Add D6

D6/D6.tex

@@ -0,0 +1,283 @@
+%Dokumentinnstillinger:---------------------------------
+\documentclass[11pt,norsk]{elsys-design}
+
+
+\heading{Designnotat}
+\title{Bufferkrets}
+\author{Øyvind Skaaden}
+\version{2.0}
+\date{\today}
+
+\begin{document}
+
+\maketitle
+
+%Automatisk generert innholdsfortegnelse:------------------
+\toc
+
+%Selve rapporten:------------------------------------------
+\section{Problembeskrivelse}
+\label{sec:innledning}
+
+I mange situasjoner klarer ikke en signalkilde å levere nok strøm til en last. 
+Spenningsnivået er høyt nok, men lasten krever en viss effekt, og da må den leverte strømstyrken også være tilstrekkelig.
+I slike tilfeller trengs en buffer, det vil si et system med en inngang $v_1$ og en utgang $v_2$ som kobles mellom kilde og last som vist i \autoref{fig:problem}.
+
+\begin{figure}[!htbp]
+	\centering
+	\includegraphics[width=0.7\textwidth]{Figurer/D6Problem.pdf}
+	\caption{Blokkdiagram for systemet med en buffer.}
+	\label{fig:problem}
+\end{figure}
+
+I mange tilfeller kan problemet lett løses ved å bruke en operasjonsforsterker,
+men i tilfeller hvor tilgjengelige operasjonsforsterker ikke kan gi tilstrekkelig effekt, ikke har stor nok båndbredde eller av andre grunner ikke oppfyller tilleggskrav i problemstillingen, er det aktuelt å designe en buffer ved hjelp av diskrete komponenter (transistorer, motstander, kondensatorer) som da kan oppnå ønsket effekt eller båndbredde.
+
+Vi vil derfor lage et design på en buffer som baserer seg på diskete komponenter, slik at vi kan drive en større last, levere mer strøm eller høyere effekt.
+
+\section{Prinsipiell løsning}
+\label{sec:prinsipielllosning}
+
+For å lage en transistorbasert buffer, kan vi starte med kretsen i \autoref{fig:buffer}. Den baserer seg på en NPN-transistor, og kretstopologien er en forenklet emitter-følger. Kretsen kan konfigureres slik at inngangsmotstanden er tilstrekkelig stor og utgangsmotstanden er tilstrekkelig liten. Dette er ønskelig om vi skal drive en større last og bruke en kilde som har en større eller ikke ideell utgangsmotstand. Kretstopologien har også den viktige egenskapen for en buffer, som er at forsterkningsfaktoren er på ca 1, altså det kommer det samme ut som inn.
+
+\begin{figure}[!hbtp]
+    \centering
+    \begin{circuitikz}
+   		\draw
+		(0,0) 		node 	[npn] (npn1) 			{}
+		(npn1.C) 	to 		[short, -*] ++(0,1) 	coordinate(top)
+		-- ++(1,0) 	node 	[midway, above] 		{$V_{CC}$}
+
+		(npn1.B) 	to 		[short, i<_=$I_B$] 		++(-0.1,0) node[below] {$V_B$} 
+					--		++(-1,0)				coordinate (base)
+					to 		[R, l_=$R_B$, *-] 		(base|-top) -- (top)
+		(base) 		to 		[C, l=$C_1$,-o] 		++(-2,0) node[left] {$V_1$}
+
+		(npn1.E)	-- 		++(0,-.25)
+					to 		[short,i<_=$I_E$] 		++(0,0) node[left] {$V_E$} 
+					--		++(0,-.75)				coordinate(emitter)
+		(emitter)	to 		[R, l=$R_E$, *-] 		++ (0,-2) node[ground] {}
+		(emitter) 	--		++(.5,0)
+					to 		[C, l=$C_2$, -o] 		++(2,0) node [right] {$V_2$}
+
+		(npn1.C) 	to 		[short, i<_=$I_C$] 		(npn1.C) node[left] {$V_C$}
+		;
+    \end{circuitikz}
+    \caption{kretstopologi av en buffer, konfigurert som en emitter-følger.}
+    \label{fig:buffer}
+\end{figure}
+
+For at vi skal kunne bruke den største mulige amplituden på inngangen $V_1 $ må vi velge arbeidspunktene nøye. 
+Vi velger arbeidspunktet $V_E$, \eqref{eq:V_E}, basert på at arbeidspunktet $V_{BE}$ slik at vi har like mye spenning opp til $V_{CC}$ som ned til terskelspenningen $V_{BE}$.
