72 BELL SYSTEM TECHNICAL JOURNAL 



Both current and voltage jump, at time t^x/v, to their steady values. 

 If an e.m.f./(/) is impressed on the line at time / = 0, the corresponding 

 current and voltage waves are 



/ = ior t<x/v, 



- yj-^f{i-x/v) for t>x/v, 



V=0 for t<x/v, 

 =f{t — x/v) for / > x/v. 



Consequently the ideal non-dissipative line transmits the waves 

 with finite velocity v, without attenuation or distortion. Such a line 

 is, of course, the ideal transmission system. 



The non-dissipative line is, of course, purely theoretical and un- 

 realizable in practice; the distortionless line is, however, approxi- 

 mately realizable, and as the name implies, transmits without distortion 

 of wave form. The distortionless line is one in which the line con- 

 stants are so related that 



If this condition is satisfied, formulas (210) and (211) become 

 7 = for t<x/v, 



-^ 



^e^"* ior t^x/v, 



V=Qior t<x/v, 



= e~°^ for t>x/v. 



Furthermore, if the impressed e.m.f. isj{t), the corresponding current 

 and voltage waves are: — 



7 = for t<x/v, 

 = A^e-^^'fit-x/v) for t>x/v, 



V=Qiov t<x/v, 

 = 6'"'' fit — x/v) for t>xlv. 



The distortionless line, therefore, transmits the waves without dis- 

 tortion of wave form, but attenuates the waves by the factor e""^ . 

 Such a line is an ideal transmission system as regards preservation 

 of wave form, but introduces serious attenuation losses. For example, 

 if a line has normally negligible leakage, and leakage is introduced 



