1. Electrical Engineering and Industrial Electronics
Hu Ailing
Tel:
Office: Yifu Building 104

2. Review What is superposition principle?
The general steps to apply superposition principle?
What is the source transformation?

3. Solution for the Wednesday assignment.

4. 2.7 Thevenin and Norton Equivalent Circuits
Now that we have been introduced to the superposition principle and source transformation, it is possible to develop two more techniques that will greatly simplify the analysis of many linear circuits.

5. 1.Thevenin’s Theorem
It often occurs in practice that a particular element in a circuit is variable (usually called the load) while other elements are fixed.
As a typical example, a household outlet terminal may be connected to different appliances constituting a variable load.
Each time the variable element is changed, the entire circuit has to be analyzed all over again.
To avoid this problem, Thevenin’s theorem provides a technique by which the fixed part of the circuit is replaced by an equivalent circuit.

6. The load in the figure may be a single resistor or another circuit. I
Linear
Two-terminal
Circuit a b I
According to Thevenin’s theorem, the linear circuit in Fig.(a) can be replaced by that in Fig.(b).
Load + _ v
Figure (a)
vTh
RTh + –
The load in the figure may be a single resistor or another circuit. I a
Linear
Two-terminal
Circuit
Load + v _
The circuit to the left of the terminals a-b in Fig.(b) is known as the Thevenin equivalent circuit; b
Figure (b)
It was developed in 1883 by M.Leon Thevenin ( ), a French telegraph engineer.

7. Thevenin’s theorem states that a linear two-terminal circuit can be replaced by an equivalent circuit consisting of a voltage source vTh in series with a resistor RTh, where vTh is the open-circuit voltage at the terminals and RTh is the equivalent resistance at the terminals when the independent sources are turned off.
Our major concern right now is how to find the Thevenin equivalent voltage vTh and resistance RTh.
Linear
Two-terminal
Circuit a b
Linear circuit with
all independent
sources set
equal to zero a b +
Req
vOC _
vTh = vOC
RTh = Req

8. 2.Norton’s Theorem
In 1926, about 43 years after Thevenin published his theorem, E.L. Norton, an American engineer at Bell Telephone Laboratories, proposed a similar theorem.
Norton’s theorem states that a linear two-terminal circuit can be replaced by an equivalent circuit consisting of a current source IN in parallel with a resistor RN, where IN is the short-circuit current through the terminals and RN is the equivalent resistance at the terminals when the independent sources are turned off.

9. Linear Two-terminal Circuit a b I Load + _ v vTh RTh + – I a Linear
According to Norton’s theorem, the linear circuit in Fig.(a) can be replaced by that in Fig.(c). + _ v
Figure (a)
vTh
RTh + – I a
Linear
Two-terminal
Circuit
Load +
The circuit to the left of the terminals a-b in Fig.(c) is known as the Norton equivalent circuit; v _ b
Figure (b) I a
Linear
Two-terminal
Circuit
Load IN RN + v _ b
Figure (c)

10. Please notice the current direction!
For now, we are mainly concerned with how to get the Norton equivalent current IN and resistance RN.
Linear
Two-terminal
Circuit a b
Linear circuit with
all independent
sources set
equal to zero a b
Req
ISC
IN = ISC
RN = Req
Please notice the current direction!
We find RN in the same way we find RTh.

11. ∵ ∴ RTh I a + Load + vTh – v _ b I a IN + Load RN v _ b RN = RTh = Req
In fact, from what we know about source transformation, for the external circuit load, Fig.(b) is equivalent to Fig.(c).
Load + v _ b
Figure (b)
For this reason, source transformation is often called Thevenin-Norton transformation. I a
Load IN RN + v _ b
According to source transformation
Figure (c)
RN = RTh = Req ∵
vTh = vOC
IN = ISC ∴
We can calculate any two of the three using the method that takes the least effort and use them to get the third using Ohm’s law.

12. 3. The general steps for finding the Thevenin (or Norton) equivalent circuit
① Find vOC or ISC
By any method we have learned before
Three steps
② Find Req
③ Draw the equivalent circuit, please notice the directions about vOC or ISC.

13. Example ：
Find the Thevenin equivalent circuit of the circuit shown in the figure, to the left of the terminals a-b. _ a 2Ω 1A b 4Ω + 3V
Three steps
Solution:
①Find voc 3V + 2Ω 4Ω
By source transformation, we can obtain _ a - b +
voc 2Ω I
By KVL
-2+(2+2+4)I+3 = 0 2V +
I = A _
By Ohm’s law
voc = 4I = -0.5V

14. By turning off the independent sources Req= 4∥4 = 4/2 = 2Ω
2 Find Req
By turning off the independent sources
Req= 4∥4 = 4/2 = 2Ω a 2Ω b 4Ω
Req
③Draw the equivalent circuit a a Or 2Ω 2Ω
-0.5V
0.5V _ + _ + b b

15. ③Draw the equivalent circuit 2Ω 0.25A
If it is desired to Find the Norton equivalent circuit of the same circuit, to the left of the terminals a-b.
①Find ISC
ISC = -0.25A a
② Find Req
Req = 2Ω
③Draw the equivalent circuit 2Ω
0.25A b

16. Simulation :
video:

17. Assignment:
P142. practice 4.8; P147,practice 4.11

18. Thank you!