diff --git a/Øvinger/LF/LF_Ø3.pdf b/Øvinger/LF/LF_Ø3.pdf new file mode 100644 index 0000000..37dbb96 Binary files /dev/null and b/Øvinger/LF/LF_Ø3.pdf differ diff --git a/Øvinger/Ø1/ESDAI_Ø1.pdf b/Øvinger/Ø1/ESDAI_Ø1.pdf new file mode 100644 index 0000000..cdea427 Binary files /dev/null and b/Øvinger/Ø1/ESDAI_Ø1.pdf differ diff --git a/Øvinger/Ø1/Fukka.ggb b/Øvinger/Ø1/Fukka.ggb new file mode 100644 index 0000000..6d0a7fd Binary files /dev/null and b/Øvinger/Ø1/Fukka.ggb differ diff --git a/Øvinger/Ø1/LF_ø1.pdf b/Øvinger/Ø1/LF_ø1.pdf new file mode 100644 index 0000000..353c52b Binary files /dev/null and b/Øvinger/Ø1/LF_ø1.pdf differ diff --git a/Øvinger/Ø1/Oppgave1.ggb b/Øvinger/Ø1/Oppgave1.ggb new file mode 100644 index 0000000..011e98d Binary files /dev/null and b/Øvinger/Ø1/Oppgave1.ggb differ diff --git a/Øvinger/Ø1/Oppgave1_a.ggb b/Øvinger/Ø1/Oppgave1_a.ggb new file mode 100644 index 0000000..409df9d Binary files /dev/null and b/Øvinger/Ø1/Oppgave1_a.ggb differ diff --git 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file mode 100644 index 0000000..dff6c25 Binary files /dev/null and b/Øvinger/Ø1/Oppgave4Python/4c2.png differ diff --git a/Øvinger/Ø1/Oppgave4Python/Graftegning.py b/Øvinger/Ø1/Oppgave4Python/Graftegning.py new file mode 100644 index 0000000..33445e4 --- /dev/null +++ b/Øvinger/Ø1/Oppgave4Python/Graftegning.py @@ -0,0 +1,83 @@ +#!/usr/bin/env python3 +# -*- coding: utf-8 -*- +""" +Created on Fri Jan 18 22:30:00 2019 + +@author: oyvind +""" +import math +import matplotlib.pyplot as plt + +# Name for the saved graph +filename = "4b" + +# Tau in microseconds +tau = 10 + +# Square wave freq in kHz +sqWFreq = 5 + +# How many taus you want +periods = 40 + +# The resolution of each tau +resolution = 1000 + +# Calculates the length of each squarewave in taus +sqTime = (1/sqWFreq) * 10**3 +sqTau = sqTime / tau + +# Creats the square wave +# Default values are in the argument list +def CreateSquareWave(amp=0.5, offset=0.5, symetry=0.5): + squareWave = [] + # Only generates as many datapoints we need + while len(squareWave) < periods * resolution: + # First generate the first half + for r in range(int(resolution*sqTau * symetry)): + squareWave.append(amp + offset) + # Then the second + for r in range(int(resolution*sqTau * (1 - symetry))): + squareWave.append(offset - amp) + squareWave = squareWave[:(resolution*periods)] + return squareWave + + +# Generate all the time-ticks +def GenerateTime(): + times = [] + for t in range(periods * resolution): + times.append(t/resolution) + print(len(times)) + return(times) + + +def CapVoltage(wave, times): + cP = wave[0] # Start voltage-supply + v0 = 0 # Start voltage + cT = 0 #Start time + volt = [] + for p in range(len(wave)): + # If the voltage-supply changes, recalculate startvalues + if wave[p] != cP: + v0 = volt[-1] # New start voltage, uses the last voltage calculated + cP = wave[p] # Variable so the array is not accessed. + cT = times[p] # Offset time for each period + # Calculate the voltage over the CAPACITOR with the start values + volt.append(cP + (v0 - cP) * math.exp(-(times[p] - cT))) + return(volt) + + +SquareWave = CreateSquareWave() +time = GenerateTime() +CapWave = CapVoltage(SquareWave, time) + +plt.figure(figsize=(15,5)) +plt.plot(time, SquareWave, time, CapWave) +plt.xlabel("Time [Ï„]") +plt.ylabel("Voltage [V]") +plt.legend(["Supply voltage", "Capacitor voltage"], loc="lower right") +plt.savefig(filename + ".png", dpi = 300) +plt.show() + + \ No newline at end of file diff --git a/Øvinger/Ø1/Oppgave4Python/cap.png b/Øvinger/Ø1/Oppgave4Python/cap.png new file mode 100644 index 0000000..dff6c25 Binary files /dev/null and b/Øvinger/Ø1/Oppgave4Python/cap.png differ diff --git a/Øvinger/Ø1/TauMaaling.png b/Øvinger/Ø1/TauMaaling.png new file mode 100644 index 0000000..00a11be Binary files /dev/null and b/Øvinger/Ø1/TauMaaling.png differ diff --git a/Øvinger/Ø1/grafer/3b.png b/Øvinger/Ø1/grafer/3b.png new file mode 100644 index 0000000..1482206 Binary files /dev/null and b/Øvinger/Ø1/grafer/3b.png 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end of file diff --git a/Øvinger/Ø1/grafer/condisO1a.tex b/Øvinger/Ø1/grafer/condisO1a.tex new file mode 100644 index 0000000..b123ff9 --- /dev/null +++ b/Øvinger/Ø1/grafer/condisO1a.tex @@ -0,0 +1,401 @@ + + +\definecolor{uuuuuu}{rgb}{0.26666666666666666,0.26666666666666666,0.26666666666666666} +\definecolor{qqwuqq}{rgb}{0.,0.39215686274509803,0.