Pcb Layout For Power Electronics

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Review of Power Electronic Solutions for Dielectric

Barrier Discharge Applications

Abstract—This paper presents a comprehensive review of dielectric barrier discharge (DBD) power supply topologies, aiming to bridge the gap between DBD applications and power electronics design. Two key aspects are examined: the dependence of the DBD electrical model on reactor geometry, and application- driven requirements for injected waveform characteristics, in- cluding shapes, voltage amplitude, frequency, and modulation techniques. On this basis, the paper systematically reviews two major categories of power supplies: sinusoidal types comprising transformerless and transformer-based resonant inverters, and pulsed power supplies (PPSs). The review summarizes perfor- mance trade-offs, highlights untested topologies and emerging ap- plications, and offers guidance for advancing high-performance DBD power supply design for next-generation systems.

Index Terms—Dielectric barrier discharge (DBD), resonant inverter, flyback, push-pull, Marx generator, pulsed power supply

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IELECTRIC barrier discharge (DBD) generates stable, low-temperature plasma under atmospheric conditions by incorporating a dielectric layer on metal electrodes –.

DBD systems typically consist of two electrodes separated by a discharge gap and insulated by dielectric materials such as glass, ceramics, polymers, or metal oxides –. This configuration prevents arc formation and supports a uniform electric field distribution.

Due to its capability to generate non-thermal plasma under atmospheric pressure, DBD technology is recognized as an effective solution for plasma-based processing applications.

Unlike high-temperature plasma systems, DBD produces re- active species such as radicals and ions without the need for expensive vacuum infrastructure or the risk of thermal dam- age to temperature-sensitive materials, while achieving higher energy efficiency –. These characteristics make DBD particularly effective for applications involving polymers, bi- ological tissues, and other delicate substrates . With the advent of DBD structures featuring flexible geometries, the range of applications has expanded significantly, offering po- tential solutions for biomedical applications, including wound healing –. Furthermore, the ability of DBD to operate under atmospheric conditions broadens its applicability across various industries, including food sterilization –, and catalytic reactions –.

These diverse and expanding applications demand precise and reliable plasma generation, which is fundamentally gov- erned by the operation of the power supply. As a critical component of DBD systems, the power supply directly influ- ences key parameters such as discharge uniformity and plasma dynamics. To support the wide range of DBD applications, power supply designs must address the unique challenges posed by the capacitive and dynamic load behavior of DBD systems while meeting application-specific requirements.

The increasing scope of DBD applications has introduced diverse operational requirements, such as high-frequency (HF), high-voltage (HV), and pulsed- or AC-excitation modes. A variety of power supplies have been proposed in the literature, over the years to drive DBDs with unique characteristics.

However, a comprehensive review of the state-of-the-art in power supply technologies for DBD systems has not yet been presented. It is essential to summarize recent advancements, address challenges such as energy losses, reactor geometry compatibility, and cost constraints, and finally identify oppor- tunities for further research.

This paper presents an extensive review of the power elec- tronics solutions developed for various DBD applications. It firstly identifies different DBD applications/reactor geometries and corresponding power supply requirements and presents a comprehensive review of the existing power supplies for DBD systems. Such a review would provide a systematic foundation, offering insights into the design and selection of power supplies for DBD systems. Furthermore, it would highlight performance trade-offs, optimization strategies, and underexplored areas, thereby advancing the development of ro- bust and efficient DBD systems for a broad range of industrial and research applications.

The remainder of this paper is structured as follows: Sec- tion II provides an overview of DBD reactor geometries and modeling approaches. To address the waveform requirements of DBD applications and guide the development of suitable power supplies, Section III and Section IV discuss the unique characteristics of DBD systems, focusing on waveform shapes, frequency considerations, and power supply requirements.

Building on this foundation, Sections V and VI present a detailed examination of sinusoidal supply and pulsed power supply (PPS) topologies, along with their operational charac- teristics. Sections VII and VIII highlight remaining challenges and future research directions. Finally, Section IX presents the conclusions.

Ii. Overview Of Dbd Applications

An important advantage of DBD technology lies in its energy efficiency and flexibility in controlling plasma chem- istry. This section presents the equivalent impedance model of

(B)

Fig. 1. DBD equivalent circuits. (a) Threshold-based. (b) Rectifier-based. 2.

Ideal Q-V plot. DBD systems followed by different DBD geometries and their equivalent model considerations. There can be various config- urations of DBD systems, such as Volume DBD (VDBD), Surface DBD (SDBD), Floating-Electrode DBD (FE-DBD), and Flexible DBD (FX-DBD), each optimized for specific applications. The power supply requirements for these systems are strongly influenced by the reactor design and the intended application. Consequently, a review of the DBD setup is essen- tial to ensure proper alignment of power supply specifications with reactor configurations and operational demands.

A. The Classical Equivalent Model Of Dbd

Fig. 1 shows the classical equivalent circuit model for DBD. This model consists of the dielectric capacitance (Cd) and gas gap capacitance (Cg) arranged in series, with the plasma represented as a resistive element during active discharge phases . This resistive element is often replaced with a threshold component, as shown in Fig. 1(a), or a constant voltage source with a full-bridge rectified configuration, as depicted in Fig. 1(b).

In the passive phase, when the applied voltage remains below the threshold voltage, Vth, the entire circuit—referred to as the ”cell”—operates predominantly as a capacitive network.

The total impedance of the cell is determined by the combined effects of its components, including the two capacitances (Cd and Cg) and the threshold component. In contrast, during the active phase, when the applied voltage across the gas material, vg, surpasses the threshold voltage, Vth, plasma conduction alters the circuit dynamics, which are then dominated by the dielectric capacitance in conjunction with the voltage source.

