsen, både utregnet og justert for standardverdier.} + \label{tab:komponenterEndelig} + \begin{tabular}{|l|c|c|} + \hline \hline + Komponent & Verdi & Justert for standardverdier \\ \hline + $R_1$ & $870\Omega$ & $1k\Omega$ \\ \hline + $R_2$ & $1k\Omega$ & $1k\Omega$ \\ \hline + $R_3$ & $1k\Omega$ & $1k\Omega$ \\ \hline + $C$ & $112$nF & $100\text{nF}||10\text{nF}||1\text{nF}||1\text{nF}$ \\ \hline + $R$ & $1k\Omega$ & $1k\Omega$ \\ \hline + $C_1$ & $43$nF & $10\text{nF}||10\text{nF}||10\text{nF}||10\text{nF}||1\text{nF}||1\text{nF}||1\text{nF}$ \\ \hline + $C_2$ & $36$nF & $10\text{nF}||10\text{nF}||10\text{nF}||(10\text{nF}+10\text{nF})||1\text{nF}$ \\ \hline + $C_3$ & $103$nF & $100\text{nF}||1\text{nF}||1\text{nF}||1\text{nF}$ \\ \hline + $C_4$ & $15$nF & $10\text{nF}||(10\text{nF}+10\text{nF})$ \\ \hline + OP1 & \multicolumn{2}{c|}{MC34082P} \\ \hline + OP2 & \multicolumn{2}{c|}{MC34082P} \\ \hline + OP3 & \multicolumn{2}{c|}{MC34082P} \\ \hline + \hline + \end{tabular} +\end{table} + +\begin{figure}[!htpb] + \centering + \begin{circuitikz}[scale=0.92, every node/.style={transform shape}] + \draw + (0,0) node[op amp,yscale=1](opamp){OP1} + + (opamp.-) to [short] ++(0,1) coordinate(C) + to [R, l=$870\Omega$, *-] (C-|opamp.out) + to (opamp.out) + (C) to [C, l_=$112\text{nF}$] ++(-2,0) node[ground] {} + + (opamp.+) to [short] ++(0,-1) coordinate(R_b) + to [R, l_=$1k\Omega$, *-] (R_b-|opamp.out) + to (opamp.out) + (R_b) to [R, l=$1k\Omega$] ++(-2,0) node[ground] {} + + + %% Filter 1 + (9,3) node[op amp,yscale=-1](opamp2){\raisebox{\depth}{\scalebox{1}[-1]{OP2}}} + + (opamp2.+) to [short] ++(-1,0) coordinate(C2) + to [C, l_=$36 \text{nF}$, *-] ++(0,-2) + to ++(0,0) node[ground]{} + + (C2) to [R, l_=$1k\Omega$] ++(-2,0) coordinate(R2) + to [short, *-] ++(0,1) coordinate(C1) + to [C, l=$43$nF] (C1-|opamp2.out) + to [short, -*] (opamp2.out) + + (R2) to [R, l_=$1k\Omega$] ++(-2,0) coordinate(koblingInn) + + (opamp2.-) to [short] ++(0,-1) coordinate(fb) + to [short] (fb-|opamp2.out) + to [short] (opamp2.out) + to [short] ++(1,0) coordinate(filter1ut) + + (opamp.out) to [short, *-o] (opamp.out-|koblingInn) node[below]{$v_1$} + to (koblingInn) + + % Filter 2 + (10,-3) node[op amp,yscale=-1](opamp3){\raisebox{\depth}{\scalebox{1}[-1]{OP3}}} + + (opamp3.+) to [short] ++(-1,0) coordinate(C4) + to [C, l_=$15 \text{nF}$, *-] ++(0,-2) + to ++(0,0) node[ground]{} + + (C4) to [R, l_=$1k\Omega$] ++(-2,0) coordinate(R4) + to [short, *-] ++(0,1) coordinate(C3) + to [C, l=$103 \text{nF}$] (C3-|opamp3.out) + to [short, -*] (opamp3.out) + + (R4) to [R, l_=$1k\Omega$] ++(-2,0) coordinate(koblingInn) + + (opamp3.-) to [short] ++(0,-1) coordinate(fb) + to [short] (fb-|opamp3.out) + to [short] (opamp3.out) + to [short, -o] ++(1,0) node[right] {$v_2$} + + (filter1ut) -- (filter1ut|-opamp.out) -- (opamp.out-|koblingInn) -- (koblingInn) + ; + \end{circuitikz} + \caption{Komplett fungerende krets med alle komponentverdier.