+
+\begin{align}
+	V_E = \frac{V_{CC} - V_{BE}}{2} = R_E \cdot I_E \label{eq:V_E}
+\end{align}
+
+Dermed blir spenningen $V_B$ som i \eqref{eq:V_B}, gitt at spenningsfallet over $V_{BE}$, fordi vi bruker en npn-transistor.
+
+\begin{align}
+	V_B = V_E + V_{BE} = \frac{V_{CC} + V_{BE}}{2} = V_{CC} - I_B \cdot R_B \label{eq:V_B}
+\end{align}
+
+En NPN-transistor har også egenskapen at $I_C = I_B \cdot \beta $, der $\beta$ er forsterkningsfaktoren til transistoren og $I_B$ er basestrømmen gitt ved \eqref{eq:I_B}. Dermed får vi \eqref{eq:I_E} for strømmen $I_E$. 
+
+\begin{align}
+	I_B = \frac{V_{CC} - V_B}{R_B} \label{eq:I_B}
+\end{align}
+\begin{align}
+	I_E = I_B + I_B \cdot \beta = I_B \left(1 + \beta\right) = \frac{V_{CC} - V_B}{R_B} \left(1 + \beta\right)\label{eq:I_E}
+\end{align}
+
+Setter vi \eqref{eq:I_E} inn i \eqref{eq:V_E}, og løser for $R_B$ for vi sammenhengen mellom $R_E$ og $R_B$ i .
+
+\begin{align}
+	R_B = R_E \cdot \frac{V_{CC} - \left(V_E + V_{BE}\right)}{V_E}\cdot\left(1 + \beta\right) \label{eq:R_B}
+\end{align}
+
+Ut i fra dette ser vi at $ R_B >> R_E$.
+
+For å se at forsterkningsfaktoren blir riktig, kan vi se på småsignalsjemaet for kretsen.
+
+\begin{figure}[!hbtp]
+    \centering
+    \begin{circuitikz}
+   		\draw
+   		(0,0) coordinate(v1)
+		(v1) 	to 		[open, v_=$v_1$] 					++(0,-2)
+		(v1) 	to 		[short, o-] 						++(1,0) 	coordinate(p1)
+				to 		[R, l=$R_B$] 						++(0,-2) 	coordinate(g1)
+				to 		[short, -o] 						++(-1,0)
+		(g1) 	-- 											++(2,0) 	coordinate(g2)
+				to 		[cisource, l_=$i_b\beta$, i_=$i_c$] ++(0,2) 	coordinate(p2)
+				to 		[R, l_=$r_\pi$, i<_=$i_b$] 			++(-2,0) 
+		(p2) 	to 		[short, i=$i_e$] 					++(2,0) 	coordinate(p3)
+				to 		[R, l=$R_E$] 						++(0,-2) 	coordinate(g3)
+				-- 											(g2) 
+		(g3) 	to 		[short, -o] 						++(2,0) 	coordinate(g4)
+		(p3) 	to 		[short, -o] 						++(2,0) 	coordinate(p4)
+		(p4) 	to 		[open, v=$v_2$] 					(g4)
+		;
+    \end{circuitikz}
+    \caption{Småsignalskjema for kretsen i \autoref{fig:buffer}.}
+    \label{fig:smaasignal}
+\end{figure}
+
+Vi ser i skjemaet i \autoref{fig:smaasignal} at vi får følgende sammenhenger. I skjemaet er det en motstand $r_\pi$ som er en slags intern motstand i transistoren, transkonduktansen. Det går kun strøm i den ene retningen, mot $v_2$, altså $i_b > 0$. Den er i ordenen noen tusen ohm, og forsterkningsfaktoren $\beta$ er i ordenen noen hundre. 
+
+\begin{align}
+	v_2 &= i_e \cdot R_E 
+	\qquad \qquad
+	i_e = i_b\left(1+\beta\right) \nonumber\\
+	&\Rightarrow 
+	v_2 = i_b\left(1+\beta\right) R_E \label{eq:v2}
+\end{align}
+\begin{align}
+	i_b &= \frac{v_1 - v_2}{r_\pi} = \frac{v_1 - i_b\left(1+\beta\right) R_E}{r_\pi} 
+	\qquad \qquad
+	v_1 = i_b \cdot r_\pi + i_b\left(1+\beta\right) R_E \nonumber \\
+	&\Rightarrow 
+	v_1 = i_b\left(1+\beta\right) \left(\frac{r_\pi}{1 + \beta} + R_E\right) \label{eq:v1}
+\end{align}
+
+Forsterkningsfaktoren $A$ er forholdet mellom \eqref{eq:v2} of \eqref{eq:v1} som i 
+
+\begin{align}
+	A = \frac{v_2}{v_1} = \frac{i_b\left(1+\beta\right) R_E}{i_b\left(1+\beta\right) \left(\frac{r_\pi}{1 + \beta} + R_E\right)} = \frac{R_E}{\frac{r_\pi}{1 + \beta} + R_E} \label{eq:forsterkning}
+\end{align}
+
+Vi har at faktoren $R_E$ er typisk i noen hundre ohm, og $\frac{r_\pi}{1 + \beta} $ i noen titalls ohm, ser vi at forsterkningen er litt under 1.
