420 



BELL SYSTEM TECIISICAL JOURNAL 



Besides depending on the frequency /, the quantities K, II, Z, W 

 and K', 11', Z', W depend on the relative terminations o- and c' 

 respectively (Fig. 1). This dependence will not usually need to be 

 indicated explicitly, but in case of such need the subscript notation 

 will be found convenient. Thus, Ka will denote the a-section char- 

 acteristic impedance (Fig. la); and Ki-a ihe "complementary char- 

 acteristic impedance," that is, the characteristic impedance of the 

 same loaded line if beginning at the "complementary termination" — 

 namely, (l — o-) -section. As an application of this notation we maN' 

 note here the relations 



Ko = Ki , 



Ih = Ih', 



A-, = AV, //.=//o'; 



(2.2) 



the first two relations subsisting because of the coincidence of the 

 points (T-section and cr'-load for a = and c'=l, and the second two 

 because of the coincidence for a = l and a' = 0. 



FART II 



Impkd.wce of N'oN-Dissii'ATivE Loaded Lines without 

 DisTRiRiTKD Inductance 



Traiisi)!!tli)ig Band mid Attouialinfi Band 



As already stated, a periodically loaded line without distributed 

 inductance (Fig. 1, with L=0) has only one transmitting band and 

 only one attenuating band; the former extending from zero fre- 

 quency to the critical frequency ft, and the latter from the critical 

 frequency' to infinite frequencies. The formula for /r is 



f,= \/-Ky/T'C. 



(3) 



L' denoting tiie inductance of each load aiul C' the capacity of each 

 line-section between loads. 



From the energy considerations alreach- adduced, it is known tiiat 

 the characteristic impedance must be pure reactance througiiout tlie 

 attenuating band, but cannot be pure reactance anywhere in the 

 transmit ting hand. 



Formulas for the Relative Impedances 



The impedance of e\en a loailecl line wiliioul distributed inductance 

 (Fig. 1, with L = 0) depends on no less than four independent variables 

 —namely, the frequency /, load inductance L', section-capacity C, 

 and one or the other of the relative terminations a and a' . But it is 

 found that these quantities enter in such a way that the relative 



