Extensions to the Theory and Design of 

 Electric Wave-Filters 



By OTTO J. ZOBEL 



'l"he problem of terminal wave-filter impedance characteristics is con- 

 sidered in this paper, in particular that of obtaining an approximately con- 

 stant wave-filter impedance in the transmitting bands of a wave-filter of any 

 class, which is of importance where the wave-filter is terminated by a 

 constant resistance, the usual case. The solution obtained is based upon the 

 repeated use of the methods of deriving wave-filter structures which gave the 

 .l/-types, combined with composite wave-filter principles. The results are 

 wave-filter transducers which at one end have standard "constant k" iniage 

 impedances and at the other have image impedances which can theoretically 

 be made constant in the transmitting bands to any degree of approximation 

 desired. Practical fixed structures are shown. 



Parts I and II give this derivation and composition of wave-filter struc- 

 tures. Two allied subjects, respectively, the designs of networks which 

 simulate the impedances of wave-filters, and of loaded lines, are dealt with in 

 Parts III and IV, such designs making use of the previous results. 



The four Appendices contain new reactance and wave-filter frequency 

 theorems, particular fixed transducer designs and certain equivalents; also, a 

 chart for determining terminal losses at the junction of such a fixed wave- 

 filter transducer and a resistance termination. This chart siipplements 

 those previously given in a chart method of calculating wave-filter trans- 

 mission losses. 



o 



Introduction 



NE important problem which frequently arises in wave-hlter 

 design is that of obtaining a terminal wave-filter impedance 

 which is approximately a constant resistance at all frequencies in the 

 transmitting bands. This ideal impedance characteristic is desirable 

 where a wave-filter is terminated by such a constant resistance, as is 

 usually the case. Under these ideal conditions, for frequencies in the 

 transmitting bands all terminal reflection losses are avoided, and there 

 are no impedance irregularities at the terminal junction to be reflected 

 back through the wave-filter and produce objectionable impedance 

 irregularities at the other end. 



The design of ladder type wave-filters of any class, ^ regarded from 

 either the theoretical or the practical standpoint, involves taking into 

 consideration two standard image impedances; and the internal or 

 main part of a composite wave-filter structure, called the mid-part, 

 usually has the equivalent of one or the other of these image impedances 

 at each terminal. These two standard image impedances are the image 



^"Theory and Design of Uniform and Comi)usile IClcclric W a\ c-Filters," (J. J. 

 Zobcl, B. S. T. J., January, 1923. 



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