DISTORTION CORRECTION 511 



from computed results are representative and serve to give an idea 

 of the possibilities of the network for design purposes. All networks 

 except the last have a constant resistance iterative impedance R. 

 Networks la-12 have attenuation so that they will usually be designed 

 from their attenuation characteristics in terms of which the formulae 

 are given. There is usually more than one physical solution from the 

 same attenuation characteristic, and in Networks 9 and 10 as many 

 as four have been found possible. These multiple solutions all have 

 different phase constants. A possible practical advantage of one solu- 

 tion over another may lie either in its phase constant or the magnitudes 

 of its elements. It is of interest to point out that if these networks were 

 designed from the phase characteristic some of them might have mul- 

 tiple solutions with different attenuation characteristics. For example, 

 Networks 3a and 36 corresponding to the phase characteristics 1' and 

 2' each can have two such solutions. 



The Networks \h, 2b, etc., with their output terminals interchanged 

 are, respectively, identical with Networks la, 2a, etc. Hence, any 

 pair of these networks have the same attenuation constants but phase 

 constants differing by tt radians. An extension of this list to include 

 Networks 6b, lb, etc., was not thought to be necessary. 



Several networks may have the same form of frequency function 

 for F or H. Some values of the attenuation or phase coefficients will 

 give a physical structure to one network but not to another. Whether 

 a network having a definite A- or 5- characteristic is physical or 

 not can be determined most readily by a direct substitution of the 

 coefficients in the formulae for the elements. In certain cases these 

 latter formulae show easily that one network may give a physical result 

 where another cannot. For example. Networks 6 and 10 both have 

 the same F formula, but when one network is physical the other is not; 

 similarly with Networks 7 and 9. These particular results would be 

 expected from the fact that those pairs of networks cannot have the 

 same attenuation characteristics, as seen from their structures. 



Networks 13-17 have no attenuation and are designed from their 

 phase characteristics. Network 18 represents a somewhat general 

 form of artificial line and has other types of formulae. 



Examples of networks which are potentially complementary are 

 Networks la and 2b; lb and 2a; 3a and 3b; 11 and 12. 



Transformations of impedance branches to equivalent ones can be 

 made in some of the networks by means of the general transformation 

 formulae given in B. S. T. J., January, 1923, pages 45 and 46. 