Achieving vg > Vth, typically in the range of several kV to 100 kV, is critical because surpassing Vth initiates gas ionization. At this point, the observed current corresponds to

(E)

Fig. 3. VDBD reactor geometries. Cyan: dielectric material. Orange: generated plasma. Black: electrical connection including electrodes. Green: package. Blue: packed material. (a) Plate-to-plate. (b) Cylindrical. (c) In-package. (d) Packed-bed. (e) Fluidized-bed.

the discharge process, marking the active plasma generation phase. This model is often analyzed using charge-voltage (Q−V ) characteristics, visualized as Lissajous plots, as shown in Fig. 2. These plots represent the energy dissipated per cycle and enable back-calculation of parameters such as Cd and Cg for DBD modeling .

Overall, the DBD system can be simplified into two distinct operating modes with different capacitances: the passive mode, governed by the capacitive network of Cd and Cg, and the ac- tive mode, dominated by the dielectric capacitance and plasma conduction. While the classical model is effective for basic diagnostics and power analysis, it assumes uniform discharge characteristics, neglecting complexities such as filamentary be- havior, non-uniform charge distributions, and parasitic effects.

For more detailed investigations and applications involving intricate discharge dynamics, extensions of the classical model are necessary to accurately capture these phenomena and adapt to diverse geometrical configurations –.

B. Volume Dbd

VDBD systems, as shown in Fig. 3, represent a foundational configuration of DBD technology, characterized by plasma generation within a confined volume between two dielectric- covered electrodes. This configuration is widely used in gas- phase applications, such as catalysis and thin-film treatments, where precise plasma generation within a controlled environ- ment is essential .

However, the limited discharge volume inherent to VDBD systems presents challenges in treating large or irregularly shaped samples, restricting their applicability in certain indus- trial processes. To address these limitations, advanced adapta- tions such as Packed-Bed DBD (PB-DBD) and Fluidized-Bed

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Fig. 4. Non-ideal Lissajous plot. 5.

Augmented Dbd

equivalent circuit.

(C)

Fig. 6. Exemplary reactor geometries. Red: treatment target. (a) SDBD. (b) In-package SDBD. (c) FE-DBD.

DBD (FB-DBD) have been developed, significantly enhancing functionality and extending the range of applications. Fig. 3(d) illustrates an example of PB-DBD, where dielec- tric or catalytic materials are introduced into the discharge zone. This configuration enhances plasma-catalyst interactions by increasing the available surface area and redistributing the electric field .

Building On The Principles Of Pb-Dbd, Fb-Dbd (See

Fig. 3(e)) incorporates fluidized particles within the plasma discharge zone to overcome challenges associated with static packed beds such as clogging and poor gas flow, especially due to the accumulation of solid byproducts like carbon nanofibers,

And Non-Uniform Heat And Mass Transfer –. Fb-Dbd

not only improves plasma penetration but also minimizes localized arcing, creating a consistent and stable reaction environment.

It Should Be Noted That Pb-Dbd And Fb-Dbd Systems

deviate from ideal VDBD behaviors, as evident in their Lissajous plots. Fig. 4 shows a lens-shaped trajectory for PB-DBD, diverging from the ideal parallelogram associated with symmetrical VDBD designs . This deviation un- derscores the classical equivalent circuit model’s limitations in capturing PB-DBD’s time-varying characteristics . In FB-DBD, dynamic capacitance changes due to varying gas velocities and fluidized geometries further complicate the modeling. For reactors with non-parallelogram Lissajous plots, equivalent circuit models incorporating variable resistors, as shown in Fig. 5, provide more accurate representations but add complexity to the analysis. This is important to note, as it guides the control design of the power converter driving

C. Surface Dbd

SDBD addresses the spatial limitations of VDBD by en- abling plasma generation over larger surface areas. Fig. 6 shows typical geometries of SDBD including in-package ge- ometry. By embedding electrodes within a dielectric barrier, Fig. 7.

FE-DBD system for human skin treatment. SDBD creates a planar discharge area ideal for extensive surface treatments, such as sterilization and wound healing.

The co-planar electrode design reduces the gap between elec- trodes, lowering voltage requirements and enhancing energy efficiency for surface-based plasma applications.

FX-DBD, on the other hand, extends this concept by incor- porating flexible materials, enabling plasma treatment of non- planar or irregular surfaces. It functions as both an SDBD and VDBD alternative, leveraging flexible electronics to conform to complex geometries for uniform plasma exposure .

However, like PB-DBD, SDBD exhibits lens-shaped Lissajous plots, as shown in Fig. 4, which can be modeled using a variable resistor , . Additionally, the asymmetrical geometry of SDBD causes Q-V trajectory discrepancies be- tween cycles at low voltages, emphasizing the importance of maintaining sufficient voltage levels for symmetric reactor operation.

D. Floating-Electrode Dbd

FE-DBD enhances the classical DBD geometry by introduc- ing a floating electrode concept, where the treated sample or a floating electrode forms capacitive coupling with the other electrode, as shown in Fig. 6(c). This eliminates the need for a direct ground connection, reducing electrical hazards and enabling localized plasma generation at the target surface. This configuration is particularly suitable for sensitive applications such as wound healing, combining simplified electrode struc- tures with efficient plasma generation.

However, the dynamic interaction between the floating elec- trode and the actual ground node demands careful considera- tion. In applications like human skin treatment, the positioning of the ground node relative to the body significantly impacts system performance . As shown in Fig. 7, directly connect- ing the transformer’s secondary winding to the body bypasses capacitive coupling, leading to unsafe current levels, while grounding the secondary node causes impedance mismatch and instability .

