664 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1952 



placing (84) by 



D 



me / _2\ n' ' — n> 



(121) 



Fig. 14 illustrates an application of the technique to the simulation of 

 a coaxial cable attenuation (which is nearly proportional to -^/w)- 



29. RECAPITULATION 



Tchebycheff polynomial series may be applied advantageously to a 

 very ^dde range of network synthesis applications. The scope of their 

 usefulness may depend upon the skill of the designer, as with any 

 synthesis tools, but the underlying principles are reasonably simple. 

 The most important principles are perhaps the following: 



A Tchebycheff polynomial series in frequency may be related to a 

 power series in a new variable z. When the Tchebycheff polynomial 

 series corresponds to a finite network gain or phase, the power series 

 corresponds to an analytic function of 2, quite similar in form to the 

 network function of p, with singularities at 2;-plane mappings of the 







0.005 



■ 0.010 



■ 0.015 



0.3 0.4 0.5 0.6 0.8 1.0 2 3 



FREQUFNCY IN MEGACYCLES PER SECOND 



Fig. 14 — Simulation of a coa.xial cable attenuation — Attenuation at top useful 

 frequency = 46 db; Network = four constant-resistance sections. 



