1、Active Filter Circuit:Bessel,Butterworth,Linkwitz.Active Filter Circuit:Bessel,Butterworth,Linkwitz.Active Filter Circuit:Bessel,Butterworth,Linkwitz.Active Filter Circuit:Bessel,Butterworth,Linkwitz.Bessel 12dB HighpassBessel 12dB HighpassBessel 12dB HighpassBessel 12dB Highpass(2st order,12 dB/oct
2、ave,Highpass)C=4.7n-10nF Ra=1.1017/(2*pi*Fc*C)Rb=1.4688/(2*pi*Fc*C)Units:Rx Ohm,C F,Fc Hz Bessel 12dB LowpassBessel 12dB LowpassBessel 12dB LowpassBessel 12dB Lowpass(2nd order,12 dB/octave,Lowpass)R=4.7k-10 kOhm Ca=0.9076/(2*pi*Fc*R)Cb=0.6809/(2*pi*Fc*R)Units:R Ohm,Cx F,Fc Hz Bessel 18dB HighpassBe
3、ssel 18dB HighpassBessel 18dB HighpassBessel 18dB Highpass(3st order,18 dB/octave,Highpass)C=4.7n-10nF Ra=1.0474/(2*pi*Fc*C)Rb=2.0008/(2*pi*Fc*C)Rc=1.3228/(2*pi*Fc*C)Units:Rx Ohm,C F,Fc Hz Bessel 18dB LowpassBessel 18dB LowpassBessel 18dB LowpassBessel 18dB Lowpass (3st order,18 dB/octave,Lowpass)R=
4、4.7k-10 kOhm Ca=0.9548/(2*pi*Fc*R)Cb=0.4998/(2*pi*Fc*R)Cc=0.7560/(2*pi*Fc*R)Units:R Ohm,Cx F,Fc Hz Bessel 24dB HighpassBessel 24dB HighpassBessel 24dB HighpassBessel 24dB Highpass(4th order,24 dB/octave,Highpass)C=4.7n-10nF Ra=1.3701/(2*pi*Fc*C)Rb=1.4929/(2*pi*Fc*C)Rc=0.9952/(2*pi*Fc*C)Rd=2.5830/(2*
5、pi*Fc*C)Units:Rx Ohm,C F,Fc Hz Bessel 24dB LowpassBessel 24dB LowpassBessel 24dB LowpassBessel 24dB Lowpass(4th order,24 dB/octave,Lowpass)R=4.7k-10 kOhm Ca=0.7298/(2*pi*Fc*R)Cb=0.6699/(2*pi*Fc*R)Cc=1.0046/(2*pi*Fc*R)Cd=0.3872/(2*pi*Fc*R)Units:R Ohm,Cx F,Fc Hz Linkwitz 24dB HighpassLinkwitz 24dB Hig
6、hpassLinkwitz 24dB HighpassLinkwitz 24dB Highpass(4st order,24 dB/octave,Highpass)C=4.7n-10nF Ra=Rc=1/(2*sqr(2)*pi*Fc*C)Rb=Rd=2Ra Units:Rx Ohm,C F,Fc Hz Linkwitz 24dB LowpassLinkwitz 24dB LowpassLinkwitz 24dB LowpassLinkwitz 24dB Lowpass(4th order,24 dB/octave,Lowpass)R=4.7k-10 kOhm Ca=Cc=2*Cb Cb=Cd
7、=1/(2*sqr(2)*pi*Fc*R)Units:R Ohm,Cx F,Fc Hz Butterworth 6dB HighpassButterworth 6dB HighpassButterworth 6dB HighpassButterworth 6dB Highpass(1st order,6 dB/octave,Highpass)C=4.7n-10nF R=1.000/(2*pi*Fc*C)Units:R Ohm,C F,Fc Hz Butterworth 6dB LowpassButterworth 6dB LowpassButterworth 6dB LowpassButter
8、worth 6dB Lowpass(1st order,6 dB/octave,Lowpass)R=4.7k-10 kOhm C=1.000/(2*pi*Fc*R)Units:R Ohm,C F,Fc Hz Butterworth 12dB HighpassButterworth 12dB HighpassButterworth 12dB HighpassButterworth 12dB Highpass (2st order,12 dB/octave,Highpass)C=4.7n-10nF Ra=0.7071/(2*pi*Fc*C)Rb=1.414/(2*pi*Fc*C)Units:Rx
9、Ohm,C F,Fc Hz Butterworth 12dB LowpassButterworth 12dB LowpassButterworth 12dB LowpassButterworth 12dB Lowpass (2nd order,12 dB/octave,Lowpass)R=4.7k-10 kOhm Ca=1.414/(2*pi*Fc*R)Cb=0.7071/(2*pi*Fc*R)Units:R Ohm,Cx F,Fc Hz Butterworth 18dB HighpassButterworth 18dB HighpassButterworth 18dB HighpassBut
