9/14/041 elec and comp tech 62b circuits and systems chapter 9 active filters

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

Chapter 9Chapter 9

Active FiltersActive Filters

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OverviewOverviewOverviewOverviewBasic filter responsesBasic filter responses

Filter response characteristicsFilter response characteristics

Active low-pass filtersActive low-pass filters

Active high-pass filtersActive high-pass filters

Active band-pass filtersActive band-pass filters

Active band-stop filtersActive band-stop filters

Filter response measurementsFilter response measurements

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

defines the end of the defines the end of the passbandpassband, and is , and is

where the output has dropped –3 dBwhere the output has dropped –3 dB70.7% 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 RateRoll-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 RegionTransition 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 FiltersHigh-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 FiltersBand-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 FiltersBand-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 CharacteristicsCharacteristicsFilter 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 ResponseFilter ResponseFilter Response

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Damping FactorDamping FactorDamping 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, the

damping 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 FilterSallen-Key Low-Pass FilterSallen-Key Low-Pass Filter

A 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 ParametersSallen-Key ParametersSallen-Key Parameters

For 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 ParametersSallen-Key ParametersSallen-Key Parameters

For 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 Filter33rdrd & 4 & 4thth-Order Low-Pass Filter-Order Low-Pass Filter

All 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)

9/14/041 elec and comp tech 62b circuits and systems chapter 9 active filters

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