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Thévenin Equivalent Circuits with Dependent Sources Module

Learn how to find Thévenin Equivalent with Dependent Sources. Explore methods, problems, and solutions in this in-depth module.

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Thévenin Equivalent Circuits with Dependent Sources Module

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  1. Port Resistors and Independent Sources Only Module 10Thévenin Equivalent Circuitswith Dependent Sources Up until now… + _

  2. VTh Review: Find the Thévenin Equivalent • Find Open Circuit Voltage VTh + _

  3. + RTh _ • Set sources to zero • Find net resistance RTh seen at the port

  4. iB RB  iB v1 + _ RE Set to zero (short ckt) Do NOT set to zero Port What happens when circuit has a Dependent Source? Example

  5. Vtest RTh Itest = + + _ _ Vtest Test source Set to zero (short ckt) Dependent Source: Must Use“Test Source” Method to find RTh Rationale: RTh VTh

  6. RTh Itest Vtest Itest = RTh + RTh _ Vtest Vtest = Itest RTh + Method B Itest _ In the Test Source method: = Vtest / RTh Method A

  7. iB RB  iB Itest = ? v1 Vtest + _ + _ RE Apply to Our Circuit Circuit with independent source set to zero • Solve the circuit for Itest • Compute Vtest /Itestto find RTh

  8. Vtest RB – iB = iB _ Vtest RB  iB + v1 + Vtest _ + RE _ + _ Apply KVL: Itest = ? Vtest

  9. Apply KCL:   Vtest RE Vtest RB Vtest RB Vtest RB Vtest RB Vtest RE KCL + _ + _ + + 1 RB  RB 1 RE + + = Vtest RB Itest = ? Vtest RE Itest =

  10. Vtest RB Vtest RB  RB Itest Vtest RE Vtest RE + _ + 1 RB  RB 1 RE _ Itest = Vtest + + Itest Vtest = 1 RB  RB 1 RE + + Solve for RTh = Vtest/Itest

  11. 1 R1R2 R1||R2 = = R1 + R2 Resistors in Parallel 1 1 R2 1 R1 + 1 RB  RB 1 RE = + + 1  + 1 RB 1 RE + RB + 1 RE Back to the main problem… Let’s look at the denominator…

  12. Vtest RB Vtest RB  RB Itest Vtest RE Vtest RE + _ + _ RB + 1 RB + 1 = Itest RE RE Vtest RTh = = Itest Solve for RTh = Vtest/Itest Itest Vtest = 1 RB  RB 1 RE + +

  13. Vtest RB Vtest RE + _ + _ X RB RTh = = RE But why? Wrong! Vtest Itest What happens if we erroneously set Dependent Source to zero? RB Itest Vtest RE

  14. Vtest RB _ Vtest + Vtest RE + _ + _  iB RB Itest Vtest RE Vtest sets the voltage across RB Vtest across RBsets the value of iB iB sets the value of the dependent source

  15. Itest Port + _ Find the Thévenin Equivalent Resistance of this circuit: Another Example • Set the independent source to zero • Apply a test current source iB RC RB  iB V1 RE

  16. iB = Itest + ItestRE – + Vtest = Itest RB + (+1)RE – Itest+ Itest (+1) Vtest RB + (+ 1)RE RTh = = Itest RC + ItestRB –  iB RB Itest RE pause Done!

  17. End of This Module Don’t forget to do the homework!

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