Iii. Waveforms On Dbd Systems

The choice of waveform in DBD systems, both in terms of shape and frequency, is highly application-dependent, as different waveforms uniquely influence discharge behavior, energy efficiency, and process outcomes. Specific plasma characteristics, such as discharge uniformity, energy transfer efficiency, and temporal behavior can be optimized by adjust- ing waveform parameters like shape, amplitude, frequency, rise

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time and modulation. Consequently, the selection of power supply setups in DBD systems must align closely with the specific requirements of the intended application.

A. Effect Of Waveform Shapes

For DBD systems, excitation waveforms can be sinusoidal, square, or pulsed. Square and pulsed waveforms can be realized as either bipolar or unipolar excitations. For in- stance, in ozone generation, which is a common intermediate reactive species determining performance of DBD applica- tions, sinusoidal and pulsed voltage waveforms have been extensively studied. Pulsed waveforms are preferred for their sharp rise times, which enhance ionization and energy transfer efficiency, while sinusoidal waveforms produce more stable discharges, making them ideal for continuous ozone produc- tion setups , . The different characteristics of AC and short-pulse excited DBDs arise mainly from their differ- ing discharge dynamics. In AC-excited DBDs, the discharge typically consists of multiple microdischarges (as shown in Fig. 8) that occur randomly across different locations and times during both the positive and negative half-cycles of the voltage waveform . In contrast, short-pulse excited DBDs produce a single and simultaneous discharge across the entire area, resulting in an almost homogeneous discharge appearance .

Similarly, in aerodynamic applications using DBD plasma actuators, waveform selection plays a critical role in determin- ing thrust generation and electric wind characteristics. Square waveforms produce the highest thrust output but at the cost of increased power consumption. Conversely, sinusoidal wave- forms yield smoother electric wind velocity profiles, which are advantageous for precise flow control applications – . DBD ionization in portable mass spectrometry systems benefits from square waveforms, which minimizes power con- sumption while achieving homogeneous plasma for efficient ion detection .

Moreover, unipolar pulses are preferred for certain appli- cations due to their ability to suppress reverse discharges, resulting in more uniform and stable plasma generation. In contrast, bipolar pulses tend to introduce secondary reverse discharges, which disrupt discharge uniformity and lead to increased energy dissipation . Thus, unipolar pulses are particularly advantageous for applications requiring precise energy control, such as surface treatments and thin-film de- position.

However, it is not evident which waveform shapes outper- form others, as this depends strongly on the DBD operating mode, which in turn is heavily influenced by application char- acteristics, electrode geometry, frequency, voltage amplitude, and rise and fall times. These dependencies will be discussed in detail in the following subsections.

B. Effect Of Frequency

As mentioned before, the selection of the excitation wave- form frequency also plays a critical role in the operation of DBD systems. The frequency requirement can range from tens of Hz to even several MHz. And the requirements for the applications also vary due to distinct operational characteristic of DBD depending on the frequency.

Fig. 8. Filamentary discharge of sinusoidal excitation. 9.

Example waveforms of GDBD and TDBD. Fig. 10. Typical waveform of burst-mode excitation.

At low frequencies, typically in the range of tens of Hz to a few kHz, the discharge operates in a filamentary mode, characterized by discrete microdischarges, as shown in Fig. 8.

These are formed through localized streamer breakdown, re- sulting in filamentary discharge channels with high current density. This mode is advantageous for applications where higher ionization efficiency and reactive species production are critical . However, localized streamer breakdown induces thermal effects due to localized heating, which can degrade overall system performance and efficiency.

As the frequency increases to the tens of kHz range, the number of filaments decreases due to a memory effect—the residual influence of previous discharge cycles, which stabi- lizes discharges in this frequency range . This transition leads to more homogeneous DBD types, often referred to as diffuse DBD. Depending on the reactor configuration, dielectric material, the gas used, and even gas flow rate, this can manifest as Glow DBD (GDBD), driven by a combination of Townsend ionization and secondary electron emission, or Townsend DBD (TDBD), dominated by slow electron avalanches associated with Townsend ionization . As shown in Fig. 9, the output waveforms of GDBD and TDBD show suppressed microdischarges. These diffuse modes offer improved plasma uniformity and suppressed microdischarges, making them well-suited for applications requiring consistent plasma exposure, such as thin-film deposition and surface treatment.

At even higher frequencies, in the MHz range—referred to as Radio Frequency (RF) DBD—the dynamics of gas ioniza-

Ionization In Discrete

filaments.

Uniform, Low-Density

ionization via avalanches.

Ionization Near The

cathode.

Driven By Oscillating

electric fields.

By Microdischarge

filaments.

Highly Uniform Across

the discharge gap.

With Distinct Plasma

regions.

Highly Uniform;

no microdischarges.

Moderate; Frequency Depends On Gas

composition and velocity.

High-Intensity Discharges

(e.g., ozone generation).

Uniform, Low-Energy

plasma treatments.

And Power, Suitable

for surface treatment.

Breakdown Voltage

and high plasma density. 1 Filamentary DBD can occur at any frequency if the applied voltage is sufficiently high. tion and charge carrier behavior shows a notable shift . The shorter voltage cycles limit ion recombination time, allowing the oscillating electric field to maintain a higher density of free electrons. This enhances ionization efficiency and significantly reduces breakdown voltages compared to low-frequency op- eration . Studies of atmospheric-pressure gas breakdown in the 1–100 MHz range confirm that higher frequencies improve ionization efficiency and lower the voltage threshold for discharge initiation , .

C. Effect Of Rising And Falling Times

For pulsed excitation, the rising time and falling time significantly impact plasma dynamics. A shorter rising time enhances the ionization rate and electric field strength, re- sulting in higher peak currents and improved plasma unifor- mity. This suppresses filamentary discharges and promotes a more diffuse plasma layer . Unlike filamentary discharge mode—where a trade-off typically exists between high ion- ization rate and plasma uniformity—pulsed excitation with a fast rising time enables both to be achieved simultaneously.