} + \label{circ:ferdig} +\end{figure} + +\begin{figure}[!htbp] + \centering + \includegraphics[width=\textwidth]{figurer/irlKrets.jpg} + \caption{Fysisk oppkobling av kretsen.} + \label{fig:irl} +\end{figure} + +Den målte frekvensen til sinusen er $f=4.100kHz$, se \autoref{fig:maaling}, som er godt innenfor avviket på $10000$ppm. Kretsen hadde et avvik på $0$ ppm. Ved måling av harmonisk forvrengning, se \autoref{fig:maalingSpec}, fant vi at den totale forvrengningen er på $2.0\%$, som også er innenfor kravene. + +\begin{figure}[!htpb] + \centering + \includegraphics[width=\textwidth]{figurer/maalingavsinus.png} + \caption{Måling av sinusgeneratoren. Oransje er firkantgeneratoren og blå er den rene sinusen.} + \label{fig:maaling} +\end{figure} + +\begin{figure}[!htpb] + \centering + \includegraphics[width=\textwidth]{figurer/maalingavsinusspektrum.png} + \caption{Måling av sinusgeneratorens harmoniske forvrengning. Blå linje er spektrumet til sinusgeneratoren.} + \label{fig:maalingSpec} +\end{figure} + + + +\section{Konklusjon} +\label{sec:konklusjon} + +Ut i fra spesifikasjonene som ble oppgitt var kretsen velfungerende. Frekvensen hadde et avvik på ca $0$ ppm, og sinusen ser ut som en sinus, med en total harmonisk forvrengning på $2\%$. For å få til en enda bedre sinus, vil det fungere å ha et enda høyere ordens filter. Den vil da fjerne mer av de uønskede frekvensene. + + +%Bibliografi: Legg til flere elementer ved å legge til flere \bibitem:-------- +\phantomsection +\addcontentsline{toc}{section}{Referanser} +\begin{thebibliography}{99} + +\bibitem{sallan-key} + Wikipedia contributors. (2019, August 6). \textit{Sallen–Key topology}. In Wikipedia, The Free Encyclopedia. Retrieved 11:21, October 8, 2019, from \url{https://en.wikipedia.org/w/index.php?title=Sallen%E2%80%93Key_topology&oldid=909548354} + +\bibitem{butterworth} + Wikipedia contributors. (2019, September 27). \textit{Butterworth filter}. In Wikipedia, The Free Encyclopedia. Retrieved 10:22, October 8, 2019, from \url{https://en.wikipedia.org/w/index.php?title=Butterworth_filter&oldid=918135860} + +\bibitem{notat} + L. Lundheim. (23.10.2018). \textit{Teknisk Notat: Sinus-generator}. NTNU, Elsys-2018-LL-1. + +\bibitem{anti-alias} + Ø. Skaaden. (09.10.2019). \textit{Designnotat: Anti-Alias-filter}. NTNU, elsys. Hentet 24.11.2019 fra \url{https://glados.no/files/ntnu/h19/ttt4265/D7.pdf} + +\bibitem{opamp} + On Semiconductors. (03.2002). \textit{MC34080 thru MC34085 - High performance JFET input operational amplifiers}. On Semiconductors. MC34080/D. \url{https://www.digchip.com/datasheets/download_datasheet.php?id=643869&part-number=MC34082P} + +\end{thebibliography}{} + +\clearpage +\appendix +%Tillegg. Flere tillegg legges til ved å lage flere sections:----------------- + + + +\end{document} diff --git a/D8/D8.tex.old b/D8/D8.tex.old new file mode 100644 