DISTORTION CORRECTION 447 



combinations are most useful, since the bridge structures require at 

 least five elements in each network. Some networks may have other 

 equivalent structures, as well. 



If zii = rn + ixn and Zoi = ^21 + ^^"21 are inverse networks such 

 that 



S11S21 = R\ (10) 



a number of simple relations exist among their impedance components; 

 namely, 



.2: rn (jl) 



and 



Jf2i _ Xn 



|22l|- R"' 



In a smooth line the condition (6) which makes it distortionless is 

 actually the one making the series and shunt impedances per unit 

 length inverse networks of impedance product i?" = R'/G' = L'/C 



2.4. Types of Constant Resistance Recurrent Netivorks and Their 

 Propagation Constants 



The types of recurrent networks considered in this paper are the 

 three simplest ones, the ladder, lattice, and bridged-T types whose 

 general structures are shown in Fig. 2. Propagation constant and 

 iterative impedance formulae for these types in terms of general 

 impedance elements are given in Appendix III for possible future 

 reference. 



By introducing in each of these types the use of inverse networks 

 with Zii and Z21 satisfying relation (10), and assuming various relations 

 in the general formulae, it is possible to derive general network struc- 

 tures whose iterative impedances are a constant resistance, R, at all 

 frequencies.^" The structures are of such general nature as to permit 

 a very wide range of propagation constants. Any one of them when 

 closed by a resistance, R, presents at the other terminals the impedance 

 R at all frequencies. They will now be considered. 



The networks of the ladder type are shown in Fig. 3 as six complete 

 sections, each designated by the termination at which it has the 

 iterative impedance R; one at full-series, one at full-shunt, and two 



loSee U. S. Patent No. 1,603,305 to O. J. Zobel, dated October 19, 1926. Also 

 British Patent Specification No. 236,189, dated July 8, 1926. 



