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8. ac Power

8. ac Power. CIRCUITS by Ulaby & Maharbiz. Overview. Linear Circuits at ac. Average power. Instantaneous power. Power at any instant of time. Average of instantaneous power over one period. Note: Power is not a linear function, cannot apply superposition.

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8. ac Power

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  1. 8. ac Power CIRCUITS by Ulaby & Maharbiz

  2. Overview

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

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

  5. Average Value • Sine wave Truncated sawtooth

  6. Average Value for These properties hold true for any values of φ1 and φ2

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

  8. Average Power Note dependence on phase difference

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

  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 Pav to load Power factor relates S to Pav

  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 Théveninequivalent Set derivatives equal to zero Max power transfer when

  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

  23. Multisim Measurement of Power

  24. Multisim Measurement of Complex Power Complex Power S

  25. Summary

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