+
+Fra \autoref{fig:smaasignal} at inngangsmotstanden er gitt i \eqref{eq:inngangsmot}, og utgangsmotstanden er gitt i \eqref{eq:utgansmot}.
+\begin{align}
+	R_{inn} &= R_B || (r_\pi + R_E) = \frac{1}{\frac{1}{R_B} + \frac{1}{r_\pi + R_E}} \label{eq:inngangsmot} \\
+	R_{ut} &= R_E \label{eq:utgansmot}
+\end{align}
+
+
+\section{Realisering og test}
+\label{sec:realisering}
+\subsection{Realisering}
+
+I bufferkretsen har vi brukt transistoren BC547 \cite{trans}, som er en NPN-transistor. Den har en nominell forsterkningsfaktor på $\beta \approx 330$, og spenningsfall $V_{BE} = \SI{0.7}{\volt} $. 
+Kilden har utgangsmotstand på $R_K = 6.8k\Omega$, og lastmotstand er $R_L = 330\Omega$. Spenningskilden som skal brukes leverer $V_{CC} = 9V$. 
+
+Arbeidspunktet $V_E$ finner vi med \eqref{eq:V_E}.
+\begin{align}
+	V_E = \frac{\SI{9}{\volt} - \SI{0.7}{\volt}}{2} = \SI{4.15}{\volt} 
+\end{align}
+
+Vi finner forholdet mellom $R_B$ og $R_E$ ved hjelp av \eqref{eq:R_B}. 
+
+\begin{align}
+	R_B = R_E \cdot \frac{\SI{9}{\volt} - \left(\SI{4.15}{\volt} + \SI{0.7}{\volt}\right)}{\SI{4.15}{\volt}}\cdot\left(1 + 330\right) = 331\cdot R_E \label{eq:R_B_verdi}
+\end{align}
+
+Velger $R_E = \SI{1.5}{\kilo\ohm}$ for å oppnå nok inngangsmotstand. Dermed blir $R_B$ gitt ved \eqref{eq:R_B_verdi}.
+
+\begin{align*}
+	R_B = 331\cdot\SI{1.5}{\kilo\ohm} \approx \SI{500}{\kilo\ohm}
+\end{align*}
+
+Kondensatorene $C_1$ og $C_2$ trenger kun å være tilstrekkelig store, så velger $C_1 = C_2 = \SI{1}{\micro\farad} $
+
+Den ferdige kretsen har er da gitt som i 
+
+\begin{figure}[!hbtp]
+    \centering
+    \begin{circuitikz}
+   		\draw
+		(0,0) 		node 	[npn] (npn1) 											{}
+		(npn1.C) 	to 		[short, -*] ++(0,1) 									coordinate(top)
+					-- 											++(1,0) 	
+					node 	[midway, above] 										{$\SI{9}{\volt}$}
+
+		(npn1.B) 	--		++(-1,0)												coordinate (base)
+					to 		[R, l_=$\SI{500}{\kilo\ohm}$, *-] 	(base|-top) 
+					-- 											(top)
+		(base) 		to 		[C, l=$\SI{1}{\micro\farad}$,-o] 	++(-2,0) 			node[left] {$V_1$}
+
+		(npn1.E)																	coordinate(emitter)
+		(emitter)	to 		[R, l=$\SI{1.5}{\kilo\ohm}$, *-] 		++ (0,-2) 			node[ground] {}
+		(emitter) 	--											++(.5,0)
+					to 		[C, l=$\SI{1}{\micro\farad}$, -o] 	++(2,0) 			node [right] {$V_2$}
+		;
+    \end{circuitikz}
+    \caption{Ferdig bufferkrets med komponentverdier.}
+    \label{fig:bufferKomponenter}
+\end{figure}
+
+
+\subsection{Test}
+
+For å teste kretsen bruker vi en Analog Discovery oscilloskop for å både å levere spenning, måle signaler og generere testsignaler. 
+Kretsen kobles opp som i \autoref{fig:problem}.
