EXPONENTIAL TRANSMISSION LINE 565 



except for a phase factor. In order that the current will not increase, 

 5 = — 2a. The actual attenuation "constant," 



will increase with distance down the line so that the current will 

 decrease but not as rapidly as with a uniform line. The total attenua- 

 tion in nepers is approximately 



1 /'\ r' o„., /i , 1 P\/e'"oi - 1 



1 +-,U a^'-'-dx = 1 +-i- 1 ^— — ^ . (14) 



At the point where the attenuation of the uniform line is 6 db the 

 tapered line has an additional attenuation of 7 db above the uniform 

 Une or a total attenuation of more than twice. The current has been 

 reduced to less than half. Here an improvement may be made by 

 increasing the dissipation by either changing the wire size or resistivity 

 of the conductor. A greater improvement would result from changing 

 the resistivity because then the capacity for heat dissipation would be 

 the same. Suppose, however, that one conductor material is to be 

 used throughout and the dissipation capacity is proportional to the 

 wire surface; then at this point the wire size could be reduced to 1/2, 

 doubling the attenuation factor. It is already 4 times that for the 

 uniform line, so this increases it to 8 times. The resulting total attenua- 

 tion is 30 db in a length that would have less than 7 db if the line were 

 uniform. If this attenuation were required the length of line could be 

 reduced by a factor of about 4.4. Of course the spacing is very close 

 at the end of this line, but the line could be shorted at the end. This 

 would approximately double the current at the end, but here again the 

 current carrying capacity of the line is more than double the current 

 traveling down the line. With the line shorted the reflected current 

 would be 60 db down, which would not affect the input impedance 

 appreciably. For the first 13 db of attenuation the impedance of the 

 line would be relatively free from changes due to changes in spacing 

 resulting from wind, etc. When the spacing is small enough to be 

 affected by wind, vibration, etc., the attenuation will be great enough 

 to suppress these small irregularities. 



Experiment 



In order to verify the foregoing theoretical development, measure- 

 ments have been made on several experimental lines. Figure 4 shows 

 the results of measurements on two such lines. These lines were 



