TL/H/11221 A Basic Introduction to Filters—Active, Passive, and Switched-Capacitor AN-779 National Semiconductor Application Note 779 Kerry Lacanette April 1991 A Basic Introduction to Filters—Active, Passive, and Switched-Capacitor 1.0 INTRODUCTION Filters of some sort are essential to the operation of most electronic circuits. It is therefore in the interest of anyone involved in electronic circuit design to have the ability to develop filter circuits capable of meeting a given set of specifications. Unfortunately, many in the electronics field are uncomfortable with the subject, whether due to a lack of familiarity with it, or a reluctance to grapple with the mathe- matics involved in a complex filter design. This Application Note is intended to serve as a very basic introduction to some of the fundamental concepts and terms associated with filters. It will not turn a novice into a filter designer, but it can serve as a starting point for those wishing to learn more about filter design. 1.1 Filters and Signals: What Does a Filter Do? In circuit theory, a filter is an electrical network that alters the amplitude and/or phase characteristics of a signal with respect to frequency. Ideally, a filter will not add new fre- quencies to the input signal, nor will it change the compo- nent frequencies of that signal, but it will change the relative amplitudes of the various frequency components and/or their phase relationships. Filters are often used in electronic systems to emphasize signals in certain frequency ranges and reject signals in other frequency ranges. Such a filter has a gain which is dependent on signal frequency. As an example, consider a situation where a useful signal at fre- quency f 1 has been contaminated with an unwanted signal at f 2 . If the contaminated signal is passed through a circuit (Figure 1) that has very low gain at f 2 compared to f 1 , the undesired signal can be removed, and the useful signal will remain. Note that in the case of this simple example, we are not concerned with the gain of the filter at any frequency other than f 1 and f 2 . As long as f 2 is sufficiently attenuated relative to f 1 , the performance of this filter will be satisfacto- ry. In general, however, a filter’s gain may be specified at several different frequencies, or over a band of frequencies. Since filters are defined by their frequency-domain effects on signals, it makes sense that the most useful analytical and graphical descriptions of filters also fall into the fre- quency domain. Thus, curves of gain vs frequency and phase vs frequency are commonly used to illustrate filter characteristics,and the most widely-used mathematical tools are based in the frequency domain. The frequency-domain behavior of a filter is described math- ematically in terms of its transfer function or network function. This is the ratio of the Laplace transforms of its output and input signals. The voltage transfer function H(s) of a filter can therefore be written as: (1) H(s) e V OUT (s) V IN (s) where V IN (s) and V OUT (s) are the input and output signal voltages and s is the complex frequency variable. The transfer function defines the filter’s response to any arbitrary input signal, but we are most often concerned with its effect on continuous sine waves. Especially important is the magnitude of the transfer function as a function of fre- quency, which indicates the effect of the filter on the ampli- tudes of sinusoidal signals at various frequencies. Knowing the transfer function magnitude (or gain) at each frequency allows us to determine how well the filter can distinguish between signals at different frequencies. The transfer func- tion magnitude versus frequency is called the amplitude response or sometimes, especially in audio applications, the frequency response. Similarly, the phase response of the filter gives the amount of phase shift introduced in sinusoidal signals as a function of frequency. Since a change in phase of a signal also rep- resents a change in time, the phase characteristics of a filter become especially important when dealing with complex signals where the time relationships between signal compo- nents at different frequencies are critical. By replacing the variable s in (1) with j0, where j is equal to 0 b1 , and 0 is the radian frequency (2qf), we can find the filter’s effect on the magnitude and phase of the input sig- nal. The magnitude is found by taking the absolute value of (1): (2) l H(j0) l e V OUT (j0) V IN (j0) and the phase is: (3) arg H(j0) e arg V OUT (j0) V IN (j0) TL/H/11221 – 1 FIGURE 1. Using a Filter to Reduce the Effect of an Undesired Signal at Frequency f 2 , while Retaining Desired Signal at Frequency f 1 C1995 National Semiconductor Corporation RRD-B30M75/Printed in U. S. A.
