1. EE301 AC Thèvenin and Max Power Transfer

2. Learning Objectives Apply Thèvenin’s Theorem to AC circuits
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. Thévenin’s theorem for AC
ETh is the open circuit voltage at the terminals,
ZTh is the input or equivalent resistance at the terminals when the independent sources are turned off.

4. Determining ETh Review
Remove the load (open-circuit) and measure the resulting voltage.
Eth = open ckt voltage

5. Determining ZTh
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.
ZTh is the equivalent resistance looking into the “dead” circuit through terminals a-b.
Zth

6. Applying Thévenin equivalent
Once ETh and ZTh have been found, the original circuit is replaced by its equivalent and solving for ILD and VLD becomes trivial.

7. Example Problem 1
Convert the source below into a Thévenin equivalent and determine the current through load Zab.

8. Example Problem 2 Convert the source below into a Thévenin equivalent.
ZLOAD

9. Example Problem 3
Convert the source below into a Thévenin equivalent and determine the power dissipated by the load.

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

11. Maximum power transfer theorem
Review
Maximum power transfer theorem
Maximum power is transferred to the load when RLD = RTh.

12. Max Power Transfer in AC Circuits
In AC circuits, max power transfer occurs when load impedance (ZL) is the complex conjugate of the Thévinin equivalent impedance (ZTh).
This means the load has a capacitor if the Thèvenin impedance includes an inductor
XLD cancels out XTH!

13. Max Power Transfer in AC Circuits
Since RLD=RTH, and the reactances cancel out, the resulting PMAX equation is the same as with DC!

14. Max Power Transfer in AC Circuits
#1 Mistake with AC Max Power is not using the REAL value of resistance when calculating Pmax
Transform ZTH into rectangular form to determine RTH X

15. Example Problem 4
Determine the load ZLOAD that will allow maximum power to be delivered to the load the circuit below. Find the power dissipated by the load.

16. Example Problem 5
Determine the load ZLD that will allow maximum power to be delivered to the load the circuit below. Frequency is Hz. Find the maximum power. What will happen to power if the frequency is changed to ?