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GNU GENERAL PUBLIC LICENSE
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GNU GENERAL PUBLIC LICENSE
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Version 3, 29 June 2007
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Version 3, 29 June 2007
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Copyright © 2007 Free Software Foundation, Inc. <http://fsf.org/>
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Copyright © 2007 Free Software Foundation, Inc. <https://fsf.org/>
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Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed.
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Everyone is permitted to copy and distribute verbatim copies of this license
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document, but changing it is not allowed.
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Preamble
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Preamble
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The GNU General Public License is a free, copyleft license for software and other kinds of works.
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The GNU General Public License is a free, copyleft license for software and
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other kinds of works.
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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.
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The licenses for most software and other practical works are designed to take
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away your freedom to share and change the works. By contrast, the GNU General
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Public License is intended to guarantee your freedom to share and change all
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versions of a program--to make sure it remains free software for all its users.
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We, the Free Software Foundation, use the GNU General Public License for most
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of our software; it applies also to any other work released this way by its
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authors. You can apply it to your programs, too.
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When we speak of free software, we are referring to freedom, not price. Our General Public Licenses are designed to make sure that you have the freedom to distribute copies of free software (and charge for them if you wish), that you receive source code or can get it if you want it, that you can change the software or use pieces of it in new free programs, and that you know you can do these things.
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When we speak of free software, we are referring to freedom, not price. Our
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General Public Licenses are designed to make sure that you have the freedom
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to distribute copies of free software (and charge for them if you wish), that
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you receive source code or can get it if you want it, that you can change
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the software or use pieces of it in new free programs, and that you know you
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can do these things.
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To protect your rights, we need to prevent others from denying you these rights or asking you to surrender the rights. Therefore, you have certain responsibilities if you distribute copies of the software, or if you modify it: responsibilities to respect the freedom of others.
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To protect your rights, we need to prevent others from denying you these rights
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or asking you to surrender the rights. Therefore, you have certain responsibilities
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if you distribute copies of the software, or if you modify it: responsibilities
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to respect the freedom of others.
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||||||
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||||||
For example, if you distribute copies of such a program, whether gratis or for a fee, you must pass on to the recipients the same freedoms that you received. You must make sure that they, too, receive or can get the source code. And you must show them these terms so they know their rights.
|
For example, if you distribute copies of such a program, whether gratis or
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for a fee, you must pass on to the recipients the same freedoms that you received.
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You must make sure that they, too, receive or can get the source code. And
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you must show them these terms so they know their rights.
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Developers that use the GNU GPL protect your rights with two steps: (1) assert copyright on the software, and (2) offer you this License giving you legal permission to copy, distribute and/or modify it.
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Developers that use the GNU GPL protect your rights with two steps: (1) assert
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copyright on the software, and (2) offer you this License giving you legal
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permission to copy, distribute and/or modify it.
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For the developers' and authors' protection, the GPL clearly explains that there is no warranty for this free software. For both users' and authors' sake, the GPL requires that modified versions be marked as changed, so that their problems will not be attributed erroneously to authors of previous versions.
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For the developers' and authors' protection, the GPL clearly explains that
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there is no warranty for this free software. For both users' and authors'
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sake, the GPL requires that modified versions be marked as changed, so that
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their problems will not be attributed erroneously to authors of previous versions.
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Some devices are designed to deny users access to install or run modified versions of the software inside them, although the manufacturer can do so. This is fundamentally incompatible with the aim of protecting users' freedom to change the software. The systematic pattern of such abuse occurs in the area of products for individuals to use, which is precisely where it is most unacceptable. Therefore, we have designed this version of the GPL to prohibit the practice for those products. If such problems arise substantially in other domains, we stand ready to extend this provision to those domains in future versions of the GPL, as needed to protect the freedom of users.
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Some devices are designed to deny users access to install or run modified
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versions of the software inside them, although the manufacturer can do so.
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This is fundamentally incompatible with the aim of protecting users' freedom
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to change the software. The systematic pattern of such abuse occurs in the
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area of products for individuals to use, which is precisely where it is most
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unacceptable. Therefore, we have designed this version of the GPL to prohibit
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the practice for those products. If such problems arise substantially in other
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domains, we stand ready to extend this provision to those domains in future
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versions of the GPL, as needed to protect the freedom of users.
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Finally, every program is threatened constantly by software patents. States should not allow patents to restrict development and use of software on general-purpose computers, but in those that do, we wish to avoid the special danger that patents applied to a free program could make it effectively proprietary. To prevent this, the GPL assures that patents cannot be used to render the program non-free.
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Finally, every program is threatened constantly by software patents. States
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should not allow patents to restrict development and use of software on general-purpose
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computers, but in those that do, we wish to avoid the special danger that
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patents applied to a free program could make it effectively proprietary. To
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prevent this, the GPL assures that patents cannot be used to render the program
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non-free.
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The precise terms and conditions for copying, distribution and modification follow.
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The precise terms and conditions for copying, distribution and modification
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follow.
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TERMS AND CONDITIONS
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TERMS AND CONDITIONS
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||||||
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||||||
0. Definitions.
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0. Definitions.
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“This License” refers to version 3 of the GNU General Public License.
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"This License" refers to version 3 of the GNU General Public License.
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“Copyright” also means copyright-like laws that apply to other kinds of works, such as semiconductor masks.
|
"Copyright" also means copyright-like laws that apply to other kinds of works,
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|
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.
|
|
||||||
|
"The Program" refers to any copyrightable work licensed under this License.
|
||||||
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.
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Each licensee is addressed as "you". "Licensees" and "recipients" may be individuals
|
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or organizations.
|
||||||
A “covered work” means either the unmodified Program or a work based on the Program.
|
|
||||||
|
To "modify" a work means to copy from or adapt all or part of the work in
|
||||||
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.
|
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
|
||||||
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.
|
or a work "based on" the earlier work.
|
||||||
|
|
||||||
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.
|
A "covered work" means either the unmodified Program or a work based on the
|
||||||
|
Program.
|
||||||
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.
|
To "propagate" a work means to do anything with it that, without permission,
|
||||||
|
would make you directly or secondarily liable for infringement under applicable
|
||||||
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.
|
copyright law, except executing it on a computer or modifying a private copy.
|
||||||
|
Propagation includes copying, distribution (with or without modification),
|
||||||
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.
|
making available to the public, and in some countries other activities as
|
||||||
|
well.
|
||||||
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.
|
|
||||||
|
To "convey" a work means any kind of propagation that enables other parties
|
||||||
The Corresponding Source need not include anything that users can regenerate automatically from other parts of the Corresponding Source.
