NETWORK ANALYSIS (3)

Nodal equation and superposition theorem

Nodal equation method:

Nodal equation method makes the calculation of a network easier.  This is somewhat similar to the 1^st KCL, but little bit different. Actually the first law of KCL gives a relation of current flowing in to a node. See the previous post on KCL for more. Here we use the equation to find the potential of a point referred to another point (most usually a grounded point).

As the name implies, this method is applying to a node in the network. See figure 9.1

In this case we assume that current in each branch is leaving the point. See point B in figure 9.1. Current is leaving the point.

We mark the potential of point b is V and point D is grounded. Usually in networks we ground the circuit.

So we can write following equations,

(V-V₁)/R₁ = I₁

 (V-V₂)/R₂ = I₂

 (V-0)/R₃ = I₃

From KCL 1

I₁ + I₂ + I₃ = 0

By combining these equations we get the nodal equation

Apply nodal equation to point B

(V-V₁)/R₁  +  (V-V₂)/R₂  + (V-0)/R₃ = 0

So if we know the R values, V₁ & V₂ we can find V.

This method is frequently usin0g in network analyzing. Of course it is a very easier method to apply. We will use this method in many of our examples in future.

Super position theorem:

When there are number of voltage or current sources acting simultaneously in a network, we can use this theorem to simplify the calculation.

According to this theorem each source can be treated as if it acts independently of the other. Hence we can calculate the effect of one source at a time and then add them algebraically. Figure 9.2 will clearly clarify this theorem.

 So we can write the equation,

I = I1 + I2

This way you can calculate the current in any branch.

Using this method we can simplify our calculation though the network is too much complicated.

If you have any problems please leave it as a comment. I wii reply as soon as possible.

pabindu lakshitha

B.Sc (engineering undergraduate)