434 BELL SYSTEM TECHNICAL JOURNAL 



in parallel. It is useful where for other reasons the unbalanced cur- 

 rents cannot be reduced to a desirably low value. The device shown 

 to the right of Fig. 15 is suitable for measurements on concentric lines. 

 In order to employ this device openings at regular intervals are re- 

 quired in the outer sheath. An important precaution to be observed in 

 employing this last device is that the shielding be sufficiently thorough 

 to assure no pick-up from stray currents flowing upon the outside of 

 the sheath. 



It is of course essential that all portable devices of this kind extract 

 a very small proportion of the power in the line; otherwise, the device 

 becomes a source of reflection and spurious results are obtained. 



Another method of measuring the attenuation of a line which is 

 particularly useful in studying the effects of current unbalances is to 

 employ a small portable horizontal antenna the impedance of which 

 matches the characteristic impedance of the line. The antenna is con- 

 nected in a short section and then in a long section of the line. It is 

 essential that the height of the antenna above ground be equal for the 

 two positions. Also, the location for the experiment should be such 

 that the same ground losses are present for the two positions. The 

 ratio of the antenna currents for the two positions and for the condition 

 of equal power input is a measure of the total line losses. 



One of the most satisfactory schemes for measuring line attenuation 

 is the direct measurement of the line sending end impedance by means 

 of the familiar resistance substitution method. It has been used ex- 

 tensively in measurements of concentric lines. For this purpose it is 

 necessary to employ lines either open- or short-circuited at the far 

 end and to restrict the measurements to lines which contain an integral 

 number of quarter wave-lengths. 



Conventional transmission line theory indicates that under these 

 conditions the impedance is either: 



Zi =Zotanh(a^^ , (12) 



or: 



where: 



4 



Z, = ZoCOth ( a^), (13) 



Zo = characteristic impedance, 

 a = attenuation factor; i.e., the real part of the propagation 



constant, 

 X = wave-length, and 

 w = an integer denoting the number of quarter wave-lengths. 



