Biomedical Engineering Reference
In-Depth Information
Many good topics and articles have been written on the design of active
fi
filters, and we
will not try to duplicate their e
ff
orts. In our view, the topics with the most practical approach
for the experimentalist are:
D. Lancaster, Active Filter Cookbook , Synergistics Press, 1995.
P. Horowitz and W. Hill, The Art of Electronics , 2nd ed., Cambridge University Press,
New York, 1989.
H. M. Berlin, The Design of Active Filters, with Experiments , Howard W. Sams,
Indianapolis, IN, 1974.
cult. There are a number of free software packages
that will take your input parameters and provide you automatically with a schematic dia-
gram and calculate capacitor and resistor values for speci
Designing active
fi
filters is not di
filter implementations. This
doesn't mean that the programs will do everything for you. You still have to decide what
type of
fi
c
fi
filter response and implementation suit your application.
Filter response refers to the shape of a
fi
fi
filter's transfer function. Everyone's
fi
rst approx-
imation to
filtering physiological signals is to assume a frequency-domain rectangular
passband containing the spectral components of interest while excluding potential inter-
ference sources. However, real-world
fi
filters do not yield a perfect step in the frequency
domain. In fact, to produce such a response would require an in
fi
fi
nite number of poles
(implemented through an in
fi
nite number of ampli
fi
ers, resistors, and capacitors) and
would result in a
fi
filter that is inherently unstable in the time domain. Because of these rea-
sons, real-world
filters make use of stable approximations to a perfect step in the frequency
domain. Some of the most common
fi
fi
filter responses are the Butterworth, Chebyshev, and
Bessel. Each of these
fi
filter responses has advantages and disadvantages, and it is the
designers task to
fits the task at hand. Table 2.5 sum-
marizes the frequency- and time-domain characteristics of these
fi
find a suitable compromise that best
fi
filters, and Figure 2.13
shows the magnitude and phase responses for fourth-order Chebyshev, Butterworth, and
Bessel transfer functions with a
fi
frequency of 30 Hz.
The Butterworth response (also known as maximally
3-dB cuto
ff
fl
at ) is nearly
fl
flat in the passband
and rolls off
smoothly and monotonically. In addition, it has virtually no ripple in either
the passband or the stopband. For these reasons, many designers regard the Butterworth
fi
ff
filter transfer function as the best compromise between attenuation and phase response for
general-purpose applications. This transfer function is certainly the most commonly used
in the design of analog biopotential signal
filters. Despite this, applications that require a
precise estimation of phase shift are better served by Bessel
fi
filters, since its phase shift is
linear, a property that is not shared by Butterworth or Chebyshev
fi
fi
filters.
filter is to select a suitable implementation. Here again,
a compromise has to be made to achieve the desired
The next step to designing a
fi
fi
filter transfer function with real-
world analog components. The most common active
fi
filter topologies are described
below.
TABLE 2.5
Characteristics of Some Common Filter Transfer Functions
Frequency-Domain Characteristics
Time-Domain Characteristics
Transfer
Function
Ripple
Stopband
Phase
Group Delay
Chebyshev
Equal ripple flat
Steep
Poor
Poor
Butterworth
Smooth
Moderate
Moderate
Moderate
Bessel
Maximum smoothness
Weak
Very flat
Very flat
 
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