index 0000000..69ed8b2 --- /dev/null +++ b/D8/D8.tex.old @@ -0,0 +1,359 @@ +%Dokumentinnstillinger:--------------------------------- +\documentclass[11pt,norsk]{elsys-design} + + +\heading{Designnotat} +\title{Sinus-generator} +\author{Øyvind Skaaden} +\version{1.0} +\date{\today} + +\begin{document} + +\maketitle + +%Automatisk generert innholdsfortegnelse:------------------ +\toc + +%Selve rapporten:------------------------------------------ +\section{Problembeskrivelse} +\label{sec:innledning} + +I veldig mange sammenhenger er det å kunne generere et periodisk signal en veldig nyttig ting. I de fleste tilfeller ønsker vi at signalet skal ha en enkel tone, og da må vi bruke et sinussignal. +For å generere et sinussignal er det flere måter å gjøre det på, men her vil vi ta utganspunk i systemet i \autoref{fig:introsystem}. + +\begin{figure}[!htbp] + \centering + \includegraphics[width=0.7\textwidth]{figurer/D8_Innledning.pdf} + \caption{Blokkdiagram for sinus-generatoren. Spenningene $v_1$ og $v_2$ er henholdsvis til utgangen på firkantsignalgeneratoren og lavpassfilteret.} + \label{fig:introsystem} +\end{figure} + +Vi ønsker å ikke være veldig langt unna frekvensen som velges, så vi ønsker å være innenfor $10 000$ ppm av frekvensen $f_0 $ til sisnussignalet. + +Siden vi lager sinusen fra en firkantpuls ønsker vi også at signalet ikke er veldig ødelagt av de overharmoniske svingningene. Derfor velger vi at harmonisk forvrengning, $D$, ikke skal være større enn $D_{max} = 2\% $. + +\section{Prinsipiell løsning} +\label{sec:prinsipielllosning} + +For å generere et firkantsignal er det flere måter å gjøre det på. Her vil det bli tatt utganspunkt i en type generator som heter relaksjonsgenerator. Den genererer et firkantsignal basert på opp- og utladning av en kondensator i et $RC$-ledd. Vi kan da styrefrekvensen ved å velge riktig tidskonstant. + + +\begin{figure}[!htpb] + \centering + \begin{circuitikz}[scale=0.92, every node/.style={transform shape}] + \draw + (0,0) node[op amp,yscale=1](opamp){} + + (opamp.-) to [short] ++(0,1) coordinate(C) + to [R, l=$R_1 $, *-] (C-|opamp.out) + to (opamp.out) + (C) to [C, l_=$C$,] ++(-2,0) node[ground] {} + + (opamp.+) to [short] ++(0,-1) coordinate(R_b) + to [R, l_=$R_3 $, *-] (R_b-|opamp.out) + to (opamp.out) + (R_b) to [R, l=$R_2$] ++(-2,0) node[ground] {} + + (opamp.out) to [short, -o] ++(1,0) node[right] {$v_1$} + +; + \end{circuitikz} + \caption{Relaksjonsgenerator. Genererer et firkantsignal basert på tidskonstanten $\tau = R_1 \cdot C$.