26 BELL SYSTEM TECHNICAL JOURNAL 



Modifications for Very Low Frequencies 



Thus far the present paper has dealt with the characteristic im- 

 pedance of smooth lines as distinguished from their sending-end 

 impedance, strictly speaking. The two are closely equal when the 

 lines are electrically long, which is usually the case for the telephonic 

 frequency range; but at very low frequencies the sending-end im- 

 pedance of even a rather long line may depend very greatly on the 

 distant terminating impedance and hence depart widely from the 

 characteristic impedance. In case the terminating impedance is 

 conductive to direct current the sending-end impedance of even a 

 strictly non-leaky line would have a finite value at zero frequency; its 

 resistance component evidently being equal to the total line-wire 

 resistance plus the terminating resistance, while its reactance com- 

 ponent would, of course, be zero. Actually, on account of line leak- 

 ance, the resistance component would be somewhat less; and in case 

 the distant terminating impedance permits no passage of direct cur- 

 rent the sending-end impedance of the line at zero frequency would 

 depend largely on the line leakance. 



Most of the simulating networks thus far described were devised 

 primarily with regard to the voice range of frequencies, without refer- 

 ence to frequencies very far below that range. At very low fre- 

 quencies these networks become unsuitable because their impedance 

 is not only much too large but also has not even approximately the 

 proper angle. There have not been many occasions for modifying 

 the networks so as to extend their range of simulation down toward 

 zero frequency; but it seems likely that in most cases the requisite 

 modification in the network impedance could be attained, at least 

 roughly, by shunting the excess-simulator (Fig. 5b) with a mere 

 resistance S' approximately equal to the zero-frequency sending-end 

 resistance of the line diminished by the resistance R x of the basic 

 resistance element. Clearly this modification will give the network 

 the desired impedance at zero-frequency, without affecting its im- 

 pedance at infinite frequencies; since the impedance of the unshunted 

 excess-simulator is infinite 13 at zero-frequency and is zero at infinite 

 frequencies. At the intermediate frequencies the resulting modifi- 

 cation would doubtless be slight except toward the lower frequencies, 

 where it would increase, more and more rapidly as zero-frequency is 

 approached. Of course, the addition of the modifying element S' 

 would usually entail some alterations in the proportioning of the 



13 Except for the limiting form in Fig. 10b. 



