1. CIRCUITS by Ulaby & Maharbiz
7. AC Analysis
CIRCUITS by Ulaby & Maharbiz

2. Overview

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

4. Sinusoidal Signals
Useful relations

5. Phase Lead/Lag

6. Complex Numbers
We will find it is useful to represent sinusoids as complex numbers
Rectangular coordinates
Polar coordinates
Relations based on Euler’s Identity

7. Relations for Complex Numbers
Learn how to perform these with your calculator/computer

8. 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.

9. Phasor Domain
Phasor counterpart of

10. 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 w.

11. Phasor Relation for Resistors
Current through a resistor
Time domain
Time Domain
Frequency Domain
Phasor Domain

12. Phasor Relation for Inductors
Current through inductor in time domain
Time domain
Phasor Domain
Time Domain

13. Phasor Relation for Capacitors
Voltage across capacitor in time domain is
Time domain
Time Domain
Phasor Domain

14. Summary of R, L, C

15. ac Phasor Analysis General Procedure
Using this procedure, we can apply our techniques from dc analysis

16. Example 1-4: RL Circuit
Cont.

17. Example 1-4: RL Circuit cont.

18. Impedance and Admittance
Impedance is voltage/current
Admittance is current/voltage
R = resistance = Re(Z)
G = conductance = Re(Y)
X = reactance = Im(Z)
B = susceptance = Im(Y)
Resistor
Inductor
Capacitor

19. Impedance Transformation

20. Voltage & Current Division

21. Cont.

22. Example 7-6: Input Impedance (cont.)

23. Example 7-9: Thévenin Circuit

24. Linear Circuit Properties
Thévenin/Norton and Source Transformation Also Valid

25. Phasor Diagrams

26. Phase-Shift Circuits

27. Example 7-11: Cascaded Phase Shifter
Solution leads to:

28. Node 1
Cont.

29. (cont.)
Cont.

30. (cont.)

31. Example 7-14: Mesh Analysis by Inspection

32. Example 7-16: Thévenin Approach

33. Example 7-16: Thévenin Approach (Cont.)

34. Example 7-16: Thévenin Approach (Cont.)

35. Power Supply Circuit

36. Ideal Transformer

37. Half-Wave Rectifier

38. Full-Wave Rectifier Current flow during first half of cycle
Current flow during second half of cycle

39. Smoothing RC Filter

40. Complete Power Supply

42. Example 7-20: Multisim Measurement of Phase Shift

43. Example 7-20 (cont.)
Using Transient Analysis

44. Summary