EE40Lecture 18Venkat AnantharamTransfer FunctionFrequency ResponseExample CircuitFiltersCommon Filter Transfer Function vs. FreqSlide 1EE40 Spring 2008 Venkat AnantharamEE40Lecture 18Venkat Anantharam3/07/08 Reading: Chap. 6: Filters, two-terminal elements, Bode plots.Slide 2EE40 Spring 2008 Venkat AnantharamTransfer Function• Transfer function is a function of frequency– Complex quantity– Both magnitude and phase are functions of frequencyTwo Port filter networkVinVout()()()outout ininVfVHfθθθ==∠−=∠outinVHVH(f)Slide 3EE40 Spring 2008 Venkat AnantharamFrequency Response• The shape of the frequency response of the complex ratio of phasors VOUT/VIN(i.e. both the magnitude and the phase) is a convenient means of classifying a circuit behavior and identifying key parameters. We will soon discuss quick and dirty ways of approximating this shape via a piecewise linear approximation based on asymptotes, as in the magnitude plot approximations below:FrequencyLow PassINOUTVVGainBreak pointINOUTVVFrequencyHigh PassGainBreak pointFYI: These are usually log of the ratio vs log frequency plotsMagnitude ofMagnitude ofOnly positive frequencies need be considered, since the plots for negative frequencies can be inferred from thisSlide 4EE40 Spring 2008 Venkat AnantharamExample Circuit−+AVTR2R1+VT+VOUTCVIN+A = 100INOUTnctionTransferFuVV=R1= 100,000 OhmscRcINOUTZZAZ+=VVR2= 1000 OhmsC = 10 uF)1()/1)/1(22CRjACjRjwCAINOUTωω+=+=VVSlide 5EE40 Spring 2008 Venkat AnantharamFilters• Filters are circuits designed to retain a certain frequency range and discard othersLow-pass: pass low frequencies and reject high frequenciesHigh-pass: pass high frequencies and reject low frequenciesBand-pass: pass some particular range of frequencies, reject other frequencies outside that bandNotch: reject a range of frequencies and pass all other frequenciesSlide 6EE40 Spring 2008 Venkat AnantharamCommon Filter Transfer Function vs. Freq()HfFrequencyHigh Pass()HfFrequencyLow Pass()HfFrequencyBand PassFrequencyBand Reject()HfMagnitude ofMagnitude ofMagnitude ofMagnitude
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