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ELECTRONIC FILTERS

ELECTRONIC FILTERS. Celso José Faria de Araújo, Dr. CONCEPTS. A “Ideal Electronic Filters” allow distortionless transmission of a certain band of frequencies and suppress all the remaining frequencies of the spectrum of the input signal.

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ELECTRONIC FILTERS

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  1. ELECTRONIC FILTERS Celso José Faria de Araújo, Dr.

  2. CONCEPTS • A “Ideal Electronic Filters” allow distortionless transmission of a certain band of frequencies and suppress all the remaining frequencies of the spectrum of the input signal. • The frequency spectrum is a representation of amplitude versus frequencies of this signal. Electronic Filters Electrical Circuits - Celso José Faria de Araújo, M.Sc.

  3. CLASSIFICATION Electronic Filters Electrical Circuits - Celso José Faria de Araújo, M.Sc.

  4. FUNCTION ACCOMPLISHED Electronic Filters Electrical Circuits - Celso José Faria de Araújo, M.Sc.

  5. Advantage: Suppress use of inductors; Easy Design of Complex Filters by cascade of simple stage; A considerable amplification of input signal is possible; Design Flexibility. Disadvantages: Power supply is necessary; The frequency response is limited by active devices (Op-Amps, Transistors) frequency response; It’s not often apply in medium and high power system. Despite these disadvantages it’s widely used in several application, such as: telecommunication and industrial instrumentation. ACTIVES FILTERS Electronic Filters Electrical Circuits - Celso José Faria de Araújo, M.Sc.

  6. STANDARD REQUIREMENTS FOR DESIGN OF APPROXIMATION FUNCTIONLOW-PASS FILTER Electronic Filters Electrical Circuits - Celso José Faria de Araújo, M.Sc.

  7. NON-FLAT STOPBAND REQUIREMENTS FOR LOW-PASS FILTER Electronic Filters Electrical Circuits - Celso José Faria de Araújo, M.Sc.

  8. STANDARD REQUIREMENTS FOR DESIGN OF APPROXIMATION FUNCTIONHIGH-PASS FILTER Electronic Filters Electrical Circuits - Celso José Faria de Araújo, M.Sc.

  9. NON-FLAT STOPBAND REQUIREMENTS FOR HIGH-PASS FILTER Electronic Filters Electrical Circuits - Celso José Faria de Araújo, M.Sc.

  10. STANDARD REQUIREMENTS FOR DESIGN OF APPROXIMATION FUNCTIONBAND-PASS FILTER • B is the passband width of BP filter • o is the center (geometric mean) of the passband of BP filter Electronic Filters Electrical Circuits - Celso José Faria de Araújo, M.Sc.

  11. NONSYMMETRICAL REQUIREMENTS FOR BAND-PASS FILTER • B is the passband width of BP filter • o is the center (geometric mean) of the passband of BP filter Electronic Filters Electrical Circuits - Celso José Faria de Araújo, M.Sc.

  12. STANDARD REQUIREMENTS FOR DESIGN OF APPROXIMATION FUNCTIONBAND-REJECT FILTER • B is the passband width of BR filter • o is the center (geometric mean) of the stopband of BR filter Electronic Filters Electrical Circuits - Celso José Faria de Araújo, M.Sc.

  13. NONSYMMETRICAL REQUIREMENTS FOR BAND-REJECT FILTER • B is the passband width of BR filter • o is the center (geometric mean) of the stopband of BR filter Electronic Filters Electrical Circuits - Celso José Faria de Araújo, M.Sc.

  14. A SECOND-ORDER GAIN FUNCTION FOR LOW-PASS FILTER Electronic Filters Electrical Circuits - Celso José Faria de Araújo, M.Sc.

  15. A SECOND-ORDER GAIN FUNCTION FOR HIGH-PASS FILTER Electronic Filters Electrical Circuits - Celso José Faria de Araújo, M.Sc.

  16. A SECOND-ORDER GAIN FUNCTION FOR BAND-PASS FILTER Electronic Filters Electrical Circuits - Celso José Faria de Araújo, M.Sc.

  17. A SECOND-ORDER GAIN FUNCTION FOR BAND-REJECT FILTER Electronic Filters Electrical Circuits - Celso José Faria de Araújo, M.Sc.

  18. A SECOND-ORDER GAIN FUNCTION FOR LOW-PASS NOTCH FILTER Electronic Filters Electrical Circuits - Celso José Faria de Araújo, M.Sc.

  19. A SECOND-ORDER GAIN FUNCTION FOR HIGH-PASS NOTCH FILTER Electronic Filters Electrical Circuits - Celso José Faria de Araújo, M.Sc.