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TL/H/11221
AB
asic
Intro
ductio
nto
Filte
rsÐ
Activ
e,Passiv
e,and
Sw
itched-C
apacito
rA
N-7
79
National SemiconductorApplication Note 779Kerry LacanetteApril 1991
A Basic Introduction toFiltersÐActive, Passive,and Switched-Capacitor
1.0 INTRODUCTION
Filters of some sort are essential to the operation of most
electronic circuits. It is therefore in the interest of anyone
involved in electronic circuit design to have the ability to
develop filter circuits capable of meeting a given set of
specifications. Unfortunately, many in the electronics field
are uncomfortable with the subject, whether due to a lack of
familiarity with it, or a reluctance to grapple with the mathe-
matics involved in a complex filter design.
This Application Note is intended to serve as a very basic
introduction to some of the fundamental concepts and
terms associated with filters. It will not turn a novice into a
filter designer, but it can serve as a starting point for those
wishing to learn more about filter design.
1.1 Filters and Signals: What Does a Filter Do?
In circuit theory, a filter is an electrical network that alters
the amplitude and/or phase characteristics of a signal with
respect to frequency. Ideally, a filter will not add new fre-
quencies to the input signal, nor will it change the compo-
nent frequencies of that signal, but it will change the relative
amplitudes of the various frequency components and/or
their phase relationships. Filters are often used in electronic
systems to emphasize signals in certain frequency ranges
and reject signals in other frequency ranges. Such a filter
has a gain which is dependent on signal frequency. As an
example, consider a situation where a useful signal at fre-
quency f1 has been contaminated with an unwanted signal
at f2. If the contaminated signal is passed through a circuit
(Figure 1) that has very low gain at f2 compared to f1, the
undesired signal can be removed, and the useful signal will
remain. Note that in the case of this simple example, we are
not concerned with the gain of the filter at any frequency
other than f1 and f2. As long as f2 is sufficiently attenuated
relative to f1, the performance of this filter will be satisfacto-
ry. In general, however, a filter’s gain may be specified at
several different frequencies, or over a band of frequencies.
Since filters are defined by their frequency-domain effects
on signals, it makes sense that the most useful analytical
and graphical descriptions of filters also fall into the fre-
quency domain. Thus, curves of gain vs frequency and
phase vs frequency are commonly used to illustrate filter
characteristics,and the most widely-used mathematical
tools are based in the frequency domain.
The frequency-domain behavior of a filter is described math-
ematically in terms of its transfer function or network
function. This is the ratio of the Laplace transforms of its
output and input signals. The voltage transfer function H(s)
of a filter can therefore be written as:
(1)H(s) e
VOUT(s)
VIN(s)
where VIN(s) and VOUT(s) are the input and output signal
voltages and s is the complex frequency variable.
The transfer function defines the filter’s response to any
arbitrary input signal, but we are most often concerned with
its effect on continuous sine waves. Especially important is
the magnitude of the transfer function as a function of fre-
quency, which indicates the effect of the filter on the ampli-
tudes of sinusoidal signals at various frequencies. Knowing
the transfer function magnitude (or gain) at each frequency
allows us to determine how well the filter can distinguish
between signals at different frequencies. The transfer func-
tion magnitude versus frequency is called the amplitude
response or sometimes, especially in audio applications,
the frequency response.
Similarly, the phase response of the filter gives the amount
of phase shift introduced in sinusoidal signals as a function
of frequency. Since a change in phase of a signal also rep-
resents a change in time, the phase characteristics of a filter
become especially important when dealing with complex
signals where the time relationships between signal compo-
nents at different frequencies are critical.
