646 
ec 
The response R(t) resulting from the admittance function [Eq. (2)] is 
then the transform 
R(t) = «| F(p) mw (s(t)]| 
five Nieeh 
“M laapr + pF 176 | 
Therefore 
(lL) R(t) = +. je-*/ lappa | 5 (C-F, Pair },48] 
eee 
The result [Eq. ()] is plotted in Fig. 2 as a function of the reduced 
time t/@ for various values of the ratio 0/7. If @ —* o, corresponding 
to an input pulse in the form of a stepwise charge of infinite duration, the 
response is R(t) =A [1 - ey and it is evident that i is the time con= 
stant of the rise to the limiting value A, Unless this time constant 7 is 
much smaller than the time constant @ of the applied pulse (9/7 >> 1) it is 
evident from Fig. 2 that considerable distortion of the initial part of the 
curve and loss of peak height result. From the plot it can be seen that 
the maximum of the response curve lies on the true response curve (the curve 
marked 9/7 = o in Fig. 2). This is readily shown by the usual means from 
Eqe (4): setting the derivative of Eq. (4) equal to zero gives for time ty 
of the maximum 
(5) t= 
and substitution of this value in Eq. () gives for the maximum response - 
1/9 
~ 
(6) R(ty) = A(z) T= 7, 
-tii/9 
It is easily seen from Eq. (6) that R(t.) = Ae w/ - S(ty). 
Plots of R(ty)/A and ty/9 2s functions of the time-constant ratio 9/7 
are shown in Fig. 3. It can be seen that the maximum response R(t,,)/A 
approaches unity asymptotically as 0/7 approaches infinity, and that this 
