Accurate Mathematical Parameter Determination for Double-Exponential Impulse Waveforms With Specified Parameters

A double-real-exponential function is extensively utilized in high-power electromagnetics, encompassing research on high-altitude electromagnetic and ultrawide-band pulses, lightning, and high-voltage tests. There is a substantial demand for converting pulse waveform parameters such as rise time, full width at half maximum, fall time, front time, time to peak, time to half peak, and peak value into the first- and second-time constants and a peak factor of a mathematical function. The article introduces an accurate method named the time normalization technique for mathematically generating impulse waveforms with a set of waveform parameters, including: the rise time, the full width at half maximum, and the peak value and the front time, the time to half peak, and the peak value. The validation of the proposed method reveals that estimation errors below 10<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−6</sup>% can be achieved. Using the results obtained from this method, expressions for mathematical parameter estimation in a wide range of time parameters are developed, which yields estimation errors below 0.02% for converting the rise time, the full width at half maximum, and the peak value to the first- and second-time constants and the peak factor, and below 0.01% for converting the front time, the time to half peak, and the peak value to the first- and second-time constants and the peak factor. Additionally, the utilization of these expressions for waveform generation to evaluate the measurement uncertainty of a voltage measuring system is demonstrated.