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).