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

2 Review: Find the Thévenin Equivalent Find Open Circuit Voltage V Th + _ V Th

3 Set sources to zero R Th Find net resistance R Th seen at the port + _

4 What happens when circuit has a Dependent Source? iBiB  iB iB + _ RBRB v1v1 RERE Port Set to zero (short ckt) Do NOT set to zero Example

5 V Th Dependent Source: Must Use “Test Source” Method to find R Th Rationale: + _ Set to zero (short ckt) + _ V test I test R Th V test R Th = Test source

6 In the Test Source method: V test I test = R Th + _ V test = V test / R Th R Th Method B I test Method A + _ V test = I test R Th I test

7 + _ V test Apply to Our Circuit iBiB  iB iB + _ RBRB v1v1 RERE Circuit with independent source set to zero I test = ? Solve the circuit for I test Compute V test / I test to find R Th

8 iBiB  iB iB + _ RBRB v1v1 RERE Apply KVL: + _ V test I test = ? V test + _ + _ R B – i B =

9 + _ RBRB RERE + _ V test I test = ? V test R B V test R B  Apply KCL: KCL I test = V test R B V test R B  + V test R E + V test R E 1 R B  RB  RB + 1 R E + = V test

10 Solve for R Th = V test / I test + _ RBRB RERE + _ V test I test V test R B V test R B  V test R E I test = 1 R B  RB  RB + 1 R E + V test I test 1 R B  RB  RB + 1 R E + V test =

11 1 R B  RB  RB + 1 R E + 1 Let’s look at the denominator… 1 R E  + 1 R B + 1 RERE  + 1 = Back to the main problem… Resistors in Parallel R 1 ||R 2 = R1R2R1R2 R 1 + R 2 = 1R11R1 1R21R2 + 1

12 Solve for R Th = V test / I test + _ RBRB RERE + _ V test I test V test R B V test R B  V test R E I test 1 R B  RB  RB + 1 R E + V test = = I test RERE R B  + 1 = V test I test RERE R B  + 1 R Th =

13 What happens if we erroneously set Dependent Source to zero? + _ RBRB RERE + _ V test I test V test R B V test R E = V test I test RERE R B R Th = Wrong! X But why?

14 + _ RBRB RERE + _ V test I test V test R B V test R E V test + _  iB iB V test sets the voltage across R B V test across R B sets the value of i B i B sets the value of the dependent source

15 Another Example iBiB  iB iB RBRB RERE + _ V1V1 RCRC Find the Thévenin Equivalent Resistance of this circuit: Set the independent source to zero Apply a test current source Port I test

16 i B = I test  iB iB RBRB RERE RCRC I test I test + I test + I test R B – + I test R E – (  +1) + V test = I test R B + (  +1)R E – = V test I test RBRB + (  + 1)R E R Th = Done! pause

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