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GNU GENERAL PUBLIC LICENSE
Version 3, 29 June 2007
Copyright © 2007 Free Software Foundation, Inc. <http://fsf.org/>
Copyright © 2007 Free Software Foundation, Inc. <https://fsf.org/>
Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed.
Everyone is permitted to copy and distribute verbatim copies of this license
document, but changing it is not allowed.
Preamble
The GNU General Public License is a free, copyleft license for software and other kinds of works.
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other kinds of works.
The licenses for most software and other practical works are designed to take away your freedom to share and change the works. By contrast, the GNU General Public License is intended to guarantee your freedom to share and change all versions of a program--to make sure it remains free software for all its users. We, the Free Software Foundation, use the GNU General Public License for most of our software; it applies also to any other work released this way by its authors. You can apply it to your programs, too.
The licenses for most software and other practical works are designed to take
away your freedom to share and change the works. By contrast, the GNU General
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versions of a program--to make sure it remains free software for all its users.
We, the Free Software Foundation, use the GNU General Public License for most
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TERMS AND CONDITIONS
0. Definitions.
“This License” refers to version 3 of the GNU General Public License.
“Copyright” also means copyright-like laws that apply to other kinds of works, such as semiconductor masks.
“The Program” refers to any copyrightable work licensed under this License. Each licensee is addressed as “you”. “Licensees” and “recipients” may be individuals or organizations.
To “modify” a work means to copy from or adapt all or part of the work in a fashion requiring copyright permission, other than the making of an exact copy. The resulting work is called a “modified version” of the earlier work or a work “based on” the earlier work.
A “covered work” means either the unmodified Program or a work based on the Program.
To “propagate” a work means to do anything with it that, without permission, would make you directly or secondarily liable for infringement under applicable copyright law, except executing it on a computer or modifying a private copy. Propagation includes copying, distribution (with or without modification), making available to the public, and in some countries other activities as well.
To “convey” a work means any kind of propagation that enables other parties to make or receive copies. Mere interaction with a user through a computer network, with no transfer of a copy, is not conveying.
An interactive user interface displays “Appropriate Legal Notices” to the extent that it includes a convenient and prominently visible feature that (1) displays an appropriate copyright notice, and (2) tells the user that there is no warranty for the work (except to the extent that warranties are provided), that licensees may convey the work under this License, and how to view a copy of this License. If the interface presents a list of user commands or options, such as a menu, a prominent item in the list meets this criterion.
1. Source Code.
The “source code” for a work means the preferred form of the work for making modifications to it. “Object code” means any non-source form of a work.
A “Standard Interface” means an interface that either is an official standard defined by a recognized standards body, or, in the case of interfaces specified for a particular programming language, one that is widely used among developers working in that language.
The “System Libraries” of an executable work include anything, other than the work as a whole, that (a) is included in the normal form of packaging a Major Component, but which is not part of that Major Component, and (b) serves only to enable use of the work with that Major Component, or to implement a Standard Interface for which an implementation is available to the public in source code form. A “Major Component”, in this context, means a major essential component (kernel, window system, and so on) of the specific operating system (if any) on which the executable work runs, or a compiler used to produce the work, or an object code interpreter used to run it.
The “Corresponding Source” for a work in object code form means all the source code needed to generate, install, and (for an executable work) run the object code and to modify the work, including scripts to control those activities. However, it does not include the work's System Libraries, or general-purpose tools or generally available free programs which are used unmodified in performing those activities but which are not part of the work. For example, Corresponding Source includes interface definition files associated with source files for the work, and the source code for shared libraries and dynamically linked subprograms that the work is specifically designed to require, such as by intimate data communication or control flow between those subprograms and other parts of the work.
The Corresponding Source need not include anything that users can regenerate automatically from other parts of the Corresponding Source.
The Corresponding Source for a work in source code form is that same work.
2. Basic Permissions.
All rights granted under this License are granted for the term of copyright on the Program, and are irrevocable provided the stated conditions are met. This License explicitly affirms your unlimited permission to run the unmodified Program. The output from running a covered work is covered by this License only if the output, given its content, constitutes a covered work. This License acknowledges your rights of fair use or other equivalent, as provided by copyright law.
You may make, run and propagate covered works that you do not convey, without conditions so long as your license otherwise remains in force. You may convey covered works to others for the sole purpose of having them make modifications exclusively for you, or provide you with facilities for running those works, provided that you comply with the terms of this License in conveying all material for which you do not control copyright. Those thus making or running the covered works for you must do so exclusively on your behalf, under your direction and control, on terms that prohibit them from making any copies of your copyrighted material outside their relationship with you.