By replacing the variable s in (1) with j0, where j is equal to0b1 , and 0 is the radian frequency (2qf), we can find the
filter’s effect on the magnitude and phase of the input sig-
nal. The magnitude is found by taking the absolute value of
(1):
(2)lH(j0)l e ÀVOUT(j0)
VIN(j0) Àand the phase is:
(3)arg H(j0) e argVOUT(j0)
VIN(j0)
TL/H/11221–1
FIGURE 1. Using a Filter to Reduce the Effect of an Undesired Signal at
Frequency f2, while Retaining Desired Signal at Frequency f1
C1995 National Semiconductor Corporation RRD-B30M75/Printed in U. S. A.
As an example, the network of Figure 2 has the transfer
function:
(4)H(s) e
s
s2 a s a 1
TL/H/11221–2
FIGURE 2. Filter Network of Example
This is a 2nd order system. The order of a filter is the high-
est power of the variable s in its transfer function. The order
of a filter is usually equal to the total number of capacitors
and inductors in the circuit. (A capacitor built by combining
two or more individual capacitors is still one capacitor.)
Higher-order filters will obviously be more expensive to
build, since they use more components, and they will also
be more complicated to design. However, higher-order fil-
ters can more effectively discriminate between signals at
different frequencies.
Before actually calculating the amplitude response of the
network, we can see that at very low frequencies (small
values of s), the numerator becomes very small, as do the
first two terms of the denominator. Thus, as s approaches
zero, the numerator approaches zero, the denominator ap-
proaches one, and H(s) approaches zero. Similarly, as the
input frequency approaches infinity, H(s) also becomes pro-
gressively smaller, because the denominator increases with
the square of frequency while the numerator increases lin-
early with frequency. Therefore, H(s) will have its maximum
value at some frequency between zero and infinity, and will
decrease at frequencies above and below the peak.
To find the magnitude of the transfer function, replace s with
j0 to yield:
(5)A(0) e lH(s)l e À j0
b02 a j0 a 1 Àe
0
002 a (1 b 02)2
The phase is:
(6)i(0) e arg H(s) e 90§ b tanb102
(1 b 02)
The above relations are expressed in terms of the radian
frequency 0, in units of radians/second. A sinusoid will
complete one full cycle in 2q radians. Plots of magnitude
and phase versus radian frequency are shown in Figure 3.
When we are more interested in knowing the amplitude and
phase response of a filter in units of Hz (cycles per second),
we convert from radian frequency using 0 e 2qf, where f is
the frequency in Hz. The variables f and 0 are used more or
less interchangeably, depending upon which is more appro-
priate or convenient for a given situation.
Figure 3(a) shows that, as we predicted, the magnitude of
the transfer function has a maximum value at a specific fre-
quency (00) between 0 and infinity, and falls off on either
side of that frequency. A filter with this general shape is
known as a band-pass filter because it passes signals fall-
ing within a relatively narrow band of frequencies and atten-
uates signals outside of that band. The range of frequencies
passed by a filter is known as the filter’s passband. Since
the amplitude response curve of this filter is fairly smooth,
there are no obvious boundaries for the passband. Often,
the passband limits will be defined by system requirements.
A system may require, for example, that the gain variation
between 400 Hz and 1.5 kHz be less than 1 dB. This specifi-
cation would effectively define the passband as 400 Hz to
1.5 kHz. In other cases though, we may be presented with a
transfer function with no passband limits specified. In this
case, and in any other case with no explicit passband limits,
the passband limits are usually assumed to be the frequen-
cies where the gain has dropped by 3 decibels (to 02/2 or
0.707 of its maximum voltage gain). These frequencies are
therefore called the b3 dB frequencies or the cutoff fre-
quencies. However, if a passband gain variation (i.e., 1 dB)
is specified, the cutoff frequencies will be the frequencies at
which the maximum gain variation specification is exceed-
ed.
TL/H/11221–3(a)
TL/H/11221–5(b)
FIGURE 3. Amplitude (a) and phase (b) response curves
for example filter. Linear frequency and gain scales.
