3.5 Sequential RC Filters

Chapter 3.5 Sequential RC Filters

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

  • CHAPTER 3. FILTER CIRCUITS52Figure 3.6: The transfer function from the table above.3.5Sequential RC FiltersSingle-pole filters are rather limited (6 dB/octave slope). For better band-pass and band-reject filters we require more poles and zeros and thus more reactive circuit elements. Asimple solution is to connect two or more single-pole RC filters in sequence. If filter H2draws no current from filter H1, the transfer function for the combined filter isH = H1H2(= H2H1).(3.43)One way to do this is to choose a large impedance for H2. Hence H has more poles andzeros than H1 or H2.The corner frequency for a high-pass filter is ωH =1/(RC) and the transfer function maybe written asHhigh =jωRC1+ jωRC=jω/ωH1+ jω/ωH.(3.44)For a low-pass filter the corner frequency is ωL =1/(RC) andHlow =11+ jωRC=11+ jω/ωL.(3.45)We may build a two-section low-pass filter by requiring R2 >R1 and 1/C2 > 1/C1,asshown in figure 3.7, so that