1. Lesson 25 AC Thèvenin Max Power Transfer

2. Learning Objectives Explain under what conditions a source transfers maximum power to a load. Determine the value of load impedance for which maximum power is transferred from the circuit.

3. Determining E Th Remove the load (open-circuit) and measure the resulting voltage. Review E th = open ckt voltage

4. Determining Z Th With the load disconnected, turn off all independent sources.  Voltage sources – 0 V is equivalent to a short-circuit.  Current sources – 0 A is equivalent to a open-circuit. Z Th is the equivalent resistance looking into the “dead” circuit through terminals a-b. Z th Review

5. Example Problem 1 Convert the source below into a Thévenin equivalent and determine the power dissipated by the load.

6. Conjugates The conjugate of C is written as C *, which has the same real value but the opposite imaginary part: Review

7. Maximum power transfer theorem Maximum power is transferred to the load when R LD = R Th. Review

8. In AC circuits, max power transfer occurs when load impedance ( Z L ) is the complex conjugate of the Thévinin equivalent impedance ( Z Th ). This means the load has a capacitor if the Thèvenin impedance includes an inductor X LD cancels out X TH ! Max Power Transfer in AC Circuits

9. Since R LD =R TH, and the reactances cancel out, the resulting P MAX equation is the same as with DC! Max Power Transfer in AC Circuits

10. #1 Mistake with AC Max Power is not using the REAL value of resistance when calculating P max Transform Z TH into rectangular form to determine R TH Max Power Transfer in AC Circuits X

11. Example Problem 2 Determine the load Z LOAD that will allow maximum power to be delivered to the load the circuit below. Find the power dissipated by the load.

12. Example Problem 3 Determine the load Z LD that will allow maximum power to be delivered to the load the circuit below. Frequency is 191.15 Hz. Find the maximum power. What will happen to power if the frequency is changed to 95.575?