The precise shape of a band-pass filter’s amplitude re-
sponse curve will depend on the particular network, but any
2nd order band-pass response will have a peak value at the
filter’s center frequency. The center frequency is equal to
the geometric mean of the b3 dB frequencies:
fc e 0fI fh (8)
where fc is the center frequency
fI is the lower b3 dB frequency
fh is the higher b3 dB frequency
Another quantity used to describe the performance of a filter
is the filter’s ‘‘Q’’. This is a measure of the ‘‘sharpness’’ of
the amplitude response. The Q of a band-pass filter is the
ratio of the center frequency to the difference between the
2
b3 dB frequencies (also known as the b3 dB bandwidth).
Therefore:
(9)Q e
fc
fh b fI
When evaluating the performance of a filter, we are usually
interested in its performance over ratios of frequencies.
Thus we might want to know how much attenuation occurs
at twice the center frequency and at half the center frequen-
cy. (In the case of the 2nd-order bandpass above, the atten-
uation would be the same at both points). It is also usually
desirable to have amplitude and phase response curves
that cover a wide range of frequencies. It is difficult to obtain
a useful response curve with a linear frequency scale if the
desire is to observe gain and phase over wide frequency
ratios. For example, if f0 e 1 kHz, and we wish to look at
response to 10 kHz, the amplitude response peak will be
close to the left-hand side of the frequency scale. Thus, it
would be very difficult to observe the gain at 100 Hz, since
this would represent only 1% of the frequency axis. A loga-
rithmic frequency scale is very useful in such cases, as it
gives equal weight to equal ratios of frequencies.
Since the range of amplitudes may also be large, the ampli-
tude scale is usually expressed in decibels (20loglH(j0)l).Figure 4 shows the curves of Figure 3 with logarithmic fre-
quency scales and a decibel amplitude scale. Note the im-
proved symmetry in the curves of Figure 4 relative to those
of Figure 3.
1.2 The Basic Filter Types
Bandpass
There are five basic filter types (bandpass, notch, low-pass,
high-pass, and all-pass). The filter used in the example in
the previous section was a bandpass. The number of possi-
ble bandpass response characteristics is infinite, but they all
share the same basic form. Several examples of bandpass
amplitude response curves are shown in Figure 5. The
curve in 5(a) is what might be called an ‘‘ideal’’ bandpass
response, with absolutely constant gain within the pass-
band, zero gain outside the passband, and an abrupt bound-
ary between the two. This response characteristic is impos-
sible to realize in practice, but it can be approximated to
varying degrees of accuracy by real filters. Curves (b)
through (f) are examples of a few bandpass amplitude re-
sponse curves that approximate the ideal curves with vary-
ing degrees of accuracy. Note that while some bandpass
responses are very smooth, other have ripple (gain varia-
tions in their passbands. Other have ripple in their stop-
bands as well. The stopband is the range of frequencies
over which unwanted signals are attenuated. Bandpass fil-
ters have two stopbands, one above and one below the
passband.
TL/H/11221–4(a)
TL/H/11221–6(b)
FIGURE 4. Amplitude (a) and phase (b) response curves for example bandpass filter.
Note symmetry of curves with log frequency and gain scales.
TL/H/11221–7
(a) (b) (c)
TL/H/11221–8
(d) (e) (f)
FIGURE 5. Examples of Bandpass Filter Amplitude Response
3
Just as it is difficult to determine by observation exactly
where the passband ends, the boundary of the stopband is
also seldom obvious. Consequently, the frequency at which
a stopband begins is usually defined by the requirements of
a given systemÐfor example, a system specification might
require that the signal must be attenuated at least 35 dB at
1.5 kHz. This would define the beginning of a stopband at
1.5 kHz.
The rate of change of attenuation between the passband
and the stopband also differs from one filter to the next. The
slope of the curve in this region depends strongly on the
order of the filter, with higher-order filters having steeper
cutoff slopes. The attenuation slope is usually expressed in
dB/octave (an octave is a factor of 2 in frequency) or dB/
decade (a decade is a factor of 10 in frequency).