|
to make or receive copies. Mere interaction with a user through a computer
|
||||||
|
network, with no transfer of a copy, is not conveying.
|
||||||
The Corresponding Source for a work in source code form is that same work.
|
|
||||||
|
An interactive user interface displays "Appropriate Legal Notices" to the
|
||||||
2. Basic Permissions.
|
extent that it includes a convenient and prominently visible feature that
|
||||||
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.
|
(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
|
||||||
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.
|
provided), that licensees may convey the work under this License, and how
|
||||||
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to view a copy of this License. If the interface presents a list of user commands
|
||||||
Conveying under any other circumstances is permitted solely under the conditions stated below. Sublicensing is not allowed; section 10 makes it unnecessary.
|
or options, such as a menu, a prominent item in the list meets this criterion.
|
||||||
|
|
||||||
3. Protecting Users' Legal Rights From Anti-Circumvention Law.
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1. Source Code.
|
||||||
No covered work shall be deemed part of an effective technological measure under any applicable law fulfilling obligations under article 11 of the WIPO copyright treaty adopted on 20 December 1996, or similar laws prohibiting or restricting circumvention of such measures.
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|
||||||
|
The "source code" for a work means the preferred form of the work for making
|
||||||
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.
|
modifications to it. "Object code" means any non-source form of a work.
|
||||||
|
|
||||||
4. Conveying Verbatim Copies.
|
A "Standard Interface" means an interface that either is an official standard
|
||||||
You may convey verbatim copies of the Program's source code as you receive it, in any medium, provided that you conspicuously and appropriately publish on each copy an appropriate copyright notice; keep intact all notices stating that this License and any non-permissive terms added in accord with section 7 apply to the code; keep intact all notices of the absence of any warranty; and give all recipients a copy of this License along with the Program.
|
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
|
||||||
You may charge any price or no price for each copy that you convey, and you may offer support or warranty protection for a fee.
|
working in that language.
|
||||||
|
|
||||||
5. Conveying Modified Source Versions.
|
The "System Libraries" of an executable work include anything, other than
|
||||||
You may convey a work based on the Program, or the modifications to produce it from the Program, in the form of source code under the terms of section 4, provided that you also meet all of these conditions:
|
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)
|
||||||
a) The work must carry prominent notices stating that you modified it, and giving a relevant date.
|
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
|
||||||
b) The work must carry prominent notices stating that it is released under this License and any conditions added under section 7. This requirement modifies the requirement in section 4 to “keep intact all notices”.
|
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
|
||||||
c) You must license the entire work, as a whole, under this License to anyone who comes into possession of a copy. This License will therefore apply, along with any applicable section 7 additional terms, to the whole of the work, and all its parts, regardless of how they are packaged. This License gives no permission to license the work in any other way, but it does not invalidate such permission if you have separately received it.
|
(if any) on which the executable work runs, or a compiler used to produce
|
||||||
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the work, or an object code interpreter used to run it.
|
||||||
d) If the work has interactive user interfaces, each must display Appropriate Legal Notices; however, if the Program has interactive interfaces that do not display Appropriate Legal Notices, your work need not make them do so.
|
|
||||||
|
The "Corresponding Source" for a work in object code form means all the source
|
||||||
A compilation of a covered work with other separate and independent works, which are not by their nature extensions of the covered work, and which are not combined with it such as to form a larger program, in or on a volume of a storage or distribution medium, is called an “aggregate” if the compilation and its resulting copyright are not used to limit the access or legal rights of the compilation's users beyond what the individual works permit. Inclusion of a covered work in an aggregate does not cause this License to apply to the other parts of the aggregate.
|
code needed to generate, install, and (for an executable work) run the object
|
||||||
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code and to modify the work, including scripts to control those activities.
|
||||||
6. Conveying Non-Source Forms.
|
However, it does not include the work's System Libraries, or general-purpose
|
||||||
You may convey a covered work in object code form under the terms of sections 4 and 5, provided that you also convey the machine-readable Corresponding Source under the terms of this License, in one of these ways:
|
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
|
||||||
a) Convey the object code in, or embodied in, a physical product (including a physical distribution medium), accompanied by the Corresponding Source fixed on a durable physical medium customarily used for software interchange.
|
Source includes interface definition files associated with source files for
|
||||||
|
the work, and the source code for shared libraries and dynamically linked
|
||||||
b) Convey the object code in, or embodied in, a physical product (including a physical distribution medium), accompanied by a written offer, valid for at least three years and valid for as long as you offer spare parts or customer support for that product model, to give anyone who possesses the object code either (1) a copy of the Corresponding Source for all the software in the product that is covered by this License, on a durable physical medium customarily used for software interchange, for a price no more than your reasonable cost of physically performing this conveying of source, or (2) access to copy the Corresponding Source from a network server at no charge.
|
subprograms that the work is specifically designed to require, such as by
|
||||||
|
intimate data communication or control flow between those subprograms and
|
||||||
c) Convey individual copies of the object code with a copy of the written offer to provide the Corresponding Source. This alternative is allowed only occasionally and noncommercially, and only if you received the object code with such an offer, in accord with subsection 6b.
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other parts of the work.
|
||||||
|
|
||||||
d) Convey the object code by offering access from a designated place (gratis or for a charge), and offer equivalent access to the Corresponding Source in the same way through the same place at no further charge. You need not require recipients to copy the Corresponding Source along with the object code. If the place to copy the object code is a network server, the Corresponding Source may be on a different server (operated by you or a third party) that supports equivalent copying facilities, provided you maintain clear directions next to the object code saying where to find the Corresponding Source. Regardless of what server hosts the Corresponding Source, you remain obligated to ensure that it is available for as long as needed to satisfy these requirements.
|
The Corresponding Source need not include anything that users can regenerate
|
||||||
|
automatically from other parts of the Corresponding Source.
|
||||||
e) Convey the object code using peer-to-peer transmission, provided you inform other peers where the object code and Corresponding Source of the work are being offered to the general public at no charge under subsection 6d.
|
|
||||||
|
The Corresponding Source for a work in source code form is that same work.
|
||||||
A separable portion of the object code, whose source code is excluded from the Corresponding Source as a System Library, need not be included in conveying the object code work.
