SUPER NODE

SUPER NODE:

           Consider a circuit shown in figure. In this circuit the nodes labelled V and V are connected directly through a voltage source without any circuit element. The region surrounding a voltage source which connects the two nodes directly is called super node.

 

        In such a case the nodes in a super node region can be analyzed separately and the relation between such node voltage's and a source voltages connecting then can be separately obtained in this circuit shown in figure we can write .

At super node:

V2-Vx-V3=0

V2-V3=Vx...................1equation

Applying KCL at node V2 and V3:

i1+i2+i3+i4=0

((V2-V1)/R2)+(V2/R3)+(V3/R4)+(V3-V1)/R1 ...........2rquation

Applying KCL at node V1:

i+i1+i4=0

i+((V2-V1)/R2)+((V3-V1)/R1)=0

((V2-V1)/R2)+((V3-V1)/R1)=-i .................3equation

 

NODE ANALYSIS

NODE ANALYSIS:

The method is mainly based on KCL this method uses the analysis of the different nodes of the network. We have already denoted a node. Every junction point in a network where two(or)more branches meet is called a node one of the nodes is assumed as referenced node whose potential is assumed to zero potential node(or)datum node. A other nodes the different voltages are to be measured with respect to this reference node the advantages of this method lies in the fact that we get (n-1) equations to solve. If there are 'n' nodes this reduces calculation work ,consider the following network shown in figure.

 

At node V1 applying KCL:

i1=i3+i4

i1=(V1-V0)/R1+(V1-V2)/R2

(V1/R1)+(V1/R2)-(V2/R2)=i1

((1/R1)+(1/R2))V1-(1/R2)V2=i1  ..........................1 equation

Applying KCL at node V2:

i2=i4+i5

=((V2-V1)/R2)+((V2-V0)/R3)

=(V2/R2)-(V1/R2)+(V2/R3)

=((1/R2)+(1/R3))V2-(V1/R2)

i2=(-V1/R2)+((1/R2)+(1/R3)V2 .......2equation

          As i1 and i2 are known we get two equations 1 and 2 with the two unknown V1 and V2 solving this equations simultaneously the node voltages V1 and V2 can be determined once V1 and V2 are known current through any branch of the network can be determined.