Bandpass filters are used in electronic systems to separate
a signal at one frequency or within a band of frequencies
from signals at other frequencies. In 1.1 an example was
given of a filter whose purpose was to pass a desired signal
at frequency f1, while attenuating as much as possible an
unwanted signal at frequency f2. This function could be per-
formed by an appropriate bandpass filter with center fre-
quency f1. Such a filter could also reject unwanted signals at
other frequencies outside of the passband, so it could be
useful in situations where the signal of interest has been
contaminated by signals at a number of different frequen-
cies.
Notch or Band-Reject
A filter with effectively the opposite function of the band-
pass is the band-reject or notch filter. As an example, the
components in the network ofFigure 3 can be rearranged to
form the notch filter of Figure 6, which has the transfer func-
tion
(10)HN(s) e
VOUT
VIN
e
s2 a 1
s2 a s a 1
TL/H/11221–9
FIGURE 6. Example of a Simple Notch Filter
The amplitude and phase curves for this circuit are shown in
Figure 7. As can be seen from the curves, the quantities fc,
fI, and fh used to describe the behavior of the band-pass
filter are also appropriate for the notch filter. A number of
notch filter amplitude response curves are shown in Figure8. As in Figure 5, curve (a) shows an ‘‘ideal’’ notch re-
sponse, while the other curves show various approximations
to the ideal characteristic.
TL/H/11221–10(a)
TL/H/11221–11(b)
FIGURE 7. Amplitude (a) and Phase (b) Response
Curves for Example Notch Filter
Notch filters are used to remove an unwanted frequency
from a signal, while affecting all other frequencies as little as
possible. An example of the use of a notch flter is with an
audio program that has been contaminated by 60 Hz power-
line hum. A notch filter with a center frequency of 60 Hz can
remove the hum while having little effect on the audio sig-
nals.
TL/H/11221–12
(a) (b) (c)
TL/H/11221–13
(d) (e) (f)
FIGURE 8. Examples of Notch Filter Amplitude Responses
4
Low-Pass
A third filter type is the low-pass. A low-pass filter passes
low frequency signals, and rejects signals at frequencies
above the filter’s cutoff frequency. If the components of our
example circuit are rearranged as in Figure 9, the resultant
transfer function is:
(11)HLP(s) e
VOUT
VIN
e
1
s2 a s a 1
TL/H/11221–14
FIGURE 9. Example of a Simple Low-Pass Filter
It is easy to see by inspection that this transfer function has
more gain at low frequencies than at high frequencies. As 0approaches 0, HLP approaches 1; as 0 approaches infinity,
HLP approaches 0.
Amplitude and phase response curves are shown in Figure10, with an assortment of possible amplitude reponse
curves in Figure 11. Note that the various approximations to
the unrealizable ideal low-pass amplitude characteristics
take different forms, some being monotonic (always having
a negative slope), and others having ripple in the passband
and/or stopband.
Low-pass filters are used whenever high frequency compo-
nents must be removed from a signal. An example might be
in a light-sensing instrument using a photodiode. If light lev-
els are low, the output of the photodiode could be very
small, allowing it to be partially obscured by the noise of the
sensor and its amplifier, whose spectrum can extend to very
high frequencies. If a low-pass filter is placed at the output
of the amplifier, and if its cutoff frequency is high enough to
allow the desired signal frequencies to pass, the overall
noise level can be reduced.
TL/H/11221–15
(a)TL/H/11221–16
(b)
FIGURE 10. Amplitude (a) and Phase (b) Response Curves for Example Low-Pass Filter
TL/H/11221–17
(a) (b) (c)
TL/H/11221–18
(d) (e) (f)
FIGURE 11. Examples of Low-Pass Filter Amplitude Response Curves
5
High-Pass
The opposite of the low-pass is the high-pass filter, which
rejects signals below its cutoff frequency. A high-pass filter
can be made by rearranging the components of our exam-
ple network as in Figure 12. The transfer function for this
filter is:
(12)HHP(s) e
VOUT
VIN
e
s2
s2 a s a 1
TL/H/11221–19
FIGURE 12. Example of Simple High-Pass Filter
and the amplitude and phase curves are found in Figure 13.
