Ideal Wave Filters*

Abstract

The increasing usefulness of wave filters in the telephone plant, together with rising standards of quality, emphasizes the need of a systematic method for approximating ideal characteristics as closely as we please. By an ideal filter is meant a network having the properties of a distortionless transducer over a given frequency range and suppressing all other frequencies. A design method is presented whereby an arbitrarily close approximation to these properties may be realized in a physical network. Examples of actual designs illustrate the engineering features involved in the practical application of the theory.

Synthesis of Reactance 4‐Poles Which Produce Prescribed Insertion Loss Characteristics: Including Special Applications To Filter Design

“…First, if Ell is obtained by adding ~i to the image transfer constant of any filter (of pure reactances) with inverse image impedances, cosh (Ell) will be an odd rational function of frequency. Second, if El1 by itself represents an image transfer constant of any symmetrical filter, cosh (Ell) will be an even rational function of frequency.71 If the theoretical pass bands of these 11 These relations follow directly from the following equations, which can readily be derived by means of elementary network theory: and (D!r + mri) at pass band and attenuation band frequencies. As a result, the well established theory of the image transfer constants of image parameter filters of the inverse impedance and symmetrical types can be applied directly to the design of insertion loss filters of the symmetrical and inverse impedance types, respectively.…”

“…They can readily be evaluated, however, in terms of the roots of the corresponding power ratio (1). 11 In the special case under consideration these roots can be computed by means of straightforward formulae derived from the elliptic function relations (2).…”

“…Since some margin is thus usually available even though '1 has the smallest permissible value, this margin is usually best distributed among the various relations of (4). 11 If the requirement of a loss function appropriate for a symmetrical network is abandoned it is usually necessary to include also the roots of a linear function of the power ratio e 2a • (1). Of these only one set is appropriate for the mid-series low pass ladder configuration of Fig.…”

“…See, for instance, the description of Fry's isograph recently published by Dietzold(9).26 Bode developed a theory similar to Mayer's independently but published only a brief reference to it. This reference is in the paper "Ideal Wave Filters"(11) which he published in collaboration with Dietzold.…”