428 BELL SYSTEM TECHNICAL JOURNAL 



line at the near end and at the far end were obtained. The attenuation 

 in decibels was computed from average near end and far end current 

 ratios. 



It is difficult to explain the discrepancy between observed and com- 

 puted values. If the resistivity employed in the computations were to 

 be increased from 1830 to 5030 e.m.u. (a multiplication factor of 2.75) 

 the computed curve so obtained would be in good agreement with the 

 observed results. It is true that the wires were somewhat weathered. 

 There is, however, little reason to believe that an appreciable amount 

 of current flows in the oxide layer covering the wires. Effects of this 

 kind would have been evident in the measurements upon concentric- 

 tube lines. It already has been mentioned that small current unbal- 

 ances in the line may produce losses in the earth which increase the 

 real part of the propagation constant. Possibly, losses of this kind 

 may explain the discrepancy. 



IV. Notes on Matching Impedances 

 It already has been mentioned that standing waves on a transmission 

 line augment line losses. The penalty which is imposed by improper 

 impedance matches may be seen from Fig. 12. This figure plots line 

 loss as a function of the degree of matching for several attenuation 

 factors. The line loss is computed from the ratio of the power dis- 

 sipated in the load to the total power obtainable from the generator. 

 The curves were obtained from conventional transmission line theory. 

 For the purpose of simplifying calculations the line length is assumed 

 to be an integral number of one-quarter wave-lengths, thereby eliminat- 

 ing complex impedances. Otherwise the length of the line is imma- 

 terial, the product of length and attenuation per unit length being 

 the criterion of loss. 



In the diagrams of Fig. 12 A and Fig. 12B the circuit M is an ad- 

 justable ideal transformer. For every value of the resistance R the 

 transformer M is assumed to be adjusted so as to maximize the load 

 power. This process is equivalent to matching impedances at the ter- 

 minals of the line adjacent to the transformers. It is of interest to 

 observe that where R is not equal to the characteristic impedance Zo, 

 this adjustment does not yield an impedance match at the line ter- 

 minals remote from the transformers. It is of further interest to 

 observe that in the case where the load impedance is variable (Fig. 12B) 

 the optimum adjustment is a compromise between a non-reflecting 

 termination and an impedance match at the generator end. 



Conventional tuned transformers may be employed to match the 

 line impedance to the antenna and radio equipment impedances. In 



