NETWORK ANALYSIS (4) thevenin's theorem

Thevenin’s Theorem

This is a very useful theorem which was introduced by French Engineer ML Thevenin(1857-1926).

Thevenin’s Theorem:

Any linear active bilateral network can be replaced by an equivalent of a voltage source in series with a resistance. The voltage source is open circuited voltage across the open circuited load terminals and the resistance being the internal resistance of the source network looking from the open circuited load terminals.

Of course it is little bit difficult to understand at once. It can be simplify as follows

This theorem says that, a given network when viewed from its any two terminal points can be replaced by a single voltage “V^th” source in series with a single resistance “R^th”.

See figure 10.1

Consider all the elements in the black box are not visible to the out side and we only have the two terminals (AB) as the output. All the elements in this black box can be represented by an equivalent single voltage source with a single series resistance. This voltage is called thevenin’s voltage and resistance is thevenin’s resistance. Let’s see how to find the values of this voltage and resistance.

The voltage across AB is called the thevinings voltage. We can use the analysis methods and laws we have learned so far to find the voltage across AB.

In figure 10.1 I have marked the voltage of point A as ‘V^/’ . As we have grounded the point D 

(D = B)  V^/ = V^th

So we can use the nodal equation method to find V^/

Applying nodal equation to point A

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

So if V₁ , R₁ , R₂ , R₃ are given, then we can find V^/ which is equal to V^th.

Note that it is not necessary to ground the circuit. But grounding makes the calculation easier. So we have to ground the suitable point according to the problem

To find the equivalent resistance first we remove the voltage sources and short circuit it. If ant current sources are available we also remove those sources and open circuit it. Then we find the equivalent resistance as seen from the two terminals A&B.

So in this problem our  R^th  = R₁//R₂//R₃

Now we have find R^th

Finally we can simplify the network as shown in figure 10.2

Wait till my next post for solved problems of thevenin’s theorem.

 In this example we don’t have any current sources however in solved problems I will add some problems with current sources.

If you have any problems regarding this post, please leave it as a comment. I will reply you as soon as possible.

Pabindu lakshitha

B.Sc(Engineering Undergraduate)