2 BELL SYSTEM TECHNICAL JOURNAL 



will be general, and will not Involve assumptions as to the detailed 

 construction of the wave-filter; but in order to secure a certain nu- 

 merical concreteness, curves for some simple wave-filters will be in- 

 cluded. The formulas employed in calculating these curves are 

 special cases of the general formulas for the wave-filters which are, 

 in conclusion, deduced by the method employed in the physical 

 theory. 



All the physical facts which are to be presented in this paper, 

 together with many others, are implicitly contained in the compact 

 formulas of the appendix. Although only comparatively few words 

 of explanation are required to derive these formulas, they will not be 

 presented at the start, since the path of least resistance is to rely 

 implicitly upon formulas for results, and ignore the troublesome ques- 

 tion as to the physical explanation of the wave-filter. In order to 

 examine directly the nature of the wave-filter in itself, as a physical 

 structure, we proceed as though these formulas did not exist. 



It is intended that the present paper shall serve as an introduction 

 to important papers by others in which such subjects as transients on 

 wave-filters, specialized types of wave-filters, and the practical design 

 of the most efificient types of wave-filters will be discussed.^ 



Definition of Wave-Filter 



A wave-filter is a device for separating waves characterized by a dif- 

 ference in frequency. Thus, the wave-filter differentiates between 

 certain states of motion and not between certain kinds of matter, 

 as does the ordinary filter. One form of wave-filter which is well 

 known is the color screen which passes only certain bands of light 

 frequencies; diffraction gratings and Lippmann color photographs 

 also filter light. Wave-filters might be constructed and employed 

 for separating air waves, water waves, or waves in solids. This 

 paper will consider only the filtering of electric waves; the same 

 principles apply in every case, however. 



In its usual form the electric wave-filter transmits currents of all 



frequencies lying within one or more specified ranges, and excludes 



currents of all other frequencies, but does not absorb the energy of 



these excluded frequencies. Hence, a combination of two or more 



wave-filters may be employed where it is desired to separate a broad 



band of frequencies, so that each of several receiving devices is sup- 



^ I take pleasure in acknowledging my indebtedness to Mr. O. J. Zobel for specific 

 suggestions, and for the light thrown on the whole subject of wave-filters by his 

 introduction of substitutions which change the propagation constant without chang- 

 ing the iterative impedance. 



