BRANCH :- E & TC ENGINEERING

SEMESTER :- 3^RD

SUBJECT :- CIRCUIT THEORY

CHAPTER :- 2 – NETWORK THEORM

TOPIC :- THEVNIN & NORTON

AY-2021-2022

FACULTY :- Er. Biswajit Mandal(Sr. Lecturer Electrical department)

Presentation On:-

Thevenin & Norton Theorem

THEVENIN & NORTON

THEVENIN’S THEOREM:

Consider the following:

Network

1

Network

2

•

•

A

B

Figure 5.1: Coupled networks.

For purposes of discussion, at this point, we consider

that both networks are composed of resistors and

independent voltage and current sources

1

THEVENIN & NORTON

THEVENIN’S THEOREM:

Suppose Network 2 is detached from Network 1 and

we focus temporarily only on Network 1.

Network

1

•

•

A

B

Figure 5.2: Network 1, open-circuited.

Network 1 can be as complicated in structure as one

can imagine. Maybe 45 meshes, 387 resistors, 91

voltage sources and 39 current sources.

2

Network

1

•

•

A

B

THEVENIN & NORTON

THEVENIN’S THEOREM:

Now place a voltmeter across terminals A-B and

read the voltage. We call this the open-circuit voltage.

​

No matter how complicated Network 1 is, we read one

voltage. It is either positive at A, (with respect to B)

or negative at A.

​

We call this voltage V_os and we also call it V_THEVENIN = V_TH

3

THEVENIN & NORTON

THEVENIN’S THEOREM:

• We now deactivate all sources of Network 1.

​

• To deactivate a voltage source, we remove

the source and replace it with a short circuit.

​

• To deactivate a current source, we remove

the source.

4

THEVENIN & NORTON

THEVENIN’S THEOREM:

Consider the following circuit.

Figure 5.3: A typical circuit with independent sources

How do we deactivate the sources of this circuit?

5

THEVENIN & NORTON

THEVENIN’S THEOREM:

When the sources are deactivated the circuit appears

as in Figure 5.4.

Figure 5.4: Circuit of Figure 5.3 with sources deactivated

Now place an ohmmeter across A-B and read the resistance.

If R₁= R₂ = R₄= 20 Ω and R₃=5 Ω then the meter reads 5 Ω.

6

THEVENIN & NORTON

THEVENIN’S THEOREM:

We call the ohmmeter reading, under these conditions,

R_THEVENIN and shorten this to R_TH. Therefore, the

important results are that we can replace Network 1

with the following network.

Figure 5.5: The Thevenin equivalent structure.

7

THEVENIN & NORTON

THEVENIN’S THEOREM:

We can now tie (reconnect) Network 2 back to

terminals A-B.

Figure 5.6: System of Figure 5.1 with Network 1

replaced by the Thevenin equivalent circuit.

We can now make any calculations we desire within

Network 2 and they will give the same results as if we

still had Network 1 connected.

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THEVENIN & NORTON

THEVENIN’S THEOREM:

It follows that we could also replace Network 2 with a

Thevenin voltage and Thevenin resistance. The results

would be as shown in Figure 5.7.

Figure 5.7: The network system of Figure 5.1

replaced by Thevenin voltages and resistances.

9

THEVENIN & NORTON

THEVENIN’S THEOREM: Example 5.1.

Find V_X by first finding V_TH and R_TH to the left of A-B.

Figure 5.8: Circuit for Example 5.1.

5

First remove everything to the right of A-B.

THEVENIN & NORTON

THEVENIN’S THEOREM: Example 5.1. continued

Figure 5.9: Circuit for finding V_TH for Example 5.1.

Notice that there is no current flowing in the 4 Ω resistor

(A-B) is open. Thus there can be no voltage across the

resistor.

11

THEVENIN & NORTON

THEVENIN’S THEOREM: Example 5.1. continued

We now deactivate the sources to the left of A-B and find

the resistance seen looking in these terminals.

R_TH

Figure 5.5: Circuit for find R_TH for Example 5.5.

