3.3.3 High-Pass Filter

Chapter 3.3.3 High-Pass Filter

Physics Lecture Notes – Phys 395 Electronics Book
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Physics Lecture Notes – Phys 395 Electronics Book

  • CHAPTER 3. FILTER CIRCUITS48CRBADCH1omega comegaomegaslope = 1Figure 3.3: RC high-pass filter.3.3.3High-Pass FilterFigure 3.3 shows one possible high-pass filter. Mathematically we can writeH(jω)=RR +1/(jωC)=jωRC1+ jωRC.(3.25)At low and high frequenciesHlow = jωRCandHhigh =1.(3.26)At the corner frequency ω = ωc we have|Hlow| =|Hhigh|(3.27)and thereforeωc =1RC.(3.28)3.3.4Approximate DifferentiatorA high-pass filter acts as an approximate differentiator at low frequencies. Considervin = vejωt(3.29)and differentiate to obtainvout =dvindt= jωvejωt = jωvin.(3.30)We defineHdifferentiate = jω =1RCHlow.(3.31)Again the filter attenuates the signal by 1/(RC).