Energy partitioning in electrostatic discharge with variable series load resistor

TL;DR

This work extends the Rompe–Weizel nonlinear spark-resistance framework to quantify energy partitioning in quasi-static ESD events with a variable series victim load spanning $R_v\in[0.1,10^4]\Omega$. Through open-air experiments across multiple capacitive energies and gap lengths, the authors show that the fraction of energy delivered to the victim load is largely independent of gap length and can be accurately predicted by a modified RW model, enabling estimation of the final spark resistance $R_{SF}$ and the energy share $\eta_v$ from circuit parameters. Key results include the derivation and validation of $\eta_v$ via $(1-\eta_v)^2=2\eta_v\frac{R_{SFmin}}{R_v}$ and the RW-based expression for $R_{SF}$, with fitted $a_R$ values ranging roughly from $0.22$ to $2.32\,\mathrm{cm^2/(s\,V^2)}$. The findings offer a predictive framework to inform safety requirements for sensitive electronics and energetic materials and guide more accurate ESD circuit models. The work also highlights the regime where the victim absorbs most energy, and emphasizes the need to consider whether energy or power transfer governs safety-critical response.

Abstract

This paper presents an experimental investigation into the energy partitioning of quasi-static electrostatic discharge (ESD) events in air, a scenario in which the discharge occurs across a fixed gap. We systematically characterize the energy transferred to a series victim load across a broad range of resistances (0.1 to 10,000Ohm) and circuit parameters, including capacitance and gap length. Our results show that the fraction of stored energy delivered to the victim load is largely independent of gap length. We demonstrate that the classic Rompe-Weizel spark resistance model effectively predicts the scaling of this energy transfer, establishing a clear link between spark resistance and energy partitioning. These findings provide a valuable, predictive framework for guiding safety requirements for sensitive electronic components and energetic materials and will inform the development of more accurate circuit models for ESD events.

Figures (13)

• Figure 1: ESD circuit diagram highlighting the charging circuit (thin, light blue) and the discharge circuit (black). The circuit nodes $N_1$ and $N_2$ shows the possible placements of the HVP.
• Figure 2: Spatial visualization of the OAS discharge circuit, highlighting the $C_x$, $R_L$, $R_x$, $R_c$, and HVP circuit elements. $N_1$ and $N_2$ are the circuit nodes where the HVP can be connected for voltage monitoring.
• Figure 3: Voltage and current traces for ESD in the OAS with $C_x = 700$ pF, $R_c = 0.0983$$\Omega$, 3.81 mm gap, and varying $R_x$. The system transitions from underdamped to overdamped behavior as $R_x$ increases.
• Figure 4: Unadjusted (a) current and voltage traces for (b) spark resistance measurement. With the OAS, $C_x = 700$ pF, $R_\text{v}=0.0983$$\Omega$ at 1.27 mm gap. The highlighted region in (a) indicates the $I_\text{lim}$ region and applies to the current trace only.
• Figure 5: Adjusted (a) current and voltage traces and (b) measured spark resistance. With the OAS, $C_x = 700$ pF, $R_c=0.0983$$\Omega$ at 1.27 mm gap. The highlighted region in (a) indicates the $I_\text{lim}$ region and applies to the current trace only.