} +\begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=2.5cm,y=1.75cm] +\begin{axis}[ +x=2.5cm,y=1.75cm, +axis lines=middle, +xmin=-0.5, +xmax=5.5, +ymin=-0.5, +ymax=5.5, +ylabel={Spenning [V]}, +xlabel={Tid [$\tau$]}, +yticklabel={\SI[round-mode=places, round-precision=1]{\tick}{V}}, +xticklabel={\SI[round-mode=places, round-precision=0]{\tick}{\tau}}, +xtick={-0.0,1.0,...,5.0}, +ytick={-0.0,1.0,...,5.0},] +\clip(-0.5,-0.5) rectangle (5.5,5.5); +\draw[line width=2.pt,color=qqwuqq] (0,0) -- (0.010000000000000314,0.04975083125416102); +\draw[line width=2.pt,color=qqwuqq] (0.010000000000000314,0.04975083125416102) -- 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width=2.pt,color=qqwuqq] (5.409999999999981,4.9776417989432575) -- (5.42499999999998,4.977974669190957); +\draw[line width=2.pt,color=qqwuqq] (5.42499999999998,4.977974669190957) -- (5.43999999999998,4.978302583646305); +\draw[line width=2.pt,color=qqwuqq] (5.43999999999998,4.978302583646305) -- (5.45499999999998,4.978625616091437); +\draw[line width=2.pt,color=qqwuqq] (5.45499999999998,4.978625616091437) -- (5.469999999999979,4.9789438392100145); +\draw[line width=2.pt,color=qqwuqq] (5.469999999999979,4.9789438392100145) -- (5.484999999999979,4.979257324603584); +\draw[line width=2.pt,color=qqwuqq] (5.484999999999979,4.979257324603584) -- (5.499999999999979,4.97956614280768); +\draw (1.0368736470914874,3.101491777808625) node[anchor=north west] {$(1\tau, 3.16\text{V})$}; +\draw (1.6711309520023216,4.0881142521143685) node[anchor=north west] {$(2\tau, 4.32\text{V})$}; +\draw (2.563789381136088,4.616662006206731) node[anchor=north west] {$(3\tau, 4.75\text{V})$}; +\draw (3.538666349795333,4.839826613490173) node[anchor=north west] {$(4\tau, 4.91\text{V})$}; +\draw (4.548779835394068,4.910299647369155) node[anchor=north west] {$(5\tau, 4.97\text{V})$}; +\begin{scriptsize} +\draw[color=qqwuqq] (-0.2786229853161683,-2.5657146966261535) node {$v$}; +\draw [fill=uuuuuu] (1.,3.1606027941427883) circle (2.0pt); +\draw [fill=uuuuuu] (2.,4.323323583816936) circle (2.0pt); +\draw [fill=uuuuuu] (3.,4.75106465816068) circle (2.0pt); +\draw [fill=uuuuuu] (4.,4.908421805556329) circle (2.0pt); +\draw [fill=uuuuuu] (5.,4.966310265004573) circle (2.0pt); +\end{scriptsize} +\end{axis} +\end{tikzpicture} \ No newline at end of file diff --git a/Øvinger/Ø1/grafer/condisO2.tex b/Øvinger/Ø1/grafer/condisO2.tex new file mode 100644 index 0000000..c1b2a9a --- /dev/null +++ b/Øvinger/Ø1/grafer/condisO2.tex @@ -0,0 +1,433 @@ +\definecolor{uuuuuu}{rgb}{0.26666666666666666,0.26666666666666666,0.26666666666666666} +\definecolor{qqwuqq}{rgb}{0.,0.39215686274509803,0.} 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{$v_c$}; +\draw [fill=uuuuuu] (1.,0.7872620041068866) circle (2.0pt); +\draw [fill=uuuuuu] (2.,0.2896175061263512) circle (2.0pt); +\draw [fill=uuuuuu] (3.,0.10654432630722885) circle (2.0pt); +\draw [fill=uuuuuu] (4.,0.03919546722189114) circle (2.0pt); +\draw [fill=uuuuuu] (5.,0.0144192065780429) circle (2.0pt); +\end{scriptsize} +\end{axis} +\end{tikzpicture} \ No newline at end of file diff --git a/Øvinger/Ø1/oppgave4e.ggb b/Øvinger/Ø1/oppgave4e.ggb new file mode 100644 index 0000000..02528e0 Binary files /dev/null and b/Øvinger/Ø1/oppgave4e.ggb differ diff --git a/Øvinger/Ø1/Øving1.pdf b/Øvinger/Ø1/Øving1.pdf new file mode 100644 index 0000000..e9e0b51 Binary files /dev/null and b/Øvinger/Ø1/Øving1.pdf differ diff --git a/Øvinger/Ø1/Øving1.tex b/Øvinger/Ø1/Øving1.tex new file mode 100644 index 0000000..6a3b1f2 --- /dev/null +++ b/Øvinger/Ø1/Øving1.tex @@ -0,0 +1,337 @@ +\documentclass[11pt,largemargins, norsk]{homework} + +\newcommand{\hwname}{Øyvind Skaaden} +\newcommand{\hwemail}{oyvindps@ntnu.no} +\newcommand{\hwtype}{Øving} +\newcommand{\hwnum}{1} +\newcommand{\hwclass}{TTT4260} +\newcommand{\hwlecture}{} +\newcommand{\hwsection}{} + +\newcommand*{\eq}{=} + +\renewcommand{\questiontype}{Oppgave} +\newcommand{\figref}[1]{Figur \ref{#1}} + +\begin{document} +\maketitle + +\question + \begin{alphaparts} + \item Vi har krets \ref{circ:1a} som vist under med verdiene $R_1 = 1\text{k}\Omega $, $ C_1 = 100\mu\text{F} $ og $V = 5\text{V} $. + + \begin{figure} [h] + \centering + \begin{circuitikz} + + \draw + (0,3) to [V, l=$V$] (0,0) + (0,3) to [closing switch, l = $t\eq0$ ] (3,3) + to [R, l=$R_1$] (6,3) + to [C, l=$C_1$] (6,0) -- (0,0); + \end{circuitikz} + \caption{Krets