Electronic PRINCIPLES

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Pauline Wilson
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1 MALVINO & BATES Electronic PRINCIPLES SEVENTH EDITION

2 Chapter 21 Active Filters

3 Topics Covered in Chapter 21 Ideal responses Approximate responses Passive ilters First-order stages VCVS unity-gain second-order low pass ilters Higher order ilters

4 Topics Covered in Chapter 21 (Continued) VCVS equal-component low pass ilters VCVS high pass ilters MFB bandpass ilters Bandstop ilters The all-pass ilter Biquadratic and state-variable ilters

5 A V Low-pass Ideal ilter responses A V BW Bandpass c 1 2 A V All-pass A V High-pass A V Bandstop c 1 2

6 Real ilter response Ideal (brickwall) ilters do not exist Real ilters have an approximate response The attenuation o an ideal ilter is in the stopband Real ilter attenuation is v out /v out(mid) : 3 db = db = db = 01

7 Approximate responses The passband is identiied by its low attenuation and its edge requency The stopband is identiied by its high attenuation and edge requency The order o a ilter is the number o reactive components

8 The order o a ilter In an LC type, the order is equal to the number o inductors and capacitors in the ilter In an RC type, the order is equal to the number o capacitors in the ilter In an active type, the order is approximately equal to the number o capacitors in the ilter

9 Filter approximations Butterworth (maximally lat response): rollo = 20n db/decade where n is the order o the ilter Chebyshev (equal ripple response): the number o ripples = n/2 Inverse Chebyshev (rippled stopband) Elliptic (optimum transition) Bessel (linear phase shit)

10 A V Butterworth Real low-pass ilter responses A V Chebyshev A V Bessel A V Inverse Chebyshev A V Elliptic Note: monotonic ilters have no ripple in the stopband

11 A V Butterworth Real bandpass ilter responses A V Chebyshev A V Bessel A V Inverse Chebyshev A V Elliptic

12 Passive ilters A low-pass LC ilter has a resonant requency and a Q The response is maximally lat when Q = 0707 As Q increases, a peak appears in the response, centered on the resonant requency

13 A second-order low-pass LC ilter L r = 1 2π LC v in C R 600 Ω v out R Q = XL L C R Q 955 mh 265 µf 1 khz mh 531 nf 1 khz mh 187 nf 1 khz 0707

14 The eect o Q on second-order response 20 db 6 db 0 db A Q = 10 (underdamped) Q = 2 (underdamped) Q = 0707 (critically damped) α = 1 Q rollo = 40 db/decade R or 0 The Butterworth response is critically damped The Bessel response is overdamped (Q = 0577 not graphed) The damping actor is α

15 First-order stages Have a single capacitor and one or more resistors Produce a Butterworth response because peaking is only possible in second-order or higher stages Can produce either a low-pass or a highpass response

16 Sallen-Key second-order low-pass ilter C 2 R R v in C 1 v out Q = 05 C 2 C 1 1 p = 2πR C 1 C 2 A v = 1 = pole requency

17 Second-order responses Most common and easy to implement and analyze Butterworth: Q = 0707; K c = 1 Bessel: Q = 0577; K c = 0786 Cuto requency: c = K c p Peaked response: Q > 0707 * 0 = K 0 p (the peaking requency) * c = K c p (the edge requency) * 3dB = K 3 p

18 Higher-order ilters Cascade second-order stages to obtain even-order response Cascade second-order stages plus one irst-order stage to obtain odd-order response The db attenuation is cumulative Filter design can be tedious and complex Tables and ilter-design sotware are used

19 VCVS equal component low-pass ilters The Sallen-Key equal component ilters control the Q by setting the voltage gain Higher Qs are diicult to get because o component tolerance

20 Sallen-Key equal-component ilter C v in R R R 2 A v = + 1 R 1 Q = p = 1 2πRC C R 1 R A v As A v approaches v out 3, this circuit becomes impractical and may oscillate

21 VCVS high-pass ilters Have the same coniguration as low-pass, except the resistors and capacitors are interchanged The Q values determine the K values

22 Sallen-Key second-order high-pass ilter R 2 v in C C v out R 1 Q = 05 R 1 R 2 1 p = 2πC R 1 R 2 A v = 1

23 MFB bandpass ilters Low-pass and high-pass ilters can be cascaded to get a bandpass ilter i the Q is less than 1 I the Q is greater than 1, a narrowband rather than a wideband ilter results

24 Tunable MFB bandpass ilter with constant bandwidth C 2R 1 R 1 v in C v out R 3 A v = -1 BW = 0 Q 0 = 2πC 1 2R 1 (R 1 R 3 ) Q = 0707 R 1 +R 3 R 3

25 Sallen-Key second-order notch ilter R/2 v in C R 2C C R R 2 1 Q = 05 As A 0 = v approaches 2 - A v 2πRC 2, this circuit R 2 v out R 1 A v = + 1 R 1 becomes impractical and may oscillate

26 The all-pass ilter Passes all requencies with no attenuation Controls the phase o the output signal Used as a phase or time-delay equalizer

27 First-order all-pass lag ilter R R v out v in A v = 1 R 1 0 = 2πRC C φ = -2 arctan 0

28 First-order all-pass lead ilter R R v out v in A v = -1 C 1 0 = 2πRC R 0 φ = 2 arctan

29 Linear phase shit Required to prevent distortion o digital signals Constant delay or all requencies in the passband Bessel design meets requirements but rollo might not be adequate Designers sometimes use a non-bessel design ollowed by an all-pass ilter to correct the phase shit

30 Biquadratic ilter Also called a TT ilter Uses three or our op amps Complex but oers lower component sensitivity and easier tuning Has simultaneous low-pass and bandpass outputs

31 Biquadratic stage

32 State-variable ilter Also called the KHN ilter Uses three or more op amps When a ourth op amp is used, it oers easy tuning because voltage gain, center requency, and Q are all independently tunable

33 State variable stage v in R R = 2πRC R HP output R R 2 R C A v = Q = R BP output R 2 R C LP output

Introduction (cont )

Introduction (cont ) Active Filter 1 Introduction Filters are circuits that are capable of passing signals within a band of frequencies while rejecting or blocking signals of frequencies outside this band. This property of