Uncertainty of ESD Pulse Metrics Due to Dynamic Properties of Oscilloscope

This paper investigates how dynamics of an HF oscilloscope affects standardized metrics (i.e., rise time and peak value) of a recorded electrostatic discharge (ESD) current pulse and evaluates the oscilloscope measurement uncertainty. A frequency-domain dynamic model of the oscilloscope, based on measurements of the input reflection and voltage gain magnitude, is derived. The complex voltage gain is approximated with a transfer function to take into account unmeasured phase shift. A high-order discrete-time filter is designed to fit the measured voltage gain magnitude not only in the passband, but also beyond it as well. Since the measured data are burdened with measurement uncertainties, the worst-case deviations of the oscilloscope input impedance and the voltage gain (in the form of envelopes of the frequency responses) are calculated, and components of type B uncertainty of the ESD pulse metrics corresponding to these deviations are estimated using the sensitivity method.