Active Filter Circuits
ECE307-10Active Filter CircuitsZ. AliyaziciogluElectrical and Computer Engineering DepartmentCal Poly PomonaActive Filter CircuitsIntroductionFilter circuits with RLC are passive filter circuitUse op amp to have active filter circuitActive filter can produce band-pass and band-reject filter withoutusing inductor.Passive filter incapable of amplification. Max gain is 1Active filter capable of amplificationThe cutoff frequency and band-pass magnitude of passive filtercan change with additional load resistanceThis is not a case for active filtersWe look at few active filter with op amps.We look at that basic op amp filter circuits can be combined toactive specific frequency response and to attain close to idealfilter responseECE 307-10 21
Active Filter CircuitsExample w 0.1:.1:10; h 20*log10(abs(1./(1 j*w))); semilogx(w,h) grid on xlabel('\omega(rad/s)') ylabel(' H(j\omega) dB') ECE 307-10 5Active Filter CircuitsA first order high-pass filterR2R1C-ViOUT VoTransfer function of the circuitH (s ) H (s ) R2ss1 H ( s ) KR1(s )(s ω c )R1CThe GainK R2R1 ZfZiH (s ) R2 R2sC 1R1sC 1R1 sCTransfer function in jωCutoff frequencyωc 1R1CH ( j ω ) Kjωωc(1 jω)ωcECE 307-10 63
Active Filter CircuitsExampleR1ViR2C20 K 0.1 uF200KOUT Vo Find R2 and R1 values in the above active High-pass filterfor gain of 10 and cutoff frequency of 500 rad/s.From the cutoff frequencyFrom the gainK ωc 1 500R12CR1 1 20 K Ω500CR2 10 R2 R110 200 K ΩR1Transfer function in jωH ( jω ) 10jω500(1 jω500)ECE 307-10 7Active Filter CircuitsExample w 1:10000; h 20*log10(10*(abs((j*w/500)./(1 j*w/500)))); semilogx(w,h) grid on xlabel('\omega(rad/s)') ylabel(' H(j\omega) dB') ECE 307-10 84
Active Filter CircuitsScaling In filter design, we can transform RLC values in to realisticvalues, this process is called scaling Two types of scaling, magnitude and frequency scaling In magnitude scaling, we multiply all L and R by scalingfactor km, multiplying all C by 1/kmR ' kmRL ' km LC' Ckm km,is positive real numberECE 307-10 9Active Filter CircuitsScaling frequency scaling, we multiply all L, C by 1/kf where kf isscaling factor.R' RL' LkfC' Ckf A circuit can be scaled in both magnitude and frequency insimultanouslyR ' kmRkL' m LkfC' CkmkfECE 307-10 105
Active Filter CircuitsExample Example 1 , Find R2 and R1 values inthe active Low-pass filter for gain of 5and cutoff frequency of 1Khz andc 0.01 µFC1FR12R1Vi11OUT km Vokf ωc ' 2π 1000 6283.185ωc11 C1 15915.5kf C ' 6283.185(10 8 )R2 ' kmR2 15915.5(1) 15.9 K Ω For gain specification, we need to change R1R1 R2 15.9K 3.18 K ΩK5ECE 307-10 11Active Filter CircuitsExample f 1:10000; w 2*pi*f; h 20*log10(5*abs(1./(1 j*w/(2*pi*1000)))); semilogx(f,h) grid on xlabel(‘f(Hz)') ylabel(' H(jf) dB')ECE 307-10 126
Active Filter CircuitsOp Amp Band-Pass Filters Three componentsA unity gain low-pass filter, cutoff frequency is ωc2A unity gain high-pass filter , cutoff frequency ωc1A gain component to provide the desired levelωc 2 2ω c1ViLow-pass filterHigh-pass filterInverting amp.VoECE 307-10 13Active Filter CircuitsOp Amp Band-Pass FiltersCLRLRHRLRf-ViOUTRHCH- RfOUTOUT ωc 2 s Rf H (s ) s ωc 2 s ωc1 Ri H (s ) 2 K ω c 2 ss (ωc1 ωc 2 )s ωc1ωc 2ωc 2 ωc 1ωc 2 1RLCLH (s ) H (s ) ωc1 Vo K ω c 2 s(s ωc 2 )(s ωc1)βss β s ω022R1H ( j ω0 ) K fRimaxRHCHECE 307-10 147
