Introduction

Before the advent and wide-spread use of operational amplifiers, much of network theory was concerned with the analysis and synthesis of passive filters. Since vacuum tube amplifiers were bulky, required power supplies and consumed power, feedback techniques were not investigated to synthesize filters. Their potential to do so, however, was well known. Since there is a very great number of books on network synthesis, we shall limit our discussion here only to the analysis of a few interesting passive filters mainly to demonstrate the unique techniques of this book. Today, passive filters are mostly used in analog communication circuits and switching power converter circuits. Switching power converter circuits will be discussed in Chapter 8. Chapter 7, however, concludes with a section on special infinite networks in which some thoughts are presented on unifying all three linear elements, R, L and C, into a single element using fractional calculus.

RC filters with gain

The possibility of obtaining any voltage or current gain from a purely RC network may seem counterintuitive at first, simply because such a network can neither have a flat gain larger than unity nor exhibit any resonance. After a little thought, we consider if it is at all possible, starting from a flat gain, A0, to have a zero, ωz, before a pole, ωp, so that A0(ωp/ωz) > 1. For a ladder network it can be shown that this is not possible (see Problem 7.1) but for other types of networks, such as the one illustrated in Fig. 7.1a, it is indeed possible to obtain a gain larger than unity.