ScienTECH Vector Series - Numerical Integration

PN 10795T 40
The output voltage from a chart recorder can be converted to wattage at any time by:
W = V/S, W
i
= V
i
/S
V = Chart recorder voltage level in mV
S = Calorimeter sensitivity in mV/W
The total energy (E) in the pulse can be found by integrating the instantaneous wattage over time:
∞
E = ∫ W(t) dt
0
The following methods may be used to compute the total integrated energy:
Numerical Integration:
Finding the area under the curve in figure 7 is the equivalent procedure for determining pulse energy.
Choose an appropriate time interval, dt, and perform the summation:
N N
E = ∑ W
i
xdt = (dt/S)∑ V
i
I=1 i=1
The error caused by this procedure is:
N
dE = (dt/S) Σ dV
i