1. 7. AC ANALYSIS CIRCUITS by Ulaby & Maharbiz All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

2. Overview All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

3. Linear Circuits at ac Objective: To determine the steady state response of a linear circuit to ac signals  Sinusoidal input is common in electronic circuits  Any time-varying periodic signal can be represented by a series of sinusoids (Fourier Series)  Time-domain solution method can be cumbersome All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

4. Sinusoidal Signals Useful relations All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

5. Phase Lead/Lag All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

6. Phasor Domain 1. The phasor-analysis technique transforms equations from the time domain to the phasor domain. 2. Integro-differential equations get converted into linear equations with no sinusoidal functions. 3. After solving for the desired variable--such as a particular voltage or current-- in the phasor domain, conversion back to the time domain provides the same solution that would have been obtained had the original integro-differential equations been solved entirely in the time domain. All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

7. Phasor Domain Phasor counterpart of All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

8. Time and Phasor Domain It is much easier to deal with exponentials in the phasor domain than sinusoidal relations in the time domain. You just need to track magnitude/phase, knowing that everything is at frequency  All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

9. Phasor Relation for Resistors Time DomainFrequency Domain Current through a resistor Time domain Phasor Domain All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

10. Phasor Relation for Inductors Time Domain Current through inductor in time domain Time domain Phasor Domain All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

11. Phasor Relation for Capacitors Time Domain Voltage across capacitor in time domain is Time domain Phasor Domain All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

12. Summary of R, L, C All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

13. ac Phasor Analysis General Procedure Using this procedure, we can apply our techniques from dc analysis All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

14. Example 7-4: RL Circuit Cont. All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

15. Example 7-4: RL Circuit cont. All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

16. Impedance and Admittance R = resistance = Re(Z) Impedance is voltage/current X = reactance = Im(Z) Resistor Inductor Capacitor G = conductance = Re(Y) Admittance is current/voltage B = susceptance = Im(Y) All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

17. Impedance Transformation All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

18. Voltage & Current Division All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

19. Cont. All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

20. Example 7-5: Input Impedance (cont.) All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

21. Example 7-8: Thévenin Circuit All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

22. Linear Circuit Properties Thévenin/Norton and Source Transformation Also Valid All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

23. Phasor Diagrams All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

24. Phase-Shift Circuits All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

25. Example 7-10: Cascaded Phase Shifter Choose R such that output is 120 0 ahead of input Solution leads to: All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

26. Node 1Cont. All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

27. (cont.) Cont. All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

28. (cont.) All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

29. Example 7-13: Mesh Analysis by Inspection All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

30. Power Supply Circuit All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

31. Ideal Transformer All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

32. Half-Wave Rectifier All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

33. Full-Wave Rectifier Current flow during first half of cycle Current flow during second half of cycle All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

34. Smoothing RC Filter All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

35. Complete Power Supply All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

36. All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

37. Example 7-19: Multisim Measurement of Phase Shift All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

38. Example 7-19 (cont.) Using Transient Analysis All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

39. All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press

40. Summary All rights reserved. Do not copy or distribute. © 2013 National Technology and Science Press