Week Eleven: Thevenin's Theorem Part II

Thevenin's Theorem



Case 2: Independent and Dependent Sources.

          -If the circuit to be Thevenized has both dependent and independent source, the method described above cannot be used to find the Thevenin resistance. Instead, you must find the short circuit current, Isc (current through short circuit at terminals). Then the Thevenin resistance is given by RT=Voc/Isc.
                   
                       
         Example of Circuit Problem using Case 2


Another Case: Only Dependent Sources.
     -If only dependent sources are present, then the Thevenin voltage is zero, and the Thevenin resistance is determine by applying a test voltage Vtest and the terminals and determining the resulting current, Itest. The Thevenin resistance is given by RT=Vtest/Itest. (Likewise, for this third case, you can apply a test current and measure the resulting voltage).
         
 Example of Circuit Problem with Dependent Sources Only


Watch an Example using Thevenin's Theorem Case 2:



Reflection:
       Comparing Case 1 and Case 2, I find case 1 more easy than case 2. Since case 1 only involves Independent sources while case 2 involves Independent and dependent sources.


Week Ten: Thevenin's Theorem Part I

Thevenin's Theorem

     - states that it is possible to simplify any linear circuit, no matter how complex, to an equivalent circuit with just a single voltage source and series resistance connected to a load.
     
     -The theorem was independently derived in 1853 by the German scientist Hermann von Helmholtz and in 1883 by Léon Charles Thévenin (1857–1926), an electrical engineer with France's national Postes et Télégraphes telecommunications organization.

                                                 
                       Hermann von Helmholtz
                                      
                       Léon Charles Thévenin
                       
                        Thevenin Equivalent Circuit:
                                                            

Case 1: Only Independent Sources 
            -the typical case. In the typical case, there are no dependent sources in the circuit to be Thevenized. To find the Thevenin equivalent, first find the open circuit voltage, Voc, this is the Thevenin voltage. To find the Thevenin resistance, set all sources to zero and find the resistance of the resulting circuit.



Consider again the circuit from above,

              

and try to find the Thevenin circuit at the terminals (i.e., across the 1k resistor). From the discussion of superposition, we know the open circuit voltage, Voc, is 1.666 volts. The Thevenin resistance, RT, is found by finding the equivalent resistance of the circuit with all source set to zero, as shown below

   

                                      

Obviously the Thevenin resistance, RT, is 1k||500=333Ω. Therefore the resulting circuit is:

                           


  Watch Another Example using Thevenin's Theorem!



Reflection:

      I have learned that Thevenin's Theorem makes a complex circuit problem into a simpler one. According to our Professor, it is commonly used especially in Board Examinations for ECE/EE.

Wall-E