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Lecture 5 Active Filter (Part II)

Lecture 5 Active Filter (Part II). Biquadratic function filters Positive feedback active filter: VCVS Negative feedback filter: IGMF Butterworth Response Chebyshev Response. Biquadratic function filters. Realised by: Positive feedback (II) Negative feedback. (I) Low Pass (II) High Pass.

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Lecture 5 Active Filter (Part II)

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  1. Lecture 5 Active Filter (Part II) • Biquadratic function filters • Positive feedback active filter: VCVS • Negative feedback filter: IGMF • Butterworth Response • Chebyshev Response EE3110 Active Filter (Part 2)

  2. Biquadratic function filters • Realised by: • Positive feedback • (II) Negative feedback EE3110 Active Filter (Part 2)

  3. (I) Low Pass (II) High Pass (III) Band Pass (IV) Band Stop (V) All Pass Biquadratic functions EE3110 Active Filter (Part 2)

  4. Low-Pass Filter EE3110 Active Filter (Part 2)

  5. High-Pass Filter EE3110 Active Filter (Part 2)

  6. Band-Pass Filter EE3110 Active Filter (Part 2)

  7. Band-Stop Filter EE3110 Active Filter (Part 2)

  8. Voltage Controlled Votage Source (VCVS) Positive Feedback Active Filter (Sallen-Key) By KCL at Va: Therefore, we get where, Re-arrange into voltage group gives: (1) EE3110 Active Filter (Part 2)

  9. But, (2) Substitute (2) into (1) gives or (3) In admittance form: (4) * This configuration is often used as a low-pass filter, so a specific example will be considered. EE3110 Active Filter (Part 2)

  10. VCVS Low Pass Filter In order to obtain the above response, we let: Then the transfer function (3) becomes: (5) EE3110 Active Filter (Part 2)

  11. Equating the coefficient from equations (6) and (5), it gives: Now, K=1, equation (5) will then become, we continue from equation (5), EE3110 Active Filter (Part 2)

  12. Simplified Design (VCVS filter) Comparing with the low-pass response: It gives the following: EE3110 Active Filter (Part 2)

  13. Example (VCVS low pass filter) To design a low-pass filter with and Let m = 1 n = 2 Choose Then What happen if n = 1? EE3110 Active Filter (Part 2)

  14. VCVS High Pass Filter EE3110 Active Filter (Part 2)

  15. VCVS Band Pass Filter EE3110 Active Filter (Part 2)

  16. Infinite-Gain Multiple-Feedback (IGMF) Negative Feedback Active Filter substitute (1) into (2) gives (3) EE3110 Active Filter (Part 2)

  17. Value Filter rearranging equation (3), it gives, Or in admittance form: EE3110 Active Filter (Part 2)

  18. IGMF Band-Pass Filter Band-pass: To obtain the band-pass response, we let *This filter prototype has a very low sensitivity to component tolerance when compared with other prototypes. EE3110 Active Filter (Part 2)

  19. Simplified design (IGMF filter) Comparing with the band-pass response Its gives, EE3110 Active Filter (Part 2)

  20. Example (IGMF band pass filter) To design a band-pass filter with and With similar analysis, we can choose the following values: EE3110 Active Filter (Part 2)

  21. Butterworth Response (Maximally flat) Butterworth polynomials where n is the order Normalize to o = 1rad/s Butterworth polynomials: EE3110 Active Filter (Part 2)

  22. Butterworth Response EE3110 Active Filter (Part 2)

  23. Second order Butterworth response Started from the low-pass biquadratic function For EE3110 Active Filter (Part 2)

  24. Bode plot (n-th order Butterworth) Butterworth response EE3110 Active Filter (Part 2)

  25. Second order Butterworth filter Setting R1= R2 and C1 = C2 Now K = 1 + RB/ RA Therefore, we have For Butterworth response: We define Damping Factor (DF) as:  EE3110 Active Filter (Part 2)

  26. Damping Factor (DF) • The value of the damping factor required to produce desire response characteristic depends on the order of the filter. • The DF is determined by the negative feedback network of the filter circuit. • Because of its maximally flat response, the Butterworth characteristic is the most widely used. • We will limit our converge to the Butterworth response to illustrate basic filter concepts. EE3110 Active Filter (Part 2)

  27. Values for the Butterworth response EE3110 Active Filter (Part 2)

  28. + - + - C1 0.01 F C3 0.01 F +15 V +15 V R1 8.2 k R2 8.2 k R4 8.2 k R3 8.2 k Vout 741C 741C C2 0.01 F C4 0.01 F RB 1.5 k RB 27 k -15 V -15 V RA 10 k RA 22 k Forth order Butterworth Filter EE3110 Active Filter (Part 2)

  29. Chebyshev Response (Equal-ripple) Where  determines the ripple and is the Chebyshev cosine polynomial defined as EE3110 Active Filter (Part 2)

  30. Chebyshev Cosine Polynomials EE3110 Active Filter (Part 2)

  31. Example: 0.969dB ripple gives  = 0.5, Roots: Second order Chebychev Response EE3110 Active Filter (Part 2)

  32. Roots of first bracketed term Roots of second bracketed term Roots or EE3110 Active Filter (Part 2)

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