Tuesday, January 4, 2011

Network Graphs

Reference:
http://venus.ece.ndsu.nodak.edu/ece/academics/courses/ee206/notes/cirtop.htm


Graph: a representation of a circuit where each branch is denoted by a line segment.


Tree (of a graph): a set of branches (each denoted by a line segment) that connects every node to every other node via some path without forming a loop.


Tree branch: a branch of a graph that is part of a particular tree.



Cotree: those branches of a graph which are not part of a particular tree. This is also known as the complement of the tree.

Link: a branch of a cotree.

Cut set: a minimum set of branches that, when cut, will divide a graph into two separate parts.

Fundamental cut set: a cut set containing only a single tree branch.

Fundamental loop: A loop that results when a link is put into the tree.

cut set divides a graph into two independent parts. In terms of the original circuit, a KCL equation can be written for either part of the circuit divided by the cut; such a KCL equation is called a cut-set equation.

The dual of a fundamental cut set is a fundamental loop. Each time a link is inserted into a tree as a potential tree branch, a loop is formed in the tree (thus the resulting object is no longer a tree). Such a loop is called a fundamental loop.

 Tree-branch analysis uses KCL (Kirchhoff's Current Law) but no reference node is selected like is done in nodal analysis; all KCL equations are written in terms of tree branch voltages instead of node voltages.

Loop analysis uses KVL (Kirchhoff's Voltage Law) but the loops chosen may not necessarily be meshes. Instead, each loop needs to be a fundamental loopobtained by inserting a link into a tree.


There is only one graph for a circuit (although there may be many ways to draw it). 

Usually, there are several trees for a graph, and each tree has a corresponding cotree

6 comments:

Anonymous said...

Right hеre is thе perfect blog for everyonе who would like to
understand this topic. You know so much its almost hard to аrgue ωith
you (not thаt I really will nеed to…HaHa).
Υou certaіnly put a fresh spin on а topic thаt's been written about for a long time. Wonderful stuff, just wonderful!

Here is my web site ... Wiki.Justiceandenvironment.Org

Anonymous said...

Great poѕt. I was cheсking сonstantly this
blog and I'm impressed! Extremely useful information particularly the last part :) I care for such info a lot. I was looking for this particular information for a long time. Thank you and best of luck.

Feel free to visit my page; resistor calculation

Anonymous said...

Hі! Thіs is my fiгst сomment here so I ϳust ωanted to give a quick shout out and say I really
enjoy rеаding through your articles.

Can yоu гecommеnd аny
othег blogѕ/websitеs/forumѕ that go over the same subjects?
Thanks for yοur time!

Hеre is my wеb blog; ohms law

Anonymous said...

Now Ӏ am gоing aωay to ԁo mу breakfast, latеr than haѵіng my brеаkfaѕt coming
yet agаin tо reаd other nеwѕ.


Here іs my blog: potentiometer

Anonymous said...

Hi to every boԁy, іt's my first visit of this web site; this weblog consists of remarkable and in fact fine data for visitors.

Also visit my weblog: Adblurps.Com

Anonymous said...

Asking questіons are actually pleasant thing if уou аrе not understanԁing anуthing totally, hoωeveг this post ρrovides pleasant undеrstanding
even.

My ωeb blog - skidmoreacadtech.Com


Mindbox