1. CIRCUITS by Ulaby & Maharbiz
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7. AC Analysis
CIRCUITS by Ulaby & Maharbiz
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2. Overview All rights reserved. Do not copy or distribute.
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Overview

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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
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Sinusoidal Signals
Useful relations

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Phase Lead/Lag

6. Phasor Domain 1. The phasor-analysis technique transforms equations
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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.

7. Phasor Domain Phasor counterpart of
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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.

9. Phasor Relation for Resistors
Current through a resistor
Time domain
Time Domain
Frequency Domain
Phasor Domain
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10. Phasor Relation for Inductors
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Phasor Relation for Inductors
Current through inductor in time domain
Time domain
Phasor Domain
Time Domain

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

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Summary of R, L, C

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

14. Example 7-4: RL Circuit Cont.
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Example 7-4: RL Circuit
Cont.

15. Example 7-4: RL Circuit cont.
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16. 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
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17. Impedance Transformation
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Impedance Transformation

18. Voltage & Current Division
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19. Cont. All rights reserved. Do not copy or distribute.
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Cont.

20. Example 7-5: Input Impedance (cont.)
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21. Example 7-8: Thévenin Circuit
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Example 7-8: Thévenin Circuit

22. Linear Circuit Properties
Thévenin/Norton and Source Transformation Also Valid
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Phasor Diagrams

24. Phase-Shift Circuits
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Example 7-10: Cascaded Phase Shifter Choose R such that output is 1200 ahead of input
Solution leads to:

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Node 1
Cont.

27. Cont. (cont.) All rights reserved. Do not copy or distribute.
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Cont.

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29. Example 7-13: Mesh Analysis by Inspection
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Example 7-13: Mesh Analysis by Inspection

30. Power Supply Circuit
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Ideal Transformer

32. Half-Wave Rectifier
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33. Full-Wave Rectifier Current flow during first half of cycle
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Full-Wave Rectifier
Current flow during first half of cycle
Current flow during second half of cycle

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Smoothing RC Filter

35. Complete Power Supply
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37. Example 7-19: Multisim Measurement of Phase Shift
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38. Example 7-19 (cont.) Using Transient Analysis
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40. Summary
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