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Elec and Comp Tech 62B Circuits and Systems

Elec and Comp Tech 62B Circuits and Systems. Chapter 9 Active Filters. Overview. Basic filter responses Filter response characteristics Active low-pass filters Active high-pass filters Active band-pass filters Active band-stop filters Filter response measurements. Basic Filter Responses.

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Elec and Comp Tech 62B Circuits and Systems

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  1. Elec and Comp Tech 62BCircuits and Systems Chapter 9 Active Filters

  2. Overview • Basic filter responses • Filter response characteristics • Active low-pass filters • Active high-pass filters • Active band-pass filters • Active band-stop filters • Filter response measurements 62Bchap9a

  3. Basic Filter Responses • A low-pass filter passes frequencies up to certain frequency, then attenuates frequencies above that frequency. 62Bchap9a

  4. Basic Filter Responses • The cutoff or critical frequency, fc, defines the end of the passband, and is where the output has dropped –3 dB • 70.7% of the voltage • 50% of the power • Also called the “half power” or “3 dB down” point • Since the filter response is from DC to fcthe bandwidth (BW) = fc. • The attenuation slope is determined by the number of poles, or bypass circuits 62Bchap9a

  5. Roll-off Rate • A single pole (bypass circuit), such as a RC filter, rolls off at a -20 dB/decade (same as a -6 db/octave) rate • 2 poles produce a -40 db/decade, 3 poles produce -60 db/decade, and so on. 62Bchap9a

  6. Transition Region • The transition region is the span of frequencies in between the passband and the constant-slope roll-off • Cascading multiple passive filter networks produces a large and gradual transition region, an undesirable filter characteristic. • Active filters allow for multiple poles with a smaller transition region 62Bchap9a

  7. High-Pass Filters • A high-pass filter attenuates frequencies below fc and passes frequencies above fc. 62Bchap9a

  8. Band-Pass Filters • A band-pass filter has two critical frequencies, fc1 and fc2 • BW = fc2–fc1 • The center frequency fo = fc1fc2 62Bchap9a

  9. Band-Stop Filters • A band-pass filter has two critical frequencies, fc1 and fc2 • BW = fc2–fc1 • The center frequency fo = fc1fc2 62Bchap9a

  10. Filter Response Characteristics • In active filters, tailoring the feedback to alter the transition region defines the response characteristic. • The most common are Butterworth, Chebyshev, and Bessel 62Bchap9a

  11. Filter Response 62Bchap9a

  12. Damping Factor • The damping factor of an active filter circuit determines the response characteristic. • The correct damping factor for the desired response depends on the number of poles • For a 2nd-order (2 poles)Butterworth filter, thedamping factor is 1.414 • DF=2–R1/R2 62Bchap9a

  13. Sallen-Key Low-Pass Filter • A basic building-block for 2nd-order filters is the Sallen-Key filter. 62Bchap9a

  14. Sallen-Key Parameters • For simplicity, make CA=CB and RA=RB. Then, fc=1/2πRC 62Bchap9a

  15. Sallen-Key Parameters • For Butterworth damping factor of 1.414, R1/R2=.586, so if R2=1kΩ, R1=586 Ω 62Bchap9a

  16. 3rd & 4th-Order Low-Pass Filter • All R and C filter values are equal • R1 through R4 damping values are taken from tables (pg. 478) 62Bchap9a

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