LOADED LINES ASD COMI'EXSAIIXC. XE I WORKS 41'J 



Notation and Terminology 



The meanings of the fiinclainental symbols employed in this paper" 

 can be readily seen from ins|K'ction of Fig. 1. Thus, C and L denote 

 the capacity and the inductance of each whole section between loads, 

 and L' the inductance of each whole load; the ratio L L' is denoted by 

 X. Figs, la and lb represent inlinitely long loaded lines terminating 



K-Jj „, i: ^ L ; L (a) 



K--^, <t'l' ^ h ^ l: (b) 



' ' ^TTT i ^- ( Twi n ( Tmy i _ 



Z-t 2'=f W-a- W.-a: 



Fig. I — .A N'on-Dissipative Infinitels- Long Loaded Line Terminating at : (a) ir-Section, 

 (b)<r'-Load 



at a-section and a'-load respectively; the ratios a and a' will be termed 

 the "relative terminations." A' and A'' denote the corresponding 

 characteristic impedances, and // and //' the characteristic admit- 

 tances. Stated more fully, K denotes the ir-section characteristic 

 impedance, and K' the a'-load characteristic impedance; similarly 

 for the admittances // and //'. The "nominal impedance" and the 

 "nominal admittance" are denoted by k and /;, respecti\ely; that is, 



k = 1/A = a/(L+Z,')/C= V'(1 + X)LVC, (1) 



the nominal impedance of a periodically loaded line being defined 

 as equal to the nominal impedance of the corresponding smooth 

 line.' Z = A'-fjF and Z' = A'' + JF' denote relati\e impedances 

 and W=U-\-iV and \\" =U'+iV' the corresponding relative ad- 

 mittances, as defined by the equations 



Z = Kfk, Z' = K';k, lV = n/h, \V' = H'/h; (2) 



the real components being A', A'', U. U', and the imaginary compo- 

 nents Y, F', I', V, resjjectively. By (2), 



ZW = Z' II" = KII = A' 'II' = 1 . ( 2. 1 ) 



r denotes the relative frequency, namely, the ratio of any frequency 

 f=2u/2r to the critical frequency /c; that is, / '=J'fc = ui uc- i denotes 

 the imaginary operator V— 1. 



