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MALVINO

SIXTH EDITION. MALVINO. Electronic. PRINCIPLES. Active Filters. Chapter 21. A. A. f. f. f c. A. Ideal filter responses. Low-pass. Bandpass. BW. f. f 1. f 2. All-pass. A. A. High-pass. Bandstop. f. f. f c. f 1. f 2. Real filter response.

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MALVINO

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  1. SIXTH EDITION MALVINO Electronic PRINCIPLES

  2. Active Filters Chapter 21

  3. A A f f fc A Ideal filter responses Low-pass Bandpass BW f f1 f2 All-pass A A High-pass Bandstop f f fc f1 f2

  4. Real filter response • Ideal (brickwall) filters do not exist. • Real filters have an approximate response. • The attenuation of an ideal filter is  in the stopband. • Real filter attenuation is vout/vout(mid): 3 dB = 0.5 12 dB = 0.25 20 dB = 0.1

  5. The order of a filter • In an LC type, the order is equal to the number of inductors and capacitors in the filter. • In an RC type, the order is equal to the number of capacitors in the filter. • In an active type, the order is approximately equal to the number of capacitors in the filter.

  6. Filter approximations • Butterworth (maximally flat response): rolloff = 20n dB/decade where n is the order of the filter • Chebyshev (equal ripple response): the number of ripples = n/2 • Inverse Chebyshev (rippled stopband). • Elliptic (optimum transition) • Bessel (linear phase shift)

  7. A f A A Real low-pass filter responses Chebyshev Butterworth f f Bessel Inverse Chebyshev A A Elliptic f f Note: monotonic filters have no ripple in the stopband.

  8. A f A A Real bandpass filter responses Chebyshev Butterworth f f Bessel Inverse Chebyshev A A Elliptic f f

  9. 1 fr = 2p LC L C fR Q R Q = 9.55 mH 2.65 mF 1 kHz 10 XL 47.7 mH 531 nF 1 kHz 2 135 mH 187 nF 1 kHz 0.707 A second-order low-pass LC filter L R 600 W C vout vin

  10. 1 a = Q The effect of Q on second-order response Q = 10 (underdamped) A Q = 2 (underdamped) 20 dB Q = 0.707 (critically damped) 6 dB 0 dB rolloff = 40 dB/decade f fR or f0 The Butterworth response is critically damped. The Bessel response is overdamped (Q = 0.577 … not graphed). The damping factor is a.

  11. Q= 0.5 1 C2 fp = = pole frequency 2pR C1C2 C1 Sallen-Key second-order low-pass filter C2 R R vout vin C1 Av = 1

  12. Second-order responses • Butterworth: Q = 0.707; Kc = 1 • Bessel: Q = 0.577; Kc = 0.786 • Cutoff frequency: fc = Kcfp • Peaked response: Q > 0.707 • f0 = K0fp (the peaking frequency) • fc = Kcfp (the edge frequency) • f3dB = K3fp

  13. Higher-order filters • Cascade second-order stages to obtain even-order response. • Cascade second-order stages plus one first-order stage to obtain odd-order response. • The dB attenuation is cumulative. • Filter design can be tedious and complex. • Tables and filter-design software are used.

  14. R2 Av = + 1 R1 1 fp = 2pRC 1 Q = 3 - Av Sallen-Key equal-component filter C R R vout vin C R2 R1 As Av approaches 3, this circuit becomes impractical.

  15. Q= 0.5 1 R1 fp = 2pC R1R2 R2 Sallen-Key second-order high-pass filter R2 vout C C vin R1 Av = 1

  16. f0 BW = Q 1 R1+R3 f0 = Q= 0.707 2pC 2R1(R1 R3) R3 Tunable MFB bandpass filter with constant bandwidth C 2R1 R1 vout C vin R3 Av = -1

  17. R2 Av = + 1 0.5 R1 1 Q = f0 = 2 - Av 2pRC Sallen-Key second-order notch filter R/2 vin vout C C R R 2C R2 R1 As Av approaches 2, this circuit becomes impractical.

  18. f = -2 arctan 1 f f0 = 2pRC f0 First-order all-pass lag filter R’ R’ vout vin R C Av = 1

  19. 1 f0 = 2pRC First-order all-pass lead filter R’ R’ vout vin R C f0 f = 2 arctan Av = -1 f

  20. Linear phase shift • Required to prevent distortion of digital signals • Constant delay for all frequencies in the passband • Bessel design meets requirements but rolloff might not be adequate • Designers sometimes use a non-Bessel design followed by an all-pass filter to correct the phase shift

  21. R2 +1 R1 3 1 f0 = 2pRC State variable filter R vin R R Av = Q = C R C R1 R HP output LP output BP output R2

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