Upload
gordon-hood
View
216
Download
0
Embed Size (px)
Citation preview
9/14/04 1
Elec and Comp Tech 62BElec and Comp Tech 62BCircuits and SystemsCircuits and Systems
Chapter 9Chapter 9
Active FiltersActive Filters
9/14/04 62Bchap9a Page 2
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
9/14/04 62Bchap9a Page 3
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.
9/14/04 62Bchap9a Page 4
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
9/14/04 62Bchap9a Page 5
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.
9/14/04 62Bchap9a Page 6
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
9/14/04 62Bchap9a Page 7
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..
9/14/04 62Bchap9a Page 8
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
9/14/04 62Bchap9a Page 9
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
9/14/04 62Bchap9a Page 10
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
9/14/04 62Bchap9a Page 11
Filter ResponseFilter ResponseFilter ResponseFilter Response
9/14/04 62Bchap9a Page 12
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
9/14/04 62Bchap9a Page 13
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.
9/14/04 62Bchap9a Page 14
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
9/14/04 62Bchap9a Page 15
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
9/14/04 62Bchap9a Page 16
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)