+
+Ved testfrekvensen $f=\SI{1}{\kilo\hertz} $ og amplitude $A = \SI{500}{\milli\volt}$ er utgangen $V_2$, over lastmotstanden $R_L$, $1.5dB$ lavere enn inngangen $v_0$, som vist i \autoref{fig:bode}. Figuren viser også at den nedre knekkfrekvensen ligger ved $f_{\text{nedre}} = \SI{700}{\hertz}$ og øvre knekkfrekvens ved $f_{\text{øvre}} = \SI{2}{\mega\hertz}$ 
+
+\begin{figure}[!hbtp]
+	\centering
+	\includegraphics[width=\textwidth]{Maalinger/MaalingBode500mv.png}
+	\caption{Måling av frekvensrespons til bufferkretsen fra $v_0$ til $v_2$.}
+	\label{fig:bode}
+\end{figure}
+
+Vi kan også se forholdene mellom kildespenningen $V_K$, inngangsspenningen $V_1$, og utgangsspenningen $V_2$ over lastmostanden $R_L$ i \autoref{fig:osc}. Som vi ser, så er det størst demping mellom inngangen $V_1$ og utgangen $V_2$.
+
+\begin{figure}[!hbtp]
+	\centering
+	\includegraphics[width=\textwidth]{Maalinger/MaalingOsc500mv.png}
+	\caption{Måling sinussignalene gjennom kretsen, svart er kildespenningen $V_K$, oransje er inngangsspenningen $V_1$, og blå er utgangsspenningen $V_2$ over lastmotstanden $R_L$.}
+	\label{fig:osc}
+\end{figure}
+
+Kretsen begynner å klippe dersom amplituden på inngangen er større enn $\SI{800}{\milli\volt}$. Se \autoref{fig:klipp}.
+
+\begin{figure}[!hbtp]
+	\centering
+	\includegraphics[width=\textwidth]{Maalinger/MaalingOscKlipping.png}
+	\caption{Største amplitude på inngangen $V_1$ (oransje) før utgangen $V_2$ (blå) klipper.}
+	\label{fig:klipp}
+\end{figure}
+
+Den realiserte kretsen ka sees i \autoref{fig:irl}.
+\begin{figure}[!hbtp]
+	\centering
+	\includegraphics[width=\textwidth]{Figurer/krets.jpg}
+	\caption{Den realiserte kretsen.}
+	\label{fig:irl}
+\end{figure}
+
+\clearpage
+\section{Konklusjon}
+\label{sec:konklusjon}
+Bufferkretsen fungerer som forventet. Signalet inn blir nogelunde likt gjennom hele kretsen og kommer ut på $v_2 $ med kun en liten demping. Det meste av dempingen ligger ved lastmotstanden. 
+
+For å kunne ha gjort kretsen enda bedre, hadde det vært mulig å lage to etterfølgende kretser. Da ville vi hatt mer optimale inngangs- og utgangsmotstander.
+
+
+%Bibliografi: Legg til flere elementer ved å legge til flere \bibitem:--------
+\phantomsection
+\addcontentsline{toc}{section}{Referanser}
+\begin{thebibliography}{99}
+
+\bibitem{notat}
+	Hambley, Allan R., 
+	\textit{Electrical Engineering: Principles \& Applications}, 
+	6th Edition, 
+	Pearson,
+	2014.
