l.OAnED UXF.S .'IXn COMrnXS.lTlXG M-.TH-ORKS 417 



independent' of frc<|uenr\'; such a line hiuins a transniitling band 

 (that is, a non-attenuating hand) extending froni zero frequency to 

 infinite frequencies, and a characteristic impedance which is a pure 

 and constant resistance. 



In contrast, the corresponding characteristics of a non-dissipative 

 periodically loaded line depentl very greatly on the frequency; such a 

 line has an infinite sequence of alternate transmitting and attenuating 

 bands* wherein the impetlance \aries enormously with frcfiuency, 

 while at the transition frequencies its nature undergoes a sudden 

 change. In this connection it may be remarked that, because of its 

 special practical importance in being the upper boundary frequency 

 of the first or principal transmitting band, the lowest transition fre- 

 quency is termed the "critical frequency" to distinguish it from the 

 other transition frequencies; though in its essential nature each 

 transition frequency is a "critical" frequency. In the ordinary case, 

 where the distributed inductance is small compared with the load 

 inductance, each transmitting band is ver\- narrow compared with the 

 succeeding attenuating band. In the limiting case of no distributed 

 inductance there is only one transmitting band and one attenuating 

 band, the former extending from zero frequenc>' to the critical fre- 

 quency and the latter from the critical frequency to infinite frequencies. 



The characteristic impedance of any non-dissipative transmission 

 line is or is not pure reactance according as the contemplated frequency 

 is in an attenuating band or in a transmitting band. For in an at- 

 tenuating band the line cannot receive energ>', since it cannot dissipate 

 any energ>" and cannot transmit any energy- to an infinite distance; 

 while in a transmitting band the line must receive energy, because it 

 does transmit. Thus, at the transition frequency between an attenu- 

 ating band and a transmitting band the characteristic impedance 

 undergoes a sudden change in its nature; the frequency-derivative 

 of the impedance (namely, the derivative of the impedance with 

 respect to the frequency) is discontinuous, so that the graph of 

 the impedance has a corner (salient point) at a transition frequency. 

 Moreover, at certain of the transition frequencies of a non-dissipative 

 periodically loaded line the impedance is zero, and at others is infinite. 

 The mid-point impedances are pure resistances throughout every 

 transmitting band. (The "mid-point" terminations are "mid-load" 

 and "mid-section," that is, "half-load" and "half-section" respectively.) 



' Except for slight change of the inductance, and even of the capacity, with 

 frequencj-. 



• For distinction, the first (lowest) or principal transmitting band may be termed 

 the "major" transmitting band; the others, the "minor" transmitting bands. 