til oppgave 1} + \label{circ:1a} + \end{figure} + + $\tau$ er gitt ved + + $$ \tau = R \cdot C $$ + + Da er $\tau$ i denne kretsen er da + + $$ \tau = R_1 \cdot C_1 = 1\text{k}\Omega \cdot 100\mu\text{F} = 100\text{ms}$$ + + En funksjon for spenningen over kondensatoren er da + + $$ v_c(t) = 5 \text{V} \cdot ( 1 - e ^ {\frac{-t}{100\text{ms}}}) $$ + \pagebreak + \begin{figure}[!ht] + \centering + \input{grafer/condisO1a} + \caption{Utvikling av spenning over kondensator $v_c$} + \label{graph:kondensator1} + \end{figure} + + + \item + + Etter Ã¥ ha koblet opp kretsen ser vi at spenningen (se \figref{graph:1b}) over kondensatoren nÃ¥r $63\%$ eller $3.16$V etter $\Delta x = 94.83$ms. + + \begin{figure}[h] + \centering + \includegraphics[width=\textwidth]{TauMaaling.png} + \caption{Spennigsutvikling av krets i oppgave 1, $\tau$ er lik $\Delta x$} + \label{graph:1b} + \end{figure} + \pagebreak + + + + \item + + NÃ¥r det skjer utladning av kondensatoren har ikke strømmen noe sted Ã¥ gÃ¥, eneste er Ã¥ gÃ¥ gjennom kondensatoren litt og litt. + + \end{alphaparts} + + +\question + For Ã¥ løse kretsen i oppgave 2, vist i kretsen \figref{circ:krets2} under. + + \begin{figure}[h] + \centering + \begin{circuitikz} + \draw + (-6,3) to [V, v=V] ++(0,-3) + (-6,3) to [opening switch, l=$S_1$] ++(3,0) + to [R, l=$R_1$] +(3,0) to [short,-*] ++(0,0) + (-6,0) to [short,-*] (0,0) + (0,0) to [R, l=$R_2$] (0,3) + (0,0) -- (2,0) to [short,-*] (2,0) to [R, l=$R_3$] (2,3) to [short,-*] ++(0,0) -- (0,3) + (2,3) to [R, l=$R_4$] (6,3) + to [C, l=$C_1$, v_=$v_c$] (6,0) -- (2,0); + \end{circuitikz} + \caption{Krets i oppgave 2} + \label{circ:krets2} + \end{figure} + + + Vi mÃ¥ finne spenningen som ligger over $R_2||R_3$ for Ã¥ finne startspenningen pÃ¥ $C_1$. + + Begynner med Ã¥ finne $$R_2||R_3 = \frac{470\ohm \cdot 220\ohm}{470\ohm + 220\ohm} = \frac{10340}{69} \ohm $$ + + $$ v_{R_2||R_3} = \frac{V}{R_1 + R_2||R_3} \cdot (R_2||R_3) = \frac{5\text{V}}{200\ohm + \frac{10340}{69} \ohm} \cdot \frac{10340}{69} \ohm = \frac{2585}{1207}\text{V} \approx 2.14\text{V} $$ + + Dette er da startspenningen pÃ¥ $c_1$. + + NÃ¥r bryteren brytes, vi vi fÃ¥ en forenklet krets, som vist i \figref{circ:oppgave2} + + \begin{figure} + \centering + \begin{circuitikz} + \draw + (0,0) to [R, l=$R_2$] (0,3) + (0,0) -- (2,0) to [short,-*] (2,0) to [R, l=$R_3$] (2,3) to [short,-*] ++(0,0) -- (0,3) + (2,3) to [R, l=$R_4$] (6,3) + to [C, l=$C_1$, v_=$v_c$] (6,0) -- (2,0); + \end{circuitikz} + \caption{Foreklet krets i oppgave 2} + \label{circ:oppgave2} + \end{figure} + + Vi kan da regne ut $R$ i kretsen + + $$ R = R_4 + R_2||R_3 = 300\ohm + \frac{10340}{69} \ohm = \frac{31040}{69}\ohm \approx 449.9\ohm $$ + + $\tau$ er da gitt ved $\tau = R \cdot C_1 = = 4.5\mu\text{s}$. + + Funksjonen for spenningen over $v_c$: + + $$ v_c(t) = 2.14e^{\frac{-t}{4.5\mu\text{s}}} $$ + + \begin{figure}[h] + \centering + \input{grafer/condisO2} + \caption{Graf for oppgave 2} + \label{graph:oppg2} + \end{figure} + +\clearpage +\question + \begin{alphaparts} + \item + Vi har kretsen som gitt i oppgave 3, men tegnet pÃ¥ en forenklet mÃ¥te i \figref{circ:3a1}. + + \begin{figure}[h] + \centering + \begin{circuitikz} + \draw + (0,3) to [V, v_=V] (0,0) + (0,3) to [R, l=$R_1\eq1\text{k}\ohm$] (3,3) + to [closing switch, l=$S_1$] (5,3) + to [R, l_=$R_2\eq1\text{k}\ohm$] (5,0) -- (0,0) + (5,3) to [short,*-] ++(2,0) + to [C, l=$C_1\eq100\mu\text{F}$] ++(0,-3) + to [short,-*] (5,0); + \end{circuitikz} + \caption{Forenklet krets til oppgave 3a} + \label{circ:3a1} + \end{figure} + + + Vi skriver om til en Norton ekvivalent ved Ã¥ regne ut $I_n = \tfrac{V}{R_1}$ + + $$ I_n = \frac{1\text{V}}{1\text{k}\ohm} = 1\text{mA} $$ + + Vi har da to like motstander i parallell. Siden de er like er den totale motstanden lik halvparten av den ene. SÃ¥ + $$ R_{eq} = 0.5\text{k}\ohm $$ + Vi regner deretter den nye kretsen tilbake til en thevenin-ekvivalent krets. + + $$ V_{th} = I_n \cdot R_{eq} = 1\text{mA}\cdot 0.5\text{k}\ohm = 0.5\text{V}$$ + + Vi har da den nye kretsen under i \figref{circ:3a2} + + \begin{figure}[h] + \centering + \begin{circuitikz} + \draw + (0,3) to [V, v_=V$_{th}$] (0,0) + (0,3) to [R, l=$R_{eq}\eq0.5\text{k}\ohm$] ++(3,0) + to [C, l=$C_1\eq100\mu\text{F}$, v=$v_{C_1}$] ++(0,-3) + -- (0,0); + \end{circuitikz} + \caption{Thevenin-ekvivalent krets til oppgave 3a} + \label{circ:3a2} + \end{figure} + + Det er