1. CIRCUITS by Ulaby & Maharbiz
12. Fourier Analysis
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CIRCUITS by Ulaby & Maharbiz

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3. Analysis Techniques Circuit Excitation Method of Solution Chapter
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Analysis Techniques
Circuit Excitation Method of Solution Chapter
1. dc (w/ switches) Transient analysis 5 & 6
2. ac Phasor-domain analysis
( steady state only)
3. Any waveform LaplaceTransform
(single-sided only) (transient + steady state)
4. Any waveform Fourier Transform
(double-sided) (transient + steady state) This chapter
single-sided: defined over [0,∞] double-sided: defined over [−∞,∞]

4. Fourier Analysis 1. Periodic Excitation:
Solution Method: Fourier series + Phasor Analysis
2. Nonperiodic Excitation:
Solution Method: Fourier Transform
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5. Fourier Series Analysis Technique
Example
(details later)
Cont.
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6. Fourier Series Analysis Technique (cont.)
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Cont.

7. Fourier Series Analysis Technique (cont.)
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8. Fourier Series: Cosine/Sine Representation
The Fourier theorem states that a periodic function f(t) of period T can be cast in the form
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9. Example Fourier series:
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10. Example 12-1: Sawtooth Waveform
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11. Fourier Series: Amplitude/Phase Representation
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12. Example 12-2: Line Spectra (cont.)
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Example 12-2: Line Spectra (cont.)

13. Symmetry Considerations
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Symmetry Considerations dc

14. Even & Odd Symmetry All rights reserved. Do not copy or distribute.
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16. Example 12-3: M-Waveform This oscillatory behavior of the Fourier
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This oscillatory behavior of the Fourier
series in the neighborhood of
discontinuous points is called the Gibbs phenomenon.

17. Circuit Applications All rights reserved. Do not copy or distribute.
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18. Cont. All rights reserved. Do not copy or distribute.
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Cont.

19. Example 12-5: RC Circuit cont.
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Cont.

20. Example 12-5: RC Circuit cont.
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Cont.

21. Average Power
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22. Fourier Series: Exponential Representation
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Fourier Transform
Fourier Series Analysis Technique
Fourier Series Analysis Technique
Fourier Transform Analysis Technique

25. Example 12-8: Pulse Train Note that:
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26. Line Spectrum of Pulse Train
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Line Spectrum of Pulse Train
Spacing between adjacent harmonics is :
spectrum becomes continuous

27. Derivation Of Fourier Transform
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Derivation Of Fourier Transform
Fourier Transform Pair

28. Example 12-9: Rectangular Pulse
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Example 12-9: Rectangular Pulse
The wider the pulse, the narrower is its spectrum, and vice versa

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31. Circuit Analysis with Fourier Transform
Example 12-11
vs(t) = cos 4t
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Cont.

32. Circuit Analysis with Fourier Transform
Applying Inverse Fourier Transform:
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33. Summary
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