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BELL SYSTEM TECHNICAL JOURNAL 



B. Condition for Obtaining Lumped Constants from a Distortionless Line 

 In a distortionless line there is only one necessary relation between 

 the constants, equation (11). Hence, we are at liberty to vary the 

 constants subject only to this relation. In the following work we wish 

 to make the distortionless line degenerate into resistances, inductances, 

 and capacities, or combinations of these. 



For example, suppose that we wish to obtain a resistance from a 

 distortionless line. To obtain this we take a short circuited line as 

 shown on Fig. 1-A and let R be finite, L -> 0, G -^ 0, and C -> 0^ in 

 order to satisfy equation (11). The shunt elements will all vanish 

 and the series inductance disappears, leaving only the series resistance 

 in the line. Since the line is short circuited, the line degenerates into 

 a resistance. The line parameters for this case become 



^ = J^ -> oo 1/2 ; p = ^jRG + > VLC -> (0^/2 + jo:0^n) 



and 



RoP = ^S i^lRG) + . /? (jcoVLCO -> R. 



(14) 



There are three combinations of lumped elements which can be 

 obtained from the short circuited line and three combinations which 

 can be obtained from the open circuited line. These are listed in the 

 following table, together with the resulting line parameters. 



Limiting Cases of the Distortionless Line 

 A . Limitinp Values with Short Circuited Line 



The first three cases result from the suppression of the shunt 

 elements in the short circuited line, and the line parameters are 

 characterized by Ro -^ ^ ; P -^ 0. The last three cases result from 

 the suppression of the series elements in the open circuited line, and 

 are characterized by Ro -^0; P -> 0. 



