Idealized external current components ...
... for lightning testing are defined in standards and in the literature for aerospace and defense [1, 2, 3].
Component
- A - First return stroke
- AH - First return strokes at higher altitudes
- B - Intermediate current
- C - Continuing current
- D - First of the subsequent strokes
- D/2 - One of the remaining subsequent strokes
- H - Current pulses in leader development, attachment and detachment process and similar pulses occurring throughout the flash duration
Except for component C, which is a rectangular pulse, all other components are aperiodic pulses with specified rise and decay times as shown in Fig. 1 for the lightning current component A.
For the electromagnetic simulation of lightning indirect effects ...
... closed form expressions of current component waveforms are required. The latest waveform specified in [1] is the quadruple exponential (QE):
In older standards and in particular in the MIL-STD [2] the double exponential (DE) is used:
For the QE waveform the maximum rate change at t > 0 is a more realistic representation of a real lightning currents and despite that reduces numerical instabilities. The first derivative of the DE waveform at t = 0 is unequal 0 and with it its' maximum rate change. The additional last term of the QE waveform impacts only the rising slope.
To make use of the QE waveform in CST Studio Suite ...
... a VBA macro is available for download from the knowledge base article QA00000306492. Instructions how to add it to the VBA macros are also provided. The macro calculates waveform values on a logarithmic time scale and an error control makes sure to reach a user specified accuracy. It allows to select among the fore mentioned current component as shown in Fig. 2 and to also switch to the DE waveform. The USER waveform allows for a customized specification of QE and DE lightning pulses, respectively.
When to use this macro?
The macro can be used to define QE waveform excitations in CST Studio Suite for transient simulation and analysis in 3D and Schematic. As this macro makes use of the ASCII import the sampling is critical - in particular during the rising slope - and for that logarithmic sampling is required and implemented. Please note: The built-in feature "User defined" in CST Studio Suite to define excitation signals does not offer logarithmic sampling and I recommend to make use of this macro for lightning indirect effects analysis with injected current pulses.
References
[1] "Aircraft Lightning Environment and Related Test Waveforms," SAE ARP5412B (EUROCAE ED-84A), SAE International, 2013.
[2] "Electromagnetic Environmental Effects, Requirements for System," SMIL-Std-464C, Department of Defense, Interface Standard, 2010.
[3] R. J. Perez, "Handbook of Aerospace Electromagnetic Compatibility," Wiley, New Jersey, 2019.