da veldig lett Ã¥ lage en funksjon som besrkiver spenningen, $v_{C_1}$, over $C_1$. + + \begin{align*} + v_{C_1}(t)&= V_{th}\left(1-e^\frac{-t}{R_{eq}C_1}\right) \\ + v_{C_1}(t)&= 0.5\text{V}\left(1-e^\frac{-t}{0.5\text{ms}}\right)\\ + v_{C_1}(t)&= 0.5\text{V}\left(1-e^\frac{-t}{\tau}\right) + \end{align*} + + \clearpage + \item + Etter $6\tau$ har kondensatoren nÃ¥dd ``steady-state'', da er spenningen $v_{C_1} = V_{th} = 0.5\text{V}$. NÃ¥r bryteren $S_2$ lukkes fÃ¥r vi en veldig lik krets som i opgpave 3a. Se \figref{circ:3b1} + + \begin{figure}[h] + \centering + \begin{circuitikz} + \draw + (0,3) to [V, v_=V$\eq1\text{V}$] (0,0) + (0,3) to [R, l=$R_1\eq1\text{k}\ohm$] (4,3) + to [R, l_=$R_2\eq1\text{k}\ohm$] ++(0,-3) -- (0,0) + (4,3) to [short,*-] ++(3,0) + to [R, l_=$R_3\eq1\text{k}\ohm$] ++(0,-3) + to [short,-*] (4,0) + (7,3) to [short,*-] ++(3,0) + to [C, l=$C_1\eq100\mu\text{F}$] ++(0,-3) + to [short,-*] ++(-3,0); + \end{circuitikz} + \caption{Forenklet krets til oppgave 3a} + \label{circ:3b1} + \end{figure} + + Vi gjør det samme som sist, gjør om til norton-ekvivalent, samler motstandene og gÃ¥r tilbake til en thevenin-ekvivalent. + + Siden det her er tre like motstander i parallell er den totale motstanden lik $1/3$ av en av motstandene. Vi fÃ¥r da $V_{th} = \frac{1}{3}\text{V}=\approx 333.3\text{mV}$ og $R_{eq} \approx 333.3\ohm$. + + Kretsen ser da ut som \figref{circ:3b2} + + \begin{figure}[h] + \centering + \begin{circuitikz} + \draw + (0,3) to [V, v_=V$_{th}\approx 333.3\text{mV}$] (0,0) + (0,3) to [R, l=$R_{eq}\approx 333.3\ohm$] ++(3,0) + to [C, l=$C_1\eq100\mu\text{F}$, v=$v_{C_1}$] ++(0,-3) + -- (0,0); + \end{circuitikz} + \caption{Thevenin-ekvivalent krets til oppgave 3a} + \label{circ:3b2} + \end{figure} + + Da er det enkelt Ã¥ sette opp likningen for spenningen $v_{C_1}$ + Vi setter $\tau = 1$ for at det skal være lettere Ã¥ lese grafene. Grafene ser helt like ut men tidsenheten blir da $\tau$ i steden for ms. + + \begin{align*} + v_{C_1}(t) &= V_{th}+\left[v_{C_1}(t_0) - V_{th} \right]e^{-\frac{t-t_0}{R_{eq}C_1}}\\ + &\downarrow \\ + v_{C_1}(t) &= \frac{1}{3}\text{V} + \frac{1}{6}\text{V} \cdot e^{-\frac{t-6\tau}{\tau}} + \end{align*} + + En skisse av spenningsutviklingen kan sees i \figref{fig:3b}. + + \pagebreak + \begin{figure}[h] + \centering + \includegraphics[width=\textwidth]{grafer/3b.png} + \caption{Spenningen $V_{C_1}$ som graf, der $S_2$ lukkes etter $6\tau$} + \label{fig:3b} + \end{figure} + + \item + + For Ã¥ lage en funksjon for kretsen nÃ¥r bryter $S_2$ lukkes nÃ¥r $t=0.5\tau$, tar vi utgangspunkt i funksjonen fra oppgave 3b og spenningen $v_{C_1}(0.5\tau)\approx \frac{1}{5}\text{V}$. + + Funksjonen for spenningen over $C_1$ fra $t=0.5\tau$ blir da + + \begin{align*} + v_{C_1}(t) &= V_{th}+\left[v_{C_1}(t_0) - V_{th} \right]e^{-\frac{t-t_0}{R_{eq}C_1}}\\ + &\downarrow \\ + v_{C_1}(t) &=\frac{1}{3}\text{V}+\left[\frac{1}{5}\text{V} - \frac{1}{3}\text{V} \right]e^{-\frac{t-0.5\tau}{\tau}}\\ + v_{C_1}(t) &= \frac{1}{3}\text{V} - \frac{2}{15}\text{V} \cdot e^{-\frac{t-0.5\tau}{\tau}} + \end{align*} + + En skisse av spenningsutviklingen kan sees i \figref{fig:3c}. + + \pagebreak + + \begin{figure}[h] + \centering + \includegraphics[width=\textwidth]{grafer/3c.png} + \caption{Spenningen $V_{C_1}$ som graf, der $S_2$ lukkes etter $0.5\tau$} + \label{fig:3c} + \end{figure} + + \end{alphaparts} + +\question + \begin{alphaparts} + \item + Tidskonstanten $\tau$ er gitt ved + + $$ \tau = R \cdot C $$ + + I denne kretsen vil $\tau$ bli følgende. + + $$ \tau = 1\text{k}\ohm \cdot 1\text{nF} = 1\mu\text{s} $$ + + \pagebreak + \item + Graf ved $f=5$kHz + + \begin{figure}[h] + \centering + \includegraphics[width=\textwidth]{Oppgave4Python/4b.png} + \caption{Graf for kretsen i oppgave 4, ved $f=5\text{kHz}$} + \label{graph:4b} + \end{figure} + \item + Graf ved $f=30$kHz + + \begin{figure}[h] + \centering + \includegraphics[width=\textwidth]{Oppgave4Python/4c2.png} + \caption{Graf for kretsen i oppgave 4, ved $f=30\text{kHz}$} + \label{graph:4c} + \end{figure} + + \item + + Etter oppkobling av kretsen ser vi at kondensatoren oppfører seg veldig likt som regnet ut i oppgave 4b. 4c ($30$kHz) er litt mer ulik da kondensatoren lades og utlades litt raskere enn beregnet. Den nÃ¥r litt høyere og litt lavere spenninger enn beregnet. + + \pagebreak + \item + Vi ser fra \figref{graph:4b} at firkantpulsen er $1$V i $10\tau = 10 \cdot 10\mu\text{s} = 100\mu\text{s}$. + + Vi ønsker da at likningen $v_{C_1}(100\mu\text{s}) = 0.8$V. Vi setter kondensatorverdien konstant og regner ut motstanden $R$ i kretsen. + + \begin{align*} + v_{C_1}(t) &= V_1+\left[v_{C_1}(t_0) - V_1 \right]e^{-\frac{t-t_0}{R\cdot C_1}}\\ + 0.8\text{V} &= 1\text{V}\cdot\left(1-e^{-\frac{100\mu\text{s}}{R\cdot10\text{nF}}}\right) \\ + R &= \frac{10000}{\ln 5}\\ + R&\approx 6213 \ohm + \end{align*} + + Tester dette og ser at den lader seg litt for mye opp. + + Etter Ã¥ har justert til $6300\ohm$ ser det ut som at spenningen nÃ¥r ca $0.8$V pÃ¥ firkantpulsen. + + + \end{alphaparts} + + +\end{document} diff --git a/Øvinger/Ø2/LF_Ø2.pdf b/Øvinger/Ø2/LF_Ø2.pdf new file mode 100644 index 0000000..94a2405 Binary files /dev/null and b/Øvinger/Ø2/LF_Ø2.pdf differ diff --git a/Øvinger/Ø2/bilder/oppg2_a1.png b/Øvinger/Ø2/bilder/oppg2_a1.png new file mode 100644 index 0000000..68818e3 Binary files /dev/null and b/Øvinger/Ø2/bilder/oppg2_a1.png differ diff --git a/Øvinger/Ø2/bilder/oppg2_a2.png b/Øvinger/Ø2/bilder/oppg2_a2.png new file mode 100644 index 0000000..a1035f3 Binary files /dev/null and b/Øvinger/Ø2/bilder/oppg2_a2.png differ diff --git a/Øvinger/Ø2/grafOppg1.png b/Øvinger/Ø2/grafOppg1.png new file mode 100644 index 0000000..dd06993 Binary files /dev/null and b/Øvinger/Ø2/grafOppg1.png differ diff --git a/Øvinger/Ø2/grafoppg1.ods b/Øvinger/Ø2/grafoppg1.ods new file mode 100644 index 0000000..0d42d40 Binary files /dev/null and b/Øvinger/Ø2/grafoppg1.ods differ diff --git a/Øvinger/Ø2/Øving2.pdf b/Øvinger/Ø2/Øving2.pdf new file mode 100644 index 0000000..e0d495b Binary files /dev/null and b/Øvinger/Ø2/Øving2.pdf differ diff --git a/Øvinger/Ø2/Øving2.tex b/Øvinger/Ø2/Øving2.tex new file mode 100644 index 0000000..e0b1af6 --- /dev/null +++ b/Øvinger/Ø2/Øving2.tex @@ -0,0 +1,128 @@ +\documentclass[11pt,largemargins, norsk]{homework} + +\newcommand{\hwname}{Øyvind Skaaden} +\newcommand{\hwemail}{oyvindps@ntnu.no} +\newcommand{\hwtype}{Øving} +\newcommand{\hwnum}{2} +\newcommand{\hwclass}{TTT4260} +\newcommand{\hwlecture}{} +\newcommand{\hwsection}{} + +\renewcommand{\questiontype}{Oppgave} +\newcommand{\figref}[1]{Figur \ref{#1}} + +\begin{document} +\maketitle + +\question + \begin{alphaparts} + \item + NÃ¥r $A$ er logisk høy, er $C$ logisk lav. NÃ¥r $A$ er logisk lav, er $C$ logisk høy. + + \item + + Kretsen i oppgave 1 er en inverter fordi den tar inn et logisk signal, og sender ut det motsatte ut etter kretsen. Dersom inngangen er 1 er utgangen 0, og nÃ¥r inngangen er 0 er utgangen 1. + + \item + NÃ¥r det er $0$V pÃ¥ inngangen $A$ er det $5$V pÃ¥ utgangen $C$. + + \item Vi gjør mÃ¥linger pÃ¥ kretsen, setter spenning pÃ¥ $A$ lik $v_A $ og mÃ¥ler spenningen $v_C $ pÃ¥ utgangen $C$. 43 + + \begin{table}[h] + \centering + \begin{tabular}{|c|c|} + \hline + $v_A$ & $v_C $ \\ \hline + \hline + 0 & 4.98 \\ + 0.5 & 4.95 \\ + 1 & 4.95 \\ + 1.5 & 4.95 \\ + 2 & 4.93 \\ + 2.1 & 4.89 \\ + 2.2 & 4.79 \\ + 2.3 & 4.56 \\ + 2.4 & 4.13 \\ + 2.5 & 3.4 \\ + 2.6 & 2.32 \\ + 2.7 & 1.11 \\ + 2.8 & 0.23 \\ + 2.9 & 0.12 \\ + 3 & 0.08 \\ + 3.5 & 0.03 \\ + 4 & 0.02 \\ + 4.5 & 0.018 \\ + 5 & 0.014 \\ + \hline + \end{tabular} + \caption{MÃ¥lte spenninger pÃ¥ $C$, alle verdier har enhet V} + \label{tab:oppg1} + \end{table} + + \begin{figure}[h!] + \centering + \includegraphics[width=\textwidth]{grafOppg1.png} + \caption{Spenning $v_C$ som funksjon av $v_A$} + \label{graph:oppg1} + \end{figure} + + \item + Vi ser i \figref{graph:oppg1} at transistoren begynner Ã¥ lede rundt $2.2$V til $2.3$V. Den er som en kortslutning ved ca $3.0$V. + + \item + Dioden begynner Ã¥ lyse nÃ¥r $A$ er ca $2$V. Da er $C$ lik $2.42$V. + + \end{alphaparts} + +\question + \begin{alphaparts} + \item + + Her er begge grafene skisserte. + + \begin{figure}[h] + \centering + \includegraphics[width=\textwidth]{bilder/oppg2_a1.png} + \caption{Graf ved $T=10\tau$} + \label{graph:2a1} + \end{figure} + \begin{figure}[h] + \centering + \includegraphics[width=\textwidth]{bilder/oppg2_a2.png} + \caption{Graf ved $T=2\tau$} + \label{graph:2a2} + \end{figure} + + \clearpage + \item + + Vi ønsker at kretsen skal nÃ¥ $2$V. Vi ønsker Ã¥ finne tiden det tar. + + $$ 2\text{V} = 5V(1-e^{\frac{-t}{\tau}})$$ + Som gjør at + $$ t = \frac{1}{2}\tau $$ + + Vi vet ogsÃ¥ at perioden er $T=1$ms. Vi vet ogsÃ¥ at $v_1 $ er $5$V i $1/2$ periode. Som betyr at + $$ \frac{1}{2}T = \frac{1}{2}\tau \Leftrightarrow \tau = 1\text{ms}$$ + + Vi mÃ¥ lage $\tau$. Velger kondensator lik $100\mu$F. + + $$ \frac{1\text{ms}}{100\mu\text{F}} = 10\ohm$$ + + + \item + + Kobler opp kretsen og oppladning nÃ¥r maksimalt $2$V. + + \item + Ved frekvensen $1$kHz vil dioden lyse, og samme for frekvenser over. + + For lave frekvenser, feks $1$Hz vil dioden blinke med frekvensen $1$Hz. + + \item + Dioden lyser hele tiden egentlig. Ved veldig lave frekvenser blinker dioden, desto høyere frekvenser jo serkere lys, men veldig lite forskjell. + + + + \end{alphaparts} +\end{document} diff --git a/Øvinger/Ø3/ESDAI_ø3.pdf b/Øvinger/Ø3/ESDAI_ø3.pdf new file mode 100644 index 0000000..c1217a9 Binary files /dev/null and b/Øvinger/Ø3/ESDAI_ø3.pdf differ diff --git a/Øvinger/Ø3/LF_Ø3.pdf b/Øvinger/Ø3/LF_Ø3.pdf new file mode 100644 index 0000000..37dbb96 Binary files /dev/null and b/Øvinger/Ø3/LF_Ø3.pdf differ diff --git a/Øvinger/Ø3/graf/0.1V1K.csv b/Øvinger/Ø3/graf/0.1V1K.csv new file mode 100644 index 0000000..360d84a --- /dev/null +++ b/Øvinger/Ø3/graf/0.1V1K.csv @@ -0,0 +1,8193 @@ +Time (s),Channel 1 (V),Channel 2 (V) +-0.00258017,0.527682,-0.0551345 +-0.00257954,0.521671,-0.0544654 +-0.00257891,0.520001,-0.0544654 +-0.00257828,0.516328,-0.0537963 +-0.00257765,0.511652,-0.0531272 +-0.00257702,0.506643,-0.0531272 +-0.00257639,0.505307,-0.0534618 +-0.00257576,0.504639,-0.0531272 +-0.00257513,0.49796,-0.0524582 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in data] +ch2 = [p[2] for p in data] + +plt.plot(time,ch1, time,ch2) +plt.xlabel("Tid (ms)") +plt.ylabel("Spenning (V)") +plt.legend(["Forsterket signal","Inngangssignal"]) +plt.savefig(filename + ".png", dpi=200) +plt.show() \ No newline at end of file diff --git a/Øvinger/Ø3/pic/SkissetTegning.png b/Øvinger/Ø3/pic/SkissetTegning.png new file mode 100644 index 0000000..33f87a6 Binary files /dev/null and b/Øvinger/Ø3/pic/SkissetTegning.png differ diff --git a/Øvinger/Ø3/pic/vanligForsterker (copy).JPG b/Øvinger/Ø3/pic/vanligForsterker (copy).JPG new file mode 100644 index 0000000..e0d3ecd Binary files /dev/null and b/Øvinger/Ø3/pic/vanligForsterker (copy).JPG differ diff --git a/Øvinger/Ø3/pic/vanligForsterker.JPG b/Øvinger/Ø3/pic/vanligForsterker.JPG new file mode 100644 index 0000000..d9a0232 Binary files /dev/null and b/Øvinger/Ø3/pic/vanligForsterker.JPG differ diff --git a/Øvinger/Ø3/pic/varierendeForsterker (copy).JPG b/Øvinger/Ø3/pic/varierendeForsterker (copy).JPG new file mode 100644 index 0000000..43d0444 Binary files /dev/null and b/Øvinger/Ø3/pic/varierendeForsterker (copy).JPG differ diff --git a/Øvinger/Ø3/pic/varierendeForsterker.JPG b/Øvinger/Ø3/pic/varierendeForsterker.JPG new file mode 100644 index 0000000..1453394 Binary files /dev/null and b/Øvinger/Ø3/pic/varierendeForsterker.JPG differ diff --git a/Øvinger/Ø3/Øving3.pdf b/Øvinger/Ø3/Øving3.pdf new file mode 100644 index 0000000..d454de0 Binary files /dev/null and b/Øvinger/Ø3/Øving3.pdf differ diff --git a/Øvinger/Ø3/Øving3.tex b/Øvinger/Ø3/Øving3.tex new file mode 100644 index 0000000..d246ca3 --- /dev/null +++ b/Øvinger/Ø3/Øving3.tex @@ -0,0 +1,177 @@ +\documentclass[11pt,largemargins, norsk]{homework} + +\newcommand{\hwname}{Øyvind Skaaden} +\newcommand{\hwemail}{oyvindps@ntnu.no} +\newcommand{\hwtype}{Øving} +\newcommand{\hwnum}{10} +\newcommand{\hwclass}{TTT4260} +\newcommand{\hwlecture}{} +\newcommand{\hwsection}{} + +\renewcommand{\questiontype}{Oppgave} +\newcommand{\figref}[1]{Figur \ref{#1}} + +\begin{document} +\maketitle + +\question +\begin{alphaparts} + \item + For Ã¥ finne utgangsspenningen $v_2 $ mÃ¥ vi først finne spenningen over $R_i $, $v_1 $. Den er + + $$ v_1 = \frac{R_i}{R_i + R_s} v_s \quad\Rightarrow\quad v_1 = \frac{100\text{k}\Omega}{100\text{k}\Omega + 33\Omega} \cdot 0.6\text{mV} \approx 0.6\text{mV}$$ + + Spenningen $Av_1 $, der $A = 10^4 $ blir $Av_1 = 6$V. + + Spenningen $v_2 $ blir da spenningen over $R_L $. Den er + + $$ v_2 = \frac{R_L}{R_L + R_0} Av_1 \quad\Rightarrow\quad v_2 = \frac{1\text{k}\Omega}{1\text{k}\Omega + 200\Omega} = 5\text{V}$$ + + \item Se \figref{graph:oppgave1b} + + + \begin{figure}[h] + \centering + \includegraphics[width=0.8\textwidth]{pic/SkissetTegning.png} + \caption{Skissert spenning $v_2 $ med ikke-ideell op-amp} + \label{graph:oppgave1b} + \end{figure} + + \item + Signalet er klippet fra 5V og oppver. Dette kan forhindres ved Ã¥ senke amplituden til inngangssignalet