} + \label{circ:relaksjonStart} +\end{figure} + +Vi antar forsyningsspenningen til operasjonsforsterkeren i generatoren er lik positiv og negativ. Da er perioden $T$ til signalet som blir generert som i \eqref{eq:periodeGenerator}. + +\begin{align} + T = 2 \cdot R_1 \cdot C \cdot \ln\left(1 + \frac{R_2}{R_3}\right) \label{eq:periodeGenerator} +\end{align} + +Vi kan også anta at $1k\Omega < R_2 = R_3 < 100k\Omega$, og skriver om fra periode $T$ til frekvens $f = \frac{1}{T}$ i \eqref{eq:frekvensGenerator}. + +\begin{align} + f = \frac{1}{2 \cdot R_1 \cdot C \cdot \ln\left(3\right)} \label{eq:frekvensGenerator} +\end{align} + +Siden en firkantpuls består av en grunnfrekvens og mange overtoner av grunnfrekvensen, kan vi hente ut et sinussignal fra firkantsignalgeneratoren ved å fjerne overtonene. Dette kan gjøres med et lavpass-filter. + +Igjen så finnes det mange varianter av et lavpassfilter, men her tas det utganspunkt i en Sallan-Key-topologi \cite{sallan-key} med en Butterworth-form\cite{butterworth} på dempningen. + +Sallan-key-filteret er et andreordens-filter og disse kan seriekobles for å legge til flere ordener. Dersom det er to i serie vil vi kunne ha opp til et fjerdeordens-filter, tre så får vi sjetteordens o.s.v. + +\begin{figure}[!htpb] + \centering + \begin{circuitikz} + \draw + (0,0) node[op amp,yscale=-1](opamp){} + + (opamp.+) to [short] ++(-1,0) coordinate(C2) + to [C, l_=$C_2$, *-] ++(0,-2) + to ++(0,0) node[ground]{} + + (C2) to [R, l_=$R$] ++(-2,0) coordinate(R2) + to [short, *-] ++(0,1) coordinate(C1) + to [C, l=$C_1 $] (C1-|opamp.out) + to [short, -*] (opamp.out) + + (R2) to [R, l_=$R$, -o] ++(-2,0) node[left] {$v_1$} + + (opamp.-) to [short] ++(0,-1) coordinate(fb) + to [short] (fb-|opamp.out) + to [short] (opamp.out) + to [short, -o] ++(1,0) node[right] {$v_2$} + + ; + \end{circuitikz} + \caption{Kretstopologi for et andregrads lavpass-filter i Sallen-Key topologi.} + \label{circ:sallen-key-start} +\end{figure} + + +For å regne ut de forskjellige komponentverdiene har vi noen formler. Siden vi bruker operasjonsforsterkere (opamp) er det ganske standard å bruke motstandsverdier mellom $1k\Omega$ og $100k\Omega$. Motstandene kan da velges fritt innenfor disse grenser. + +$\omega_0 $ er knekkfrekvensen i radianer og gitt i (\ref{eq:knekkfreq}). +\begin{align} + \omega_0 = 2\pi \cdot f_0 \label{eq:knekkfreq} +\end{align} + +To tidskonstanter $\tau_1$ og $\tau_2$ i (\ref{eq:tidskonstanter}). + +\begin{align} + \tau_1 = \frac{1}{\omega_0 \zeta} \quad \text{og} \quad \tau_2 = \frac{1}{\omega_0^2\tau_1} \label{eq:tidskonstanter} +\end{align} + +Da er kondensatorverdiene gitt som i (\ref{eq:kondiser}). + +\begin{align} + C_1 = \frac{\tau_1}{R} \quad \text{og} \quad C_2 = \frac{\tau_2}{R} \label{eq:kondiser} +\end{align} + +Verdiene for $\zeta$ kan regnes ut eller så er de gitt for et normal Butterworth-filter for orden 1 til 6 i \autoref{tab:sallenKeyLosning}. Her kommer $\zeta$-verdiene i par som gjelder for et sett med et Sallen-Key-filter. + + +\begin{table}[!htpb] +\centering +\caption{$\zeta$-verdier for forskjellige ordener $n$ for et butterwurth-filter med et Allan-Key-filter topologi.