Scaling of energy delivered through an electrostatic discharge to a small series load

TL;DR

This study investigates energy transfer during quasi-static electrostatic discharges in air, modeling the spark channel as a resistive path in series with a small victim load. Using a controlled circuit with variable external capacitance $C_x$, inductance, and electrode geometries, the authors measure voltage and current traces to quantify energy partition between the spark and the victim load, and they test the Rompe-Weizel (RW) model’s scaling predictions. The key finding is that, for gap lengths $h$ exceeding about 1 mm, the fraction of stored energy delivered to the victim load scales with the product $C R_v$ and becomes independent of $h$, with the normalized energy limited by $oxed{\overline{\eta}_v= a_R E_{th}^2/4}$. This provides a simple, practical framework to bound energy delivery to low-resistance components during ESD, informing safety margins for sensitive electronics and energetic-material interfaces; deviations at small gaps and geometry effects highlight areas for future refinement of the model.

Abstract

We study the energy delivered through a small-resistance series ``victim'' load during electrostatic discharge events in air. For gap lengths over 1~mm, the fraction of the stored energy delivered is mostly gap-length independent, with a slight decrease at larger gaps due to electrode geometry. The energy to the victim scales linearly with circuit capacitance and victim load resistance but is not strongly dependent on circuit inductance. This scaling leads to a simple approach to predicting the maximum energy that will be delivered to a series resistance for the case where the victim load resistance is lower than the spark resistance.

Figures (10)

• Figure 1: ESD circuit diagram highlighting the charging circuit (thin, light blue), the safety circuit (thick dark gray) and the discharge circuit (black).
• Figure 2: Graphical depiction of the discharge circuit elements $C_x$, CVR ($R_\text{v}$) and spark gaps of the (a) open-air system (OAS) and the (b) symmetric grounded system (SGS). For the SGS, the image is a cross-sectional view of the chamber to visualize the circuit components
• Figure 3: SGS example voltage and current traces with $C_x=100$ pF, $R_\text{v}=0.0983$$\Omega$, 1.27 cm diameter brass spherical electrodes and Cal Test voltage probe. The legend in (a) applies to both plots.
• Figure 4: The average current (dashed line) and integrated charge (solid line) for 20 individual discharge events, using the SGS with a 100 pF $C_x$ and 0.0983 $\Omega$ CVR at a 4.2 mm gap. The stored charge $Q_0$ is indicated by the horizontal line and marked on the charge axis.
• Figure 5: For 20 individual discharge events, shown here is the (a) voltage (solid lines) and current trace (dashed line), and the (b) dissipated energy through the circuit, using the SGS with $C_x=100$ pF and $R_v=0.0983$$\Omega$ at a 3.0 mm gap. The analysis is shown for three different cable delays, emphasizing the importance of the time shift between the voltage and current signals. The shaded areas around the curves show the spread in signal, and the horizontal line in (b) indicates the stored energy. The legend in (a) applies to both plots.