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Maxim > Design
support > App notes
> Filter
Circuits (Analog) > APP 4422

Nov 04, 2009

Keywords: analog filters, bessel, Butterworth and
Elliptic filters, switched capacitor analog filters

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APPLICATION NOTE 4422

Integrated solutions make analog filter design
easy

By:

Joseph
Shtargot, Strategic Applications Engineer

Alex
Dean, Business Manager

Abstract: This
application note explains advances of switched-capacitor
analog filters for anti-aliasing and noise filtering for ADCs
(analog-to-digital converters), as well as "reconstruction"
post-filtering for DACs (digital-to-analog converters). The
article summarizes the unique benefits of the MAX74xx series
filter vs. continuous-time active filters and provides
application examples.

A
similar version of this article appeared in the October 2009
issue of Electronic Products magazine.

Analog
filters play an important part in electronic signal-synthesis
subsystems, providing functions such as anti-aliasing and
noise filtering for ADCs, and reconstruction post-filtering
for DACs.¹ Different design specifications and requirements
dictate the use of the particular filter configurations. The
most popular filters include Bessel, Butterworth, and
elliptic.

Bessel lowpass filters provide a linear
phase response with a ripple-free passband and monotonic
rolloff. These characteristics make Bessel filters ideal for
time domain applications. Butterworth lowpass filters have a
maximally flat frequency response in the passband with a
monotonic rolloff that is much sharper than the Bessel filter.
Their phase response varies nonlinearly with frequency. These
characteristics present no problems for amplitude-based
applications. Finally, elliptic lowpass filters have a nearly
flat passband response with an extremely sharp rolloff
characteristic. Elliptic filters are ideally suited to
amplitude-based anti-aliasing applications.

Design and
construction of continuous-time active filters pose
substantial design challenges and require the use of multiple
high-performance op amps surrounded by many matched
tight-tolerance passive components. Design challenges include
selection of the optimal filter configuration, as well as the
use of specialized software for filter synthesis.² A simpler
approach might include the use of highly integrated SCFs
(switched-capacitor filters)—such circuits can reduce the
number of components, make it easier to tune the filter, and
trim system power. This article will examine a filter
implementation, first using a continuous-time filter and then
with an SCF
approach to show the differences in performance and
complexity.

As mentioned previously, due to their
characteristics, Bessel filters are ideal for time domain
applications, as they have no distortion in the
oscilloscope/analyzer type measurements. However, the cost for
the perfect characteristic filter is that the designer must
construct a higher order Bessel filter (having more poles than
a Butterworth or elliptic filter) to achieve a suitable level
of stopband attenuation.

Figure 1 shows a
schematic for a 5th-order, 1.0kHz, lowpass Bessel filter. This
design is based on Sallen-Key architecture, is optimized for
minimum component count, and uses standard-value 1%-tolerance
resistors and 5%-tolerance ceramic capacitors. To determine
the component values, the design was created using FilterPro™
software and "tested" using PSPICE simulation
tools.

Figure
1. Two op amps and a handful of passive parts comprise this
5th-order, 1.0kHz, lowpass Bessel filter.

In many
cases, input and output RC filters also require additional op
amp buffers, particularly if the signal source
impedance
is relatively high (above a few hundred ohms) and the output
of the filter is connected to the relatively low impedance
circuit (below several hundred kilohms).

SPICE
simulations run on the Bessel filter circuit are shown in
Figure 2. These frequency response plots are the result
of a Monte Carlo run of 100 different virtual manufacturing
builds for the same filter. The SPICE simulator randomly
varies the component values within their specified tolerances
to account for manufacturing variances. The results of the
simulation demonstrate a passband variation around
fC = fIN -3dB ± 0.6dB due to capacitor
and resistor values spread in their tolerance
ranges.

Figure
2. These frequency response plots show the results of SPICE
simulations of the five-pole Bessel filter.

To
achieve acceptable filter characteristics at 1kHz to 15kHz
cutoff frequencies (for 80dB dynamic
range or better), designers must use components with even
tighter tolerances and better temperature stability. For
example:

Amplifiers must exhibit a required unity gain of 0.5MHz
to 6.5MHz for 1kHz to 15kHz cutoff frequencies and a THD+N
(total
harmonic distortion plus noise) factor of better than
0.005%.

Capacitors should be precision ceramic or film
capacitors. These capacitors should hold their nominal value
over wide temperature and voltage ranges.

Resistors should be the metal film type with ±1% or
better tolerances and a low temperature coefficient.