+
+\bibitem{trans}
+	Fairchild Semiconductor. (August, 2002). \textit{BC546/547/548/549/550}. Rev. A2, \url{https://www.sparkfun.com/datasheets/Components/BC546.pdf}
+
+
+\end{thebibliography}{}
+
+\clearpage
+\appendix
+%Tillegg. Flere tillegg legges til ved å lage flere sections:-----------------
+
+
+
+\end{document}

D6/Krets2.txt

@@ -0,0 +1,25 @@
+$ 1 0.000005 0.37936678946831776 48 5 43
+c 240 272 160 272 0 0.000001 6.265913281204941
+t 272 272 320 272 0 1 -5.039488104225576 0.6258621997512086 330
+r 320 288 320 368 0 330
+c 320 288 416 288 0 0.00009999999999999999 5.601340268766997
+v 528 368 528 176 0 0 40 9 0 0 0.5
+w 528 176 320 176 0
+w 528 368 320 368 0
+w 320 368 256 368 0
+w 320 256 320 176 0
+g 320 368 320 400 0
+r 80 272 160 272 0 6800
+r 416 288 528 368 0 330
+v 80 368 80 272 0 1 1000 3 0 0 0.5
+w 80 368 256 368 0
+w 320 176 256 176 0
+174 256 368 240 176 1 500000 0.9158000000000001 Resistance
+w 240 272 208 304 0
+w 208 304 272 304 0
+w 272 304 272 272 0
+p 160 272 80 368 1 0
+w -80 224 0 224 0
+o 11 4 0 20483 5 0.025 0 2 11 3
+o 1 4 6 20483 10 0.1 1 1
+o 19 4 0 20483 5 0.1 2 1

D6/Maalinger/MaalingBode500mv.csv

@@ -0,0 +1,152 @@
+Frequency (Hz),Kilde Magnitude (dB),Lastmotstand Magnitude (dB),Lastmotstand Phase (*)
+500,0.004934299677427263,-4.141332559712486,41.92484728080767
+531.6632858185809,0.00505266960785139,-3.909979774835126,40.24739099697555
+565.3316989748193,0.005647553705630371,-3.693211265849722,38.58034141506414
+601.1322173087066,0.005089914568660925,-3.492566965586881,36.94330986364498
+639.1998597315115,0.005522480296053013,-3.306015296810397,35.3256953753292
+679.6781954392627,0.004561057904826714,-3.132600870918113,33.74222604514446
+722.719885372964,0.004194254873752756,-2.971994970936488,32.1980607311274
+768.4872579676354,0.005306099902990438,-2.824801869429785,30.68469493998201
+817.1529213615688,0.004788768649034057,-2.690045960810123,29.21636628779666
+868.9004143746881,0.005135906628180547,-2.566339342190086,27.79295580417244
+923.9248987111453,0.005519328212682429,-2.454792473195988,26.41957179361516
+982.433894996734,0.005317047917228632,-2.350259533150457,25.09003250511464
+1044.648065427019,0.00421928590941858,-2.256322299498154,23.81559296245666
+1110.802045977906,0.005596804867503785,-2.171415142339117,22.5868513627542
+1181.145331317231,0.005989163543959564,-2.094373982718611,21.42104817892459
+1255.94321575479,0.00617620279886057,-2.024434600404039,20.29805305566545
+1335.477793779493,0.004871918997360811,-1.960715765931731,19.2156502973351
+1420.049023957107,0.005975072383172633,-1.903141729181185,18.19096778081797
+1509.975860201008,0.00695106406458061,-1.850789639792812,17.21954666378534
+1605.597454682412,0.005264828738351971,-1.8036269598333,16.2949935030322
+1707.2744369168,0.005357978527561806,-1.761160741701984,15.41813811134273
+1815.390273850507,0.005440833960226152,-1.721076138090882,14.5846127817219
+1930.352716076907,0.007312326745218989,-1.685636426162642,13.7914665917109
+2052.595335636539,0.005047794373348172,-1.653109406957302,13.03383244961915
+2182.579161200831,0.00770408044738205,-1.623810033889997,12.31900009711404
+2320.794416806389,0.007914191135959309,-1.595921969361862,11.64008359552923
+2467.762370697403,0.006404690751653556,-1.572229377775245,11.00975795058449
+2624.037301248861,0.007941951969087844,-1.549193802401504,10.38210324809313
+2790.208587384981,0.008213983164102004,-1.527971774983906,9.802385376136499
+2966.90293137664,0.006968744125454801,-1.508904384281624,9.262394774497807
+3154.786722400965,0.01042702023881925,-1.491770959561209,8.733496967275993
+3354.568549777056,0.009619030894434302,-1.475683906934238,8.241309024473477
+3567.001875356283,0.01048715158151549,-1.462232485965415,7.773070069459862
+3792.887875145918,0.00998353889279982,-1.448104758108025,7.333219940851819
