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 = 0.512 dB = 0.2520 dB = 0.1
5 The order of a filterIn 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 filterChebyshev (equal ripple response): the number of ripples = n/2Inverse Chebyshev (rippled stopband).Elliptic (optimum transition)Bessel (linear phase shift)
7 Real low-pass filter responses Inverse Chebyshev ButterworthffAfBesselInverseChebyshevAAEllipticffNote: monotonic filters have no ripple in the stopband.
8 Real bandpass filter responses Inverse Chebyshev ButterworthffAfBesselInverseChebyshevAAEllipticff
10 The effect of Q on second-order response Q = 10 (underdamped)AQ = 2 (underdamped)20 dB6 dBQ = (critically damped)0 dBa =Q1rolloff = 40 dB/decadeffR or f0The Butterworth response is critically damped.The Bessel response is overdamped (Q = … not graphed).The damping factor is a.
11 Sallen-Key second-order low-pass filter voutvinC1Q = 0.5C2C1Av = 12pRC1C21fp == pole frequency
13 Higher-order filtersCascade 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 Sallen-Key equal-component filter voutvinCAv =R2R1R2R1Q =13 - AvAs Av approaches3, this circuitbecomes impractical.2pRC1fp =
20 Linear phase shift Required to prevent distortion of digital signals Constant delay for all frequencies in the passbandBessel design meets requirements but rolloff might not be adequateDesigners sometimes use a non-Bessel design followed by an all-pass filter to correct the phase shift
21 State variable filter R2 R vin R +1 R R1 Av = Q = 3 C R C R1 R 1 f0 = HPoutputLPoutputf0 =2pRC1R2BPoutput