Furthermore, shorter rising times intensify pressure waves by increasing their amplitude and propagation distance, making them highly effective for aerodynamic applications such as flow control and plasma mixing .

While less influential than the rising time, the falling time governs the discharge termination behavior and energy dissipa- tion. A shorter falling time allows for faster quenching of the discharge, reducing recombination processes and minimizing energy losses. This contributes to maintaining plasma unifor- mity and ensuring efficient energy deposition. Additionally, shorter falling times sharpen the wavefront of induced pressure waves, enhancing their aerodynamic effects . However, shorter rising and falling times can also increase stress on the electrodes due to abrupt changes in current, necessitating careful consideration of trade-offs between performance and component longevity .

D. Effect Of Modulation Techniques

Modulation techniques enhance the flexibility and controlla- bility of DBD operation by enabling the use of custom wave- form profiles and tunable discharge characteristics. Among them, burst-mode excitation has been studied in excimer lamps and ozone generation. At HF operation, the memory effect generally improves discharge uniformity. However, over time,particularly in filamentary discharge regimes or without periodic zero-voltage intervals, non-uniform charge accumu- lation occurs. This eventually leads to localized overcharg- ing, reinforcing filamentary discharges, and degradation in spatial uniformity. Consequently, burst mode, a hybrid wave- form between continuous sinusoidal and short-pulse excitation methods (shown in Fig. 10), provides zero-voltage (or low- frequency) idle intervals. These intervals facilitate ion recom- bination on barrier surfaces, lateral drift in surface electric fields, and charge diffusion driven by gradients, improving overall discharge performance.

Burst mode is typically realized using HF AC pulses sep- arated by zero-voltage idle intervals (see Fig. 10) or via am- plitude modulation with a HF carrier. By adjusting parameters such as the burst duty ratio (Dburst) and base frequency (fb), a reset operation is enabled, allowing efficient distribution of DBD power. For example, in Xenon DBD excimer lamps, burst-mode excitation achieves improved vacuum-ultraviolet efficiency and uniform, filament-free discharge . In ozone generation, periodic idle intervals reduce gas temperature and the rate of ozone decomposition, improving energy efficiency and enabling stable, tunable ozone concentrations –.

E. Discussion

These findings emphasize that power supply configurations for DBD systems cannot be universal but must be designed to the specific requirements of each application. Table I summa- rizes the generalized characteristics of different DBD operating modes, each offering distinct advantages suited to particular applications. Notably, filamentary discharges, often occurring at excessively high voltage levels, may bypass intermediate diffuse modes (i.e., TDBD and GDBD). Thus, the careful selection of waveforms, operating frequencies, and voltage levels is essential to optimize energy efficiency, discharge uniformity, and system stability.

(D)

Fig. 11. Specifications of DBD setups from the reported cases. Each data point occupies the same position across all four subfigures to represent the same case. (a) Voltage vs. frequency with average output power levels. Gray markers indicate cases where power is not reported. (b) Voltage vs. frequency for various applications. (c) Voltage vs. frequency for sinusoidal and pulsed excitation methods. (d) Voltage vs. frequency for different DBD geometries.

Applications

A. Clarifying DBD-Enabled Processes and Applications Conventionally, ozone generation and excimer lamp emis- sion are treated as applications of DBD technology. However, a more accurate description considers these as underlying physical processes enabled by DBD. In contrast, activities such as food sterilization, CO2/CH4 conversion, volatile or- ganic compound (VOC) abatement, and surface treatment are best categorized as end-use applications of DBD-enabled processes.

Since DBD produces a non-thermal plasma environment, it enables various plasma-chemical and plasma-photonic pro- cesses, including ozone generation (O2 →O3), excimer for- mation (rare-gas dimers emitting UV light), radical generation, and molecular dissociation. These effects can be used, for ex- ample, through direct ozone treatment , plasma-activated water, or UV irradiation from DBD-excimer lamps to inactivate bacteria and viruses. Such plasma processes are therefore central to applications ranging from sterilization, chemical conversion, and pollution abatement to surface mod- ification. This clarification helps align the terminology with the perspective of power electronics engineers.

B. Power Supply Requirements: Voltage, Frequency, Power Accordingly, Table II summarizes the specifications of the power supplies in various applications, including ongoing research in food sterilization, CH4 and CO2 conversion, VOC abatement, and surface treatment. To meet the diverse require- ments discussed in Sec. III, DBD power supplies are catego- rized into sinusoidal AC sources and pulsed bipolar/unipolar sources. The table highlights excitation waveform shapes, frequencies, and voltage and power requirements for different DBD applications. As shown, voltage requirements range from several kV to over 100 kV, while operating frequencies span from a few Hz to several MHz.

Power demand is primarily influenced by the reactor’s load configuration, including electrode and reactor geometry. Larger systems, such as VDBD setups, require higher power levels due to increased electrode separation and larger reaction volumes, which necessitate higher energy input for sustaining effective plasma generation. In contrast, SDBD systems typ- ically operate at only a few watts because of their smaller discharge areas and closer electrode spacing.

Fig. 11 shows the specifications of various DBD systems. It shows that high power levels—ranging from kW to MW— are rarely reported in the literature –. However, 100 kW-level power for surface treatment and several MW-level power for industrial ozone generation were documented as early as the 2000s . Additionally, several commercial systems with power ratings in the tens of kW have been re- ported –. As research and industrial interest in DBD applications continues to expand, the power requirements for these systems are anticipated to increase significantly.