ned til $0.5$mV. Dette kan gjøres ved Ã¥ øke motstanden $R_s $ og senke $R_i $. + +\end{alphaparts} + + +\question + +\begin{alphaparts} + \item + Kretsen i figur 3 er en buffer. Den vil kunne ta inn et inngangssignal og levere akkurat det samme tilbake til kretsen. Den har en forsterkning pÃ¥ 1, altsÃ¥ det samme signalet inn som ut. Den brukes ofte der kretsen som leverer signalet ikke klarer Ã¥ levere nok strøm til det den leverer til. Bufferen klarer da Ã¥ levere nok strøm. + + + \item + + Kretsen i figur 4 er en inverterende forsterker. Det gÃ¥r ingen strøm gjennom forsterkeren, men det gÃ¥r en strøm fra $v_i $ til $v_o $. Vi kan da sette opp KVL, basert pÃ¥ at det gÃ¥r en strøm fra $v_i $ til $v_o $. + + \begin{align} + -v_i + R_1 \cdot i + R_2 \cdot i + v_o = 0 + \label{eq:2b} + \end{align} + Vi har ogsÃ¥ at spenningen til terminalene er like mellom seg, og at den ikke inverterende er koblet til jord. + + $$ -v_i + R_1\cdot i = 0 \qquad\Leftrightarrow\qquad i = \frac{v_i}{R_1} $$ + + Setter vi dette inn i (\ref{eq:2b}), fÃ¥r vi + + \begin{align*} + -v_i + R_1 \cdot \frac{v_i}{R_1} + R_2 \cdot \frac{v_i}{R_1} + v_o &= 0 \\ + \frac{v_o}{v_i} &= -\frac{R_2}{R_1} + \end{align*} + + \item + + Kretsen i figur 5 er en ikke inverterende forsterker. Spenningen over terminalene er lik. Bruker nodespenning. + + \begin{align*} + \frac{v_i}{R_1} + \frac{v_i + v_o}{R_2} &= 0 \\ + \frac{R_2}{R_1} &= \frac{-v_i + v_o}{v_i} \\ + \frac{v_o}{v_i} - 1 &= \frac{R_2}{R_1} \\ + \frac{v_o}{v_i} &= \frac{R_2 + R_1}{R_1} + \end{align*} + + \item + + Kretsen i figur 6 er en derivator. Vi vet at strømmen gjennom en kondensator er $ i_c = C\frac{dv_c}{dt} $ Vi vet ogsÃ¥ at det ikke gÃ¥r noe strøm gjennom forsterkeren, sÃ¥ all strøm mÃ¥ gÃ¥ gjennom motstanden $R_1 $. Siden det ikke er noen spenning mellom terminalene pÃ¥ forsterkeren, og den ikke inverterende er koblet til jord vil spenningen over motstanden $R_1 $ være $-v_o $ + + Setter dette lik hverandre. + + \begin{align*} + C\frac{dv_i}{dt} &= \frac{-v_o}{R_1}\\ + v_o &= -RC\frac{dv_i}{dt} + \end{align*} + + \item + + Kretsen i figur 7 er en integrator. Her er det tilsvarende som oppgaven over. + + Finner strømmen gjennom $R $ og $C $. + + \begin{align*} + \frac{v_i}{R_1} &= -C\frac{dv_o}{dt} \\ + \frac{dv_o}{dt} &= -\frac{v_i}{RC} \\ + v_o &= -\frac{1}{RC}\int v_i\ dt + \end{align*} + + \item + + Kretsen i figur 8 er en komparator. Den har en terskelspenning som kan settes pÃ¥ den inverterende inngangen. Dersom inngangssignalet er mindre enn terskelspenningen vil utgangssignalet trekkes ned mot det nedre spenningsforsyningen. + Dersom den er større, vil utgangssignalet trekkes til den øvre spenningsforsyning. + +\end{alphaparts} + +\question + +\begin{alphaparts} + \item Kretsen i figur 9 fungerer ikke pÃ¥ samme mÃ¥te som kretsen i figur 4 (inverterende forsterker). Denne kretsen vil vokse veldig fort oppover nÃ¥r inngangsspenning er positiv og omvendt nÃ¥r inngangen er negativ. + + Etter litt søking pÃ¥ internettet er dette en ``Schmitt-trigger'' \footnote{Wikipedia contributors. (2019, January 20). Operational amplifier. In Wikipedia, The Free Encyclopedia. Retrieved 10:43, February 7, 2019, from \url{https://en.wikipedia.org/w/index.php?title=Operational_amplifier&oldid=879387924}} + + \item + Dersom $v_1 $ er et trekantsignal vil signalet ut pÃ¥ $v_2 $ bli et firkantsignal. + + \item + + Dersom vi integrerer et firkantsignal vil vi fÃ¥ en kurve som alternerer mellom et konstant stignigstall som er positivt og et negativt. Den eneste kurven som passer dette, er en trekantbølge. + + +\end{alphaparts} + + +\question + +\begin{alphaparts} + \item Krets koblet opp. Inngangsamplitude er pÃ¥ $0.1$V. Forventet utgangsamplitude er $1$V, forsterkingen er pÃ¥ -10. Valgte motstander $R_1 = 1\text{k}\Omega $ og $R_2 = 10\text{k}\Omega$ + Vi kan se forsterkningssignalet i \figref{graph:oppgave4a} + + \begin{figure}[h] + \centering + \includegraphics[width=0.7\textwidth]{pic/vanligForsterker.JPG} + \caption{Oppkoblet krets etter Figur 4 i oppgavetekten, en inverterende forsterker} + \label{pic:oppgave4a} + \end{figure} + + + \begin{figure}[h] + \centering + \includegraphics[width=\textwidth]{graf/0.1V1K.png} + \caption{OP-Amp med inngangsspenning $0.1$V og forventet utgangsspenning pÃ¥ $1$V} + \label{graph:oppgave4a} + \end{figure} + + \item + Forsterkeren blir mettet nÃ¥r inngangssignalet overstiger 0.5V. Vi kan