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Maximally-Flat Filters in Waveguide

01 October 1948

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W E USUALLY associated the word filter with any device which is selective. The electric wave filter has that property which enables it to transmit energy in one band or bands of frequencies and to inhibit energy in other bands. Selectivity is the result of either selective absorption 1 , 2 * or selective reflection. This paper discusses a special case of the classical lossless transducer which derives its selective properties entirely from selective reflection. The insertion loss of this type of filter can be analyzed in terms of the input reflection coefficient and the input standing wave ratio. In many applications of lossless filters it is desirable to obtain a characteristic such that the insertion loss, and hence the reflection coefficient, is small over as wide a band as possible. A special case described here, referred to as a maximally-flat filter, has a loss characteristic such that a maximum number of its derivatives are zero at midband. While the maximally-flat type of characteristic does not give the smallest possible reflections over a finite pass band, it does give small reflections, and has added advantages of simplicity in design and in many cases less transient distortion than filters giving smaller reflections. The desirable characteristics of maximally-flat filters have long been realized.1 ยท 3 Mr. W. R. Bennett 4 of these Laboratories derived the constants for a maximally-flat ladder network in the late 20's, and gave simple expressions for the element values.