Scientech S200 Vector - Manual (Page 20)

1. Numerical Integration
Finding the area under the curve in Figure 4 is the equivalent procedure for determining pulse energy.
Choose an appropriate time interval, dt, and perform the summation:
N N
E=
Σ
W
i
xdt=(dt/S)
Σ
V
i
i=1 i=1
The error caused by this procedure is:
N
dE=(dt/S)
Σ
dV
i
i=1
The error, in theory, is only dependent upon the value of
Σ
dV
i
, that is the cumulative random error of V
i
.
This number should approach zero if data is carefully taken. The accuracy is also increased if the time
interval, dt, is minimized. Numerical integration can
yield accurate results, but is a tedious task.
2. Initial Voltage Interpolation
A method used to eliminate the tedious numerical integration task is to project the
thermal decay envelope on to the voltage axis, determine the 1/e decay time constant T, and estimate the
total energy value (E):
E=(V
o
/S) x T
The change from thermal absorption to thermal transport phenomena near the peak causes difficulty in
accurately projecting the envelope on to the voltage axis introducing an error, dV
o
. Further, the determination
of the time constant T, introduces another error, dT. The total error is the sum of the two errors.
dE=(V
o
/S)dT + (T/S)dV
o
The difficulty in eliminating the potential error makes this method typically less accurate than numerical
integration, but much faster in application.
3. Peak Voltage Estimate
The peak voltage method requires using an independent determination of total energy and referencing it
back to the peak voltage value, V
p
.
For a given pulse, use the numerical integration method to obtain E. Note the peak voltage, V
p
. Compute the
value, F:
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