ni.i'.CTRic c/h'crir ■riir.oRv i\ 



velocitN' of propagation of the \va\e is v'l^. Now since /3 is greater 

 than unity and only approaches unit>' as the frequency becomes 

 indefinitely great, the inference is freciucnlK- made that the \elocit\- 

 of propagation depends upon and increases to a limiting value v, 

 with the frequency. This velocity, however, is not the true velocity 

 of propagation, which is always v, but is the velocity oj phase propagation 

 in the steady-state. This distinction is quite important and failure 

 to bear it in mind has led to serious mistakes. 



Returning to equation (211) and (210) we see that after a time 

 interval t = x/v has elapsed since the unit e.m.f. was impressed on the 

 cable, the voltage at point x suddenly jumps from zero to the 

 value g"''"'" while the current correspondingly jumps to the value 

 C 



^ 



— e ''^'^'. The exponential factor px/v is 



■Ki + 1^) ^•^^"=K f \l L + f ^l§) ="" 



which will be recognized as the steady-state attenuation factor for high 

 frequencies. Similarly \^C/L is the steady-state admittance of the 

 line for high frequencies. The sudden jumps in the current and 

 voltage at time t = x/v are called the heads of the current and voltage 

 waves. If, instead of a unit e.m.f., a voltage /(/) is impressed on the 

 line at time / = 0, the corresponding heads of the waves are f(o)e~'"' 

 and -s/ CjL /(o)g"'" for voltage and current respectively. These 

 expressions follow at once from the integral formula 



'(0 = ^Jj(t-r)h{T)dT 



=/(o)//(0+ f'f'it-T)h{r)di 

 Jo 



The tails of the waves, that is, the parts of the waves subsequent 

 to the time t = x/v, are more complicated and will depend on the 

 distance x along the line and on the line parameters p and a. The two 

 simplest cases are the non-dissipative line, and the distortionless line. 



The ideal non-dissipative line, quite unrealizable in practice, is one 

 in which both R and G are zero. In this case p = o- = 0, and formulas 

 (210) and (211) become 



7 = for t<x/v, 



= -Jy- for t>x/v, 



V = for t<x/v, 

 = 1 for / > x/v. 