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When you convey a covered work, you waive any legal power to forbid circumvention of technological measures to the extent such circumvention is effected by exercising rights under this License with respect to the covered work, and you disclaim any intention to limit operation or modification of the work as a means of enforcing, against the work's users, your or third parties' legal rights to forbid circumvention of technological measures.
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“Additional permissions” are terms that supplement the terms of this License by making exceptions from one or more of its conditions. Additional permissions that are applicable to the entire Program shall be treated as though they were included in this License, to the extent that they are valid under applicable law. If additional permissions apply only to part of the Program, that part may be used separately under those permissions, but the entire Program remains governed by this License without regard to the additional permissions.
When you convey a copy of a covered work, you may at your option remove any additional permissions from that copy, or from any part of it. (Additional permissions may be written to require their own removal in certain cases when you modify the work.) You may place additional permissions on material, added by you to a covered work, for which you have or can give appropriate copyright permission.
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A contributor's “essential patent claims” are all patent claims owned or controlled by the contributor, whether already acquired or hereafter acquired, that would be infringed by some manner, permitted by this License, of making, using, or selling its contributor version, but do not include claims that would be infringed only as a consequence of further modification of the contributor version. For purposes of this definition, “control” includes the right to grant patent sublicenses in a manner consistent with the requirements of this License.
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In the following three paragraphs, a “patent license” is any express agreement or commitment, however denominated, not to enforce a patent (such as an express permission to practice a patent or covenant not to sue for patent infringement). To “grant” such a patent license to a party means to make such an agreement or commitment not to enforce a patent against the party.
If you convey a covered work, knowingly relying on a patent license, and the Corresponding Source of the work is not available for anyone to copy, free of charge and under the terms of this License, through a publicly available network server or other readily accessible means, then you must either (1) cause the Corresponding Source to be so available, or (2) arrange to deprive yourself of the benefit of the patent license for this particular work, or (3) arrange, in a manner consistent with the requirements of this License, to extend the patent license to downstream recipients. “Knowingly relying” means you have actual knowledge that, but for the patent license, your conveying the covered work in a country, or your recipient's use of the covered work in a country, would infringe one or more identifiable patents in that country that you have reason to believe are valid.
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Nothing in this License shall be construed as excluding or limiting any implied license or other defenses to infringement that may otherwise be available to you under applicable patent law.
12. No Surrender of Others' Freedom.
If conditions are imposed on you (whether by court order, agreement or otherwise) that contradict the conditions of this License, they do not excuse you from the conditions of this License. If you cannot convey a covered work so as to satisfy simultaneously your obligations under this License and any other pertinent obligations, then as a consequence you may not convey it at all. For example, if you agree to terms that obligate you to collect a royalty for further conveying from those to whom you convey the Program, the only way you could satisfy both those terms and this License would be to refrain entirely from conveying the Program.
13. Use with the GNU Affero General Public License.
Notwithstanding any other provision of this License, you have permission to link or combine any covered work with a work licensed under version 3 of the GNU Affero General Public License into a single combined work, and to convey the resulting work. The terms of this License will continue to apply to the part which is the covered work, but the special requirements of the GNU Affero General Public License, section 13, concerning interaction through a network will apply to the combination as such.
14. Revised Versions of this License.
The Free Software Foundation may publish revised and/or new versions of the GNU General Public License from time to time. Such new versions will be similar in spirit to the present version, but may differ in detail to address new problems or concerns.
Each version is given a distinguishing version number. If the Program specifies that a certain numbered version of the GNU General Public License “or any later version” applies to it, you have the option of following the terms and conditions either of that numbered version or of any later version published by the Free Software Foundation. If the Program does not specify a version number of the GNU General Public License, you may choose any version ever published by the Free Software Foundation.
If the Program specifies that a proxy can decide which future versions of the GNU General Public License can be used, that proxy's public statement of acceptance of a version permanently authorizes you to choose that version for the Program.
Later license versions may give you additional or different permissions. However, no additional obligations are imposed on any author or copyright holder as a result of your choosing to follow a later version.
15. Disclaimer of Warranty.
THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM “AS IS” WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING, REPAIR OR CORRECTION.
16. Limitation of Liability.
IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES.
17. Interpretation of Sections 15 and 16.
