A Modified Description of Early Time High-altitude Electromagnetic Pulse Waveform (E1)

The mathematical description of High-altitude Electromagnetic Pulse (HEMP) waveform (E1) in the standard of IEC 61000-2-9 is the difference of double exponentials (DEXP). However, in this description there is a discontinuity of the first derivative at the initial time of waveform. Another analytic waveform description, the quotient of double exponentials (QEXP) has the advantage of all time derivatives continuous, but an additional time shift parameter must be used since the amplitude is nonzero for negative time. To address these problems, this paper offers a modified description, namely p-power of double exponentials (PEXP). The parameter values in PEXP description corresponding to IEC 61000-2-9 have been fitted by means of varied power of double exponentials. The analysis results demonstrate that the PEXP description has two advantages of the continuous derivative at initial time of waveform and no need of the time shift factor. Key Words— HEMP Waveform Description, Discontinuity, Difference of Double Exponentials (DEXP), Quotient of Double Exponentials (QEXP), p-power of Double Exponentials (PEXP)