+4033.078460883068,0.01313767398905539,-1.435929909802621,6.913804693406149
+4288.479492954473,0.01162475891410919,-1.427075454179144,6.511977453252157
+4560.054196779548,0.01298780024625838,-1.415387423951257,6.132432505151066
+4848.826795541248,0.0124385204142419,-1.405840990911923,5.78406066714642
+5155.88637296528,0.01406934745588136,-1.397829343238713,5.437185727592976
+5482.390980715926,0.01571146305982906,-1.390632149925257,5.109744940432378
+5829.572005899156,0.01536524628629926,-1.383773765511573,4.807409244297745
+6198.73881514472,0.01744560492718117,-1.378296679363528,4.524740245160501
+6591.283692782037,0.01693160360518591,-1.373116248013424,4.246828199126256
+7008.687091733847,0.02076371879594231,-1.367583870797127,3.990585642684074
+7452.52321693098,0.00646305189027809,-1.362883388502584,3.746561257078255
+7924.46596230557,0.02156657731662993,-1.358462463928693,3.509212522834872
+8426.295223753756,0.01459536256537091,-1.354565156742321,3.294619199694861
+8959.903611876669,0.02279821520822838,-1.3507157775165,3.082786419990128
+9527.303589816242,0.01994962575596314,-1.347055690078227,2.882349436716027
+10130.63506310572,0.01950215477879605,-1.343542254130174,2.688813143022566
+10772.17345015941,0.02741703446394789,-1.342439620672519,2.513381018201613
+11454.33826383887,0.02853061341284478,-1.339926779717606,2.347607042145441
+12179.70223646013,0.02783506071790952,-1.337605080625124,2.17835237190809
+12951.00102265661,0.02974179414277833,-1.336431453867741,2.028036528606421
+13771.14351669083,0.03108317853639755,-1.333832986370894,1.886746713798459
+14643.22282312619,0.03404354597373638,-1.332868378379574,1.741411971261698
+15570.52792223379,0.02801038288632726,-1.330897785380293,1.594246066958505
+16556.55607412956,0.03500348721818894,-1.330454449162901,1.464339872860457
+17605.0260084226,0.03506119701744338,-1.32891509530866,1.3480853165958
+18719.89194911905,0.03858468921603775,-1.327566282916492,1.223358593126477
+19905.35852767487,0.03754341724459559,-1.325512492081898,1.103829613778032
+21165.89664044106,0.0380034211324761,-1.324356496021401,0.9832145027822889
+22506.26031030668,0.03496589327244327,-1.323387467514378,0.8802183168675413
+23931.5046161319,0.04008161066758985,-1.322397700794651,0.7718826898148734
+25447.00475759047,0.04178691240518875,-1.322705342301614,0.6626152754390127
+27058.47632732319,0.04484654318606993,-1.321902521102382,0.5710215411997552
+28771.99686685783,0.03153551009588505,-1.318180108673138,0.4636355898904014
+30594.02878759109,0.03891838644517456,-1.318641470698893,0.3644940941360346
+32531.44374327787,0.04815746828989879,-1.318271320382075,0.2688684319482491
+34591.54854594681,0.05169138074394734,-1.316707828454503,0.1692753651419849
+36782.11272298207,0.05374328431466807,-1.315185986115048,0.07228916262663709
+39111.39781930015,0.05351610599877252,-1.314956733169347,-0.01984140055164119
+41588.18855513354,0.05633668616159242,-1.314109035118557,-0.1123768849958378
+44221.82595692999,0.06020615699181164,-1.314416927328817,-0.2270921249322555
+47022.24258631762,0.0648027020624642,-1.316934476609867,-0.3235240175614327
+50000,0.06133660223366334,-1.313698807063205,-0.4154103428634226
+53166.32858185808,0.05862170819032597,-1.315233856520499,-0.526191134034363
+56533.16989748193,0.05698107494630021,-1.315151317603417,-0.6261191180716299
+60113.22173087066,0.07317705068804146,-1.313501812005142,-0.7356193219616074
+63919.98597315115,0.07631280171840961,-1.314717141627109,-0.8479745085236772
+67967.81954392628,0.07813874140820321,-1.311705539193134,-0.956992805578281
+72271.98853729639,0.0818740239552512,-1.314100834302277,-1.070854616052515
+76848.72579676354,0.08529714196539756,-1.313154573241603,-1.221622514267906
+81715.29213615687,0.08934025044103884,-1.315068895128191,-1.34326182738701
+86890.04143746881,0.08785086459916161,-1.313470061498897,-1.466830472554335
