Handbook for Sound Engineers

794 Chapter 23

filter sections to be connected together without concerns
for mutual interference.

More advanced active filters use filter components in
the feedback loop of a gain stage to add functionality
with fewer components. Active filters have advantages
over passive filters in that they can be made much
smaller, especially for low-frequency filters that would
otherwise use bulky inductors. The removal of inductors
also makes active filters less prone to low-frequency
hum interference. The disadvantages of active filters are
that they are more complex, having more components to
fail; require a power supply; and have a dynamic range
limited at the top by the power supply and at the bottom
by high-frequency self-noise in the amplifiers.

23.3.1 Filter Topologies

23.3.1.1 Sallen-Key

Sallen-Key filters are second-order high-pass or low-

pass sections exhibiting a 12 dB per octave cutoff slope

in the stop band. Equal component value filters are the

easiest to design, with the frequency-determining resis-

tors being of equal value and the frequency-determining

capacitors being of equal value. They have the advan-

tage of being able to high pass or low pass simply by

interchanging their positions.

In the second-order low pass of Fig. 23-15,

frequency is changed by scaling the values of R and C

in the input network in accordance with Eq. 23-42. To

keep the offset at a minimum, it is best to have R 0 equal

to the input impedance of 2R. Damping factor, d, is

controlled by the ratio of R (^) f and R 0 such that
(23-46)
The gain of the circuit is fixed at
Figure 23-13. Effects of termination impedance on three types of filter sections.
Frequency–Hz
Response–db
Response–db Response
db
Response
db
A. T network B. P network
Frequency–Hz
Matched source (6007

Voltage source (0 7 )
Matched source (6007

Voltage source (0 7 )
Frequency–Hz
Matched source (6007)
Voltage source (0 7 )
Voltage source (0 7 )
12 dB/octave
Response
db
Response
db
Matched source (6007)
Voltage source (0 7 )
Frequency–Hz
Voltage source (0 7 )
Matched source (6007)
Frequency–Hz
Frequency–Hz

.. C. Bridged-T network.

Rs Rs

Rs

RL RL

RL

V V

V

Matched source (60018 dB/octave 7  

Figure 23-14. Simple buffering of an active filter.

R

C

Amp Amp

Rf= 2 – dR 0