DESIGN AND DEVELOPMENT OF MEDICAL ELECTRONIC ...

ACTIVE FILTERS 59Many good books and articles have been written on the design of active filters, and wewill not try to duplicate their efforts. In our view, the books with the most practical approachfor 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.Designing active filters is not difficult. There are a number of free software packagesthat will take your input parameters and provide you automatically with a schematic diagramand calculate capacitor and resistor values for specific filter implementations. Thisdoesn’t mean that the programs will do everything for you. You still have to decide whattype of filter response and implementation suit your application.Filter response refers to the shape of a filter’s transfer function. Everyone’s first approximationto filtering physiological signals is to assume a frequency-domain rectangularpassband containing the spectral components of interest while excluding potential interferencesources. However, real-world filters do not yield a perfect step in the frequencydomain. In fact, to produce such a response would require an infinite number of poles(implemented through an infinite number of amplifiers, resistors, and capacitors) andwould result in a filter that is inherently unstable in the time domain. Because of these reasons,real-world filters make use of stable approximations to a perfect step in the frequencydomain. Some of the most common filter responses are the Butterworth, Chebyshev, andBessel. Each of these filter responses has advantages and disadvantages, and it is thedesigners task to find a suitable compromise that best fits the task at hand. Table 2.5 summarizesthe frequency- and time-domain characteristics of these filters, and Figure 2.13shows the magnitude and phase responses for fourth-order Chebyshev, Butterworth, andBessel transfer functions with a 3-dB cutoff frequency of 30 Hz.The Butterworth response (also known as maximally flat) is nearly flat in the passbandand rolls off smoothly and monotonically. In addition, it has virtually no ripple in eitherthe passband or the stopband. For these reasons, many designers regard the Butterworthfilter transfer function as the best compromise between attenuation and phase response forgeneral-purpose applications. This transfer function is certainly the most commonly usedin the design of analog biopotential signal filters. Despite this, applications that require aprecise estimation of phase shift are better served by Bessel filters, since its phase shift islinear, a property that is not shared by Butterworth or Chebyshev filters.The next step to designing a filter is to select a suitable implementation. Here again,a compromise has to be made to achieve the desired filter transfer function with realworldanalog components. The most common active filter topologies are describedbelow.TABLE 2.5Characteristics of Some Common Filter Transfer FunctionsTransferFrequency-Domain CharacteristicsTime-Domain CharacteristicsFunction Ripple Stopband Phase Group DelayChebyshev Equal ripple flat Steep Poor PoorButterworth Smooth Moderate Moderate ModerateBessel Maximum smoothness Weak Very flat Very flat