Energy partitioning in electrostatic discharge with variable series load resistor

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 gap length that can be considered fixed. 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 our extension of 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 predictive framework that should be valuable for guiding safety requirements for energetic materials and ignition scenarios and will inform the development of more accurate circuit models that can be applied to a wider range of ESD events such as those found in the electronics industry.

💡 Research Summary

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This paper presents a comprehensive experimental study of how the stored electrical energy in a quasi‑static electrostatic discharge (ESD) event is divided between the spark plasma and a series‑connected resistive “victim” load. The authors extend their previous work, which examined only low‑resistance loads, by exploring a five‑order‑of‑magnitude range of victim resistances (0.1 Ω to 10 kΩ) together with variations in capacitance, gap length, and breakdown voltage.

The experimental platform consists of a high‑voltage power supply charging an external capacitor (Cₓ) through a 100 MΩ current‑limiting resistor (R_L). A spark gap formed by two graphite spheres is placed in series with a low‑inductance resistor (Rₓ) and a current‑viewing resistor (R_c). The total victim resistance is R_v = Rₓ + R_c. Voltage is measured with a high‑bandwidth high‑voltage probe (HVP) that can be connected either before (node N₁) or after (node N₂) the current‑limiting resistor. Current is recorded with the CVR.

A key methodological contribution is the extraction of the time‑dependent spark resistance R_S(t). Simple division of voltage by current yields spurious spikes because the inductive voltage drop (L_S · dI/dt) is not accounted for. The authors therefore subtract the inductive term, using an effective series inductance L_S (330 nH–1.25 µH, calibrated for each configuration), and compute the total resistance as

 R_T(t) =