10、terworth 18dB Highpass(3st order,18 dB/octave,Highpass)C=4.7n-10nF Ra=0.500/(2*pi*Fc*C)Rb=2.000/(2*pi*Fc*C)Rc=1.000/(2*pi*Fc*C)Units:Rx Ohm,C F,Fc Hz Butterworth 18dB LowpassButterworth 18dB LowpassButterworth 18dB LowpassButterworth 18dB Lowpass(3st order,18 dB/octave,Lowpass)R=4.7k-10 kOhm Ca=2.00
11、0/(2*pi*Fc*R)Cb=0.500/(2*pi*Fc*R)Cc=1.000/(2*pi*Fc*R)Units:R Ohm,Cx F,Fc Hz Butterworth 24dB HighpassButterworth 24dB HighpassButterworth 24dB HighpassButterworth 24dB Highpass(4th order,24 dB/octave,Highpass)C=4.7n-10nF Ra=0.9239/(2*pi*Fc*C)Rb=1.0824/(2*pi*Fc*C)Rc=0.3827/(2*pi*Fc*C)Rd=2.6130/(2*pi*
12、Fc*C)Units:Rx Ohm,C F,Fc Hz Butterworth 24dB LowpassButterworth 24dB LowpassButterworth 24dB LowpassButterworth 24dB Lowpass (4th order,24 dB/octave,Lowpass)R=4.7k-10 kOhm Ca=1.0824/(2*pi*Fc*R)Cb=0.9239/(2*pi*Fc*R)Cc=2.6130/(2*pi*Fc*R)Cd=0.3827/(2*pi*Fc*R)Units:R Ohm,Cx F,Fc Hz http:/ TypeTypeTypeTy
13、pe PropertiesPropertiesPropertiesProperties Transfer FuncTransfer FuncTransfer FuncTransfer Function(Lowpass)tion(Lowpass)tion(Lowpass)tion(Lowpass)Butterworth Maximally flat near the center of the band.Smooth transition from passband to stopband.Moderate out-of-band rejection.Low group delay variat
14、ion near center of band.Moderate group delay variation near band edges.Table of poles for N=1 to 10.Chebyshev Equiripple in passband.Abrupt transition from passband to stopband.High out-of-band rejection.Rippled group delay near center of band.Large group delay variation near band edges.Table of pol
15、es for N=1 to 10.Bessel Rounded amplitude in passband.Gradual transition from passband to stopband.Low out-of-band rejection.Very flat group delay near center of band.Flat group delay variation near band edges11.Note:BN,PN,and boN must be Table of poles for N=1 to 10.placed in a loop from 0 through
16、N.Ideal Flat in the passband.Step function transition from passband to stopband.Infinite out-of-band rejection.Zero group delay everywhere.(Heaviside step function)Filters Website:Filters Website:Filters Website:Filters Website:http:/ AutoAutoAutoAuto-calculation Formula calculation Formula calculat
17、ion Formula calculation Formula for Filters:for Filters:for Filters:for Filters:http:/beis.de/Elektronik/Filter/ActiveLPFilter.html http:/beis.de/Elektronik/Filter/ActiveHPFilter.html http:/beis.de/Elektronik/Filter/Act3PoleLP.html Filter TopologyFilter TopologyFilter TopologyFilter Topology The mos
18、t common filter topologies are Sallen-Key and Multiple Feedback filters.The major differences are:S S S Sallenallenallenallen-KeyKeyKeyKey Multiple FeedbackMultiple FeedbackMultiple FeedbackMultiple Feedback Non-inverting Inverting Very precise DC-gain of 1 Any gain is dependent on the resistor precision Less components for gain=1 Less components for gain 1 or 1 Op-amp input capacity must possibly be taken into account Op-amp input capacity has almost no effect Resistive load for sources even in high-pass filters Capacitive loads can become very high for sources in high-pass filters