C. Voltage-Fed Vs. Current-Fed Power Supplies

DBD power supplies can also be classified based on their power delivery method: voltage-fed or current-fed. Voltage-fed power supplies have long been the primary choice for DBD applications due to their simplicity, scalability, and efficiency in delivering HV excitation. Their straightforward design, often incorporating a step-up transformer, enables reliable operation with minimal complexity. Furthermore, voltage-fed supplies are cost-effective for high-power applications, making them a practical choice for industries requiring robust and scalable plasma systems. Unlike current-fed systems, voltage- fed converters do not rely on input inductors or a front- end current regulator, reducing their size and complexity—an advantage for cost-sensitive or space-constrained applications.

Furthermore, implementing soft-switching schemes in voltage- fed converters enables a more compact design by minimizing switching losses and enhancing efficiency .

However, voltage-controlled systems face challenges in maintaining precise current control, particularly with the varying capacitive loads characteristic of DBD systems. For uncontrolled or discontinuous voltage waveforms—such as square-wave voltages with undefined slew rates or arbitrary non-sinusoidal waveforms—it becomes difficult to predict idis given the discharge current of a DBD system is the derivative of the applied voltage as shown in (1).

(1)

In contrast, current-controlled converters enable well- regulated idis, making it possible to accurately predict the energy dissipation of the DBD load, while the voltage across the electrodes can be well predicted even for arbitrary current waveforms, as described by (2).

(2)

This precise current control allows current-fed power sup- plies to offer significant advantages in applications where stability and uniformity of plasma discharge are critical. By directly regulating the injected current, these systems ensure consistent plasma generation and improved discharge uni- formity. Such capability is particularly vital in applications like excimer lamps and biomedical treatments, where pre- cise plasma characteristics are essential to achieving optimal results. A key benefit of current-fed designs is their ability to regulate power delivery independently of the capacitive load’s varying properties. By employing a constant current source, the energy delivered to the DBD reactor is accurately controlled.

Moreover, the capacitive load characteristics of DBD appli- cations pose significant challenges. For instance, under square- voltage excitation with an uncontrolled slew rate, the voltage retained by the DBD load can create a significant voltage difference relative to the applied voltage. This leads to large dV/dt, resulting in uncontrolled inrush currents and potential short-circuit behavior. To address this, the converter must accommodate the capacitive characteristic of the DBD load and incorporate short-circuit-tolerant properties—a feature in- herently supported by current-fed converters.

Beyond general capacitive effects, a particularly critical challenge arises from the threshold-triggered, nonlinear behav- ior of DBD loads—especially during filamentary discharge. In

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such cases, the abrupt collapse of load impedance upon plasma initiation can induce severe current surges in voltage-fed systems, placing significant stress on switching devices, trans- formers, and resonant components. In contrast, current-fed inverters—typically incorporating an input choke inductor— naturally limit these transient current spikes by maintaining a quasi-constant or regulated input current, thereby enhancing system reliability under abrupt discharge events.

This quasi-constant or constant input current behavior often leads to reduced harmonic distortion and better input power factor, compared to voltage-fed systems. Although compre- hensive input power quality analyses specifically targeting current-fed DBD power supplies remain scarce , nu- merous studies on general current-fed converter topologies demonstrate their inherent capability to shape input current waveforms and achieve near-unity power factor –.

A DBD-specific implementation employing a passive current- fed rectifier has also reported improved input power quality compared to conventional diode-rectifier systems .

D. Voltage Step-Up: Non-Isolated vs. Isolated Power Supplies The HV demand of DBD loads necessitates the inclusion of a voltage-boosting stage to address the limitations of input power supply voltage. This can be accomplished using either transformer-based (isolated) and transformerless (non-isolated) configurations.

In transformerless designs, HV amplifier structures, such as those based on operational amplifiers and driven by function generators, can be utilized for DBD applications . How- ever, such designs are constrained by limited power output, making them unsuitable for high-power applications. To ad- dress this limitation, sinusoidal or pulse-generating stages with HV gain can be implemented, thereby meeting the threshold voltage levels for DBD applications. This stage typically comprises resonant pulse generators for pulse excitation (e.g., half-bridge or full-bridge configurations) or resonant inverters for sinusoidal excitation –.

A primary design challenge is the precise tuning of the resonant circuit, as DBD loads exhibit complex and nonlinear characteristics. Specifically, DBD loads are not only capacitive but also possess a threshold voltage. This threshold-dependent behavior causes the load’s characteristics to shift dramatically once the applied voltage exceeds the threshold, as shown in Fig. 1. Moreover, the capacitive nature of the load contributes to a low output power factor, presenting additional challenges for system efficiency . Furthermore, in transformerless configurations, switching devices are subjected to the same HV levels as the amplified output, necessitating components with higher blocking voltage ratings.

Beyond HV requirements, power specifications introduce additional design complexities. The power rating is deter- mined by several factors, including application type, reactor geometry, electrode design, and material properties. For high- power applications exceeding tens of kW—such as large ozone generators with power densities ranging from 1 to 10 kW/m2 or surface treatment systems requiring over 50 kW —transformerless designs are not practical. These applications demand robust isolation, typically achieved by incorporating transformers to decouple the primary power supply from the secondary load. This approach ensures com- pliance with operational safety standards and supports reliable performance in high-power systems. Additionally, as switching solid-state devices are typically positioned on the primary side with lower voltage levels, the blocking voltage requirements can be significantly reduced.

However, one challenge with the HV transformer is the need for isolation in the design process. Thick dielectric materi- als are commonly used between windings and between the windings and the core to ensure isolation. Achieving sufficient isolation often requires increasing the spacing between wind- ings or enlarging winding areas to meet voltage breakdown limits. While thicker insulation reduces direct capacitance, the use of high-permittivity materials to meet isolation standards can inadvertently increase parasitic capacitance. Given that the DBD load is typically modeled as a capacitive element, typically ranging in tens of pF, the interaction between the transformer’s parasitic capacitance and the load capacitance creates a current divider effect, thereby reducing overall power efficiency .

