CHAPTER FIVE
Filter Design and Approximation
5.1 INTRODUCTION
The development of filters has been extensively studied and refined in the twentieth century by engineers and scientists in Germany and the United States. This work was associated with the development of telephony and used simple mathematics. In the 1930s and 1940s major progress was made in filter theory and optimum filter designs. To work through that body of knowledge would be beyond the present purpose of reviewing filter design and filter synthesis techniques. New types of analog filters emerged in the 1950s and 1960s called active filters, which for the most part used operational amplifiers. At this point in time, operational amplifiers have not made a significant inroad to the RF range. Active filter design discussions can be found in Chen [1].
The present chapter concentrates on basic filter types and techniques. The solutions to the filter approximation problem and implementations that have arisen because of special requirements are treated in this chapter. The treatment is further limited to filters that perform certain tasks on continuous time-varying analog signals by way of linear time-invariant circuit elements.
5.2 IDEAL AND APPROXIMATE FILTER TYPES
The function of a filter is to separate different frequency components of the input signal that passes through the filter network. The characteristics of the network are specified by a transfer function, H(jω) or H(s), where s = +jω represents the complex ...
