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E E 2415

E E 2415. Lecture 15 Introduction to Frequency Response, Poles & Zeroes, Resonant Circuit. Low-Pass Filter Example: (1/2). Low-pass Filter:. Low-Pass Filter Example: (2/2). Gain in Decibels. Using the Low-pass filter example:. Drops at 20 db per decade. Bode Plot of Low-Pass Filter.

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E E 2415

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  1. E E2415 Lecture 15 Introduction to Frequency Response, Poles & Zeroes, Resonant Circuit

  2. Low-Pass Filter Example: (1/2) Low-pass Filter:

  3. Low-Pass Filter Example: (2/2)

  4. Gain in Decibels Using the Low-pass filter example: Drops at 20 db per decade

  5. Bode Plot of Low-Pass Filter

  6. Phase Plot of Low-Pass Filter

  7. High-Pass Filter Example: (1/2)

  8. High-Pass Filter Example: (2/2)

  9. High-Pass Gain in Decibels

  10. Bode Plot of High-Pass Filter

  11. Phase Plot of High-Pass Filter

  12. Definition: Poles & Zeroes A zero at the origin A pole at jw1 A zero at jw1 A pole at jw2 A pole at the origin

  13. Effect of a Pole on the Bode Plot • A pole causes the asymptotic slope to decrease by 20 db/decade. • A pole at the origin causes the slope to start at –20 db/decade. • A pole not at the origin causes a corner to appear at the pole’s frequency; then the slope is 20 db/decade less for frequencies greater than the pole’s frequency.

  14. Effect of a Zero on the Bode Plot • A zero causes the asymptotic slope to increase by 20 db/decade. • A zero at the origin causes the slope to start at +20 db/decade. • A zero not at the origin causes a corner to appear at the pole’s frequency; then the slope is 20 db/decade more for frequencies greater than the zero’s frequency.

  15. Examples: (1/3) A zero at the origin A pole at jw1

  16. Examples: (2/3) A zero at jw1 A pole at jw2 A pole at the origin

  17. Examples: (3/3)

  18. Resonant Bandpass Filter (1/2)

  19. Resonant Bandpass Filter (2/2)

  20. Resonant BandPass Poles & Zeroes Zero at origin Two poles

  21. Bode Plot for Resonant Bandpass

  22. Phase Plot for Resonant Bandpass

  23. Bandwidth of Resonant Bandpass (1/2) at half power Take square and reciprocal of both sides Need both solutions for positive values of w

  24. Bandwidth of Resonant Bandpass (2/2) Positive w for -1 Positive w for +1 Bandwidth for a series resonant bandpass filter

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