|
|
||||||
|
2. Basic Permissions.
|
||||||
A “User Product” is either (1) a “consumer product”, which means any tangible personal property which is normally used for personal, family, or household purposes, or (2) anything designed or sold for incorporation into a dwelling. In determining whether a product is a consumer product, doubtful cases shall be resolved in favor of coverage. For a particular product received by a particular user, “normally used” refers to a typical or common use of that class of product, regardless of the status of the particular user or of the way in which the particular user actually uses, or expects or is expected to use, the product. A product is a consumer product regardless of whether the product has substantial commercial, industrial or non-consumer uses, unless such uses represent the only significant mode of use of the product.
|
|
||||||
|
All rights granted under this License are granted for the term of copyright
|
||||||
“Installation Information” for a User Product means any methods, procedures, authorization keys, or other information required to install and execute modified versions of a covered work in that User Product from a modified version of its Corresponding Source. The information must suffice to ensure that the continued functioning of the modified object code is in no case prevented or interfered with solely because modification has been made.
|
on the Program, and are irrevocable provided the stated conditions are met.
|
||||||
|
This License explicitly affirms your unlimited permission to run the unmodified
|
||||||
If you convey an object code work under this section in, or with, or specifically for use in, a User Product, and the conveying occurs as part of a transaction in which the right of possession and use of the User Product is transferred to the recipient in perpetuity or for a fixed term (regardless of how the transaction is characterized), the Corresponding Source conveyed under this section must be accompanied by the Installation Information. But this requirement does not apply if neither you nor any third party retains the ability to install modified object code on the User Product (for example, the work has been installed in ROM).
|
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
|
||||||
The requirement to provide Installation Information does not include a requirement to continue to provide support service, warranty, or updates for a work that has been modified or installed by the recipient, or for the User Product in which it has been modified or installed. Access to a network may be denied when the modification itself materially and adversely affects the operation of the network or violates the rules and protocols for communication across the network.
|
acknowledges your rights of fair use or other equivalent, as provided by copyright
|
||||||
|
law.
|
||||||
Corresponding Source conveyed, and Installation Information provided, in accord with this section must be in a format that is publicly documented (and with an implementation available to the public in source code form), and must require no special password or key for unpacking, reading or copying.
|
|
||||||
|
You may make, run and propagate covered works that you do not convey, without
|
||||||
7. Additional Terms.
|
conditions so long as your license otherwise remains in force. You may convey
|
||||||
“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.
|
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,
|
||||||
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.
|
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
|
||||||
Notwithstanding any other provision of this License, for material you add to a covered work, you may (if authorized by the copyright holders of that material) supplement the terms of this License with terms:
|
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
|
||||||
a) Disclaiming warranty or limiting liability differently from the terms of sections 15 and 16 of this License; or
|
material outside their relationship with you.
|
||||||
|
|
||||||
b) Requiring preservation of specified reasonable legal notices or author attributions in that material or in the Appropriate Legal Notices displayed by works containing it; or
|
Conveying under any other circumstances is permitted solely under the conditions
|
||||||
|
stated below. Sublicensing is not allowed; section 10 makes it unnecessary.
|
||||||
c) Prohibiting misrepresentation of the origin of that material, or requiring that modified versions of such material be marked in reasonable ways as different from the original version; or
|
|
||||||
|
3. Protecting Users' Legal Rights From Anti-Circumvention Law.
|
||||||
d) Limiting the use for publicity purposes of names of licensors or authors of the material; or
|
|
||||||
|
No covered work shall be deemed part of an effective technological measure
|
||||||
e) Declining to grant rights under trademark law for use of some trade names, trademarks, or service marks; or
|
under any applicable law fulfilling obligations under article 11 of the WIPO
|
||||||
|
copyright treaty adopted on 20 December 1996, or similar laws prohibiting
|
||||||
f) Requiring indemnification of licensors and authors of that material by anyone who conveys the material (or modified versions of it) with contractual assumptions of liability to the recipient, for any liability that these contractual assumptions directly impose on those licensors and authors.
|
or restricting circumvention of such measures.
|
||||||
|
|
||||||
All other non-permissive additional terms are considered “further restrictions” within the meaning of section 10. If the Program as you received it, or any part of it, contains a notice stating that it is governed by this License along with a term that is a further restriction, you may remove that term. If a license document contains a further restriction but permits relicensing or conveying under this License, you may add to a covered work material governed by the terms of that license document, provided that the further restriction does not survive such relicensing or conveying.
|
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
|
||||||
If you add terms to a covered work in accord with this section, you must place, in the relevant source files, a statement of the additional terms that apply to those files, or a notice indicating where to find the applicable terms.
|
exercising rights under this License with respect to the covered work, and
|
||||||
|
you disclaim any intention to limit operation or modification of the work
|
||||||
Additional terms, permissive or non-permissive, may be stated in the form of a separately written license, or stated as exceptions; the above requirements apply either way.
|
as a means of enforcing, against the work's users, your or third parties'
|
||||||
|
legal rights to forbid circumvention of technological measures.
|
||||||
8. Termination.
|
|
||||||
You may not propagate or modify a covered work except as expressly provided under this License. Any attempt otherwise to propagate or modify it is void, and will automatically terminate your rights under this License (including any patent licenses granted under the third paragraph of section 11).
|
4. Conveying Verbatim Copies.
|
||||||
|
|
||||||
However, if you cease all violation of this License, then your license from a particular copyright holder is reinstated (a) provisionally, unless and until the copyright holder explicitly and finally terminates your license, and (b) permanently, if the copyright holder fails to notify you of the violation by some reasonable means prior to 60 days after the cessation.
|
You may convey verbatim copies of the Program's source code as you receive
|
||||||
|
it, in any medium, provided that you conspicuously and appropriately publish
|
||||||
Moreover, your license from a particular copyright holder is reinstated permanently if the copyright holder notifies you of the violation by some reasonable means, this is the first time you have received notice of violation of this License (for any work) from that copyright holder, and you cure the violation prior to 30 days after your receipt of the notice.
|
on each copy an appropriate copyright notice; keep intact all notices stating
|
||||||
|
that this License and any non-permissive terms added in accord with section
|
||||||
Termination of your rights under this section does not terminate the licenses of parties who have received copies or rights from you under this License. If your rights have been terminated and not permanently reinstated, you do not qualify to receive new licenses for the same material under section 10.
|
7 apply to the code; keep intact all notices of the absence of any warranty;
|
||||||
|
and give all recipients a copy of this License along with the Program.
|
||||||
9. Acceptance Not Required for Having Copies.
|
|
||||||
You are not required to accept this License in order to receive or run a copy of the Program. Ancillary propagation of a covered work occurring solely as a consequence of using peer-to-peer transmission to receive a copy likewise does not require acceptance. However, nothing other than this License grants you permission to propagate or modify any covered work. These actions infringe copyright if you do not accept this License. Therefore, by modifying or propagating a covered work, you indicate your acceptance of this License to do so.
