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Elec and Comp Tech 62BElec and Comp Tech 62BCircuits and SystemsCircuits and Systems

Chapter 9Chapter 9Active FiltersActive Filters

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OverviewOverviewBasic filter responsesBasic filter responsesFilter response characteristicsFilter response characteristicsActive low-pass filtersActive low-pass filtersActive high-pass filtersActive high-pass filtersActive band-pass filtersActive band-pass filtersActive band-stop filtersActive band-stop filtersFilter response measurementsFilter response measurements

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Basic Filter ResponsesBasic Filter ResponsesA low-pass filter passes frequencies up to A low-pass filter passes frequencies up to

certain frequency, then attenuates certain frequency, then attenuates frequencies above that frequency.frequencies above that frequency.

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Basic Filter ResponsesBasic Filter ResponsesThe The cutoffcutoff or or critical frequencycritical frequency, , ffcc, defines , defines

the end of the the end of the passbandpassband, and is where the , and is where the output has dropped –3 dBoutput has dropped –3 dB

70.7% of the voltage70.7% of the voltage 50% of the power50% of the powerAlso called the “half power” or “3 dB down” pointAlso called the “half power” or “3 dB down” point

Since the filter response is from DC to Since the filter response is from DC to ffcc the the bandwidthbandwidth (BW) = (BW) = ffcc..

The attenuation slope is determined by The attenuation slope is determined by the number of the number of polespoles, or bypass circuits, or bypass circuits

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Roll-off RateRoll-off RateA single pole (bypass circuit), such as a A single pole (bypass circuit), such as a

RC filter, rolls off at a -20 dB/decade RC filter, rolls off at a -20 dB/decade (same as a -6 db/octave) rate(same as a -6 db/octave) rate

2 poles produce a 2 poles produce a -40 db/decade, 3 -40 db/decade, 3 poles produce -60 poles produce -60 db/decade, and so db/decade, and so on.on.

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Transition RegionTransition RegionThe transition region is the span of The transition region is the span of

frequencies in between the passband and frequencies in between the passband and the constant-slope roll-offthe constant-slope roll-off

Cascading multiple passive filter Cascading multiple passive filter networks produces a large and gradual networks produces a large and gradual transition region, an undesirable filter transition region, an undesirable filter characteristic.characteristic.

Active filters allow for multiple poles with Active filters allow for multiple poles with a smaller transition regiona smaller transition region

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High-Pass FiltersHigh-Pass FiltersA high-pass filter attenuates A high-pass filter attenuates frequencies below ffrequencies below fcc and passes and passes frequencies above ffrequencies above fcc..

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Band-Pass FiltersBand-Pass FiltersA band-pass filter has two critical A band-pass filter has two critical

frequencies, ffrequencies, fc1c1 and f and fc2c2

BW = fBW = fc2c2–f–fc1c1

The center The center frequency frequency ffoo = = f fc1c1ffc2c2

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Band-Stop FiltersBand-Stop FiltersA band-pass filter has two critical A band-pass filter has two critical

frequencies, ffrequencies, fc1c1 and f and fc2c2

BW = fBW = fc2c2–f–fc1c1

The center The center frequency frequency ffoo = = f fc1c1ffc2c2

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Filter Response Filter Response CharacteristicsCharacteristics

In active filters, tailoring the In active filters, tailoring the feedback to alter the transition feedback to alter the transition region defines the response region defines the response characteristic.characteristic.

The most common are The most common are Butterworth, Chebyshev, and Butterworth, Chebyshev, and BesselBessel

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Filter ResponseFilter Response

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Damping FactorDamping FactorThe damping factor of an active filter circuit The damping factor of an active filter circuit

determines the response characteristic.determines the response characteristic.The correct damping factor for the desired The correct damping factor for the desired

response depends on response depends on the number of polesthe number of poles

For a 2nd-order (2 poles)For a 2nd-order (2 poles)Butterworth filter, theButterworth filter, thedamping factor is 1.414damping factor is 1.414

DF=2–RDF=2–R11/R/R22

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Sallen-Key Low-Pass FilterSallen-Key Low-Pass FilterA basic building-block for 2nd-order A basic building-block for 2nd-order filters is the Sallen-Key filter.filters is the Sallen-Key filter.

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Sallen-Key ParametersSallen-Key ParametersFor simplicity, make CFor simplicity, make CAA=C=CBB and and RRAA=R=RBB. Then, f. Then, fcc=1/2πRC=1/2πRC

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Sallen-Key ParametersSallen-Key ParametersFor Butterworth damping factor of 1.414, For Butterworth damping factor of 1.414,

RR11/R/R22=.586, so if R=.586, so if R22=1kΩ, R=1kΩ, R11=586 Ω=586 Ω

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33rdrd & 4 & 4thth-Order Low-Pass Filter-Order Low-Pass FilterAll R and C All R and C

filter values filter values are equalare equal

RR11 through through RR44 damping damping values are values are taken from taken from tables tables (pg. 478)(pg. 478)