1. E E 2415 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 j  1 A zero at j  1 A pole at j  2 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 j  1

16. Examples: (2/3) A zero at j  1 A pole at j  2 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 

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