418 BELL SYSTEM TECHNICAL JOURNAL 



Clearly the characteristic impedance of any dissipative line cannot 

 be pure reactance at any frequency; for the line receives at its sending 

 end the energy dissipated within itself. Also, the presence of dis- 

 sipation renders the frequency -derivative of the impedance continu- 

 ous at all frequencies; that is, it rounds off the corners on the graph 

 of the impedance. Dissipation prevents the impedance from becoming 

 either zero or infinite at any frequency; and in general it prevents the 

 mid-point impedances from being pure resistances in the trans- 

 mitting bands. 



In the neighborhood of the transition frequencies of the loaded line, 

 the effects of even ordinary amounts of dissipation may be very large, 

 thus preventing the impedance from attaining the very extreme values 

 of the non-dissipative line; but with that exception it may be said 

 that the contrast between a loaded line and the corresponding smooth 

 line is merely softened or dulled by the presence of ordinary amounts of 

 dissipation: The impedance of the smooth line is no longer pure 

 resistance, and it varies somewhat or even considerably with the 

 frequency.' The impedance of the loaded line no longer varies quite 

 so rapidly with the frequency nor attains such extreme values; but, 

 except at low frequencies, it continues to depart widely from 

 the impedance of the corresponding smooth line, and to vary 

 much more rapidly than the smooth line with frequency, besides 

 varying greatly with its relative termination (fractional end-section 

 or end-load). 



Non-Dissipative Loaded Lines 



Except in the neighborhood of zero frequency and of the transition 

 frequencies, the characteristic impedance of an efficient loaded line 

 is dependent mainly on the inductance and capacity, only relatively 

 little on the wire resistance and load resistance, and very much less 

 still on the leakance. The present paper is confined mainly to non- 

 dissipative loaded lines; it deals first with the limiting case of no 

 distributed inductance, and then with the case where distributed 

 inductance is present. By the neglect of all dissipation the number of 

 independent variables is sufficiently reduced to enable a compre- 

 hensive, though only approximate, view to be obtained of the char- 

 acteristic impedance of loaded lines. Such a view is a valuable guide 

 in engineering work even though in most cases it may be necessar\ , 

 for final calculations or verifications, to resort to exact formulas 

 (Appendix D) or graphs thereof. 



