Background: Lightning electromagnetic pulse (LEMP) and high-altitude electromagnetic
pulse (HEMP) are widely described by three physical parameters (rise time tr, full-width at halfmaximum
pulse width tw, and maximum electric field strength E0). These pulse shapes are often given
by a double exponential form concerning four mathematical parameters, namely α, β, k and Ep.
Objective: The transformation from physical parameters into mathematical parameters is necessary
in waveform simulation and is traditionally accomplished by linear fit functions regarding the two
groups of parameters. However, traditional methods commonly rely on data analysis and calculation.
In order to obtain the mathematical parameters more concisely and clearly.
Methods: In this paper, a numerical method to calculate the mathematical parameters by solving
nonlinear equations with three key constraints is proposed. Firstly, we establish the nonlinear system
of equations regarding four variables, namely t1, t2, α and β. Then, three constraints are given to
converge the solutions of the equations. Lastly, select the minimal value of the convergent solution
of each equation.
Results: Comparing the solutions obtained by our proposed method to the iterated ones, the overall
relative error is less than 2×10-8.
Conclusion: The results show that our proposed method not only simplifies the transformation from
physical parameters to mathematical parameters, but also keeps the solutions high accurate.