146 Chapter 7 7.11 Filter Characteristics There are many different types of recognised filter response, each with their own special properties. Their study is complicated by the fact that some of them go by several different names, and you need to keep a close eye on the terminology that an author is using. The well-known filter types are shown in Table 7.1 below. Some lesser known types are shown in Table 7.2. We will look at some of these filter types, in each case first examining the simplest possible instances, the second-order versions; there are no first-order versions because a first-order filter is just a first-order filter, in other words a simple single time-constant. All the filters in this section are lowpass filters with a cutoff frequency of 1 kHz. In every case there is an equivalent highpass filter. For the simpler filters--the Butterworth, Linkwitz-Riley, and the Bessel--we will look at the amplitude response, the phase-shift response, the response to a step input, and the group-delay curve; we then go on to compare the response of the higher-order versions. Chebyshev filters have a more complicated response and some explanation of this is required before we get into the same details as for the earlier filters. The filters used to generate the information are shown in Figure 7.1. They are all unity-gain Sallen and Key configurations, differing only in Q. Full details of how