se dette i grafen i \figref{graph:oppgave4b} + + \begin{figure}[h] + \centering + \includegraphics[width=\textwidth]{graf/0.5V1K.png} + \caption{OP-Amp med inngangsspenning $0.5$V. Her klipper forsterkeren pÃ¥ ca 4V} + \label{graph:oppgave4b} + \end{figure} + +\end{alphaparts} + +\clearpage +\question + +Kobler opp kretsen i oppgave 5. Bruker inngangsspenning 1V og spenningskilde 5V og -5V. Bruker et 10k potmeter. Kan variere forsterkningen fra 3.45V til 0.18V, eller i dB, ca +10db til -14.9dB + +\begin{figure}[h] + \centering + \includegraphics[width=0.7\textwidth]{pic/varierendeForsterker.JPG} + \caption{Fysisk krets for en varierende inverterende forserker} + \label{pic:oppgave5} +\end{figure} + + +\end{document} diff --git a/Øvinger/Ø4/Ø4.pdf b/Øvinger/Ø4/Ø4.pdf new file mode 100644 index 0000000..97e1ad2 Binary files /dev/null and b/Øvinger/Ø4/Ø4.pdf differ diff --git a/Øvinger/Ø5/Analyse_5(1).pdf b/Øvinger/Ø5/Analyse_5(1).pdf new file mode 100644 index 0000000..2168c68 Binary files /dev/null and b/Øvinger/Ø5/Analyse_5(1).pdf differ diff --git a/Øvinger/Ø5/BodeDiagram b/Øvinger/Ø5/BodeDiagram new file mode 100644 index 0000000..3e9c51f --- /dev/null +++ b/Øvinger/Ø5/BodeDiagram @@ -0,0 +1,28 @@ +#!/usr/bin/env python3 +# -*- coding: utf-8 -*- +""" +Created on Thu Feb 28 11:00:18 2019 + +@author: oyvind +""" + +import numpy as np +import matplotlib.pyplot as plt + +def H(f): + w = 2 * np.pi * f + + return (w * 10**(-4))/np.sqrt(1+(w*10**(-4))**2) + +frq = [] +values = [] +for i in range(2*10**5): + frq.append(i) + value = 20 * np.log10(abs(H(i))) + values.append(value) + +plt.plot(frq, values) +plt.xscale('log') +plt.gca().xaxis.grid(True) + + diff --git a/Øvinger/Ø5/BodeDiagram.py b/Øvinger/Ø5/BodeDiagram.py new file mode 100644 index 0000000..70f0ebf --- /dev/null +++ b/Øvinger/Ø5/BodeDiagram.py @@ -0,0 +1,44 @@ +#!/usr/bin/env python3 +# -*- coding: utf-8 -*- +""" +Created on Thu Feb 28 11:00:18 2019 + +@author: oyvind +""" + +import numpy as np +import matplotlib.pyplot as plt + +def H13(f): + w = 2 * np.pi * f + + return (w * 10**(-4))/np.sqrt(1+(w*10**(-4))**2) + +def H2(f): + w = 2 * np.pi * f + + return (1/np.sqrt(1+(w*100*10**(-9)*10**4)**2)) + +def H4(f): + w = 2 * np.pi * f + + R = 99.76 + L = 100 * 10**(-3) + + t = L / R + + return (1/np.sqrt(1+(w*t)**2)) + +frq = [] +values = [] +for i in range(2*10**4): + frq.append(i) + value = 20 * np.log10(abs(H4(i))) + values.append(value) + +plt.plot(frq, values) +plt.xscale('log') +plt.gca().xaxis.grid(True) +plt.gca().yaxis.grid(True) + + diff --git a/Øvinger/Ø5/Frekvensrespons.py b/Øvinger/Ø5/Frekvensrespons.py new file mode 100644 index 0000000..2735297 --- /dev/null +++ b/Øvinger/Ø5/Frekvensrespons.py @@ -0,0 +1,44 @@ +#!/usr/bin/env python3 +# -*- coding: utf-8 -*- +""" +Created on Thu Feb 28 11:00:18 2019 + +@author: oyvind +""" + +import numpy as np +import matplotlib.pyplot as plt + +def H13(f): + w = 2 * np.pi * f + + return np.arctan(1/(w * 10**-4)) * 180 / np.pi + + +def H2(f): + w = 2 * np.pi * f + + return np.arctan(w * 100*10**(-9) * 10**4) * 180 / np.pi + +def H4(f): + w = 2 * np.pi * f + + R = 99.76 + L = 100 * 10**(-3) + + t = L / R + + return np.arctan(w * t) * 180 / np.pi + +frq = [] +values = [] +for i in range(1, 2*10**4): + frq.append(i) + value = H4(i) + values.append(value) + +plt.plot(frq, values) +plt.xscale('log') +plt.gca().xaxis.grid(True) + + diff --git a/Øvinger/Ø6/Bode Oppgave 1b Pic.png b/Øvinger/Ø6/Bode Oppgave 1b Pic.png new file mode 100644 index 0000000..ad80196 Binary files /dev/null and b/Øvinger/Ø6/Bode Oppgave 1b Pic.png differ diff --git a/Øvinger/Ø6/BodeOppgave1b.csv b/Øvinger/Ø6/BodeOppgave1b.csv new file mode 100644 index 0000000..4e83292 --- /dev/null +++ b/Øvinger/Ø6/BodeOppgave1b.csv @@ -0,0 +1,172 @@ +#Digilent WaveForms Network Analyzer - Bode +#Device Name: Discovery2NI +#Serial Number: SN:210321A36D3D +#Date Time: 2019-03-04 13:47:34.600 +#Start: 10 Hz +#Stop: 20000 Hz +#Steps: 151 +#Wavegen: Wavegen1 +#Amplification: 1 X +#Settle: 10 ms +#MinPeriods: 16 +#Channel: Channel 1 +#Range: 5.47148 V +#Offset: -3.64348e-05 V +#Relative: no +#Channel: Channel 2 +#Range: 5.48107 V +#Offset: -6.42632e-05 V +#Relative: yes + +Frequency (Hz),Channel 1 Magnitude (dB),Channel 2 Magnitude (dB),Channel 2 Phase (°) +10,-0.00537326,-0.00481132,-0.3339 +10.5198,-0.00550897,-0.00468579,-0.350273 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