Furthermore, transformer designs must account for the spe- cific waveform requirements of the application, with the sec- ondary output potentially being sinusoidal, bipolar, or unipolar square pulses. Unlike sinusoidal and bipolar pulse excitations, achieving unipolar operation with a pulse transformer presents additional design challenges. A reset circuit is necessary to prevent core saturation during unipolar operation. While this approach ensures reliable transformer functionality, it also in- troduces additional components, increases design complexity, and imposes limitations on operational frequency.

In addition to these challenges, the leakage inductance of HV transformers imposes additional challenges. Specifically, the leakage inductance restricts the minimum achievable pulse width, complicating the implementation of transformers in DBD applications requiring higher pulse repetition frequencies (PRFs). Furthermore, leakage inductance can result in higher voltage spikes across the switches during commutation, ne- cessitating a carefully designed transformer to mitigate these effects and ensure reliable operation.

V. Sinusoidal Power Supplies

While conventional bridge-based voltage-source inverters (VSIs) are commonly used for inductive loads such as motors, these are not well-suited for generating sinusoidal output volt- age waveforms when driving DBD with sinusoidal excitation.

Multi-level modular voltage inverters have been explored as a potential solution to mitigate the high dV/dt associated with such loads –. However, these inverters still suffer from uncontrolled current peaks due to the capacitive nature of the DBD load, which generates HF current spikes .

These spikes necessitate additional circuit components, such as series inductors, to stabilize the operation. Alternatively, traditional transformer-based design, achieved by connecting a transformer to the power grid, allows for HV gain at grid frequencies (e.g., at 50 Hz, see Fig. 11(a)). While

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Fig. 12. Transformerless voltage-fed full-bridge resonant inverter. 13.

Equivalent circuit of LCL resonant tank with DBD load. effective for basic setups, this method is limited by its inability to offer adjustable frequency options and variable voltage gains, reducing its suitability for advanced DBD applications requiring greater versatility.

This challenge is effectively addressed by resonant inverters, such as the class-D resonant inverter, which naturally incorpo- rates the capacitive DBD load into its design. By leveraging resonance, these inverters provide smooth sinusoidal excitation and ensure stable operation. Both voltage-fed and current-fed resonant inverters have been successfully implemented to drive DBD systems, as elaborated in this Section.

A. Voltage-Fed Resonant Inverters

1) Transformerless Topologies: The full-bridge-based in- verter with a resonant tank, as shown in Fig. 12, is a widely utilized topology for generating sinusoidal output voltages while meeting the HV requirements of DBD loads. The resonant tank facilitates voltage amplification by leveraging the intrinsic capacitances of the DBD load, including Cg and Cd. By incorporating a single inductor, the LCC (or simply LC) resonant tank can be analytically designed to integrate

The Load Impedance, As Done In , . The Resonant

tank not only facilitates voltage amplification but also pro- vides reasonable voltage gain without increasing the blocking voltage requirements of the switching devices. Transformerless implementations of this topology further reduce the cost and complexity of the power electronics.

For applications requiring higher voltage gains, the resonant tank design can be varied. Amjad et al. implemented an LCL resonant circuit (see Fig. 13), achieving greater voltage gain for ozone generation systems , . However, this design operates at a significantly lower resonant frequency than LC configurations, illustrating a trade-off between op- erating frequency and voltage gain. This trade-off provides design flexibility, allowing the resonant tank configuration to Fig. 14.

Exemplary waveforms of full-bridge LC inverter with DBD load in ZCS operation. Fig. 15.

Piezoelectric class-E push-pull resonant inverter. be decided based on the specific requirements of the DBD system.

However, environmental factors, such as temperature, can cause variations in DBD capacitances, directly affecting the achievable voltage gain of the resonant tank. To mitigate the effects of capacitance drift, compensation schemes similar to those used in LC inverter topologies can be employed, as dis- cussed in . These schemes ensure consistent performance despite fluctuations in operating conditions.

Fig. 14 shows the key waveforms of the full-bridge LC inverter with a DBD load, highlighting the zero-current switch- ing (ZCS) operation. ZCS allows for higher switching frequen- cies, a critical requirement for achieving efficient and stable plasma generation in DBD applications. Resonant inverters, particularly class-D and class-E configurations, are well-suited for HF operation, often reaching the MHz range. This enables DBD systems to operate in the RF-DBD mode, expanding their application potential. Among these, class-E inverters provide a cost-effective solution due to their single-switch design, higher voltage gain, and reduced component count, making them ideal for compact and high-performance power supply designs .

Further, the emergence of piezoelectric energy storage units represents a novel approach to integrating mechanical and electrical energy systems, leveraging the unique ability of piezoelectric materials to convert mechanical vibration into electrical resonance and vice versa. These units exhibit the high energy density and fast response of piezoelectric materi- als, enabling efficient energy capture, storage, and release with high quality factor compared to conventional resonant tank design. When utilized as a resonant tank, as shown in Fig. 15 using the equivalent Butterworth-Van Dyke (BVD) model, these units simplify system design, reduce losses, and support MHz range operation. A class-E inverter including piezoelec- tric resonator is reported in , achieving 6.41MHz opera- tion with a complementary-controlled push–pull configuration

10

Fig. 16. Transformer-based full-bridge-based topology. 17.

Transformer-based full-bridge LC resonant inverter with HF snubber. Fig. 18.

