### TOPOLOGY IN CIRCUIT ANALYSISLoop Analysis using Topology

Loop analysis is an alternative means of analysing a circuit. It is based on the mesh current technique. In this case, if the link currents are known then all the tree branch currents can be calculated. In this case  the current sources of the circuit are included, and the voltage sources of the circuit are excluded.

The independent equations that describe the circuit can be derived using the link currents as variables, by defining a loop current around each fundamental loop of the circuit.

An example circuit is shown in figure A together with its graph in figure B respectively:

figure A : the circuit

figure B : the graph of figure A

The tree is defined as shown in figure C (is the group of the black branches), together with the cotree (is the group of the green branches or  links).

figure C : tree & cotree

There are 4 nodes and 6 branches, therefore (6-(4-1)) = 3 equations are needed in order for the circuit to be analysed.

Three fundamental loops should be identified now:

figure D : loops & loop currents

 Loop Branches Associated Current a a-b-d-f ia b b-e-a ib c c-d-b ic

For loop A :

.......(1)

For loop B :

By observing loop B it is clear that ib = 7A, because of the current source that exists on the link branch e (see figures A & C). This demonstrates the advantage of placing current sources in links.

For loop C :

.................(2)

from (1) =>

.................................................(3)

from (2) =>

=>

ia = 2A

ic = 2.5A