A General Theory of Electric Wave Filters

HE growth of the field of electric wave filters since their original discovery by Dr. G. A. Campbell shows the filtering action by no means inheres in any particular physical configuration. Filters have been built, for example, as recurrent or non-recurrent ladder structures, as lattices, as bridged-T's, and in a variety of combinations of transformers with ordinary elements. No general theory uniting all these configurations has, however, been developed. Each structure has been treated by methods which are primarily adapted to that configuration alone. In consequence, such questions as the relations between filters of different types and the possibilities of securing improved characteristics by going to a still wider variety of configurations have remained unsettled. The present paper is an attempt to develop a general filter theory independent of any particular structure, by means of which these questions can be answered. For the sake of a rigorous discussion, the term "filter" has been used to signify a four-terminal network of ordinary lumped elements which, when terminated in its image impedances, transmits freely one continuous band of real frequencies and attenuates all other real frequencies. Since in actual operation the distinction between free transmission and attenuation is always more or less obscured by terminal effects and parasitic dissipation, this definition is necessarily somewhat arbitrary. It agrees, however, with common usage except in its rejection of multiple band-pass filters, which are rarely used in practice.