Exemplary frequency response of the full-bridge LC inverter with DBD load. to maximize voltage gain. It is noteworthy that the capacitive load affects the zero-voltage switching (ZVS) capability of the class-E inverters and the circulating current in resonant tank will reduce the overall efficiency of the converter, which requires careful tuning of circuit components.

Although the resonant tank reduces blocking-voltage stress on the switching devices and supports the HF demands of DBD excitation, the substantial voltage and power demands typical of DBD loads often necessitate the inclusion of a step-up transformer to meet application-specific requirements effectively.

2) Transformer-Based Topologies: The bridge-based in- verter structure with a transformer can be analyzed similarly to resonant DC-DC converter topologies but without a secondary rectifier. A key advantage is that soft-switching can be utilized in the primary bridge as in resonant DC-DC converters. Uti- lizing the inherent inductance of the transformer as a resonant component removes the need for additional inductive elements, as shown in Fig. 16. This is realized through the use of a pulse transformer, specifically designed to handle HF pulsed signals while preserving waveform integrity.

This approach minimizes component count and reduces overall system complexity. The combination of transformer leakage inductance and DBD capacitances forms a resonant tank that enables soft-switching operation. Phase-shifted con- trol is employed to achieve proper ZVS, but this requires precise timing of the switching events –.

On the other hand, to achieve ZCS, as in transformer- less LC-series designs, a series resonant inductor (Lr) can be added, forming a resonant network with the DBD load capacitance, as shown in Fig. 17. However, it necessitates careful consideration of leakage inductance. The presence of transformer leakage inductance can introduce a secondary peak in the frequency response of the voltage gain, located near the primary resonant peak, as shown in Fig. 18. This sec- ondary peak can potentially degrade the system’s performance if not properly managed. To mitigate this issue, a HF snubber circuit can be employed . The snubber circuit effectively attenuates the second peak, ensuring smoother operation and improved frequency stability.

Moreover, the parasitic capacitance of the transformer should be managed carefully. To minimize the current flowing into the parasitic capacitance of the transformer, it is crucial to reduce the effective load impedance. This can be achieved by adding an additional inductor on the secondary side, positioned between the transformer and the DBD load. This inductive component compensates for the capacitive load, effectively minimizing the load impedance relative to the parasitic ca- pacitance, as expressed in (3).

(3)

It should be noted that voltage-fed resonant inverter designs for DBD applications are particularly vulnerable to the partial short-circuit behavior inherent to the threshold-like capacitive nature of DBD loads. This behavior not only compromises the system’s reliability but also highlights the necessity of exploring alternative topologies. Current-fed resonant inverters emerge as a compelling solution, offering enhanced tolerance to short-circuit conditions and robust control over discharge dynamics, effectively addressing the limitations of voltage-fed designs.

B. Current-Fed Resonant Inverters

1) Bridge-Based Topologies: Beyond short-circuit toler- ance, compared to voltage-fed DC/DC resonant converters, current-fed resonant converters are considered a reasonable option for applications requiring HV gain in bridge-based

Designs –. This Is Attributed Not Only To Their

achievable resonant gain but also to their reduced duty-cycle losses, the elimination of snubber circuits, and the absence of pulsating input currents, which would otherwise necessitate large filter sizes in voltage-fed designs.

In bridge-based current-fed topologies, the half-bridge or full-bridge structure typically serves as a current inverter cascaded with a front-end current regulator, such as a buck converter with constant current output , , as illus- trated in Fig. 19. The primary objective of the current inverter is to generate a commutating bipolar square current waveform for the primary winding of the pulse transformer and the resonant network. The resonant design can initially be realized similarly to DC/DC resonant converters, without requiring a secondary rectifier circuit.

The output voltage waveform depends on the design of the resonant network, including the transformer and the capacitive

11

Fig. 19. Current-fed CLCC resonant inverter with front-end buck. 20.

Current-fed parallel-resonant push-pull inverter. load. For sinusoidal output waveforms, the same analysis used in the resonant tank tuning for voltage-source-fed systems can be applied; using piecewise mathematical approach , fundamental harmonic approximation (FHA), the rectifier compensated FHA (RCFHA), and state plane analysis, the initial tuning of the resonant tank can be performed to achieve the desired voltage waveform characteristics.

Fig. 19 shows current-fed full-bridge CLCC resonant in- verter, which incorporates the two capacitances of the DBD load within the resonant tank . By employing a math- ematical approach to tune the resonant tank, the inverter achieves high precision, accounting for the two states of the capacitive DBD load—an accuracy difficult to achieve using conventional approximation methods such as FHA.

However, this inverter design has certain limitations. The inability to utilize leakage inductance as a functional com- ponent of the resonant tank necessitates minimized leak- age inductance. Additionally, soft-switching is not inherently guaranteed—a common drawback in traditional current-fed bridge-based topologies . To address these challenges, the current-fed full-bridge LLCC resonant inverter, proposed in , offers a more advanced solution. By introducing three additional resonant capacitors to the lower switches of the phase legs, this design overcomes the limitations of conven- tional configurations. Validated using RCFHA, the asymmetric full-bridge structure achieves ZCS for the upper devices and ZVS for the lower devices, while effectively incorporating leakage inductance as a resonant component.

Unlike the aforementioned current-fed topologies, which primarily aim to control voltage output, direct control of the current is achievable due to the stiff input current regulation.

In , it is demonstrated that the third harmonic of the injected current influences the discharge-time ratio (DTR), which represents the duration of the discharge subinterval within a single period. This enables compressed energy deliv- ery under sinusoidal excitation. The design process leverages RCFHA. By incorporating third harmonic current injection into the reference current, the DTR becomes adjustable, pro- viding precise control over energy compression and stretching.

This capability is particularly beneficial for DBD surface treat- ment applications, where designed energy delivery is critical for achieving desired processing outcomes.