|
You may charge any price or no price for each copy that you convey, and you
|
||||||
|
may offer support or warranty protection for a fee.
|
||||||
10. Automatic Licensing of Downstream Recipients.
|
|
||||||
Each time you convey a covered work, the recipient automatically receives a license from the original licensors, to run, modify and propagate that work, subject to this License. You are not responsible for enforcing compliance by third parties with this License.
|
5. Conveying Modified Source Versions.
|
||||||
|
|
||||||
An “entity transaction” is a transaction transferring control of an organization, or substantially all assets of one, or subdividing an organization, or merging organizations. If propagation of a covered work results from an entity transaction, each party to that transaction who receives a copy of the work also receives whatever licenses to the work the party's predecessor in interest had or could give under the previous paragraph, plus a right to possession of the Corresponding Source of the work from the predecessor in interest, if the predecessor has it or can get it with reasonable efforts.
|
You may convey a work based on the Program, or the modifications to produce
|
||||||
|
it from the Program, in the form of source code under the terms of section
|
||||||
You may not impose any further restrictions on the exercise of the rights granted or affirmed under this License. For example, you may not impose a license fee, royalty, or other charge for exercise of rights granted under this License, and you may not initiate litigation (including a cross-claim or counterclaim in a lawsuit) alleging that any patent claim is infringed by making, using, selling, offering for sale, or importing the Program or any portion of it.
|
4, provided that you also meet all of these conditions:
|
||||||
|
|
||||||
11. Patents.
|
a) The work must carry prominent notices stating that you modified it, and
|
||||||
A “contributor” is a copyright holder who authorizes use under this License of the Program or a work on which the Program is based. The work thus licensed is called the contributor's “contributor version”.
|
giving a relevant date.
|
||||||
|
|
||||||
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.
|
b) The work must carry prominent notices stating that it is released under
|
||||||
|
this License and any conditions added under section 7. This requirement modifies
|
||||||
Each contributor grants you a non-exclusive, worldwide, royalty-free patent license under the contributor's essential patent claims, to make, use, sell, offer for sale, import and otherwise run, modify and propagate the contents of its contributor version.
|
the requirement in section 4 to "keep intact all notices".
|
||||||
|
|
||||||
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.
|
c) You must license the entire work, as a whole, under this License to anyone
|
||||||
|
who comes into possession of a copy. This License will therefore apply, along
|
||||||
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.
|
with any applicable section 7 additional terms, to the whole of the work,
|
||||||
|
and all its parts, regardless of how they are packaged. This License gives
|
||||||
If, pursuant to or in connection with a single transaction or arrangement, you convey, or propagate by procuring conveyance of, a covered work, and grant a patent license to some of the parties receiving the covered work authorizing them to use, propagate, modify or convey a specific copy of the covered work, then the patent license you grant is automatically extended to all recipients of the covered work and works based on it.
|
no permission to license the work in any other way, but it does not invalidate
|
||||||
|
such permission if you have separately received it.
|
||||||
A patent license is “discriminatory” if it does not include within the scope of its coverage, prohibits the exercise of, or is conditioned on the non-exercise of one or more of the rights that are specifically granted under this License. You may not convey a covered work if you are a party to an arrangement with a third party that is in the business of distributing software, under which you make payment to the third party based on the extent of your activity of conveying the work, and under which the third party grants, to any of the parties who would receive the covered work from you, a discriminatory patent license (a) in connection with copies of the covered work conveyed by you (or copies made from those copies), or (b) primarily for and in connection with specific products or compilations that contain the covered work, unless you entered into that arrangement, or that patent license was granted, prior to 28 March 2007.
|
|
||||||
|
d) If the work has interactive user interfaces, each must display Appropriate
|
||||||
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.
|
Legal Notices; however, if the Program has interactive interfaces that do
|
||||||
|
not display Appropriate Legal Notices, your work need not make them do so.
|
||||||
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.
|
A compilation of a covered work with other separate and independent works,
|
||||||
|
which are not by their nature extensions of the covered work, and which are
|
||||||
13. Use with the GNU Affero General Public License.
|
not combined with it such as to form a larger program, in or on a volume of
|
||||||
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.
|
a storage or distribution medium, is called an "aggregate" if the compilation
|
||||||
|
and its resulting copyright are not used to limit the access or legal rights
|
||||||
14. Revised Versions of this License.
|
of the compilation's users beyond what the individual works permit. Inclusion
|
||||||
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.
|
of a covered work in an aggregate does not cause this License to apply to
|
||||||
|
the other parts of the aggregate.
|
||||||
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.
|
|
||||||
|
6. Conveying Non-Source Forms.
|
||||||
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.
|
|
||||||
|
You may convey a covered work in object code form under the terms of sections
|
||||||
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.
|
4 and 5, provided that you also convey the machine-readable Corresponding
|
||||||
|
Source under the terms of this License, in one of these ways:
|
||||||
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.
|
a) Convey the object code in, or embodied in, a physical product (including
|
||||||
|
a physical distribution medium), accompanied by the Corresponding Source fixed
|
||||||
16. Limitation of Liability.
|
on a durable physical medium customarily used for software interchange.
|
||||||
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.
|
|
||||||
|
b) Convey the object code in, or embodied in, a physical product (including
|
||||||
17. Interpretation of Sections 15 and 16.
|
a physical distribution medium), accompanied by a written offer, valid for
|
||||||
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.
|
at least three years and valid for as long as you offer spare parts or customer
|
||||||
|
support for that product model, to give anyone who possesses the object code
|
||||||
END OF TERMS AND CONDITIONS
|
either (1) a copy of the Corresponding Source for all the software in the
|
||||||
|
product that is covered by this License, on a durable physical medium customarily
|
||||||
|
used for software interchange, for a price no more than your reasonable cost
|
||||||
|
of physically performing this conveying of source, or (2) access to copy the
|
||||||
|
Corresponding Source from a network server at no charge.
|
||||||
|
|
||||||
|
c) Convey individual copies of the object code with a copy of the written
|
||||||
|
offer to provide the Corresponding Source. This alternative is allowed only
|
||||||
|
occasionally and noncommercially, and only if you received the object code
|
||||||
|
with such an offer, in accord with subsection 6b.
