Ideal Wave Filters * 



By H. W. BODE and R. L. DIETZOLD 



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 applica- 

 tion of the theory. 



Introduction 



TN the phenomenal advance of telephone practice during the past 

 ■'- twenty years, almost every step has further restricted the distortion 

 which individual parts of a transmission system can be allowed to 

 introduce into the signal. The extension of circuits to great distances 

 made it necessary that each link pass on to the next a more faithful 

 copy of the signal so that the accumulated effects of many links might 

 not endanger the intelligibility. The extension of telephone circuits 

 to new uses, such as the transmission of pictures and the distribution 

 of broadcast programs, imposed new demands for accuracy. Each of 

 these has required rising standards of performance for wave filters. 

 More than anything else, however, it has been the introduction of 

 carrier methods, with their comparatively large utilization of selective 

 structures, which has given prominence to the problem of reducing 

 the distortion from wave filters. With the increase in length and com- 

 plexity of carrier systems, the problem of providing wave filters which 

 will have no harmful effect upon transmission has become one of in- 

 creasing importance. 



What this requires of the filters quickly appears if we recall that a 

 structure which transmits all signals without distortion must (1) 

 possess a characteristic impedance which is a pure resistance inde- 

 pendent of frequency; (2) attenuate steady sinusoidal signals equally 

 at all values of frequency; and (3) introduce a rotation in phase pro- 

 portional to the frequency. In filter theory we need consider these 

 requirements over only a limited band, since the signals which filters 



* The reader is referred to the preceding paper entitled "A General Theory of 

 Electric Wave Filters." 



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