+92392.48987111454,0.09258526115510016,-1.31257476914947,-1.611833240776591
+98243.38949967339,0.1008399184523324,-1.315342856072513,-1.757271396299657
+104464.8065427019,0.103086631988121,-1.314430769997616,-1.909876746512879
+111080.2045977906,0.09942289316660761,-1.314058102005165,-2.069336966999614
+118114.5331317231,0.1011569473084099,-1.314596217833695,-2.243262813805373
+125594.321575479,0.09476495734976148,-1.31717524855048,-2.405998545254675
+133547.7793779493,0.1066220786528797,-1.315382241881355,-2.592503140058483
+142004.9023957107,0.103283919261896,-1.319439970661207,-2.781380121973775
+150997.5860201008,0.1054562029653687,-1.320106219585398,-3.014208997505534
+160559.7454682412,0.1019083360604104,-1.321270243202597,-3.205934439394639
+170727.44369168,0.1023457291259851,-1.325390347872919,-3.439923891862833
+181539.0273850507,0.09955912709312323,-1.327243950025414,-3.703883419394884
+193035.2716076905,0.09720700159986544,-1.332225174542406,-3.936552958263874
+205259.5335636539,0.09849921452192432,-1.333109169373028,-4.183629169707245
+218257.9161200831,0.09148193999503706,-1.337736822783619,-4.495434892911447
+232079.4416806389,0.08680512898729326,-1.342893696253303,-4.768663868952245
+246776.2370697403,0.08381728563671217,-1.349682489750827,-5.086457802608408
+262403.7301248864,0.06223086311981925,-1.353277160544021,-5.431273480980764
+279020.8587384982,0.07550491512261172,-1.358601615943654,-5.79335215580609
+296690.293137664,0.07174097877075529,-1.368396020892196,-6.161541526375776
+315478.6722400965,0.05950480560334349,-1.370944600389946,-6.555237398936271
+335456.8549777056,0.04077448051002463,-1.383208226098833,-6.95583728413726
+356700.1875356282,0.04442683365237275,-1.389504153198174,-7.406695426726969
+379288.7875145918,0.03560965739571073,-1.395629390147462,-7.877598890924389
+403307.8460883067,0.03152072522036127,-1.409185640068662,-8.384332869174955
+428847.9492954469,0.02017955917200519,-1.424680964868159,-8.923101915472714
+456005.4196779549,0.01049679515274558,-1.436423953363186,-9.454913184120954
+484882.6795541248,0.008399142245467671,-1.4523436746973,-10.06345152823504
+515588.6372965274,-0.002848336603555058,-1.458084797252748,-10.63486772211779
+548239.0980715925,-0.01113345672364528,-1.481041193003363,-11.3506197988012
+582957.2005899161,-0.0193008770242502,-1.508450281328647,-11.97682023920722
+619873.8815144721,-0.02455735499509413,-1.534368488845306,-12.63339958479264
+659128.3692782037,-0.03168203794995797,-1.558730283249667,-13.73215998577545
+700868.7091733846,-0.04696136875595198,-1.600340573481818,-14.42956865496255
+745252.3216930979,-0.04626821414139758,-1.622825928675205,-15.33833187750858
+792446.5962305572,-0.05295842287298618,-1.673654630036064,-16.16931901380036
+842629.5223753755,-0.06205463597900539,-1.71304439823969,-17.16139459670106
+895990.361187667,-0.07400846150371559,-1.759418381538594,-18.17357345747091
+952730.3589816232,-0.07600842593474139,-1.812098969873094,-19.26401394314988
+1013063.506310572,-0.08690940273519686,-1.888730215586869,-20.35241658631412
+1077217.345015942,-0.09356128961579371,-1.94255134663982,-21.57151421991965
+1145433.826383886,-0.102677600717045,-2.024914946030169,-22.79510925029282
+1217970.223646014,-0.1112328103503125,-2.106465853385961,-23.9922062689492
+1295100.102265663,-0.1242185327941466,-2.199997720437144,-25.31892188487203
+1377114.351669083,-0.1339773618518256,-2.309367727024069,-26.74291421831168
+1464322.282312619,-0.1475609747016502,-2.41558529862597,-28.14117786798198
+1557052.792223379,-0.1719578213607708,-2.534424503554689,-29.55638414877413
+1655655.607412955,-0.18286656221203,-2.678748799160847,-31.14082220943781
+1760502.600842261,-0.1986756223698078,-2.82615877385608,-32.69554366244512
+1871989.194911905,-0.2223419247054212,-2.978822383306166,-34.29900027138573