} +\label{tab:sallenKeyLosning} +\begin{tabular}{|l|l|l|l|} +\hline \hline + & \multicolumn{3}{l|}{Polpar \textit{i}} \\ \hline +$n$ & $1$ & $2$ & $3$ \\ \hline +\hline +$1$ & $1$ & & \\ \hline +$2$ & $0.70711$ & & \\ \hline +$3$ & $1$ & $0.5$ & \\ \hline +$4$ & $0.92388$ & $0.38268$ & \\ \hline +$5$ & $1$ & $0.80902$ & $0.30902$ \\ \hline +$6$ & $0.96593$ & $0.70711$ & $0.25882$ \\ \hline +\hline +\end{tabular}% +\end{table} + +Hele sinusgeneratoren vil da være firkantgeneratoren og deretter filteret/ene i serie som vist i \autoref{circ:sinusTeori}. + +\begin{figure}[!htpb] + \centering + \begin{circuitikz}[scale=0.92, every node/.style={transform shape}] + \draw + (0,0) node[op amp,yscale=1](opamp){} + + (opamp.-) to [short] ++(0,1) coordinate(C) + to [R, l=$R_1 $, *-] (C-|opamp.out) + to (opamp.out) + (C) to [C, l_=$C$,] ++(-2,0) node[ground] {} + + (opamp.+) to [short] ++(0,-1) coordinate(R_b) + to [R, l_=$R_3 $, *-] (R_b-|opamp.out) + to (opamp.out) + (R_b) to [R, l=$R_2$] ++(-2,0) node[ground] {} + + (9,0) node[op amp,yscale=-1](opamp2){} + + (opamp2.+) to [short] ++(-1,0) coordinate(C2) + to [C, l_=$C_2$, *-] ++(0,-2) + to ++(0,0) node[ground]{} + + (C2) to [R, l_=$R$] ++(-2,0) coordinate(R2) + to [short, *-] ++(0,1) coordinate(C1) + to [C, l=$C_1 $] (C1-|opamp2.out) + to [short, -*] (opamp2.out) + + (R2) to [R, l_=$R$] ++(-2,0) coordinate(koblingInn) + + (opamp2.-) to [short] ++(0,-1) coordinate(fb) + to [short] (fb-|opamp2.out) + to [short] (opamp2.out) + to [short, -o] ++(1,0) node[right] {$v_2$} + + (opamp.out) to [short, -o] (opamp.out-|koblingInn) node[below]{$v_1$} + to (koblingInn) + + ; + \end{circuitikz} + \caption{Relaksjonsgenerator med lavpass-filter. Genererer et sinussignal på utgangen $v_2$ basert på tidskonstanten $\tau = R_1 \cdot C$.} + \label{circ:sinusTeori} +\end{figure} + + +\section{Realisering og test} +\label{sec:realisering} +\subsection{Realisering} + +Frekvensen som sinusgeneratoren skal generere er gitt ved $f_0 = 4,1kHz$. + +Velger $R_1 = R_2 = R_3 = 1k\Omega$. Kondensatoren i generatoren er gitt i \eqref{eq:generatorKondis}. Opampen som blir brukt er en LF353P, den har to opamper i samme pakke. + +\begin{align} + C = \frac{1}{2 \cdot R_1 \cdot f_0 \cdot \ln(3)} = 111\text{nF} \label{eq:generatorKondis} +\end{align} + +Siden vi har to opamper tilgjengelig, og brukte én i generatoren lager vi kun et andre-ordens filter. +Starter med å velge $R=1k\Omega$. + +Siden dette er et andre-ordens filter blir $\zeta = 0.70711$. Knekkfrekvensen $\omega_0 = 2\pi \cdot f_0 = 8,1\pi \cdot 10^3 $ rad/s. Da er tidskonstantene gitt i \eqref{eq:tid1}. + +\begin{align} + \tau_1 = \frac{1}{\omega_0 \zeta_1} \approx 55\mu\text{s} \quad &\text{og} \quad \tau_2 = \frac{1}{\omega_0^2\tau_1} \approx 27\mu\text{s} \label{eq:tid1} +\end{align} + +Dermed blir kondensatorene, og justert for standardverdier som i \eqref{eq:kond1} og \eqref{eq:kond2}. + +\begin{align} + C_1 = \frac{\tau_1}{R} \approx 55 \text{nF} \approx (100 \text{nF} + 100 \text{nF}) || (10 \text{nF} + 10 \text{nF}) \label{eq:kond1}\\ + C_2 = \frac{\tau_2}{R} \approx 27 \text{nF} \approx 10 \text{nF} || 10 \text{nF} || (10 \text{nF} + 10 \text{nF}) || 1 \text{nF} || \text{nF} \label{eq:kond2} +\end{align} + +Den fullførte kretsen er som i \autoref{circ:sinusVerdier}. + +\begin{figure}[!htpb] + \centering + \begin{circuitikz}[scale=0.92, every node/.style={transform shape}] + \draw + (0,0) node[op amp,yscale=1](opamp){} + + (opamp.