If the disclaimer of warranty and limitation of liability provided above cannot be given local legal effect according to their terms, reviewing courts shall apply local law that most closely approximates an absolute waiver of all civil liability in connection with the Program, unless a warranty or assumption of liability accompanies a copy of the Program in return for a fee.
END OF TERMS AND CONDITIONS
0. Definitions.
"This License" refers to version 3 of the GNU General Public License.
"Copyright" also means copyright-like laws that apply to other kinds of works,
such as semiconductor masks.
"The Program" refers to any copyrightable work licensed under this License.
Each licensee is addressed as "you". "Licensees" and "recipients" may be individuals
or organizations.
To "modify" a work means to copy from or adapt all or part of the work in
a fashion requiring copyright permission, other than the making of an exact
copy. The resulting work is called a "modified version" of the earlier work
or a work "based on" the earlier work.
A "covered work" means either the unmodified Program or a work based on the
Program.
To "propagate" a work means to do anything with it that, without permission,
would make you directly or secondarily liable for infringement under applicable
copyright law, except executing it on a computer or modifying a private copy.
Propagation includes copying, distribution (with or without modification),
making available to the public, and in some countries other activities as
well.
To "convey" a work means any kind of propagation that enables other parties
to make or receive copies. Mere interaction with a user through a computer
network, with no transfer of a copy, is not conveying.
An interactive user interface displays "Appropriate Legal Notices" to the
extent that it includes a convenient and prominently visible feature that
(1) displays an appropriate copyright notice, and (2) tells the user that
there is no warranty for the work (except to the extent that warranties are
provided), that licensees may convey the work under this License, and how
to view a copy of this License. If the interface presents a list of user commands
or options, such as a menu, a prominent item in the list meets this criterion.
1. Source Code.
The "source code" for a work means the preferred form of the work for making
modifications to it. "Object code" means any non-source form of a work.
A "Standard Interface" means an interface that either is an official standard
defined by a recognized standards body, or, in the case of interfaces specified
for a particular programming language, one that is widely used among developers
working in that language.
The "System Libraries" of an executable work include anything, other than
the work as a whole, that (a) is included in the normal form of packaging
a Major Component, but which is not part of that Major Component, and (b)
serves only to enable use of the work with that Major Component, or to implement
a Standard Interface for which an implementation is available to the public
in source code form. A "Major Component", in this context, means a major essential
component (kernel, window system, and so on) of the specific operating system
(if any) on which the executable work runs, or a compiler used to produce
the work, or an object code interpreter used to run it.
The "Corresponding Source" for a work in object code form means all the source
code needed to generate, install, and (for an executable work) run the object
code and to modify the work, including scripts to control those activities.
However, it does not include the work's System Libraries, or general-purpose
tools or generally available free programs which are used unmodified in performing
those activities but which are not part of the work. For example, Corresponding
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If you develop a new program, and you want it to be of the greatest possible use to the public, the best way to achieve this is to make it free software which everyone can redistribute and change under these terms.
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Copyright (C) <year> <name of author>
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ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
You should have received a copy of the GNU General Public License along with
this program. If not, see <https://www.gnu.org/licenses/>.
Also add information on how to contact you by electronic and paper mail.
If the program does terminal interaction, make it output a short notice like this when it starts in an interactive mode:
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<program> Copyright (C) <year> <name of author>
This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
This is free software, and you are welcome to redistribute it under certain conditions; type `show c' for details.
<program> Copyright (C) <year> <name of author>
The hypothetical commands `show w' and `show c' should show the appropriate parts of the General Public License. Of course, your program's commands might be different; for a GUI interface, you would use an “about box”.
This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
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This is free software, and you are welcome to redistribute it under certain
conditions; type `show c' for details.
The GNU General Public License does not permit incorporating your program into proprietary programs. If your program is a subroutine library, you may consider it more useful to permit linking proprietary applications with the library. If this is what you want to do, use the GNU Lesser General Public License instead of this License. But first, please read <http://www.gnu.org/philosophy/why-not-lgpl.html>.
The hypothetical commands `show w' and `show c' should show the appropriate
parts of the General Public License. Of course, your program's commands might
be different; for a GUI interface, you would use an "about box".
You should also get your employer (if you work as a programmer) or school,
if any, to sign a "copyright disclaimer" for the program, if necessary. For
more information on this, and how to apply and follow the GNU GPL, see <https://www.gnu.org/licenses/>.
The GNU General Public License does not permit incorporating your program
into proprietary programs. If your program is a subroutine library, you may
consider it more useful to permit linking proprietary applications with the
library. If this is what you want to do, use the GNU Lesser General Public
License instead of this License. But first, please read <https://www.gnu.org/
licenses /why-not-lgpl.html>.

