1. 8. AC POWER CIRCUITS by Ulaby & Maharbiz

2. Overview

3. Linear Circuits at ac Instantaneous power Average power Power at any instant of timeAverage of instantaneous power over one period  Power delivery (utilities)  Electronics (laptops, mobile phones, etc.)  Logic circuits Power is critical for many reasons: Note: Power is not a linear function, cannot apply superposition

4. Instantaneous Power for Sinusoids Power depends on phases of voltage and current Trig. Identity: Constant in time (dc term) ac at 2 

5. Average Value Sine wave Truncated sawtooth

6. Average Value for These properties hold true for any values of φ 1 and φ 2

7. Effective or RMS Value Equivalent Value That Delivers Same Average Power to Resistor as in dc case For current given by Effective value is the (square) Root of the Mean of the Square of the periodic signal, or RMS value Hence: Similarly,

8. Average Power Note dependence on phase difference

9. Average Power Sinceand a similar relationship applies to I, Power factor angle: 0 for a resistor = 90 degrees for inductor ‒ 90 degrees for capacitor

10. ac Power Capacitors Capacitors (ideal) dissipate zero average power = 0

11. ac Power Inductors Inductors (ideal) dissipate zero average power = 0

12. Complex Power Phasor form defining “real” and “reactive” power

13. Power Factor for Complex Load Inductive/capacitive loads will require more from the power supply than the average power being consumed Power supply needs to supply S in order to deliver P av to load Power factor relates S to P av

14. Power Factor

15. Power Factor Compensation Introduces reactive elements to increase Power Factor

16. Example 8-6: pf Compensation

17. Maximum Power Transfer Max power is delivered to load if load is equal to Thévenin equivalent Max power transfer when Set derivatives equal to zero

18. Example 8-7: Maximum Power Cont.

19. Example 8-7: Maximum Power

20. Three Phase

21. Y & Delta

22. Y-Source Connected to a Y-Load

24. Multisim Measurement of Power

25. Multisim Measurement of Complex Power Complex Power S

26. Summary