Note that the amplitude response of the high-pass is a ‘‘mir-
ror image’’ of the low-pass response. Further examples of
high-pass filter responses are shown in Figure 14, with the
‘‘ideal’’ response in (a) and various approximations to the
ideal shown in (b) through (f).
High-pass filters are used in applications requiring the rejec-
tion of low-frequency signals. One such application is in
high-fidelity loudspeaker systems. Music contains significant
energy in the frequency range from around 100 Hz to 2 kHz,
but high-frequency drivers (tweeters) can be damaged if
low-frequency audio signals of sufficient energy appear at
their input terminals. A high-pass filter between the broad-
band audio signal and the tweeter input terminals will pre-
vent low-frequency program material from reaching the
tweeter. In conjunction with a low-pass filter for the low-fre-
quency driver (and possibly other filters for other drivers),
the high-pass filter is part of what is known as a ‘‘crossover
network’’.
TL/H/11221–20(a)
TL/H/11221–21(b)
FIGURE 13. Amplitude (a) and Phase (b) Response Curves for Example High-Pass Filter
TL/H/11221–22
(a) (b) (c)
TL/H/11221–23
(d) (e) (f)
FIGURE 14. Examples of High-Pass Filter Amplitude Response Curves
6
All-Pass or Phase-Shift
The fifth and final filter response type has no effect on the
amplitude of the signal at different frequencies. Instead, its
function is to change the phase of the signal without affect-
ing its amplitude. This type of filter is called an all-pass or
phase-shift filter. The effect of a shift in phase is illustrated
in Figure 15. Two sinusoidal waveforms, one drawn in
dashed lines, the other a solid line, are shown. The curves
are identical except that the peaks and zero crossings of
the dashed curve occur at later times than those of the solid
curve. Thus, we can say that the dashed curve has under-
gone a time delay relative to the solid curve.
TL/H/11221–24
FIGURE 15. Two sinusoidal waveforms
with phase difference i. Note that this
is equivalent to a time delayi
0.
Since we are dealing here with periodic waveforms, time
and phase can be interchangedÐthe time delay can also be
interpreted as a phase shift of the dashed curve relative to
the solid curve. The phase shift here is equal to i radians.
The relation between time delay and phase shift is TD e
i/2q0, so if phase shift is constant with frequency, time
delay will decrease as frequency increases.
All-pass filters are typically used to introduce phase shifts
into signals in order to cancel or partially cancel any un-
wanted phase shifts previously imposed upon the signals by
other circuitry or transmission media.
Figure 16 shows a curve of phase vs frequency for an all-
pass filter with the transfer function
HAP(s) e
s2 b s a 1
s2 a s a 1
The absolute value of the gain is equal to unity at all fre-
quencies, but the phase changes as a function of frequency.
TL/H/11221–25
FIGURE 16. Phase Response Curve for
Second-Order All-Pass Filter of Example
Let’s take another look at the transfer function equations
and response curves presented so far. First note that all of
the transfer functions share the same denominator. Also
note that all of the numerators are made up of terms found
in the denominator: the high-pass numerator is the first term
(s2) in the denominator, the bandpass numerator is the sec-
ond term (s), the low-pass numerator is the third term (1),
and the notch numerator is the sum of the denominator’s
first and third terms (s2 a 1). The numerator for the all-pass
transfer function is a little different in that it includes all of
the denominator terms, but one of the terms has a negative
sign.
Second-order filters are characterized by four basic proper-
ties: the filter type (high-pass, bandpass, etc.), the pass-
band gain (all the filters discussed so far have unity gain in
the passband, but in general filters can be built with any
gain), the center frequency (one radian per second in the
above examples), and the filter Q. Q was mentioned earlier
in connection with bandpass and notch filters, but in sec-
ond-order filters it is also a useful quantity for describing the
behavior of the other types as well. The Q of a second-order
filter of a given type will determine the relative shape of the
amplitude response. Q can be found from the denominator
of the transfer function if the denominator is written in the
form:
D(s) e s2 a
0O
Qs a 0O
2.