|
||||||
|
|
||||||
|
d) Convey the object code by offering access from a designated place (gratis
|
||||||
|
or for a charge), and offer equivalent access to the Corresponding Source
|
||||||
|
in the same way through the same place at no further charge. You need not
|
||||||
|
require recipients to copy the Corresponding Source along with the object
|
||||||
|
code. If the place to copy the object code is a network server, the Corresponding
|
||||||
|
Source may be on a different server (operated by you or a third party) that
|
||||||
|
supports equivalent copying facilities, provided you maintain clear directions
|
||||||
|
next to the object code saying where to find the Corresponding Source. Regardless
|
||||||
|
of what server hosts the Corresponding Source, you remain obligated to ensure
|
||||||
|
that it is available for as long as needed to satisfy these requirements.
|
||||||
|
|
||||||
|
e) Convey the object code using peer-to-peer transmission, provided you inform
|
||||||
|
other peers where the object code and Corresponding Source of the work are
|
||||||
|
being offered to the general public at no charge under subsection 6d.
|
||||||
|
|
||||||
|
A separable portion of the object code, whose source code is excluded from
|
||||||
|
the Corresponding Source as a System Library, need not be included in conveying
|
||||||
|
the object code work.
|
||||||
|
|
||||||
|
A "User Product" is either (1) a "consumer product", which means any tangible
|
||||||
|
personal property which is normally used for personal, family, or household
|
||||||
|
purposes, or (2) anything designed or sold for incorporation into a dwelling.
|
||||||
|
In determining whether a product is a consumer product, doubtful cases shall
|
||||||
|
be resolved in favor of coverage. For a particular product received by a particular
|
||||||
|
user, "normally used" refers to a typical or common use of that class of product,
|
||||||
|
regardless of the status of the particular user or of the way in which the
|
||||||
|
particular user actually uses, or expects or is expected to use, the product.
|
||||||
|
A product is a consumer product regardless of whether the product has substantial
|
||||||
|
commercial, industrial or non-consumer uses, unless such uses represent the
|
||||||
|
only significant mode of use of the product.
|
||||||
|
|
||||||
|
"Installation Information" for a User Product means any methods, procedures,
|
||||||
|
authorization keys, or other information required to install and execute modified
|
||||||
|
versions of a covered work in that User Product from a modified version of
|
||||||
|
its Corresponding Source. The information must suffice to ensure that the
|
||||||
|
continued functioning of the modified object code is in no case prevented
|
||||||
|
or interfered with solely because modification has been made.
|
||||||
|
|
||||||
|
If you convey an object code work under this section in, or with, or specifically
|
||||||
|
for use in, a User Product, and the conveying occurs as part of a transaction
|
||||||
|
in which the right of possession and use of the User Product is transferred
|
||||||
|
to the recipient in perpetuity or for a fixed term (regardless of how the
|
||||||
|
transaction is characterized), the Corresponding Source conveyed under this
|
||||||
|
section must be accompanied by the Installation Information. But this requirement
|
||||||
|
does not apply if neither you nor any third party retains the ability to install
|
||||||
|
modified object code on the User Product (for example, the work has been installed
|
||||||
|
in ROM).
|
||||||
|
|
||||||
|
The requirement to provide Installation Information does not include a requirement
|
||||||
|
to continue to provide support service, warranty, or updates for a work that
|
||||||
|
has been modified or installed by the recipient, or for the User Product in
|
||||||
|
which it has been modified or installed. Access to a network may be denied
|
||||||
|
when the modification itself materially and adversely affects the operation
|
||||||
|
of the network or violates the rules and protocols for communication across
|
||||||
|
the network.
|
||||||
|
|
||||||
|
Corresponding Source conveyed, and Installation Information provided, in accord
|
||||||
|
with this section must be in a format that is publicly documented (and with
|
||||||
|
an implementation available to the public in source code form), and must require
|
||||||
|
no special password or key for unpacking, reading or copying.
|
||||||
|
|
||||||
|
7. Additional Terms.
|
||||||
|
|
||||||
|
"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.
|
||||||
|
|
||||||
|
Notwithstanding any other provision of this License, for material you add
|
||||||
|
to a covered work, you may (if authorized by the copyright holders of that
|
||||||
|
material) supplement the terms of this License with terms:
|
||||||
|
|
||||||
|
a) Disclaiming warranty or limiting liability differently from the terms of
|
||||||
|
sections 15 and 16 of this License; or
|
||||||
|
|
||||||
|
b) Requiring preservation of specified reasonable legal notices or author
|
||||||
|
attributions in that material or in the Appropriate Legal Notices displayed
|
||||||
|
by works containing it; or
|
||||||
|
|
||||||
|
c) Prohibiting misrepresentation of the origin of that material, or requiring
|
||||||
|
that modified versions of such material be marked in reasonable ways as different
|
||||||
|
from the original version; or
|
||||||
|
|
||||||
|
d) Limiting the use for publicity purposes of names of licensors or authors
|
||||||
|
of the material; or
|
||||||
|
|
||||||
|
e) Declining to grant rights under trademark law for use of some trade names,
|
||||||
|
trademarks, or service marks; or
|
||||||
|
|
||||||
|
f) Requiring indemnification of licensors and authors of that material by
|
||||||
|
anyone who conveys the material (or modified versions of it) with contractual
|
||||||
|
assumptions of liability to the recipient, for any liability that these contractual
|
||||||
|
assumptions directly impose on those licensors and authors.
|
||||||
|
|
||||||
|
All other non-permissive additional terms are considered "further restrictions"
|
||||||
|
within the meaning of section 10. If the Program as you received it, or any
|
||||||
|
part of it, contains a notice stating that it is governed by this License
|
||||||
|
along with a term that is a further restriction, you may remove that term.
|
||||||
|
If a license document contains a further restriction but permits relicensing
|
||||||
|
or conveying under this License, you may add to a covered work material governed
|
||||||
|
by the terms of that license document, provided that the further restriction
|
||||||
|
does not survive such relicensing or conveying.
|
||||||
|
|
||||||
|
If you add terms to a covered work in accord with this section, you must place,
|
||||||
|
in the relevant source files, a statement of the additional terms that apply
|
||||||
|
to those files, or a notice indicating where to find the applicable terms.
|
||||||
|
|
||||||
|
Additional terms, permissive or non-permissive, may be stated in the form
|
||||||
|
of a separately written license, or stated as exceptions; the above requirements
|
||||||
|
apply either way.
|
||||||
|
|
||||||
|
8. Termination.
|
||||||
|
|
||||||
|
You may not propagate or modify a covered work except as expressly provided
|
||||||
|
under this License. Any attempt otherwise to propagate or modify it is void,
|
||||||
|
and will automatically terminate your rights under this License (including
|
||||||
|
any patent licenses granted under the third paragraph of section 11).
