Waveform conversion and validation of transient magnetic field due to ESD using equivalent circuit of magnetic near‐field probe

With a 6 GHz band high resolution magnetic near-field probe (XF-R 3-1) produced by Langer, the transient magnetic fields due to collision ESDs (electrostatic discharges) between metal balls at a charging voltage of 600 V were measured near the spark point to investigate a dipole radiation mechanism. In this study, as an object of considering the measured magnetic field waveforms, two different equivalent circuits of the magnetic near-field probe are derived based on the probe response waveform observed by a TDR (time domain reflectometer) with a 10 ps rise-time pulse and the probe reflection coefficient measured with a 26 GHz network analyzer. Waveform conversion formulae from the probe output voltage to the magnetic field are given. The validity of the conversion methods is verified by comparing the measured conversion waveforms and their frequency spectra in addition to the converted spectra by the Langer field correction curve with the calculated waveforms of the transient magnetic far-fields from a dipole model consisting of image charge pairs and the Rompe-Weizel spark resistance formula. The probe conversion formulae presented here are valid within the frequency range of the 6 GHz probe band, however, beyond the band the resonance peaks at multiple frequencies over 8 GHz appear on the spectra, which causes damping oscillations peculiar to the probe with multiple frequencies to the time domain waveform.