Theory of electric wave filters built up of coupled circuit elements

This paper is essentially a treatment of certain types of coupled circuit networks by methods similar to those used in the discussion of the properties of long lines with distributed constants. This method of treating those coupled circuit chains to which it can be applied far surpasses other methods of treatment in several important ways. First, the number of elements in the chain can be made as large as desired without complicating the problem in any way whatsoever. Second, the very method of treatment leads directly to the rational design of selective systems of a type which the older methods of treatment did not even show to exist. Third, this method of attacking the problem is much better adapted to a transient state treatment (following the methods of J. R. Carson and T. C. Fry) than the older methods of handling the coupled circuit problem. In the second section of this paper there is developed the general theory of the properties of identical circuits coupled so as to form a chain. The equations giving the current and voltage of any circuit in the chain are identical in form with those giving the current and voltage at any point of a long line with distributed constants. The propagation constant however, instead of being an algebraic function of the circuit constants and the impressed frequency as in the case for the line with distributed constants, is a transcendental function of the circuit constants and the frequency of the current being transmitted. The nature of this transcendental function is such that sharp changes occur in the characteristic curve which portrays the attenuation constant as a function of the frequency. The third section shows how, by proper termination and design, these sharp changes in the attenuation frequency characteristic can be employed to build up filter networks. The fourth section gives an application of the general theory by presenting a detailed treatment of simple series circuits magnetically coupled so as to form a chain. In this section a number of curves is presented. These curves give a visual picture of the general theory and bring out points useful in the designing of selective networks which must meet preassigned requirements. The fifth section discusses the problem of building up filters using sections of many different types. General methods of attacking this problem are given and design formulas for three different types of filter sections which may be used together in building up a filter system, are derived. Curves are given which illustrate the methods of building up desirable characteristics. The design of selective systems is put upon a rational basis.