468 BELL SYSTEM TECHNICAL JOURNAL 



are given in Appendix IV. Any pair of the networks, such as la and 

 \b, differ only by an interchange of series and lattice elements with a 

 corresponding difference in their phase constants of an amount tt. 

 In order to simplify computations for some networks the formula? 

 were derived so as to require attenuation data at a limiting frequency, 

 but other formulae may also be obtained. By means of the relations 

 in Section 2.5, transformations can readily be made to any of the other 

 general types, if they lead to physical structures. 



The type of network which a final design is to assume will be sug- 

 gested by economic and practical considerations. However, an ap- 

 proximate statement can be made in this connection. If the sections 

 are to be dissymmetrical as regards the two pairs of terminals and 

 unbalanced as regards the two sides of the line, use the full-series or 

 full-shunt ladder types; if symmetrical and unbalanced, use the 

 bridged-T types; if symmetrical and balanced, use the bridged-T or 

 lattice types. 



Part 3. Arbitrary Impedance Recurrent Networks 



In Part 2 consideration was given entirely to recurrent networks 

 whose iterative impedances are a constant resistance at all frequencies 

 and which depend upon the use of inverse networks; that is, 211Z21 = -R'- 

 It is intended here merely to point out briefly that all the types in 

 Section 2.4 can be generalized to have iterative impedances of arbitrary 

 value K provided in them 



R is generalized to K, 

 and 



211221 = X^; (47) 



that is, 2i] and 221 are inverse networks ^- of impedance product K-. 

 The corresponding propagation constant formulae hold also with these 

 generalizations. 



Where a recurrent network of arbitrary iterative impedance K is 

 desirable, these structures would, theoretically at least, be applicable. 

 Practically, however, considerable difficulties are usually encountered 

 in physically realizing Zu and 221 to give a desired propagation con- 

 stant, and perhaps even K when K is not a simple function of fre- 

 quency. A few physical possibilities will be given here in which the 

 structures for 211 and 221 are easily identified from the forms of the 

 expressions. They may be used in the different types of networks, 

 and, of course, 211 and 221 may be interchanged. 



12 The complete qualifying statement such as given is necessary here, not just 

 simply "inverse networks." 



