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
  load
• 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
  load
• 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
  load
• 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
  load
• 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
  the load
• 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
  the load
• 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
  the load
• 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
  the load
• 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
  load
• 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
  load
• 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
  load
• 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
  load
• 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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