As was noted in the case of the bandpass and notch func-
tions, Q relates to the ‘‘sharpness’’ of the amplitude re-
sponse curve. As Q increases, so does the sharpness of the
response. Low-pass and high-pass filters exhibit ‘‘peaks’’ in
their response curves when Q becomes large. Figure 17shows amplitude response curves for second-order band-
pass, notch, low-pass, high-pass and all-pass filters with
various values of Q.
There is a great deal of symmetry inherent in the transfer
functions we’ve considered here, which is evident when the
amplitude response curves are plotted on a logarithmic fre-
quency scale. For instance, bandpass and notch amplitude
resonse curves are symmetrical about fO (with log frequen-
cy scales). This means that their gains at 2fO will be the
same as their gains at fO/2, their gains at 10fO will be the
same as their gains at fO/10, and so on.
The low-pass and high-pass amplitude response curves
also exhibit symmetry, but with each other rather than with
themselves. They are effectively mirror images of each oth-
er about fO. Thus, the high-pass gain at 2fO will equal the
low-pass gain at fO/2 and so on. The similarities between
the various filter functions prove to be quite helpful when
designing complex filters. Most filter designs begin by defin-
ing the filter as though it were a low-pass, developing a low-
pass ‘‘prototype’’ and then converting it to bandpass, high-
pass or whatever type is required after the low-pass charac-
teristics have been determined.
As the curves for the different filter types imply, the number
of possible filter response curves that can be generated is
infinite. The differences between different filter responses
within one filter type (e.g., low-pass) can include, among
Signal Processors, etc.): Switched-capacitor filters excel
in applications that require multiple center frequencies be-
cause their center frequencies are clock-controlled. More-
over, a single filter can cover a center frequency range of 5
decades. Adjusting the cutoff frequency of a continuous fil-
ter is much more difficult and requires either analog
switches (suitable for a small number of center frequen-
cies), voltage-controlled amplifiers (poor center frequency
accuracy) or DACs (good accuracy over a very limited con-
trol range).
Audio Signal Processing (Tone Controls and Other
Equalization, All-Pass Filtering, Active Crossover Net-
works, etc.): Switched-capacitor filters are usually too noisy
for ‘‘high-fidelity’’ audio applications. With a typical dynamic
range of about 80 dB to 90 dB, a switched-capacitor filter
will usuallly give 60 dB to 70 dB signal-to-noise ratio (as-
suming 20 dB of headroom). Also, since audio filters usually
need to handle three decades of signal frequencies at the
same time, there is a possibility of aliasing problems. Con-
tinuous filters are a better choice for general audio use, al-
though many communications systems have bandwidths
and S/N ratios that are compatible with switched capacitor
filters, and these systems can take advantage of the tunabil-
ity and small size of monolithic filters.
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be reasonably expected to result in a significant injury
to the user.
National Semiconductor National Semiconductor National Semiconductor National Semiconductor National Semiconductores National SemiconductorCorporation GmbH Japan Ltd. Hong Kong Ltd. Do Brazil Ltda. (Australia) Pty, Ltd.2900 Semiconductor Drive Livry-Gargan-Str. 10 Sumitomo Chemical 13th Floor, Straight Block, Rue Deputado Lacorda Franco Building 16P.O. Box 58090 D-82256 F 4urstenfeldbruck Engineering Center Ocean Centre, 5 Canton Rd. 120-3A Business Park DriveSanta Clara, CA 95052-8090 Germany Bldg. 7F Tsimshatsui, Kowloon Sao Paulo-SP Monash Business ParkTel: 1(800) 272-9959 Tel: (81-41) 35-0 1-7-1, Nakase, Mihama-Ku Hong Kong Brazil 05418-000 Nottinghill, MelbourneTWX: (910) 339-9240 Telex: 527649 Chiba-City, Tel: (852) 2737-1600 Tel: (55-11) 212-5066 Victoria 3168 Australia
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