Simplified trajectory of an impulse (like the current of lightnings) as one of two choices:
y = amplitude/eta*(exp(-time/tau1) - exp(-time/tau2))
y = amplitude/eta*(time/tau1)m/(1 + (time/tau1)m)*exp(-time/tau2)
The parameters of the trajectory are defined by:
amplitude
of the trajectoryT1
T2
m = 5..10
is recommended.
According to Fig. 1, a straight line between 0.1 and 0.9 of the amplitude is drawn.
The virtual start of the trajectory is defined by the intersection of this straight line and the abscissa.
The rise time T1
is defined as the time span between the virtual start of the trajectory and the point in time when the straight line reaches the amplitude.
The decay time to half value T2
is defined as the time span between the virtual start and the point in time when the output falls below 0.5 of the amplitude.
Note: Due to numerical reasons, for the double-exponential function T1 < 0.2*T2
is required.
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For a standard trajectory with amplitude = 100 kA, T1 = 10 µs, T2 = 350 µs
the integral of the output reaches the required charge Q = 50 C
nearly perfect.