LIGHTMXG PKOTECnOX OF BURIED TOLL CABLE 259 



where To and A'o are the propagation constant and the characteristic im- 

 pedance of the core-sheath circuit and 



Since the current must be zero at .v = 0, it is necessary that A = B. 

 To make the curent vanish when .v becomes infinity, B must equal 



z 1 



— ()(x) = —777 z I z;" . With these boundary conditions the voltage 

 zAo 1 -|- 1 



between core and sheath becomes: 



r(.v) = y p-£-j;, (r.-^^- - T,e-'n (10) 



The propagation constant To is much smaller than F, and may be taken as: 



To = \{R, + /coZo)/coCo]- 



1 . (11) 



= - [lo:{lw -f /?(, An)]-' 



An = Unit length resistance of core-sheath circuit, ohms/meter 

 An = Unit length inductance of core-sheath circuit, hy /meter 

 C = Unit length capacitance of core-sheath circuit, fd/meter 



CO = (1/AoCo)* 



1 .4 Direct Strokes — Lightning Voltage at Stroke Point 



The largest voltage between sheath and core conductors is obtained for 

 X = 0, and for this case (10) becomes: 



DXO) = -^ ' 



2 r + To 



/ A7Vsinh iiwy)^ (12) 



~ ~ \ , . 1 



- (zco -j- 1 'pk)" -f- - (ico -f Ao An)-' 

 V Vo 



For sufficiently high frequencies, so that {iooyY » 1, /w > 1 pK, /oj > A0Z.0, 



and sinh (icoyY = \ exp {iuiy)"' expression (12) becomes 



r(0) = /At- -^ (/co)--e-^'"^'* (13) 



