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**TOPOLOGY IN CIRCUIT ANALYSIS**

Terminology

The circuit of *figure A*
has **4 essential **nodes. In order for
this circuit to be analyzed, (4-1=3), **3 equations** are needed.

*figure A : example circuit*

*Figure B *
demonstrates the branch currents of *
figure A*.

*figure B*

On* figure C*, the 4
nodes of the circuit are numbered, and a
tree joins all the
nodes together creating a path.

*figure C*

A__
____tree__ is a set of
connecting branches that **connects every node to every other node**, **
passing only once from each node (does not form a **
loop**)**.

Some example trees of *figure A* can be:

*
i3-i4-i6
i2-i4-i5
*

*
i7-i6-i4*

Once a tree is defined, the remaining branches
are called** **__links__ or __chords__. A collection of these
links is called a __complementary tree__ or __cotree__.

A__ graph__ is the redrawing of the
circuit with each branch represented by a line, like *figure B *&* figure
C*.

*figure
B figure C*

A** **__cut-set__ is the **smallest**
set of branches which are** removed** from the graph in order to divide the
graph into **two groups of nodes**. Some example cut-sets, are shown in *
figure D(i) & D(ii)* below:

**
**

** **__cut-set__:
i1-i2-i3-i5-i6
* *__cut-set__:
i1-i2-i4-i6

figure D(i)
figure D(ii)

A__ fundamental loop__ is a loop
which contains one and only __one link__.
By observing *figure E*:

**
***figure E*

__fundamental loops__: i2-i4-i3,
i4-i6-i5, i1-i4-i3,

**i3-i4-i6-i7**** **

A** **__
fundamental cut-set__ is a cut-set which contains one and only **
one tree branch**. By observing *figure E*
above, an example of a fundamental cut-set is shown on *figure F* & G

* *

*
figure
F *

__fundamental cut-set__: i1-i2-i3-i7

*figure G*

__
fundamental cut-set__: i1-i2-i4-i5-i7