  20. GAIN EQUALIZERS Electronic Filters Electrical Circuits - Celso José Faria de Araújo, M.Sc.

  21. DELAY EQUALIZERS Electronic Filters Electrical Circuits - Celso José Faria de Araújo, M.Sc.

  22. DELAY EQUALIZERSSecond-order (all-pass) Electronic Filters Electrical Circuits - Celso José Faria de Araújo, M.Sc.

  23. EQUALIZATION OF CABLE DELAY Electronic Filters Electrical Circuits - Celso José Faria de Araújo, M.Sc.

  24. Filter pole-zero patterns Electronic Filters Electrical Circuits - Celso José Faria de Araújo, M.Sc.

  25. Bode Plot Approximation Technique Loss (dB) Frequency (rad/s) Electronic Filters Electrical Circuits - Celso José Faria de Araújo, M.Sc.

  26. n 1/H(S) 1 S + 1 2 S2 + 1,414S + 1 3 (S2 + S + 1) (S+1) 4 (S2 + 0,76537S + 1) (S2 + 1,84776S + 1) 5 (S2 + 0,61803S + 1) (S2 + 1,61803S + 1) (S + 1) BUTTERWORTH APPOXIMATION Requirements: p Amaxs Amin Order: Correction Factor: Roots of a third-order normalized filters Roots of the normalized filters: Denormalization: Electronic Filters Electrical Circuits - Celso José Faria de Araújo, M.Sc.

  27. Magnitude response for Butterworth filters of various order with  = 1. Note that as the order increases, the response approaches the ideal brickwall type transmission. Electronic Filters Electrical Circuits - Celso José Faria de Araújo, M.Sc.

  28. Graphical construction for determining the poles of a Butterworth filter of order N. All the poles lie in the left half of the s-plane on a circle of radius 0 = p(1/)1/N, where  is the passband deviation parameter : (a) the general case, (b)N = 2, (c)N = 3, (d)N = 4. Electronic Filters Electrical Circuits - Celso José Faria de Araújo, M.Sc.

  29. BUTTERWORTH APPOXIMATIONExample Requirements: p = 100 rad/s Amax = 0.5 dB s = 400 rad/s Amin = 12 dB Electronic Filters Electrical Circuits - Celso José Faria de Araújo, M.Sc.

  30. CHEBYSHEV APPOXIMATION Requirements: p Amaxs Amin Roots of a third-order normalized filters Roots of the normalized filters: Electronic Filters Electrical Circuits - Celso José Faria de Araújo, M.Sc.

  31. Sketches of the transmission characteristics of a representative even- and odd-order Chebyshev filters. Electronic Filters Electrical Circuits - Celso José Faria de Araújo, M.Sc.

  32. CHEBYSHEV APPOXIMATION(Order from Plot) Requirements: p Amaxs Amin Loss of LP Chebyshev approximation for Amax= 0.25dB Loss of LP Chebyshev approximation for Amax= 0.50dB Loss of LP Chebyshev approximation for Amax= 1dB Electronic Filters Electrical Circuits - Celso José Faria de Araújo, M.Sc.

  33. n n n Numerator of 1/H(S) Numerator of 1/H(S) Numerator of 1/HS) Denominator (k) Denominator (k) Denominator (k) 1 1 1 S + 1.96523 S + 2.86278 S + 4.10811 4.10811 1.96523 2.86278 2 2 2 S2 + 1.09773S + 1.10251 S2 + 1.79668S + 2.11403 S2 + 1.42562S + 1.51620 2.05405 0.98261 1.43138 3 3 3 (S2 + 0.76722S + 1.33863) (S+0.76722) (S2 + 0.62646S + 1.14245) (S+0.62646) (S2 + 0.49417S + 0.99420) (S+0.49417) 0.71570 1.02702 0.49130 4 4 4 (S2 + 0.35071S + 1.06352) (S2 + 0.84668S + 0.356412) (S2 + 0.27907S + 0.98650) (S2 + 0.67374S + 0.27940) (S2 + 0.42504S + 1.16195) (S2 + 1.02613S + 0.45485) 0.51352 0.24565 0.35785 5 5 5 (S2 + 0.22393S + 1.03578) (S2 + 0.58625S + 0.47677) (S + 0.362332) (S2 + 0.17892S + 0.98831) (S2 + 0.46841S + 0.42930) (S + 0.28949) (S2 + 0.27005S + 1.09543) (S2 + 0.70700S + 0.53642) (S + 0.43695) 0.25676 0.17892 0.12283 CHEBYSHEV APPOXIMATION(Polynominal from Table) Requirements: p Amaxs Amin Amax= 0.25dB Amax= 0.50dB Amax= 1dB Electronic Filters Electrical Circuits - Celso José Faria de Araújo, M.Sc.

  34. CHEBYSHEV APPOXIMATIONExample Requirements: p = 200 rad/s Amax = 0.5 dB s = 600 rad/s Amin = 20 dB From table H(S) normalized isobtained Bandpass Details Electronic Filters Electrical Circuits - Celso José Faria de Araújo, M.Sc.

