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audio data sheets. They are used for antialiasing in front of
ADCs or for smoothing on the output of DACs. The follow-
ing bulletin is an excellent primer on the subject. 鈥擡d.
to digitize. Very often, these filters must be very complex,
high order analog filters in order to do their job effectively.
however, oversampling may be used to reduce the filters鈥?/div>
stopband attenuation requirements
(1)(2)
. In digital audio sys-
tems, 4x oversampling may be used, and it can be shown
(3)
that for an antialiasing filter (which precedes the ADC), a
simple sixth order filter may be used. For the output side,
after the DAC, a simple third order filter may be used.
Realizing these filters in a way that maintains extremely low
noise and low distortion then becomes a challenge.
Compact disk player manufacturers began using a filter
topology that was described many years ago鈥攖he General-
ized Immittance Converter (GIC)
(4)
. This topology allows
one to easily realize active filters beginning from a passive
filter design. In addition, the GIC filter provides extremely
low distortion and noise, at a reasonable cost. Compared
with more familiar feedback filter techniques, such as Sallen
& Key filter topologies, the GIC filter can be shown to have
superior noise gain characteristics, making it particularly
suitable for audio and DSP type applications
(5)
.
We use this type of filter on our demonstration fixtures for
the PCM1750 and PCM1700, dual 18-bit ADC and DAC,
respectively. When sending out schematics of these demon-
stration fixtures, very often the first question is, 鈥淲hat are
those filters anyway?鈥?Well, they鈥檙e GIC filters, and here鈥檚
how you design them and how they perform. Stepping
through this design process will allow you to modify these
designs for a different cutoff frequency for your particular
application. A more detailed treatment of the theory behind
these filters may be found in Huelsman and Allen
(6)
.
As stated above, for oversampling digital audio applications,
third and sixth order filters are adequate. Thus, we may
design our first GIC filter by designing a third order filter.
The filter characteristic most desirable for sensitive DSP
type applications is linear-phase. The linear-phase filter is
sometimes called a Bessel (or Thomson) filter. The linear-
phase filter has constant group delay. This means that the
phase of the filter changes linearly with frequency, or that
漏
L
1
0.9852H
L
3
0.3350H
C
2
0.8746F
R
4
1鈩?/div>
1
2
3
FIGURE 1. Passive Third Order, Linear-Phase, Low-Pass
Filter Prototype.
the group delay is constant. These filters maintain phase
information for sensitive DSP applications such as correla-
tion, and preserve transient response. These characteristics
are critical in audio applications as well, because they affect
sound quality greatly.
Thus, we begin the design process by selecting a passive,
third order linear-phase filter design that will be realized
using this active approach. The passive design shown in
Figure 1 is neither a Butterworth nor a Bessel response; it is
something in between. The component values for this par-
ticular response, optimized for phase linearity and stopband
attenuation, were found through exhaustive computer simu-
lations and empirical analysis. Component values for stan-
dard Butterworth and Bessel responses may be found in
standard filter tables, such as those available in Huelsman
and Allen
(7)
. This circuit is then transformed to an active
circuit by multiplying all circuit values by 1/s, which changes
all inductors to resistors, all resistors to capacitors, and all
capacitors to Frequency Dependent Negative Resistors
(FDNRs). These FDNRs have the characteristic impedance
of
1
2
C
s
and may be realized using the GIC circuit. Thus, L
1
becomes
R
1
, C
2
becomes 1/s
2
C
2
, L
3
becomes R
3
, and the terminating
R
1
0.9852鈩?/div>
R
3
0.3350鈩?/div>
1
s
2
C
2
0.8746Fs
4
6
7
8
9
10
11
12
C
4
1F
13
14
FDNR: units are farad-seconds (Fs)
FIGURE 2. Filter of Figure 1 Transformed by Multiplying
All Component Values by 1/s.
Printed in U.S.A. March, 1991
15
16
1991 Burr-Brown Corporation
AB-026A
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2
3
4
5
6
7
