Elec and Comp Tech 62B
Circuits and Systems
Chapter 9
Active Filters
9/14/04
1
Overview
Basic
filter responses
Filter
response characteristics
Active
low-pass filters
Active
high-pass filters
Active
band-pass filters
Active
band-stop filters
Filter
9/14/04
response measurements
62Bchap9a
Page 2
Basic Filter Responses
A
low-pass filter passes frequencies up to
certain frequency, then attenuates
frequencies above that frequency.
9/14/04
62Bchap9a
Page 3
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%

50% of the power
 Also

of the voltage
called the “half power” or “3 dB down” point
Since the filter response is from DC to fc
the bandwidth (BW) = fc.
 The
attenuation slope is determined by
the number of poles, or bypass circuits
9/14/04
62Bchap9a
Page 4
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.
9/14/04
62Bchap9a
Page 5
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
9/14/04
62Bchap9a
Page 6
High-Pass Filters
A
high-pass filter attenuates
frequencies below fc and passes
frequencies above fc.
9/14/04
62Bchap9a
Page 7
Band-Pass Filters
A
band-pass filter has two critical
frequencies, fc1 and fc2
 BW
= fc2–fc1
 The
center
frequency
fo = fc1fc2
9/14/04
62Bchap9a
Page 8
Band-Stop Filters
A
band-pass filter has two critical
frequencies, fc1 and fc2
 BW
= fc2–fc1
 The
center
frequency
fo = fc1fc2
9/14/04
62Bchap9a
Page 9
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
9/14/04
62Bchap9a
Page 10
Filter Response
9/14/04
62Bchap9a
Page 11
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, the
damping factor is 1.414
 DF=2–R1/R2
9/14/04
62Bchap9a
Page 12
Sallen-Key Low-Pass Filter
A
basic building-block for 2nd-order
filters is the Sallen-Key filter.
9/14/04
62Bchap9a
Page 13
Sallen-Key Parameters
For
simplicity, make CA=CB and
RA=RB. Then, fc=1/2πRC
9/14/04
62Bchap9a
Page 14
Sallen-Key Parameters
 For
Butterworth damping factor of 1.414,
R1/R2=.586, so if R2=1kΩ, R1=586 Ω
9/14/04
62Bchap9a
Page 15
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)
9/14/04
62Bchap9a
Page 16