1 / 21

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.

hectorw
Download Presentation

MALVINO

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related