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# TTT4260
# TTT4160
Kilden til designprosjekt 1-4 i TTT4260 Elektronisk systemdesign og analyse
Kilden til designprosjekt 1-4 i TTT4160 Elektronisk systemdesign og analyse

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#!/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 [τ]")
plt.ylabel("Voltage [V]")
plt.legend(["Supply voltage", "Capacitor voltage"], loc="lower right")
plt.savefig(filename + ".png", dpi = 300)
plt.show()

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\documentclass[10pt]{article}
\usepackage{pgf,tikz,pgfplots}
\pgfplotsset{compat=1.15}
\usepackage{mathrsfs}
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View File

@ -0,0 +1,401 @@
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View File

@ -0,0 +1,433 @@
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\draw (0.9826971286425398,1.0091692065822461) node[anchor=north west] {$(\tau, 0.79\text{V})$};
\draw (1.7132719478893085,0.5951090467957184) node[anchor=north west] {$(2\tau, 0.29\text{V})$};
\draw (2.588565094705576,0.46352472684146245) node[anchor=north west] {$(3\tau, 0.11\text{V})$};
\draw (3.592848810526346,0.35387112687958255) node[anchor=north west] {$(4\tau, 0.04\text{V})$};
\draw (4.597132526347116,0.35387112687958255) node[anchor=north west] {$(5\tau, 0.01\text{V})$};
\begin{scriptsize}
\draw[color=qqwuqq] (0.14886523614914818,2.1083287262696615) node {$v_c$};
\draw [fill=uuuuuu] (1.,0.7872620041068866) circle (2.0pt);
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\draw [fill=uuuuuu] (5.,0.0144192065780429) circle (2.0pt);
\end{scriptsize}
\end{axis}
\end{tikzpicture}

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\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 å ha koblet opp kretsen ser vi at spenningen (se \figref{graph:1b}) over kondensatoren når $63\%$ 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
Når det skjer utladning av kondensatoren har ikke strømmen noe sted å gå, eneste er å gå gjennom kondensatoren litt og litt.
\end{alphaparts}
\question
For å 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 må finne spenningen som ligger over $R_2||R_3$ for å finne startspenningen på $C_1$.
Begynner med å 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 på $c_1$.
Når bryteren brytes, vi vi få 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 på en forenklet måte 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 å 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. Så
$$ R_{eq} = 0.5\text{k}\ohm $$
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 å 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 nådd ``steady-state'', da er spenningen $v_{C_1} = V_{th} = 0.5\text{V}$. Når bryteren $S_2$ lukkes får 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 går 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 får 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 å sette opp likningen for spenningen $v_{C_1}$
Vi setter $\tau = 1$ for at det skal være lettere å 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 å lage en funksjon for kretsen når bryter $S_2$ lukkes når $t=0.5\tau$, 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 når 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 å har justert til $6300\ohm$ ser det ut som at spenningen når ca $0.8$V på firkantpulsen.
\end{alphaparts}
\end{document}

