NOTE 



Some Novel Expressions for the Propagation Constant 

 of a Uniform Line 



By J. L. CLARKE 



IN a modern communication system the leakance is generally quite 

 small and can be neglected in making propagation computations. 

 Hence the case is taken of a circuit having resistance, inductance and 

 capacitance. 



Let R, L and C be the resistance, inductance and capacitance per mile 

 of the circuit. 



Now the formulae which have been developed for the real and imaginary 

 parts of P, the propagation constant, are: 



P = a + j^ 

 where 



« = VicoClV^ + co2Z-2 - wZ] (1) 



/3 = Via)C{\/^+ co2Z,2 + coL] (2) 



Inspection of these formulae does not reveal any obvious reason for the 

 particular structure of the expressions; however, they may be changed so 

 as to present themselves in a different form. 



P can be written: 



P=^(a/fi+j) (3) 



Now 



-«=/ 



VR^ + 0)2 L2 + CoL 



tan 6 (4) 



where d is the absolute value of the angle of the characteristic impedance. 

 Hence 



P = iS(tan d + j) (5) 



156 



