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Maxim > Design Support > Technical Documents > Tutorials > Filter Circuits (Analog) > APP 733
Keywords: analog filter design, second order filters, highpass, high pass, lowpass, low pass, filters,
notch, allpass, high order, filters, Butterworth, Chebychev, Bessel, elliptic, state variable, filter
TUTORIAL 733
A Filter Primer
Oct 06, 2008
Abstract: This comprehensive article covers all aspects of analog filters. It first addresses the basic
types: first- and second-order filters, highpass and lowpass filters, notch and all-pass filters, and high-
order filters. The tutorial then explains the characteristics of the different implementations, such as
Butterworth filters, Chebychev filters, Bessel filters, elliptic filters, state-variable filters, and switched-
capacitor filters.
Introduction
Ease of use makes integrated, switched-capacitor filters attractive for many applications. This article
helps you prepare for such designs by describing the filter products and explaining the concepts that
govern their operation.
Starting with a simple integrator, we first develop an intuitive approach to active filters in general. We
then introduce practical realizations such as the state-variable filter and its implementation in switched-
capacitor form. Specific integrated filters described here include Maxim's MAX7400 family of higher-order
switched-capacitor filters.
First-Order Filters
Integrator Filters
An integrator (Figure 1a) is the simplest filter mathematically, and it forms the building block for most
modern integrated filters. Consider what we know intuitively about an integrator. If you apply a DC signal
at the input (i.e., zero frequency), the output will describe a linear ramp that grows in amplitude until
limited by the power supplies. Ignoring that limitation, the response of an integrator at zero frequency is
infinite, which means that it has a pole at zero frequency. (A pole exists at any frequency for which the
transfer function's value becomes infinite.)
We also know that the integrator's gain diminishes with increasing frequency, and that at high
frequencies the output voltage becomes virtually zero. Gain is inversely proportional to frequency, so it
has a slope of -1 when plotted on log/log coordinates (i.e., -20dB/decade on a Bode plot, Figure 1b).
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