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\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
Når $A$ er logisk høy, er $C$ logisk lav. Når $A$ 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 når inngangen er 0 er utgangen 1.
\item
Når det er $0$V på inngangen $A$ er det $5$V på utgangen $C$.
\item Vi gjør målinger på kretsen, setter spenning på $A$ lik $v_A $ og måler spenningen $v_C $ på 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{Målte spenninger på $C$, 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 å lede rundt $2.2$V til $2.3$V. Den er som en kortslutning ved ca $3.0$V.
\item
Dioden begynner å lyse når $A$ 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 nå $2$V. Vi ønsker å finne tiden det tar.
$$ 2\text{V} = 5V(1-e^{\frac{-t}{\tau}})$$
Som gjør at
$$ t = \frac{1}{2}\tau $$
Vi vet også at perioden er $T=1$ms. Vi vet også 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 må lage $\tau$. Velger kondensator lik $100\mu$F.
$$ \frac{1\text{ms}}{100\mu\text{F}} = 10\ohm$$
\item
Kobler opp kretsen og oppladning når 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}

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#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Sun Jan 13 16:30:58 2019
@author: oyvind
"""
import csv
import matplotlib.pyplot as plt
header = []
data = []
filename = "0.1V1K"
with open(filename + ".csv") as csvfile:
csvreader = csv.reader(csvfile)
header = next(csvreader)
for dataplot in csvreader:
values = [float(value) for value in dataplot]
data.append(values)
time = [p[0] * 1000 for p in data]
ch1 = [p[1] for p 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()

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\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 å finne utgangsspenningen $v_2 $ må 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 å senke amplituden til inngangssignalet ned til $0.5$mV. Dette kan gjøres ved å 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 på 1, altså det samme signalet inn som ut. Den brukes ofte der kretsen som leverer signalet ikke klarer å levere nok strøm til det den leverer til. Bufferen klarer da å levere nok strøm.
\item
Kretsen i figur 4 er en inverterende forsterker. Det går ingen strøm gjennom forsterkeren, men det går en strøm fra $v_i $ til $v_o $. Vi kan da sette opp KVL, basert på at det går 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 også 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}), får 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 også at det ikke går noe strøm gjennom forsterkeren, så all strøm må gå gjennom motstanden $R_1 $. Siden det ikke er noen spenning mellom terminalene på 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 på 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 på samme måte som kretsen i figur 4 (inverterende forsterker). Denne kretsen vil vokse veldig fort oppover når inngangsspenning er positiv og omvendt når inngangen er negativ.
Etter litt søking på 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 på $v_2 $ bli et firkantsignal.
\item
Dersom vi integrerer et firkantsignal vil vi få 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 på $0.1$V. Forventet utgangsamplitude er $1$V, forsterkingen er på -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 på $1$V}
\label{graph:oppgave4a}
\end{figure}
\item
Forsterkeren blir mettet når 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 på 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}

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#!/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)

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#!/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)

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#!/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)

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#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
11.0666,-0.00553953,-0.00497733,-0.366327
11.6418,-0.00540155,-0.00537231,-0.38602
12.2469,-0.00550687,-0.00508884,-0.406273
12.8835,-0.00509335,-0.00539532,-0.427304
13.5532,-0.00553483,-0.00544864,-0.448588
14.2577,-0.00527835,-0.0057729,-0.469659
14.9987,-0.00519837,-0.00589985,-0.495311
15.7784,-0.00532765,-0.00593774,-0.520151
16.5985,-0.00538368,-0.00622925,-0.547678
17.4613,-0.00528162,-0.00670784,-0.57488
18.3689,-0.00546862,-0.00668217,-0.604199
19.3237,-0.00555204,-0.00687947,-0.634738
20.3281,-0.00533271,-0.00723183,-0.666323
21.3847,-0.00538782,-0.00742054,-0.701453
22.4962,-0.00546445,-0.00789399,-0.735715
23.6656,-0.00519679,-0.00848513,-0.774108
24.8957,-0.00538932,-0.00843235,-0.812998
26.1897,-0.00523701,-0.00917148,-0.853232
27.551,-0.00518192,-0.00980661,-0.898256
28.9831,-0.00530315,-0.00982177,-0.943569
30.4896,-0.00545199,-0.0100736,-0.991705
32.0744,-0.00528373,-0.0106913,-1.0408
33.7415,-0.00529,-0.0111226,-1.09468
35.4954,-0.0052797,-0.0118656,-1.14995
37.3404,-0.00554357,-0.0121321,-1.20827
39.2813,-0.00531512,-0.0130159,-1.27031
41.323,-0.00543937,-0.013854,-1.33445
43.471,-0.00540697,-0.0144741,-1.40109
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