We see,

R_TH = 12||6 + 4 = 8 Ω

12

THEVENIN & NORTON

THEVENIN’S THEOREM: Example 5.1. continued

After having found the Thevenin circuit, we connect this

to the load in order to find V_X.

Figure 5.11: Circuit of Ex 5.1 after connecting Thevenin

circuit.

13

THEVENIN & NORTON

THEVENIN’S THEOREM:

In some cases it may become tedious to find R_TH by reducing

the resistive network with the sources deactivated. Consider

the following:

Figure 5.12: A Thevenin circuit with the output shorted.

We see;

14

Eq 5.1

THEVENIN & NORTON

THEVENIN’S THEOREM: Example 5.2.

For the circuit in Figure 5.13, find R_TH by using Eq 5.1.

Figure 5.13: Given circuit with load shorted

The task now is to find I_SS. One way to do this is to replace

the circuit to the left of C-D with a Thevenin voltage and

Thevenin resistance.

15

THEVENIN & NORTON

THEVENIN’S THEOREM: Example 5.2. continued

Applying Thevenin’s theorem to the left of terminals C-D

and reconnecting to the load gives,

Figure 5.14: Thevenin reduction for Example 5.2.

16

THEVENIN & NORTON

THEVENIN’S THEOREM: Example 5.3

For the circuit below, find V_AB by first finding the Thevenin

circuit to the left of terminals A-B.

Figure 5.15: Circuit for Example 5.3.

We first find V_TH with the 17 Ω resistor removed.

Next we find R_TH by looking into terminals A-B

with the sources deactivated.

17

THEVENIN & NORTON

THEVENIN’S THEOREM: Example 5.3 continued

Figure 5.16: Circuit for finding V_OC for Example 5.3.

18

THEVENIN & NORTON

THEVENIN’S THEOREM: Example 5.3 continued

Figure 5.17: Circuit for find R_TH for Example 5.3.

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THEVENIN & NORTON

THEVENIN’S THEOREM: Example 5.3 continued

Figure 5.18: Thevenin reduced circuit for Example 5.3.

We can easily find that,

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THEVENIN & NORTON

THEVENIN’S THEOREM: Example 5.4: Working

with a mix of independent and dependent sources.

​

Find the voltage across the 50 Ω load resistor by first finding

the Thevenin circuit to the left of terminals A-B.

Figure 5.19: Circuit for Example 5.4

21

THEVENIN & NORTON

THEVENIN’S THEOREM: Example 5.4: continued

First remove the 50 Ω load resistor and find V_AB = V_TH to

the left of terminals A-B.

Figure 5.20: Circuit for find V_TH, Example 5.4.

22

THEVENIN & NORTON

THEVENIN’S THEOREM: Example 5.4: continued

To find R_TH we deactivate all independent sources but retain

all dependent sources as shown in Figure 5.21.

Figure 5.21: Example 5.4, independent sources deactivated.

We cannot find R_TH of the above circuit, as it stands. We

must apply either a voltage or current source at the load

and calculate the ratio of this voltage to current to find R_TH.

23

THEVENIN & NORTON

THEVENIN’S THEOREM: Example 5.4: continued

Figure 5.22: Circuit for find R_TH, Example 5.4.

Around the loop at the left we write the following equation:

From which

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THEVENIN & NORTON

THEVENIN’S THEOREM: Example 5.4: continued

Figure 5.23: Circuit for find R_TH, Example 5.4.

Using the outer loop, going in the cw direction, using drops;

or

25

THEVENIN & NORTON

THEVENIN’S THEOREM: Example 5.4: continued

The Thevenin equivalent circuit tied to the 50 Ω load

resistor is shown below.

Figure 5.24: Thevenin circuit tied to load, Example 5.4.

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THEVENIN & NORTON

THEVENIN’S THEOREM: Example 5.5: Finding

the Thevenin circuit when only resistors and dependent

sources are present. Consider the circuit below. Find V_xy

by first finding the Thevenin circuit to the left of x-y.

Figure 5.25: Circuit for Example 5.5.

For this circuit, it would probably be easier to use mesh or nodal analysis to find V_xy. However, the purpose is to illustrate Thevenin’s theorem.