-) to [short] ++(0,1) coordinate(C) + to [R, l=$1k\Omega$, *-] (C-|opamp.out) + to (opamp.out) + (C) to [C, l_=$C$,] ++(-2,0) node[ground] {} + + (opamp.+) to [short] ++(0,-1) coordinate(R_b) + to [R, l_=$1k\Omega$, *-] (R_b-|opamp.out) + to (opamp.out) + (R_b) to [R, l=$1k\Omega$] ++(-2,0) node[ground] {} + + (9,0) node[op amp,yscale=-1](opamp2){} + + (opamp2.+) to [short] ++(-1,0) coordinate(C2) + to [C, l_=$27 \text{nF}$, *-] ++(0,-2) + to ++(0,0) node[ground]{} + + (C2) to [R, l_=$1k\Omega$] ++(-2,0) coordinate(R2) + to [short, *-] ++(0,1) coordinate(C1) + to [C, l=$55 \text{nF}$] (C1-|opamp2.out) + to [short, -*] (opamp2.out) + + (R2) to [R, l_=$1k\Omega$] ++(-2,0) coordinate(koblingInn) + + (opamp2.-) to [short] ++(0,-1) coordinate(fb) + to [short] (fb-|opamp2.out) + to [short] (opamp2.out) + to [short, -o] ++(1,0) node[right] {$v_2$} + + (opamp.out) to [short, -o] (opamp.out-|koblingInn) node[below]{$v_1$} + to (koblingInn) + + ; + \end{circuitikz} + \caption{Relaksjonsgenerator med lavpass-filter. Genererer et sinussignal på utgangen $v_2$ basert på tidskonstanten $\tau = R_1 \cdot C$.} + \label{circ:sinusVerdier} +\end{figure} + +\subsection{Test} + +Etter testing må motstandsverdien $R_1$ endres til $R_1 = 870\Omega$. Ellers helt lik krets. Den endelige kretsen kan sees i + +\begin{figure}[!htpb] + \centering + \begin{circuitikz}[scale=0.92, every node/.style={transform shape}] + \draw + (0,0) node[op amp,yscale=1](opamp){} + + (opamp.-) to [short] ++(0,1) coordinate(C) + to [R, l=$1k\Omega$, *-] (C-|opamp.out) + to (opamp.out) + (C) to [C, l_=$C$,] ++(-2,0) node[ground] {} + + (opamp.+) to [short] ++(0,-1) coordinate(R_b) + to [R, l_=$1k\Omega$, *-] (R_b-|opamp.out) + to (opamp.out) + (R_b) to [R, l=$1k\Omega$] ++(-2,0) node[ground] {} + + (9,0) node[op amp,yscale=-1](opamp2){} + + (opamp2.+) to [short] ++(-1,0) coordinate(C2) + to [C, l_=$27 \text{nF}$, *-] ++(0,-2) + to ++(0,0) node[ground]{} + + (C2) to [R, l_=$1k\Omega$] ++(-2,0) coordinate(R2) + to [short, *-] ++(0,1) coordinate(C1) + to [C, l=$55 \text{nF}$] (C1-|opamp2.out) + to [short, -*] (opamp2.out) + + (R2) to [R, l_=$1k\Omega$] ++(-2,0) coordinate(koblingInn) + + (opamp2.-) to [short] ++(0,-1) coordinate(fb) + to [short] (fb-|opamp2.out) + to [short] (opamp2.out) + to [short, -o] ++(1,0) node[right] {$v_2$} + + (opamp.out) to [short, -o] (opamp.out-|koblingInn) node[below]{$v_1$} + to (koblingInn) + + ; + \end{circuitikz} + \caption{Komplett fungerende krets med alle komponentverdier.