|
||||||
|
|
||||||
|
However, if you cease all violation of this License, then your license from
|
||||||
|
a particular copyright holder is reinstated (a) provisionally, unless and
|
||||||
|
until the copyright holder explicitly and finally terminates your license,
|
||||||
|
and (b) permanently, if the copyright holder fails to notify you of the violation
|
||||||
|
by some reasonable means prior to 60 days after the cessation.
|
||||||
|
|
||||||
|
Moreover, your license from a particular copyright holder is reinstated permanently
|
||||||
|
if the copyright holder notifies you of the violation by some reasonable means,
|
||||||
|
this is the first time you have received notice of violation of this License
|
||||||
|
(for any work) from that copyright holder, and you cure the violation prior
|
||||||
|
to 30 days after your receipt of the notice.
|
||||||
|
|
||||||
|
Termination of your rights under this section does not terminate the licenses
|
||||||
|
of parties who have received copies or rights from you under this License.
|
||||||
|
If your rights have been terminated and not permanently reinstated, you do
|
||||||
|
not qualify to receive new licenses for the same material under section 10.
|
||||||
|
|
||||||
|
9. Acceptance Not Required for Having Copies.
|
||||||
|
|
||||||
|
You are not required to accept this License in order to receive or run a copy
|
||||||
|
of the Program. Ancillary propagation of a covered work occurring solely as
|
||||||
|
a consequence of using peer-to-peer transmission to receive a copy likewise
|
||||||
|
does not require acceptance. However, nothing other than this License grants
|
||||||
|
you permission to propagate or modify any covered work. These actions infringe
|
||||||
|
copyright if you do not accept this License. Therefore, by modifying or propagating
|
||||||
|
a covered work, you indicate your acceptance of this License to do so.
|
||||||
|
|
||||||
|
10. Automatic Licensing of Downstream Recipients.
|
||||||
|
|
||||||
|
Each time you convey a covered work, the recipient automatically receives
|
||||||
|
a license from the original licensors, to run, modify and propagate that work,
|
||||||
|
subject to this License. You are not responsible for enforcing compliance
|
||||||
|
by third parties with this License.
|
||||||
|
|
||||||
|
An "entity transaction" is a transaction transferring control of an organization,
|
||||||
|
or substantially all assets of one, or subdividing an organization, or merging
|
||||||
|
organizations. If propagation of a covered work results from an entity transaction,
|
||||||
|
each party to that transaction who receives a copy of the work also receives
|
||||||
|
whatever licenses to the work the party's predecessor in interest had or could
|
||||||
|
give under the previous paragraph, plus a right to possession of the Corresponding
|
||||||
|
Source of the work from the predecessor in interest, if the predecessor has
|
||||||
|
it or can get it with reasonable efforts.
|
||||||
|
|
||||||
|
You may not impose any further restrictions on the exercise of the rights
|
||||||
|
granted or affirmed under this License. For example, you may not impose a
|
||||||
|
license fee, royalty, or other charge for exercise of rights granted under
|
||||||
|
this License, and you may not initiate litigation (including a cross-claim
|
||||||
|
or counterclaim in a lawsuit) alleging that any patent claim is infringed
|
||||||
|
by making, using, selling, offering for sale, or importing the Program or
|
||||||
|
any portion of it.
|
||||||
|
|
||||||
|
11. Patents.
|
||||||
|
|
||||||
|
A "contributor" is a copyright holder who authorizes use under this License
|
||||||
|
of the Program or a work on which the Program is based. The work thus licensed
|
||||||
|
is called the contributor's "contributor version".
|
||||||
|
|
||||||
|
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.
|
||||||
|
|
||||||
|
Each contributor grants you a non-exclusive, worldwide, royalty-free patent
|
||||||
|
license under the contributor's essential patent claims, to make, use, sell,
|
||||||
|
offer for sale, import and otherwise run, modify and propagate the contents
|
||||||
|
of its contributor version.
|
||||||
|
|
||||||
|
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.
|
||||||
|
|
||||||
|
If, pursuant to or in connection with a single transaction or arrangement,
|
||||||
|
you convey, or propagate by procuring conveyance of, a covered work, and grant
|
||||||
|
a patent license to some of the parties receiving the covered work authorizing
|
||||||
|
them to use, propagate, modify or convey a specific copy of the covered work,
|
||||||
|
then the patent license you grant is automatically extended to all recipients
|
||||||
|
of the covered work and works based on it.
|
||||||
|
|
||||||
|
A patent license is "discriminatory" if it does not include within the scope
|
||||||
|
of its coverage, prohibits the exercise of, or is conditioned on the non-exercise
|
||||||
|
of one or more of the rights that are specifically granted under this License.
|
||||||
|
You may not convey a covered work if you are a party to an arrangement with
|
||||||
|
a third party that is in the business of distributing software, under which
|
||||||
|
you make payment to the third party based on the extent of your activity of
|
||||||
|
conveying the work, and under which the third party grants, to any of the
|
||||||
|
parties who would receive the covered work from you, a discriminatory patent
|
||||||
|
license (a) in connection with copies of the covered work conveyed by you
|
||||||
|
(or copies made from those copies), or (b) primarily for and in connection
|
||||||
|
with specific products or compilations that contain the covered work, unless
|
||||||
|
you entered into that arrangement, or that patent license was granted, prior
|
||||||
|
to 28 March 2007.
|
||||||
|
|
||||||
|
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
|
||||||
|
|
||||||
How to Apply These Terms to Your New Programs
|
How to Apply These Terms to Your New Programs
|
||||||
|
|
||||||
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.
|
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.
|
||||||
|
|
||||||
To do so, attach the following notices to the program. It is safest to attach them to the start of each source file to most effectively state the exclusion of warranty; and each file should have at least the “copyright” line and a pointer to where the full notice is found.
|
To do so, attach the following notices to the program. It is safest to attach
|
||||||
|
them to the start of each source file to most effectively state the exclusion
|
||||||
|
of warranty; and each file should have at least the "copyright" line and a
|
||||||
|
pointer to where the full notice is found.
|
||||||
|
|
||||||
<one line to give the program's name and a brief idea of what it does.>
|
<one line to give the program's name and a brief idea of what it does.>
|
||||||
Copyright (C) <year> <name of author>
|
|
||||||
|
|
||||||
This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.
