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Electronics Reference

Operation Amplifiers (Active Filters)

Basic Filter Responses

Low-Pass Filter:

Bandwidthlatex!encoded:base64,XHRleHRybXtCV309XHRleHRybXtmfV9j
Critical frequencylatex!encoded:base64,XHRleHRybXtmfV97Y309XGZyYWN7MX17MlxwaSBcdGV4dHJte1JDfX0=
Ideal Passbandlatex!encoded:base64,MFx0ZXh0cm17SHogdG8gZn1fe2N9

High-Pass Filter:

Critical frequencylatex!encoded:base64,XHRleHRybXtmfV97Y309XGZyYWN7MX17MlxwaSBcdGV4dHJte1JDfX0=
Ideal Passbandlatex!encoded:base64,XGdlcSBcdGV4dHJte2Z9X3tjfQ==

Band-Pass Filter:

Bandwidthlatex!encoded:base64,XHRleHRybXtCV309XHRleHRybXtmfV97Y3V9LVx0ZXh0cm17Zn1fe2NsfQ==

fcu - Upper critical frequency
fcl - Lower critical frequency
Center frequencylatex!encoded:base64,XHRleHRybXtmfV97XHRleHRybXtvfX09XHNxcnR7XHRleHRybXtmfV97Y2x9XHRleHRybXtmfV97Y3V9fQ==
Quality Factorlatex!encoded:base64,XHRleHRybXtRfT1cZnJhY3tcdGV4dHJte2Z9X3tcdGV4dHJte299fX17XHRleHRybXtCV319PVxmcmFjezF9e1x0ZXh0cm17REZ9fQ==
 > Basic Filter Responses

Filter Damping Factor

latex!encoded:base64,XHRleHRybXtEYW1waW5nIEZhY3RvciAoREYpfT0gMi1cZnJhY3tcdGV4dHJte1J9XzF9e1x0ZXh0cm17Un1fMn0=

An op-amp based active filter can be designed to have either a Butterworth, Chebyshev, or Bessel response characteristic by setting the value of the damping factor (DF).

 > Filter Damping Factor

Low-Pass Filter

Single-PoleTwo-Pole (Sallen-Key)
Critical Frequencylatex!encoded:base64,XHRleHRybXtmfV97Y309XGZyYWN7MX17MlxwaSBcdGV4dHJte1JDfX0=latex!encoded:base64,XHRleHRybXtmfV97Y309XGZyYWN7MX17MlxwaSBcc3FydHtcdGV4dHJte1J9X3tcdGV4dHJte0F9fVx0ZXh0cm17Un1fe1x0ZXh0cm17Qn19XHRleHRybXtDfV97XHRleHRybXtBfX1cdGV4dHJte0N9X3tcdGV4dHJte0J9fX19
Roll-offlatex!encoded:base64,XHRleHRybXstMjBkQi9kZWNhZGV9latex!encoded:base64,XHRleHRybXstNDBkQi9kZWNhZGV9
Note: To obtain a filter with three poles or more, single-pole or two-pole filters are cascaded.
 > Low-Pass Filter

High-Pass Filter

Single-PoleTwo-Pole (Sallen-Key)
Critical Frequencylatex!encoded:base64,XHRleHRybXtmfV97Y309XGZyYWN7MX17MlxwaSBcdGV4dHJte1JDfX0=latex!encoded:base64,XHRleHRybXtmfV97Y309XGZyYWN7MX17MlxwaSBcc3FydHtcdGV4dHJte1J9X3tcdGV4dHJte0F9fVx0ZXh0cm17Un1fe1x0ZXh0cm17Qn19XHRleHRybXtDfV97XHRleHRybXtBfX1cdGV4dHJte0N9X3tcdGV4dHJte0J9fX19
Roll-offlatex!encoded:base64,XHRleHRybXstMjBkQi9kZWNhZGV9latex!encoded:base64,XHRleHRybXstNDBkQi9kZWNhZGV9
Note: To obtain a filter with three poles or more, single-pole or two-pole filters are cascaded.
 > High-Pass Filter

Band-Pass Filter

Lower critical frequencylatex!encoded:base64,XHRleHRybXtmfV97Y2x9PVxmcmFjezF9ezJccGkgXHNxcnR7XHRleHRybXtSfV97XHRleHRybXtBMX19XHRleHRybXtSfV97XHRleHRybXtCMX19XHRleHRybXtDfV97XHRleHRybXtBMX19XHRleHRybXtDfV97XHRleHRybXtCMX19fX0=
Upper critical frequencylatex!encoded:base64,XHRleHRybXtmfV97Y3V9PVxmcmFjezF9ezJccGkgXHNxcnR7XHRleHRybXtSfV97XHRleHRybXtBMn19XHRleHRybXtSfV97XHRleHRybXtCMn19XHRleHRybXtDfV97XHRleHRybXtBMn19XHRleHRybXtDfV97XHRleHRybXtCMn19fX0=
Center frequencylatex!encoded:base64,XHRleHRybXtmfV97XHRleHRybXtvfX09XHNxcnR7XHRleHRybXtmfV97Y2x9XHRleHRybXtmfV97Y3V9fQ==
Roll-offlatex!encoded:base64,XHRleHRybXstNDBkQi9kZWNhZGV9

 > Band-Pass Filter

Multiple-Feedback Band-Pass Filter

Center frequencylatex!encoded:base64,XHRleHRybXtmfV97XHRleHRybXtvfX09XGZyYWN7MX17MlxwaSBcdGV4dHJte0N9fSBcc3FydHtcZnJhY3tcdGV4dHJte1J9X3sxfStcdGV4dHJte1J9X3szfX17XHRleHRybXtSfV97MX1cdGV4dHJte1J9X3syfVx0ZXh0cm17Un1fezN9fX0=

where C1 = C2 = C
Gainlatex!encoded:base64,XHRleHRybXtBfV97XHRleHRybXtvfX09XGZyYWN7XHRleHRybXtSfV97Mn19ezJcdGV4dHJte1J9X3sxfX0=
Quality Factorlatex!encoded:base64,XHRleHRybXtRfT0yXHBpIFx0ZXh0cm17Zn1fe1x0ZXh0cm17b319XHRleHRybXtBfV97XHRleHRybXtvfX1cdGV4dHJte0N9XHRleHRybXtSfV97MX09XHBpIFx0ZXh0cm17Zn1fe1x0ZXh0cm17b319XHRleHRybXtDfVx0ZXh0cm17Un1fezJ9
Bandwidthlatex!encoded:base64,XHRleHRybXtCV309XGZyYWN7XHRleHRybXtmfV97XHRleHRybXtvfX19e1x0ZXh0cm17UX19
 > Multiple-Feedback Band-Pass Filter
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