} + \label{circ:ferdig} +\end{figure} + +Den målte frekvensen til sinusen er $f=4.096kHz$ som er godt innenfor avviket på $10000$ppm. Kretsen hadde et avvik på $976$ppm. Harmonisk forvrengning fikk vi ikke til å måle, men antar den ikke er så stor. + +\begin{figure} + \centering + \includegraphics[width=\textwidth]{graphs/sinusmaalingWhite.png} + \caption{Måling av sinusgeneratoren. Oransje er firkantgeneratoren og blå er den rene sinusen.} + \label{fig:maaling} +\end{figure} + + + +\section{Konklusjon} +\label{sec:konklusjon} + +Ut i fra spesifikasjonene som ble oppgitt var kretsen velfungerende. Frekvensen var nære, og sinusen ser ut som en sinus. For å få til en enda bedre sinus, vil det fungere å ha et enda høyere ordens filter. Den vil da fjerne mer av de uønskede frekvensene. + + +%Bibliografi: Legg til flere elementer ved å legge til flere \bibitem:-------- +\phantomsection +\addcontentsline{toc}{section}{Referanser} +\begin{thebibliography}{99} + +\bibitem{sallan-key} + Wikipedia contributors. (2019, August 6). \textit{Sallen–Key topology}. In Wikipedia, The Free Encyclopedia. Retrieved 11:21, October 8, 2019, from \url{https://en.wikipedia.org/w/index.php?title=Sallen%E2%80%93Key_topology&oldid=909548354} + +\bibitem{butterworth} + Wikipedia contributors. (2019, September 27). \textit{Butterworth filter}. In Wikipedia, The Free Encyclopedia. Retrieved 10:22, October 8, 2019, from \url{https://en.wikipedia.org/w/index.php?title=Butterworth_filter&oldid=918135860} + +\bibitem{notat} + L. Lundheim. (23.10.2018). \textit{Teknisk Notat: Sinus-generator}. NTNU, Elsys-2018-LL-1. + +\end{thebibliography}{} + +\clearpage +\appendix +%Tillegg. Flere tillegg legges til ved å lage flere sections:----------------- + + + +\end{document} diff --git a/D8/Sinusgenerator.txt b/D8/Sinusgenerator.txt new file mode 100644 index 0000000..aa9a9da --- /dev/null +++ b/D8/Sinusgenerator.txt @@ -0,0 +1,36 @@ +$ 1 0.000005 0.8729138363720133 63 5 43 +c 384 80 384 240 0 1.0000000000000001e-7 2.447360802545873 +a 464 96 608 96 8 5 -5 1000000 2.447360802545873 -2.5002473779090226 100000 +w 384 80 464 80 0 +w 464 80 464 16 0 +r 464 16 608 16 0 1000 +w 608 16 608 96 0 +w 464 112 464 160 0 +r 464 160 464 240 0 1000 +w 384 240 464 240 0 +g 464 240 464 288 0 +r 464 160 608 160 0 1000 +w 608 160 608 96 0 +p 672 96 672 240 1 0 +w 672 240 464 240 0 +w 672 96 608 96 0 +R 256 80 256 144 0 0 40 5 0 0 0.5 +s 240 16 368 16 0 1 false +a 960 112 1056 112 9 5 -5 1000000 4.443987333865353 4.444031773738692 100000 +r 672 96 784 96 0 1000 +r 784 96 912 96 0 1000 +c 784 32 1056 32 0 5.5e-8 0.6790196142120433 +w 784 32 784 96 0 +c 912 96 912 240 0 2.7e-8 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"\url{https://en.wikipedia.org/w/index.php?title=Sallen%E2%80%93Key_topology&oldid=924138246}", + note = "[Online; accessed 24-November-2019]" +} \ No newline at end of file