+1990535.852767487,-0.2410115111440087,-3.162062922030925,-35.94515480276034
+2116589.664044104,-0.2719587310283614,-3.350990262372849,-37.60798805644744
+2250626.031030668,-0.2979857679879256,-3.554630616588227,-39.32953739317543
+2393150.461613193,-0.3249722394340721,-3.787296283936372,-41.02322549550469
+2544700.475759044,-0.3831549839077542,-4.021036958828303,-42.74814410964757
+2705847.632732319,-0.4037231559964128,-4.271710605581308,-44.45942277115347
+2877199.686685783,-0.447312571608569,-4.540977438709171,-46.20125603860517
+3059402.878759109,-0.4978915559676812,-4.820282093730665,-47.9323047916548
+3253144.374327787,-0.565342408184631,-5.123466704492302,-49.65810215806445
+3459154.854594681,-0.611868647735619,-5.443511388672176,-51.34561002039652
+3678211.272298207,-0.6771364779188405,-5.773034436298143,-53.01190764056954
+3911139.781930015,-0.7563889725824304,-6.123422661792345,-54.67239825662023
+4158818.855513354,-0.8334720251080752,-6.487571190444487,-56.28774479195334
+4422182.595693,-0.9240560106689888,-6.864304667183994,-57.86108397361413
+4702224.258631757,-1.024275124766898,-7.251175235302993,-59.40592908003066
+5000000,-1.136323280630394,-7.659815570208179,-60.88004712969874

D6/buffer.tex

@@ -0,0 +1,29 @@
+\begin{figure}[H]
+    \centering
+    \begin{circuitikz}
+    \draw
+(1,6) --  node[anchor=south] {} (4,6)
+(4,6) --  node[anchor=south] {$V_{CC}$} (5,6)
+(2,6) to [european resistor, a=$R_1$] (2,4)
+(2,4) to [short, -] (2,3.3)
+(2,3.3) to [european resistor, a=$R_2$] (2,1)
+(0,4) to [short, *-,l=$v_1$] (0.1,4)
+(0.1,4) to [C] (2,4)
+(2,4) to [short, -] (3.15,4)
+(4,6) to [short, -] (4,4.75)
+(4,3.3) to [C] (5.9,3.3)
+(5.9,3.3) to [short, -*,l=$v_2$] (6,3.3)
+(4,3.3) to [european resistor, a=$R_3$] (4,1)
+
+(1,1) --  node[anchor=south] {} (5,1)
+%(4,1) --  node[anchor=south] {$V_-$} (5,1)
+(5,1) to node[ground]{} (5,1)
+;
+\draw
+(4,4) node[npn] {}
+;
+
+    \end{circuitikz}
+    \caption{kretstopologi av en buffer, konfigurert som en emitter-følger.}
+    \label{fig:buffer}
+\end{figure}

D6/bufferkrets.tex

@@ -0,0 +1,35 @@
+\begin{figure}[H]
+    \centering
+    \begin{circuitikz}
+    \draw
+    
+   (1,2) to node[ground]{} (1,2)
+   (1,4) to [american voltage source, v=$v_0$] (1,2)
+ % (1,4) to [short, -] (1,3)
+    (1,4) to [european resistor, a=$R_k$] (3.3,4)
+    (3.3,4) to [short, -*,l=$v_1$] (3.5,4)
+    
+    (3.5,4) to [amp, a=Buffer] (6,4)    
+    
+    (6,4) to [short, -*,l=$v_2$] (6.2,4)
+    (6.2,4) to [short, -] (8,4)
+    (8,4) to [european resistor, a=$R_L$] (8,2)
+    (8,2) to node[ground]{} (8,2)
+    
+    ;
+    \draw[dashed] 
+    (0,1) to [short, -] (3,1)
+    (3,1) to [short, -] (3,5)
+    (3,5) to [short, -, l=Kilde] (0,5)
+    (0,5) to [short, -,] (0,1)
+    
+    (6.5,1) to [short, -] (9.5,1)
+    (9.5,1) to [short, -] (9.5,5)
+    (9.5,5) to [short, -, l=Last] (6.5,5)
+    (6.5,5) to [short, -] (6.5,1)
+
+    ;
+    \end{circuitikz}
+    \caption{Kretstopologi der en buffer er tatt i bruk.}
+    \label{fig:full}
+\end{figure}

D6/circuit-20190914-2012.circuitjs.txt

@@ -0,0 +1,25 @@
+$ 1 0.000005 1.0312258501325766 48 5 43
+c 240 272 160 272 0 0.000001 5.258928153175109
+t 272 272 320 272 0 1 -6.033485561231757 0.5787603741818041 330
+r 320 288 320 368 0 330
+c 320 288 416 288 0 0.00009999999999999999 4.602843295100454
+v 528 368 528 176 0 0 40 9 0 0 0.5
+w 528 176 320 176 0
+w 528 368 320 368 0
+w 320 368 256 368 0
+w 320 256 320 176 0
+g 320 368 320 400 0
+r 80 272 160 272 0 6800
+r 416 288 528 368 0 330
+v 80 368 80 272 0 1 1000 3 0 0 0.5
+w 80 368 256 368 0
+w 320 176 256 176 0
+174 256 368 240 176 1 200000 0.7574000000000001 Resistance
+w 240 272 208 304 0
+w 208 304 272 304 0
+w 272 304 272 272 0
+p 160 272 80 368 1 0
+w -80 224 0 224 0
+o 11 4 0 20483 5 0.025 0 2 11 3
+o 1 4 6 20483 10 0.1 1 1
+o 19 4 0 20483 5 0.1 2 1