|
Copyright (C) <year> <name of author>
|
||||||
|
|
||||||
This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
|
This program is free software: you can redistribute it and/or modify it under
|
||||||
|
the terms of the GNU General Public License as published by the Free Software
|
||||||
|
Foundation, either version 3 of the License, or (at your option) any later
|
||||||
|
version.
|
||||||
|
|
||||||
You should have received a copy of the GNU General Public License along with this program. If not, see <http://www.gnu.org/licenses/>.
|
This program is distributed in the hope that it will be useful, but WITHOUT
|
||||||
|
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.
|
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:
|
If the program does terminal interaction, make it output a short notice like
|
||||||
|
this when it starts in an interactive mode:
|
||||||
|
|
||||||
<program> Copyright (C) <year> <name of author>
|
<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.
|
|
||||||
|
|
||||||
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'.
|
||||||
|
|
||||||
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 <http://www.gnu.org/licenses/>.
|
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>.
|
||||||
|
|
|
||||||
|
|
@ -1,3 +1,3 @@
|
||||||
# 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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|
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|
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|
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|
After Width: | Height: | Size: 169 KiB |
|
|
@ -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 [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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|
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|
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|
After Width: | Height: | Size: 28 KiB |
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|
After Width: | Height: | Size: 16 KiB |
|
|
@ -0,0 +1,442 @@
|
||||||
|
\documentclass[10pt]{article}
|
||||||
|
\usepackage{pgf,tikz,pgfplots}
|
||||||
|
\pgfplotsset{compat=1.15}
|
||||||
|
\usepackage{mathrsfs}
|
||||||
|
\usetikzlibrary{arrows}
|
||||||
|
\pagestyle{empty}
|
||||||
|
\begin{document}
|
||||||
|
\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=2.0cm,y=3.0cm]
|
||||||
|
\begin{axis}[
|
||||||
|
x=2.0cm,y=3.0cm,
|
||||||
|
axis lines=middle,
|
||||||
|
ymajorgrids=true,
|
||||||
|
xmajorgrids=true,
|
||||||
|
xmin=-0.5,
|
||||||
|
xmax=5.5,
|
||||||
|
ymin=-0.5,
|
||||||
|
ymax=2.5,
|
||||||
|
ylabel={Spenning [V]},
|
||||||
|
xlabel={Tid [$\tau$]},
|
||||||
|
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@ -0,0 +1,401 @@
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|
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|
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|
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|
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|
@ -0,0 +1,433 @@
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
||||||
|
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|
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|
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|
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|
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||||||
|
\draw[line width=2.pt,color=qqwuqq] (5.3900000799999965,0.009762622157463333) -- (5.4037500699999965,0.00962930485663323);
|
||||||
|
\draw[line width=2.pt,color=qqwuqq] (5.4037500699999965,0.00962930485663323) -- (5.4175000599999965,0.009497808122287617);
|
||||||
|
\draw[line width=2.pt,color=qqwuqq] (5.4175000599999965,0.009497808122287617) -- (5.4312500499999965,0.009368107092969627);
|
||||||
|
\draw[line width=2.pt,color=qqwuqq] (5.4312500499999965,0.009368107092969627) -- (5.4450000399999965,0.009240177246727726);
|
||||||
|
\draw[line width=2.pt,color=qqwuqq] (5.4450000399999965,0.009240177246727726) -- (5.4587500299999965,0.009113994396479473);
|
||||||
|
\draw[line width=2.pt,color=qqwuqq] (5.4587500299999965,0.009113994396479473) -- (5.4725000199999965,0.008989534685438576);
|
||||||
|
\draw[line width=2.pt,color=qqwuqq] (5.4725000199999965,0.008989534685438576) -- (5.4862500099999965,0.008866774582604415);
|
||||||
|
\draw[line width=2.pt,color=qqwuqq] (5.4862500099999965,0.008866774582604415) -- (5.4999999999999964,0.008745690878313134);
|
||||||
|
\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);
|
||||||
|
\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}
|
||||||
Binary file not shown.
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|
|
@ -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 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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|
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|
|
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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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|
|
@ -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 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}
|
||||||
Binary file not shown.
|
|
@ -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)
|
||||||
|
|
||||||
|
|
||||||
|
|
@ -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)
|
||||||
|
|
||||||
|
|
||||||
|
|
@ -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)
|
||||||
|
|
||||||
|
|
||||||
Binary file not shown.
|
After Width: | Height: | Size: 30 KiB |
|
|
@ -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
|
||||||
|
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
|
||||||
|
45.7305,-0.00532245,-0.0151413,-1.47166
|
||||||
|
48.1075,-0.00547021,-0.0159066,-1.54728
|
||||||
|
50.6081,-0.00517615,-0.0173125,-1.62645
|
||||||
|
53.2386,-0.0050528,-0.0183198,-1.70792
|
||||||
|
56.0059,-0.00538225,-0.0192564,-1.79434
|
||||||
|
58.917,-0.0053449,-0.0202372,-1.88548
|
||||||
|
61.9794,-0.00544656,-0.0216106,-1.98053
|
||||||
|
65.201,-0.00550144,-0.022905,-2.08071
|
||||||
|
68.59,-0.00564915,-0.0243751,-2.1851
|
||||||
|
72.1552,-0.00544825,-0.0261777,-2.29628
|
||||||
|
75.9057,-0.00531167,-0.027924,-2.41336
|
||||||
|
79.8512,-0.0052448,-0.0299534,-2.53401
|
||||||
|
84.0018,-0.00539383,-0.0318696,-2.66404
|
||||||
|
88.368,-0.00566807,-0.0338469,-2.79711
|
||||||
|
92.9613,-0.00558168,-0.0361629,-2.93891
|
||||||
|
97.7933,-0.00577305,-0.0389504,-3.08796
|
||||||
|
102.876,-0.00527313,-0.0417832,-3.2438
|
||||||
|
108.224,-0.00559215,-0.0446737,-3.40746
|
||||||
|
113.849,-0.00547246,-0.048086,-3.58008
|
||||||
|
119.767,-0.00530848,-0.0517561,-3.75967
|
||||||
|
125.992,-0.00557531,-0.0552902,-3.95007
|
||||||
|
132.541,-0.00536839,-0.0594675,-4.15219
|
||||||
|
139.43,-0.00523049,-0.0641689,-4.36139
|
||||||
|
146.678,-0.00526805,-0.068836,-4.58326
