l.OADlin LINES ./iV/) COMPENSATING NETWORKS M,7 



The formulas for the mid-sivlioii and mid-Io.id cliaracli'risiic im- 

 pi'danres A.' 5 and ^'5 arc' 



(1-D) 



A". = e^(l+|coth^)(l + ^tanh^) (2-D) 



=^^^+\{iy+i''^'^^- (3-D) 



Several imitually equivalent formulas for the propagation con- 

 stant r (per periodic interval) are: 



cosh r=cosh T + TT s'"h y< (4-D) 



2g 



sinh r = ^'^'sinh 7, (5-D) 



tanh A r=— tanh J 7. (6-D) 



g 



The sending-end impedance J of any smooth line, of character- 

 istic impedance gi and total propagation constant 71, whose distant 

 end is closed through any impedance Ji, has the formula 



This enables the formula for the <r-section characteristic impedance 

 K„ of a loaded line to be established by starting with the formula 

 (l-D) for the mid-section characteristic impedance /C.5. 



' Formulas (2-D) and (^-D) for K'.5 and formula (4-D) for cosh r are given by 

 G. A. Campbell in his paper on loaded lines {Pliil. Mag., March, 1903) cited in 

 footnote 2. 



