Bol ae 647 
ratio must be very large if appreciable reduction in peak height is to be 
avoided. For example, a loss of only 2 percent of the peak requires that 
6/r = 300. Ifa pulse of time constant 9 = 50 psec is to be recorded with 
this accuracy, * = 0.17 msec, and the amplifier stage should have 70 per- 
cent of its midband response at a frequency f, = 1/2m7 = 950 ke. 
Another property of the response characteristic is that the area under 
the response curve for any value of @/r is equal to that under the applied 
transient if the integration is extended to infinite time, This appears 
reasonable from Fig. 2 and is easily proved by direct integration of Kgs. 
(3) and (4): 
bs \ i 
B(t)dt = —"— |o (i -je*/*) = (1 = ot | = AO, 
Jo Ui ibaa, c 
pe i Li 
ICTs crete E ae ae ae 
~ o 
° 
It is interesting to consider the area under the response curve for more 
gener2l conditions. let the response curve of the applied signal F(t) be R(t), 
and the response to an applied step signal be S(t). If the system is linear, 
the response R(t) may be expressed as a function of F(t) and S(t) by the 
superposition ureanemia. 
The relation may be written 
it 
(7) R(t) = S(O) F(t) | P(x) S'(t = x) dx, 
(0) 
where the prime superscript indicates differentiation with respect to the 
argument of the function, Im the present case S(0), the response at zero 
time to a step voltage, can be taken as zero. If we integrate from t = 0 
to t = +t', the area A(t") under the response curve is 
For a discussion of the superposition theorem, see Gardner and Barnes, 
Transients in linear systems (192). 
