DISTORTION CORRECTION 



445 



filters and which, together with iterative parameters, were discussed 

 generally by the writer in a previous number of this Journal.^ But 

 since here in the ladder type networks some dissymmetrical sections 

 are also considered, I shall use the iterative parameters throughout 

 this paper. 



Theorem I: Any symmetrical transducer whose attenuation constant is 

 zero at all frequencies has a phase constant which increases with fre- 

 quency and an iterative impedance which is a constant resistance through- 

 out the frequency range. 



Theorem II: Any transducer whose iterative impedance is real at all 

 frequencies has a constant resistance iterative impedance, and if in 

 addition its phase constant is proportional to frequency, it has a uniform 

 attenuation constant. 



Theorem III: Any symmetrical transducer whose attenuation constant 

 is independent of frequency and whose iterative impedance is a constant 

 resistance at all frequencies has a phase constant which is zero or increases 

 with frequency. 



The theorems, whose proofs are given in Appendix II, may be 

 represented by the following table. The variations with frequency of 

 the network parameters shown apply to the entire frequency range 

 and in each theorem the parenthesis designates the dependent property, 

 where A is the attenuation constant, B the phase constant, and K the 

 iterative impedance. 



TABLE I 



Linear Transducer Theorems 



That part of Theorem I which relates to the iterative impedance 

 explains why there is no physical ladder type network having zero 

 attenuation throughout the frequency range. For, the ladder type, 

 when non-dissipative and having zero attenuation, requires a mid-series 

 or mid-shunt iterative impedance which varies with frequency. 



* "Transmission Characteristics of Electric Wave-Filters," O. J. Zobel, B. S. T. J., 

 October, 1924. The term "characteristic impedance" used in that paper for a 

 recurrent or iterative parameter with dissymmetrical transducers is replaced here by 

 "iterative impedance." Thus, the same term "iterative" applies to the structure, 

 to the corresponding impedances, and to the kind of parameters. The use of the 

 term "characteristic impedance" will be limited to smooth Unes, or sometimes to 

 symmetrical recurrent structures. In symmetrical structures the "characteristic," 

 "iterative," and "image" impedances are identical. 



