# NORTON’S THEOREM

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```					 LECTURER 08

THEVENIN’S THEOREM
NORTON’S THEOREM
Thevenin’s Circuit
• The Thevenin’s circuit across a load is
defined as a serially connected Thevenin
Voltage source and a Thevenin resistance.

RTH
IL
VTH      RL

Lec 08                  2
Thevenin’s Theorem
Procedure
• Identify and remove the load
• Look in the load terminals and calculate VTH
• Remove all sources by replacing:
– voltage sources with a short
– current sources with an open
– If the source has an internal resistance, keep the
resistance in the circuit
• Look in the load terminals and calculate RTH
• Create a series circuit consisting of VTH, RTH, and the
• Calculate the load current or voltage as desired
Lec 08                         3
EXAMPLE 01

R1            R3

R2          RL
VS

Lec 08             4
STEP 01 & 02
• Identify and remove the load
• Look in the load terminals and calculate VTH
• Remove all sources by replacing:
– voltage sources with a short
– current sources with an open
– If the source has an internal resistance, keep the
resistance in the circuit
• Look in the load terminals and calculate RTH
• Create a series circuit consisting of VTH, RTH, and the
• Calculate the load current or voltage as desired
Lec 08                         5
+
VOC
-

VOC = VTH

Lec 08         6
STEP 03 & 04
• Identify and remove the load
• Look in the load terminals and calculate VOC
• Remove all sources by replacing:
– voltage sources with a short
– current sources with an open
– If the source has an internal resistance, keep the
resistance in the circuit
• Look in the load terminals and calculate RTH
• Create a series circuit consisting of VTH, RTH, and the
• Calculate the load current or voltage as desired
Lec 08                         7
RTH

Lec 08         8
STEP 05 & 06
• Identify and remove the load
• Look in the load terminals and calculate VOC
• Remove all sources by replacing:
– voltage sources with a short
– current sources with an open
– If the source has an internal resistance, keep the
resistance in the circuit
• Look in the load terminals and calculate RTH
• Create a series circuit consisting of VTH, RTH, and the
• Calculate the load current or voltage as desired
Lec 08                         9
RTH
IL
RL
VTH

Lec 08        10
Exercise 01: Find I

RL

Lec 08        11
A

B



   I1= (100 – 70)/40 = 0.75 A
Voc, AB = 100 – (0.75 * 20) = 85 V
VTH = 85v

Lec 08                12
A

B



   ZTH = 10

Lec 08   13
I
VTH = 85v

85
I           0.5 A
10  160

Lec 08         14
Exercise 02: Find IL

IL

Lec 08         15
Thevenin’s theorem with
dependent sources
• Identify and remove the load
• Look in the load terminals and calculate V TH
• Place a short on the load terminals and calculate
ISC, the current through the short
VTH
• Calculate RTH =
I sc
• Create a series circuit consisting of VTH, RTH, and
• Calculate the load current or voltage as desired 16
Lec 08
Example 01

Lec 08   17
STEPS 01 & 02

• Identify and remove the load
• Look in the load terminals and calculate V TH
• Place a short on the load terminals and calculate
ISC the current through the short
Vth
• Calculate RTH =
Isc
• Create a series circuit consisting of VTH, RTH, and
• Calculate the load current or voltage as desired 18
Lec 08
Calculate VTH
-VS1 + IR1 -2I + IR3 = 0
I(R1 -2 + R3) = VS1
I = 10A
VTH = IR3 = 10*6 = 60V

Lec 08     19
STEPS 03 & 04

• Identify and remove the load
• Look in the load terminals and calculate V TH
• Place a short on the load terminals and calculate
ISC the current through the short
Vth
• Calculate RTH =
Isc
• Create a series circuit consisting of VTH, RTH, and
• Calculate the load current or voltage as desired 20
Lec 08
VTH 60
RTH =        6
ISC 10

Lec 08          21
STEPS 05 & 06

• Identify and remove the load
• Look in the load terminals and calculate V TH
• Place a short on the load terminals and calculate
ISC the current through the short
Vth
• Calculate RTH =
Isc
• Create a series circuit consisting of VTH, RTH, and
• Calculate the load current or voltage as desired 22
Lec 08
RTH
IL
RL
VTH

Lec 08             23
Norton’s Circuit
• The Norton’s circuit across a load is
defined as a parallel connected Norton
Current source and a Norton resistance.

IN                 RL
RN

Lec 08               24
Norton’s Theorem
Procedure
• Identify and remove the load
• Short the load terminals and calculate IN (ISC)
• Remove all sources by replacing:
–voltage sources with a short
–current sources with an open
–If the source has an internal resistance, keep the
resistance in the circuit.
• Look in the load terminals and calculate RN
• Create a parallel circuit consisting of IN, RN, and the
• Calculate the load current or voltage as desired
Lec 08                            25
EXAMPLE 01

R1            R3

R2          RL
VS

Lec 08             26
STEPS 01 & 02
• Identify and remove the load
• Short the load terminals and calculate IN (ISC)
• Remove all sources by replacing:
–voltage sources with a short
–current sources with an open
–If the source has an internal resistance, keep the
resistance in the circuit.
• Look in the load terminals and calculate RN
• Create a parallel circuit consisting of IN, RN, and the
• Calculate the load current or voltage as desired
Lec 08                            27
ISC

ISC = IN

Lec 08         28
STEPS 03 & 04
• Identify and remove the load
• Short the load terminals and calculate IN (ISC)
• Remove all sources by replacing:
–voltage sources with a short
–current sources with an open
–If the source has an internal resistance, keep the
resistance in the circuit.
• Look in the load terminals and calculate RN
• Create a parallel circuit consisting of IN, RN, and the
• Calculate the load current or voltage as desired
Lec 08                            29
RN

Lec 08        30
STEPS 03 & 04
• Identify and remove the load
• Short the load terminals and calculate IN (ISC)
• Remove all sources by replacing:
–voltage sources with a short
–current sources with an open
–If the source has an internal resistance, keep the
resistance in the circuit.
• Look in the load terminals and calculate RN
• Create a parallel circuit consisting of IN, RN, and the
• Calculate the load current or voltage as desired
Lec 08                            31
IN            RL
RN

Lec 08        32
Exercise 01: Find IL

IL

Lec 08         33
ISC = ISC1 + ISC2

Lec 08   34
Lec 08   35
IL
IN     RN
RL

Lec 08             36

```
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