27

THEVENIN & NORTON

THEVENIN’S THEOREM: Example 5.5: continued

We first reconcile that the Thevenin voltage for this circuit

must be zero. There is no “juice” in the circuit so there cannot

be any open circuit voltage except zero. This is always true

when the circuit is made up of only dependent sources and

resistors.

To find R_TH we apply a 1 A source and determine V for

the circuit below.

Figure 5.26: Circuit for find R_TH, Example 5.5.

THEVENIN & NORTON

THEVENIN’S THEOREM: Example 5.5: continued

Figure 5.27: Circuit for find R_TH, Example 5.5.

Write KVL around the loop at the left, starting at “m”, going

cw, using drops:

29

THEVENIN & NORTON

THEVENIN’S THEOREM: Example 5.5: continued

Figure 5.28: Determining R_TH for Example 5.5.

We write KVL for the loop to the right, starting at n, using

drops and find;

or

THEVENIN & NORTON

THEVENIN’S THEOREM: Example 5: continued

We know that,

where V = 50 and I = 1.

Thus, R_TH = 50 Ω. The Thevenin circuit tied to the

load is given below.

Figure 5.29: Thevenin circuit tied to the load, Example 5.5.

Obviously, V_XY = 50 V

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THEVENIN & NORTON

NORTON’S THEOREM:

Assume that the network enclosed below is composed

of independent sources and resistors.

Network

Norton’s Theorem states that this network can be

replaced by a current source shunted by a resistance R.

33

THEVENIN & NORTON

NORTON’S THEOREM:

In the Norton circuit, the current source is the short circuit

current of the network, that is, the current obtained by

shorting the output of the network. The resistance is the

resistance seen looking into the network with all sources

deactivated. This is the same as R_TH.

THEVENIN & NORTON

NORTON’S THEOREM:

We recall the following from source transformations.

In view of the above, if we have the Thevenin equivalent

circuit of a network, we can obtain the Norton equivalent

by using source transformation.

However, this is not how we normally go about finding

the Norton equivalent circuit.

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THEVENIN & NORTON

NORTON’S THEOREM: Example 5.6.

Find the Norton equivalent circuit to the left of terminals A-B

for the network shown below. Connect the Norton equivalent

circuit to the load and find the current in the 50 Ω resistor.

Figure 5.30: Circuit for Example 5.6.

35

THEVENIN & NORTON

NORTON’S THEOREM: Example 5.6. continued

Figure 5.31: Circuit for find I_NORTON.

It can be shown by standard circuit analysis that

36

THEVENIN & NORTON

NORTON’S THEOREM: Example 5.6. continued

It can also be shown that by deactivating the sources,

We find the resistance looking into terminals A-B is

R_N and R_TH will always be the same value for a given circuit.

The Norton equivalent circuit tied to the load is shown below.

Figure 5.32: Final circuit for Example 5.6.

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THEVENIN & NORTON

NORTON’S THEOREM: Example 5.7. This example

illustrates how one might use Norton’s Theorem in electronics.

the following circuit comes close to representing the model of a

transistor.

For the circuit shown below, find the Norton equivalent circuit

to the left of terminals A-B.

Figure 5.33: Circuit for Example 5.7.

38

THEVENIN & NORTON

NORTON’S THEOREM: Example 5.7. continued

We first find;

We first find V_OS:

39

THEVENIN & NORTON

NORTON’S THEOREM: Example 5.7. continued

Figure 5.34: Circuit for find I_SS, Example 5.7.

We note that I_SS = - 25I_S. Thus,

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THEVENIN & NORTON

NORTON’S THEOREM: Example 5.7. continued

Figure 5.35: Circuit for find V_OS, Example 5.7.

From the mesh on the left we have;

From which,

41

THEVENIN & NORTON

NORTON’S THEOREM: Example 5.7. continued

We saw earlier that,

Therefore;

The Norton equivalent circuit is shown below.

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Norton Circuit for Example 5.7

THEVENIN & NORTON

Extension of Example 5.7:

Using source transformations we know that the

Thevenin equivalent circuit is as follows:

Figure 5.36: Thevenin equivalent for Example 5.7.

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