Measurement noise and signal processing

5.4.2 Active analogue filters

In the foregoing discussion on passive filters, the two main difficulties noted were those of obtaining resistance-less inductors and achieving proper matching between signal source and load through the filter sections. A further problem is that the inductors required by passive filters are bulky and relatively expensive. Active filters overcome all of these problems and so they are now used more commonly than passive filters.

The major component in an active filter is an electronic amplifier. The filter char[1]acteristics are defined by amplifier input and feedback components that consist of resistors and capacitors but not inductors. The fact that the necessary characteristics can be obtained using only resistors and capacitors, without requiring inductors, is a particular advantage of this class of filters. The circuits shown in Figure 5.8 produce the four types of filter characteristics discussed earlier. These are all known as second order filters, because the input–output relationship across each filter is described by a second order differential equation.

The characteristics of each filter in terms of attenuation behaviour in the pass- and stop-bands is determined by the choice of circuit components in Figure 5.8. A common set of design formulae is given below, although detailed derivation is not given. Further information on the derivation of these formulae can be found in specialist texts (e.g. Stephenson, 1985):

Active filters with parameters derived from the above formulae are general purpose and suitable for most applications. However, many other design formulae exist for the parameters of filters with circuit structures as given in Figure 5.8, and these yield filters with special names and characteristics. Butterworth filters, for example, optimize the pass-band attenuation characteristics at the expense of stop-band performance. Another form, Chebyshev filters, have very good stop-band attenuation characteristics but poorer pass-band performance. Again, the reader is referred to the specialist texts (e.g. Stephenson, 1985) for more information.