To ensure that the components deliver the desired
characteristics, they should be acquired from reputable
sources such as Panasonic, Rohm, Vishay, Kemet, and AVX.

Preliminary estimates show that component cost of
the 5th-order, 1kHz to 15kHz cutoff frequency, lowpass Bessel
filter could be in the range $1.50 to $2.00 (1000-up pricing).
This does not include incremental time expenses for design,
test, PCB
layout, assembly, components procurement, and so on; these
expenses are difficult to quantify and will vary from company
to company. For more detailed information regarding
component-variation sensitivity for high-order,
continuous-time filters, see application note 738, "Minimizing
Component-Variation Sensitivity in Single Op Amp
Filters."

Maxim offers a much more efficient, less
complex approach by providing an integrated solution based on
switched-capacitor technology, which allows most of the filter
function to be integrated on a single silicon IC. (Application
note 733, "A Filter
Primer," provides additional information regarding SCF
operations.) All that the designer must do to set up a
particular filter characteristic is to use a single,
inexpensive external capacitor or external clock. The result
is a compact, reliable, predictable, cost-effective filter
design that is less susceptible to temperature and other
variations.

Figures 3 and 4 show the
simple circuit implementations for 5th-order, low-pass Bessel
filter based on SCF chips (the MAX7409/MAX7413).
The decoupling, 0.1µF capacitors could be the generic,
low-cost ceramic type (dielectric type X7R or Z5U). However,
for CCLK in Figure 4, a COG
(NPO) dielectric type is recommended.

Figure
3. Setting fC (cutoff frequency) for a
switched-capacitor filter circuit can be done by using an
external clock with a 50% ± 10% duty
cycle.

Figure
4. Setting fC by using the switched-capacitor
filter's internal oscillator requires connecting the
CCLK capacitor between CLK and ground. At
CCLK = 300pF, fC =
1kHz.

Simulations and test results (shown in
Figure 5) indicate an improvement in passband variation
for a MAX7409/MAX7413-based design vs. a continuous-time,
op-amp-based design. Another advantage of these two integrated
solutions is easy tunability. The cutoff frequencies are clock
tunable with two clocking options available: self-clocking or
external clocking. In comparison, changing the cutoff
frequency in the op-amp-based design often requires
fundamental redesign.

Figure
5. Passband variation at fC = fIN is
only -3dB ± 0.4dB over temperature and
voltage.

Tables 1 and 2 illustrate a
few of the many integrated filter solutions from Maxim that
consume little power, yet deliver high-order-filter
characteristics.

Table 1. Maxim's family of
low-power, 5th-order filters

Part

Supply Voltage (V)

Filter Type

Filter Characteristics

MAX7411

+5

Elliptic

Steepest rolloff, 37dB of stopband rejection

MAX7415

+3

Elliptic

Steepest rolloff, 37dB of stopband rejection

MAX7408

+5

Elliptic

Steep rolloff, 53dB of stopband rejection

MAX7412

+3

Elliptic

Steep rolloff, 53dB of stopband rejection

MAX7409

+5

Bessel

Linear phase response

MAX7413

+3

Bessel

Linear phase response

MAX7410

+5

Butterworth

Maximally flat passband and stopband response

MAX7414

+3

Butterworth

Maximally flat passband and stopband
response

Table 2. Maxim's
family of low-power, 8th-order filters

Part

Supply Voltage (V)

Filter Type

Filter Characteristics

MAX7400

+5

Elliptic

Steepest rolloff and 83dB of stopband
rejection

MAX7401

+5

Bessel

Linear phase response

MAX7403

+5

Elliptic

Steep rolloff and 60dB of stopband rejection

MAX7404

+3

Elliptic

Steepest rolloff and 83dB of stopband
rejection

MAX7405

+3

Bessel

Linear phase response

MAX7407

+3

Elliptic

Steep rolloff and 60dB of stopband
rejection

References

Application note 3494, "The Basics of
Anti-Aliasing: Using Switched-Capacitor Filters."

Application note 738, "Minimizing
Component-Variation Sensitivity in Single Op Amp
Filters."

FilterPro
is a registered trademark of Texas Instruments.

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MAX7400

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MAX7404

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MAX7405

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MAX7407

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MAX7408

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MAX7409

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MAX7410

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MAX7412

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MAX7413

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MAX7414

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MAX7415

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Download,
PDF format (96kB)
APP 4422: Nov 04, 2009

AN4422, AN 4422, APP4422,
Appnote4422, Appnote 4422

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