|
||||||
|
154.302,-0.00551183,-0.0742347,-4.81298
|
||||||
|
162.322,-0.00520949,-0.0801541,-5.05723
|
||||||
|
170.759,-0.00539274,-0.0864603,-5.3143
|
||||||
|
179.635,-0.00590949,-0.0933259,-5.58317
|
||||||
|
188.972,-0.00538619,-0.101251,-5.86634
|
||||||
|
198.795,-0.00518577,-0.109384,-6.16444
|
||||||
|
209.128,-0.0055917,-0.118142,-6.47923
|
||||||
|
219.998,-0.00548197,-0.128142,-6.80825
|
||||||
|
231.433,-0.0056232,-0.138748,-7.15653
|
||||||
|
243.463,-0.00544606,-0.150422,-7.52181
|
||||||
|
256.118,-0.00561499,-0.163397,-7.90551
|
||||||
|
269.43,-0.00534262,-0.17782,-8.31212
|
||||||
|
283.435,-0.00570721,-0.193078,-8.74015
|
||||||
|
298.167,-0.00559709,-0.209895,-9.19166
|
||||||
|
313.666,-0.0053281,-0.228781,-9.66573
|
||||||
|
329.969,-0.00557465,-0.249558,-10.1691
|
||||||
|
347.121,-0.0054418,-0.272464,-10.6997
|
||||||
|
365.164,-0.00500028,-0.297813,-11.2592
|
||||||
|
384.144,-0.0058747,-0.325873,-11.8502
|
||||||
|
404.112,-0.00593924,-0.356397,-12.4764
|
||||||
|
425.117,-0.00577392,-0.391047,-13.144
|
||||||
|
447.214,-0.0055284,-0.429207,-13.8464
|
||||||
|
470.459,-0.00541712,-0.472221,-14.5937
|
||||||
|
494.913,-0.00561611,-0.519669,-15.3865
|
||||||
|
520.638,-0.00591756,-0.572987,-16.2316
|
||||||
|
547.7,-0.00559437,-0.633294,-17.1321
|
||||||
|
576.168,-0.00564262,-0.701158,-18.0914
|
||||||
|
606.117,-0.00572966,-0.77783,-19.1153
|
||||||
|
637.622,-0.00561941,-0.86511,-20.2107
|
||||||
|
670.764,-0.00599837,-0.964436,-21.3856
|
||||||
|
705.63,-0.00600291,-1.07843,-22.6453
|
||||||
|
742.307,-0.00597806,-1.2097,-23.9973
|
||||||
|
780.891,-0.00649728,-1.36134,-25.4537
|
||||||
|
821.481,-0.00581668,-1.53865,-27.0226
|
||||||
|
864.18,-0.00694608,-1.74573,-28.7155
|
||||||
|
909.099,-0.00683892,-1.99015,-30.5369
|
||||||
|
956.352,-0.00666713,-2.28027,-32.5032
|
||||||
|
1006.06,-0.00682924,-2.62797,-34.6139
|
||||||
|
1058.36,-0.00723345,-3.04851,-36.8706
|
||||||
|
1113.37,-0.00701525,-3.56212,-39.2585
|
||||||
|
1171.24,-0.00721427,-4.19514,-41.748
|
||||||
|
1232.12,-0.00627676,-4.98529,-44.2612
|
||||||
|
1296.16,-0.00828824,-5.98207,-46.6703
|
||||||
|
1363.53,-0.00712476,-7.26275,-48.6667
|
||||||
|
1434.41,-0.00784158,-8.93457,-49.6496
|
||||||
|
1508.97,-0.00770318,-11.161,-48.246
|
||||||
|
1587.4,-0.00798169,-14.1194,-40.9149
|
||||||
|
1669.91,-0.00749812,-17.3491,-18.5697
|
||||||
|
1756.71,-0.00623631,-17.4354,20.0198
|
||||||
|
1848.02,-0.00694516,-14.2128,43.2097
|
||||||
|
1944.08,-0.00648254,-11.192,50.8481
|
||||||
|
2045.13,-0.00745522,-8.91228,52.3001
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||||||
|
2151.43,-0.00684777,-7.19389,51.2377
|
||||||
|
2263.26,-0.00673777,-5.87635,49.1091
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||||||
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2380.9,-0.00589962,-4.84806,46.5311
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||||||
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||||||
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2634.85,-0.00510321,-3.38328,41.1268
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2771.8,-0.0047664,-2.85714,38.5313
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||||||
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2915.88,-0.00446474,-2.42779,36.0732
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||||||
|
3067.44,-0.00391824,-2.07449,33.7663
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||||||
|
3226.88,-0.00355361,-1.78134,31.6205
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||||||
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3394.61,-0.00341895,-1.53735,29.6276
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||||||
|
3571.05,-0.00350624,-1.33174,27.7739
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||||||
|
3756.67,-0.00331146,-1.1588,26.0669
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||||||
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3951.94,-0.00231351,-1.01238,24.479
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4157.36,-0.00225369,-0.886585,23.0086
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|
4373.45,-0.00139882,-0.778564,21.6437
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4600.77,-0.00102246,-0.686038,20.3781
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|
4839.91,-0.000220647,-0.606433,19.1892
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|
5091.49,0.00105067,-0.537312,18.0879
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5356.13,0.00167097,-0.476906,17.0608
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|
5634.54,0.00162972,-0.424867,16.0998
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|
5927.41,0.00207173,-0.378397,15.2028
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|
6235.51,0.00112702,-0.338463,14.3593
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|
6559.62,0.00372765,-0.302806,13.5651
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|
6900.58,0.000302864,-0.271531,12.8235
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|
7259.27,0.00538512,-0.244025,12.1227
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|
7636.59,0.00663817,-0.219858,11.4623
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|
8033.53,-0.00340019,-0.197586,10.8473
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|
8451.1,0.00407549,-0.179074,10.2594
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9838.61,0.0101511,-0.13357,8.69056
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10350,0.011041,-0.121674,8.22173
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10888,0.0111862,-0.110205,7.77288
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11453.9,0.0134568,-0.101829,7.3539
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12049.3,0.0143843,-0.0925829,6.95629
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12675.6,0.0109394,-0.0856871,6.57951
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13334.4,0.0107169,-0.0779623,6.21708
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14027.6,0.0159309,-0.0715899,5.87416
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|
14756.7,0.0168666,-0.0671844,5.55194
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15523.7,0.00627492,-0.0613767,5.23519
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|
16330.6,0.0184252,-0.0579301,4.94486
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|
17179.5,0.0197432,-0.0538634,4.65643
|
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|
18072.4,0.0210424,-0.0503017,4.38578
|
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|
19011.8,0.0220391,-0.0471414,4.13298
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|
20000,0.0186899,-0.043639,3.88622
|
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|
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Reference in New Issue