O-K-State BAE 5413 - Signal Filtering - D1760259

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O-K-State BAE 5413 - Signal Filtering

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Signal FilteringFirst Order Low Pass FilterSlide 3Plotting Frequency responseSlide 5Adding terms of Frequency ResponseSecond Order Low Pass FilterSlide 8Slide 9First Order High Pass FilterSlide 11PowerPoint PresentationSlide 13Slide 142/18/01 BAE 5413 1Signal FilteringPassive filters2/18/01 BAE 5413 2First Order Low Pass Filter•Consider the following circuit–A signal with a desired signal and an interference signal may be supplied. The interference is at a high frequency in this case and the desired at a low frequency:InputSignaloutputSignalRCCRii RviRRdtdvCioutCdtdvCRvoutRoutinCinRvvvvv dtdvCRvvoutoutinoutoutinvdtdvRCv 2/18/01 BAE 5413 3First Order Low Pass Filter•Assuming deviation variables:•First order system–Ratio of output to input will follow ideal response for a first order system–Easily calculated by substituting i for s and computing |G(i)| and G(i))()()( svsRCsvsvoutoutin1111)()(sRCssvsvinout2/18/01 BAE 5413 4Plotting Frequency response-40-35-30-25-20-15-10-500.01 0.1 1 10 100Frequency * tau ()Magnitude Ratio (db)2/18/01 BAE 5413 5Plotting Frequency response-90-80-70-60-50-40-30-20-1000.01 0.1 1 10 100Frequency * tau ()Phase Lag (degrees)2/18/01 BAE 5413 6Adding terms of Frequency Response        iGiGiGiG2121log20log20log20        iGiGiGiG2121 iG1 iG2We can simply add terms on the Bode Magnitude plotand on the Bode Phase plot to get total response2/18/01 BAE 5413 7Second Order Low Pass FilteroutputSignalInputSignalC1R1C2R211)(11ssG11)(22ssG1111)(21sssG1111)(21iiiG11log2011log20)(log2021iiiG1111)(21iiiGThis works as long as the assumption of no current flowing between R1 and R2 holds. Make R2 >> R12/18/01 BAE 5413 8Plotting Frequency response-80-70-60-50-40-30-20-1000.01 0.1 1 10 100Frequency * tau ()Magnitude Ratio (db)2/18/01 BAE 5413 9Plotting Frequency response-180-160-140-120-100-80-60-40-2000.01 0.1 1 10 100Frequency * tau ()Phase Lag (degrees)2/18/01 BAE 5413 10First Order High Pass Filter•Consider the following circuitInputSignaloutputSignalRCCRii RvioutRdtdvCiCCdtdvCRvCoutoutinRinCvvvvv dtvvdCRvoutinout)( outoutinvdtdvRCdtdvRC )()()( svsRCsvsRCsvoutoutin11)()(ssRCsRCssvsvinout2/18/01 BAE 5413 11First Order High Pass Filter 111iiiiiG 11log20log20log20iiiG220iFreq.|G(i)|20log|G(i)|.1/0.1 -201/1 010/10 202/18/01 BAE 5413 12 11iiiG01900tan i2/18/01 BAE 5413 13Plotting Frequency response-40-30-20-100102030400.01 0.1 1 10 100Frequency * tau ()Magnitude Ratio (db)1/(s+1)ss/(s+1)2/18/01 BAE 5413 14Plotting Frequency response-90-70-50-30-1010305070901100.01 0.1 1 10 100Frequency * tau ()Phase Lag

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