  35. ELLIPTIC (CAUER) APPOXIMATION Requirements: p Amaxs Amin H(s) = Loss Function Electronic Filters Electrical Circuits - Celso José Faria de Araújo, M.Sc.

  36. ELLIPTIC APPOXIMATIONExample Requirements: p = 200 rad/s Amax = 0.5 dB s = 600 rad/s Amin = 20 dB From table H(S) normalized isobtained Bandpass Details Electronic Filters Electrical Circuits - Celso José Faria de Araújo, M.Sc.

  37. Phase and delay characteristics Characteristics of a fourth-order Chebyshev (Amax = 0.5dB); (a) Loss, (b) Delay, (c) Step input, (d) Step response. Characteristics of a fourth-order Butterworth (Amax = 3dB); (a) Loss, (b) Delay, (c) Step response. Electronic Filters Electrical Circuits - Celso José Faria de Araújo, M.Sc.

  38. BESSEL APPROXIMATION H(S) normalized is Where Bn(S) is the nth order polynomial which is defined by the following recursive equation and Bessel Approximation Function in Normalized and Factored Form Loss of LP Bessel Approximations Denormalization Delay of LP Bessel Approximations Electronic Filters Electrical Circuits - Celso José Faria de Araújo, M.Sc.

  39. BESSEL APPROXIMATIONExample • Requirements: • The delay must be flat within 1 percent of the DC value up to 2KHz. • The attenuation at 6KHz must exceed 25dB. Solution • Try a fourth-order Filter. 1%  0 … p= 1.9 (from delay Bessel approximations plots) • s= (6/2)1.9 = 5.7 • Attenuation is only 22 dB  p= 5.7 (from loss Bessel approximations plots) • Try a fifth-order Filter. 1%  0 … p= 2.5 (from delay Bessel approximations plots) • s= (6/2)2.5 = 7.5 • Attenuation is 29.5 dB  p= 5.7 (from loss Bessel approximations plots) From table : Denormalization Electronic Filters Electrical Circuits - Celso José Faria de Araújo, M.Sc.

  40. DELAY EQUALIZERSFunction Approximation The number of delay sections N and their defining parameters (ai , bi) for approximating a given delay shape are usually obtained by computer optimization. Electronic Filters Electrical Circuits - Celso José Faria de Araújo, M.Sc.

  41. DELAY EQUALIZERSExample Delay Equalization of a fouth-order Chebyshev (Amax=0.25dB, passband edge = 1 rad/sec) Electronic Filters Electrical Circuits - Celso José Faria de Araújo, M.Sc.

  42. FREQUENCY TRANSFORMATIONS Block diagram of the frequency transformation procedure Electronic Filters Electrical Circuits - Celso José Faria de Araújo, M.Sc.

  43. HIGH-PASS FILTERS Requirements 1K rad/s -> -3dB • H(S)LP Normalized is obtained from LP Requirements Normalized • H(S)LP normalized can be transformed to a high-pass function by the frequency transformation 500 rad/s -> -18dB Example: Butterworth Electronic Filters Electrical Circuits - Celso José Faria de Araújo, M.Sc.

  44. BAND-PASS FILTERS Requirements Elliptic • H(S)BP Normalized is obtained from LP Requirements Normalized • H(S)LP normalized can be transformed to a band-pass function by the frequency transformation Example: Amax = 0.5dB Amin = 20 dB Passband = 500 Hz to 1000 Hz Stopbands = DC to 275 Hz and 2000 Hz to  Electronic Filters Electrical Circuits - Celso José Faria de Araújo, M.Sc.

  45. BAND-REJECT FILTERS Requirements Chebyshev • H(S)BR Normalized is obtained from LP Requirements Normalized • H(S)LP normalized can be transformed to a band-reject function by the frequency transformation Example: Amax = 1dB Amin = 20 dB Passbands = below 1000 Hz and above 6000 Hz Stopband = 2500 Hz to 3000 Hz Electronic Filters Electrical Circuits - Celso José Faria de Araújo, M.Sc.

  46. First-order filters. Electronic Filters Electrical Circuits - Celso José Faria de Araújo, M.Sc.

  47. First-order all-pass filter. Electronic Filters Electrical Circuits - Celso José Faria de Araújo, M.Sc.

  48. Second-order filtering functions. Electronic Filters Electrical Circuits - Celso José Faria de Araújo, M.Sc.

  49. Second-order filtering functions. (continued 1) Electronic Filters Electrical Circuits - Celso José Faria de Araújo, M.Sc.

  50. Second-order filtering functions. (continued 2) Electronic Filters Electrical Circuits - Celso José Faria de Araújo, M.Sc.

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