Active Filter CircuitsExample: Design a band-pass filter for a graphical equalizer that hasgain 2 within the frequency between 100 and 10,000 Hz.Use 0.1 µF capacitors For upper cutoff frequency from LP filterωc 2 1RLCLRL 1ωc 2CL 12π 10000(0.1)10 6 80 Ω For Lower cutoff frequency from HP filterωc1 1RHCHRH 11 7958 Ωωc1CL 2π 100(0.1)10 6 For gain, choose Ri 1KΩK RfRiRf Ri K 1000(2) 2 K ΩECE 307-10 15Active Filter CircuitsFrom transfer function 2π 1000 2000 jωH ( jω ) A 20log10 H ( jω ) ωπωπ j21000j2100 1000 dB f 10:80000; w 2*pi*f; H ((2*pi*10000)./(j*w 2*pi*10000)).*((j*w)./(j*w 2*pi*100))*(-2); A 20*log10(abs(H)); semilogx(f,A) grid on; ylabel ('A {dB}') xlabel ('F (Hz)')ECE 307-10 168
Active Filter CircuitsOp Amp Band-Reject Filters Three componentsA unity gain low-pass filter, cutoff frequency is ωc1A unity gain high-pass filter , cutoff frequency ωc2A gain component to provide the desired levelLow-pass filterViVoInverting amp.High-pass filterECE 307-10 17Active Filter CircuitsOp Amp Band-Reject FiltersCL ωc1 s Rf H (s ) ssωωc 2 Ri c1 RLRLOUTRf RfVi-RHRHCHOUT OUTFor ωc 2 ωc1Rf H (s ) RfRi s 2 2ω s ω ω c1c1 c 2 (s ωc1)(s ωc 2 ) Voωc1 1RLCLH ( jω )ωc 2 max1RHCH K RfRiECE 307-10 189
Active Filter CircuitsExample: Design an active band-reject filter that has gain 5 and thestop frequency between 100 and 2000 Hz. Use 0.5 µFcapacitorsFc1 100Hz and Fc 2 2000Hzωc1 1RLCLωc 2 1RHCHRL For ωc 2 ωc111 3.18 K Ωωc1CL 2π 100(0.5)10 6RH 11 159 Ωωc 2CH 2π 2000(0.5)10 6 For gain, choose Ri 1KΩK RfRiRf Ri K 1000(5) 5 K ΩECE 307-10 19Active Filter Circuits ωc1 jω Rf H ( jω ) jω ωc1 jω ωc 2 Ri AdB 20log10 H ( jω ) f 10:80000; w 2*pi*f; H (((2*pi*100)./(j*w 2*pi*100)) ((j*w)./(j*w 2*pi*2000)))*(5); A 20*log10(abs(H)); semilogx(f,A) grid on; xlabel ('F (Hz)') ylabel ('A {dB}')ECE 307-10 2010
Use op amp to have active filter circuit Active filter can produce band-pass and band-reject filter without using inductor. Passive filter incapable of amplification. Max gain is 1 Active filter capable of amplification
Cook Medical Bird’s Nest Filter: C. Vena Tech LP FIlter: D. Bard Simon Nitinol Filter: E. Bard Recovery G2 Filter: F. Cook Medical Günther Tulip Filter: G. Cook Celect Filter: H. Cordis OPTEASE Filter: I. Argon Option Elite Filter: J. Crux VCF: K. ALN Optional Filter: Many other IVC f
Filter Gallery dialog box A. Preview B. Filter category C. Thumbnail of selected filter D. Show/Hide filter thumbnails E. Filters pop‑up menu F. Options for selected filter G. List of filter effects to apply or arrange H. Filter effect selected but not applied I. Filter effects applied cumulatively but not selected J. Hidden filter effect Display the Filter Gallery
Contemporary Electric Circuits, 2nd ed., Prentice-Hall, 2008 Class Notes Ch. 9 Page 1 Strangeway, Petersen, Gassert, and Lokken CHAPTER 9 Series–Parallel Analysis of AC Circuits Chapter Outline 9.1 AC Series Circuits 9.2 AC Parallel Circuits 9.3 AC Series–Parallel Circuits 9.4 Analysis of Multiple-Source AC Circuits Using Superposition 9.1 AC SERIES CIRCUITS
cava filters, such as Greenfield filter, Vena Tech filter, Bird s nest filter, Simon-Nitinol filter, TrapEase filter, Günther tulip filter, Antheor filter, Neuhaus protect filter, and Recovery- Nitinol filter, have been develope
15 Active Filter Circuits - 416 - 15.2 Low-Pass Filter A passive low-pass filter is one can sufficiently attenuate all frequencies above a certain frequency named as critical frequency fc and passes all frequencies below fc value. It has a basic filter element consists of
EMI FILTER There are several types of filters, for example, passive EMI filter, active EMI filter and hybrid EMI filter. However, the passive EMI filter is simpler than others. A typical procedure used in [4, 5] is considered to design power line EMI filter. A basic network topology is used, C-L-C for DM filter and L-C
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