Irregularities in Broad-Band Wire Transmission Circuits 



By PIERRE MERTZ and K. W. PFLEGER 



The efifects of inhomogeneities along the length of a wire trans- 

 mission circuit are considered, affecting its use as a broad-band 

 transmission medium. These inhomogeneities give rise to reflec- 

 tions of the transmitted energy which in turn cause irregularities 

 in the measured sending or receiving end impedance of the circuit 

 in its overall attenuation, and in its envelope delay. The irregu- 

 larities comprise departures of the characteristic from the average, 

 in an ensemble of lines, or departures from a smooth curve of the 

 characteristic of a single line when this is plotted as a function 

 of frequency. These irregularities are investigated quantitatively. 



TX riRE transmission circuits in their elementary conception are 

 ^ ^ considered as perfectly uniform or homogeneous from end to 

 end. Actually, of course, they are manufactured in comparatively 

 short pieces and joined end to end, and there is a finite tolerance in the 

 deviation of the characteristics of one piece from those of the next and 

 also from one part of the same piece to another. A real transmission 

 circuit therefore has a large number of irregularities scattered along its 

 length which reflect wavelets back and forth when it is used for the 

 propagation of a signal wave. When a cable pair, coaxial conductor, 

 or similar medium is used for broad-band transmission it is important 

 to know how these irregularities influence the transmission character- 

 istics of the medium. 



The transmission characteristics which will be studied are the im- 

 pedance, the attenuation, the sinuosity of the attenuation (to be 

 defined), and the delay distortion. The derivations for the first two 

 characteristics parallel substantially those published by Didlaukis and 

 Kaden (ENT, vol. 14, p. 13, Jan., 1937). They are set forth here for 

 completeness of presentation because the steps in them illustrate the 

 more complicated steps in the derivation of the last two characteristics. 



When the characteristic impedance changes from point to point, its 

 variation from the average characteristic impedance for the whole 

 length of conductor forms the irregularities which produce reflections. 

 Assume that successive discrete elementary pieces of the circuit are 

 homogeneous throughout their length, that the lengths of these ele- 

 mentary pieces are equal throughout the length of the whole circuit, 

 and that there is no correlation between the deviations from average 



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