IRREGULARITIES IN WIRE TRANSMISSION CIRCUITS 547 

 final simplified result is 



^AK? _ VaZ? \cf>\8 



K K 2\' 



(4) 



where is the phase shift in radians in two elementary lengths, e is 

 the attenuation in nepers of two elementary lengths, and 5 is, as men- 

 tioned before, the standard deviation in C measured as a fraction of C. 

 It will be noted that as a consequence of the single reflections, the ir- 

 regularities in impedance vary as the first power of 5. 



The irregularities in attenuation have been computed in Appendix II 

 from the double reflections of the type c in Fig. 1. It is found, as 

 mentioned before, that there is a net rise in average attenuation caused 

 by the reflections, equal, in nepers, to 



2/4 



where n is the number of elementary lengths in the total line. Con- 

 sidering the factor in parentheses in the expression above, although the 

 term e is not usually wholly negligible compared with the term <^^/2, 

 nevertheless the latter is dominating and sets the order of magnitude 

 of the factor. If the e is disregarded, the expression can easily be put 

 in terms of the impedance irregularities, giving 



r Va^ 



L K 



A, (6) 



where A as before represents the loss in the total line. 



The standard deviation in the loss in nepers, when finally simplified, 

 is, for the reflections, 



Vir-^. (7) 



Expressed in terms of the impedance irregularities, this amounts to 



4m^[^]^\. (8) 



It will be noted that these irregularities in the attenuation vary with 

 the square of b, or the square of the impedance irregularities. This is a 

 consequence of the double reflections, and will continue to hold for the 

 sinuosity and irregularities in envelope delay. It will also be noted 



