filters滤波器习题讲解

[e-mail]@esat.kuleuven.beESAT-MICASAnalogbuildingblocksforsignalprocessing2Exercise1:assignment•DesignaBP-filter,usingthefilterdesignflowfromthecourse,accordingtofollowingspecifications:–BW=3kHz–f0=5kHz–Passbandgain=0dB–10dBattenuation@f03kHz•UseabutterworthfilterapproximationAnalogbuildingblocksforsignalprocessing3Exercise1:assignment•Step1:Drawabodediagramofthefilter•Step2:Normalizethefilteranddeterminethefilterorder.–Drawabodediagramofthenormalizedfilter–Determinetheminimumfilterorderforabutterworthapprox.•Step3:DeterminethefilterTF(Approximation)•Step4:Realizethefilter–Cascadeofbiquads–Passivefilter•Step5:Implementthefilter–Sallen&KeyActive-RC–leapfrogAnalogbuildingblocksforsignalprocessing4Exercise1:solutionI•Step1:drawabodediagramofthefilterExercise1:solutionIIa•Step2:Normalizethefilteranddeterminethefilterorder:–LowPassFilter(LPF)•scalethecut-offfrequencyto1–HighPassFilter(HPF)•converttoaLPFwiththesamefilterorder(i.e.thesamefilter‘steepness’)•scalethecut-offfrequencyto1–BandPassFilter(BPF)•shiftthecenterfrequencytoDC•scalethecut-offfrequencyto1–BandStopFilter(BSF)•shiftthecenterfrequencytoDC•converttoaLPFwiththesamefilterorder(i.e.thesamefilter‘steepness’)•scalethecut-offfrequencyto1Analogbuildingblocksforsignalprocessing5Analogbuildingblocksforsignalprocessing6Exercise1:solutionIIb•Step2:Normalizethefilteranddeterminethefilterorder:()()22221120log1101.58nnNnNnHjNωωωω==+⇒−+≤−⇔≥=Implementationusinga2thorderLPFRemark:εissettoone(i.e.themaximumattenuationinthepass-bandisnotgivenandisthereforesetto3dB)Analogbuildingblocksforsignalprocessing7Exercise1:solutionIII•Step3:DeterminethefilterTF(Approximation)–2thorderButterworthfilter()2121LPHsss=++()()()220024325,3:94.2459106625pBPLPsBpBPBLPBPHsHssHsssssωω+===→=⇒=++++Analogbuildingblocksforsignalprocessing8Exercise1:solutionIV•Step4:RealizethefilterusingacascadeofbiquadsSallen&Keygeneralfilter:outvvvv=⇒=+−+Analogbuildingblocksforsignalprocessing9Exercise1:solutionV•Sallen&Keygeneralfilter()341241234outinvZZvZZZZZZZ=+++Analogbuildingblocksforsignalprocessing10Exercise1:solutionVI•Low-passfilter()()3412412342212121211outinvZZvZZZZZZZCRRsCCRRs=+++=+++Analogbuildingblocksforsignalprocessing11Exercise1:solutionVI•Highpassfilter()()34124123421212211212121outinvZZvZZZZZZZRRCCsRCCsRRCCs=+++=+++Analogbuildingblocksforsignalprocessing12Exercise1:solutionVII•Bandpassfilter()3412412341112112122112121111outinbafbaffvZZvZZZZZZZRsRRCRRRssRCRCRCRRCRRRCC=++++=++++−+Analogbuildingblocksforsignalprocessing13Exercise1:solutionIX()24322294.2459106625332.5738.451.6716.25BPpHppppppppppp=++++=⋅++++•Solution1()12111112121211112222121111211121211111111211121121222122222221212222111111111bbaaBPffbbaffaffRRssRRCRRCHsRRRRRRssssRCRCRCRRCRRRCCRCRCRCRRCRRRC++=⋅+++++−++++−+222CSection1Section2Analogbuildingblocksforsignalprocessing14Exercise1:solutionVIII()243222294.2459106625912.5738.451.6716.25BPpHpppppppppp=++++=⋅++++•Solution2()()+++⋅+++=222122212221222221112111211111221112111111)(sCCRRsRRCsCCRRsCCRsCCRRsHBPSection1Section2Exercise1:solutionIX•Whichcascadeisbetter?–AcascadeofBPFismorerobusttocomponentvariations(i.e.thepositionofthepolesandzerosisdeterminedbyeachsectionandnotbyonlyonesection)–AcascadeofaLPFandaBPFislesscomplex(remark:itisevenbettertoputtheLPFsectioninthefronttofilterHFnoisefirst)Analogbuildingblocksforsignalprocessing15Analogbuildingblocksforsignalprocessing16Exercise1:solutionX•Step4finish:denormalisethefilterandchooseappropriatevaluesforRandC(dependingontheimplementation):–Denormalisation:replacepwithp’/(2*pi*scalefactor),e.g.todenormaliseanLPFwithacut-offfrequencyof1toacut-offfrequencyof2kHz:•Step5:Implementthefilterwith:–ActiveRC–MOSFET-C–Gm-C–Switchcapacitors–…20002'1111πpp+⇒+Analogbuildingblocksforsignalprocessing17Exercise1:solutionXI•Step4:Realizethefilterusingapassivefilter(usingfiltersolutions)Analogbuildingblocksforsignalprocessing18Exercise1:solutionXII•Step5:Implementthefilterwithleapfrogimplementation1332412314435244254sLVVVIIRsLIVsCIVVVsCVIsLVIR−=−−==−−==Analogbuildingblocksforsignalprocessing19Exercise1:solutionXIII'133241231'44352'442'45sLVVVVRRVRsLVVsRCVVVVsRCVVRsLVVRR−=−−==−−==•Replaceeverycurrentbyanequivalentvoltage1332412314435244254sLVVVIIRsLIVsCIVVVsCVIsLVIR−=−−==−−==Analogbuildingblocksforsignalprocessing20Exercise1::solutionXIV•Drawaflowchartscheme()1HssRC−=Analogbuildingblocksforsignalprocessing21Exercise2:assignment•Determine•FindC2if–fs=8MS/s–fp=2.5MHz–C1=0.2pF()outpinpVzVAnalogbuildingblocksforsignalprocessing22Exercise2:solutionI•2phases:Thesystemcanbedecomposedintwoseparatesystems,oneforeachphase.Thetwosystemsareinterdependentthroughthechargesonthecommonnodes.Thesechargesareassumedtoremainunchangedduringatransitionfromonephasetothenext.φ1iscalledtheevenphase,φ2istheoddphase.Analogbuildingblocksforsignalprocessing23Exercise2:soluti