and 



DISTORTION CORRECTION 473 



g-Fi — \ 2mn { — I » ("58) 



\ w + (1 + m)np ) ' 



_p _ 1 — w ^ lmn{\ — m) I p 



\ -\- m \ -\- m \ m + (1 — m)np ' 



Introducing these expressions in the general relation, where the net- 

 work is terminated by R, 



~ =J'^e-p^g{t)dt, (60) 



there results for the indicial voltage of the first section, since 



g,{t) = 1 - , g-[»a/(l+m)n] /^2) 



and for the second section 



g2(0 = \^ + T^ e-t-'/a-)»'. (63) 



1 + m 1 -f m 



These functions are given in Fig. 10. 



It will now be shown that, whereas the indicial voltage of each section 

 alone is a varying function of time, that of the composite network is a 

 constant, which represents the transient condition for no distortion 

 with zero time-of -transmission. 



For the composite network terminated by R the indicial voltage 

 gc{t) may be derived from the usual formula for such a combination, 

 equivalent to (5), 



gc{t) = g2(0)gi(0 + f g^{t - y)g2'{y)dy. (64) 



Jo 



Upon carrying through the integration we get 



ScU) = -^ — ; — er^' = constant, (65) 



1 -f w 



which agrees with the prediction from the steady state and is so shown 

 in Fig. 10. 



Obviously the two sections can be interchanged. 



The composite network appears at first hand to behave in a rather 

 remarkable manner. For if a periodic voltage is suddenly impressed 