The front-end current source design is a critical part of de- signing current-fed resonant inverter, which must address the non-linear characteristics of DBD loads by compensating for rapid voltage transients and dynamic load behavior. Average- current-mode control, commonly implemented using current- mode buck converters or two-quadrant choppers, provides fixed switching frequency and favorable EMI characteristics for closed-loop regulation . However, such approaches are fundamentally challenged by the fast, discontinuous cur- rent demand inherent to DBD systems. Average-based current regulation assumes a smooth and predictable relationship between input current and load behavior—an assumption that breaks down due to the threshold-dependent nature of DBD discharges. Moreover, the inherent delay introduced by the averaging process slows the control response, making it ill- suited for HF operation or rapidly changing load conditions.

Conversely, hysteresis control is often favored for its fast time-domain response . However, its variable switching frequency complicates EMI filtering and makes the system more sensitive to load variations. When applied to capacitive and nonlinear loads such as DBDs, hysteresis bands can induce ringing or oscillations, leading to instability or degraded performance.

As an alternative, the active front-end can be replaced with an input choke , , enabling efficient operation with improved power factor. However, such simplified current- fed configurations generally demand a large input inductance to maintain near-constant current, which can significantly increase system size and cost.

2) Push-Pull Topologies: A current-fed resonant inverter can also be realized using a parallel-resonant push-pull topol- ogy. Fig. 20 illustrates the schematic of a current-fed parallel- resonant push-pull inverter. The input inductors, L1 and L2, establish a stiff current source for the push-pull resonant network. The primary advantage of this topology lies in its ability to achieve ZCS by ensuring the current naturally drops to zero before the switching devices turn off. The low side switching devices are implemented with series-diodes to add an extra protection to block reverse current . However, this approach prevents the current induced by the transformer’s leakage inductance from finding a proper path, leading to voltage spikes on the switching devices. To address this limitation, proposes a design that eliminates the series diodes and incorporates the transformer’s leakage inductance as part of the resonant tank. This structure can be further simplified by realizing the push–pull configuration with a center-tapped transformer .

However, the limited practical inductance of the input choke often introduces harmonic content in the output waveform, reducing voltage gain and diminishing the expected benefits of current-fed resonant inverters.

Current-Mode Front-End Buck

1 L: inductor, C: capacitor, D: diode. 2 Not Reported. 3 Tested with equivalent load.

Table Iv

GENERALIZED PERFORMANCE COMPARISON OF RESONANT INVERTERS FOR DBD APPLICATIONS

+++

+++

+ Only one inductor is required. + Higher voltage gain achievable with added LC network. – Trade-off: reduced frequency.

++++

++++

+ MHz-range operation with high power capability. – Input choke size increases with power level.

+

+

+ Short-circuit tolerant. + Injected current harmonics are controllable. – Complex design.

– Requires transformer with high turn ratio.

++

++

+ Short-circuit tolerant. + No active front end required. – Requires large input choke.

– Requires transformer with high turn ratio. 1 Normalized with transformer turns ratio. 2 More plus signs (+) indicate more economical implementation.

C. Overview Of Sinusoidal Power Supplies

Table III summarizes the main converters discussed in this section, detailing the number of active switches and passive components, output characteristics, and soft-switching capabilities. Applications and compatible DBD geometries are also provided for clarity.

Although current-fed systems are more tolerant of the threshold behavior of DBD loads—where a conditional short circuit may occur depending on the applied waveform, voltage, and current—voltage-fed systems, including class-D variants (bridge-based) and class-E amplifiers, are often preferred for their simpler design, higher voltage gain, higher output frequency, and better efficiency enabled by inherent soft- switching.

Current-fed resonant inverters often include the requirement for a front-end current source, such as a buck-based converter or a large input inductor, a resonant network to facilitate soft- switching, and additional series diodes to mimic thyristor-like behavior in the switches. Typically, the input choke inductance for current-fed systems is in the mH range. At higher power levels required by DBD applications, this results in large component sizes that severely compromise power density.

Consequently, quasi-current-fed voltage-fed systems, such as class-E resonant inverters, become preferable solutions, as they reduce the required input choke inductance, enhancing power density.

Nevertheless, topological variations remain possible because conventional voltage-fed resonant inverters—including classes D, E, EFn, E/Fn, and Φ2—are generally well-characterized for inductive-resistive loads . Given the duality between voltage-driven inductive loads and current-driven capacitive loads, further analysis and novel resonant tank designs are needed to address the unique characteristics of DBD loads.

Regardless of whether voltage-fed or current-fed, a common limitation of resonant inverters is that soft-switching can only be maintained within a narrow range of operating conditions.

As the resonant tank’s soft-switching region is frequency- dependent, variations in gain or frequency can push the system out of this optimal range, reducing efficiency. Unlike DC- DC resonant converters with secondary rectifiers, the voltage

13

waveform produced by the inverter is directly applied to the DBD load, resulting in deviations from an ideal sinusoidal shape. Consequently, pulse-frequency modulation, commonly used in DC–DC resonant converters for gain regulation, cannot be directly applied to DBD resonant inverters. This limitation makes closed-loop gain control impractical, explaining why open-loop operation is predominantly adopted, with the design instead guided by the gain characteristic, soft-switching region, and frequency dependence of the resonant tank.

Sys-

tems—such as variations in gas type, application, and oper- ating conditions—significantly influence the load’s capacitive and resistive characteristics. These factors shift the optimal operating frequency away from the resonance frequency for which the inverter was initially designed. Furthermore, Cd, Cg, and Vth are frequency-dependent, complicating impedance matching for the resonant network. As research on load- independent resonant inverters progresses, extending these concepts to dynamic-independent resonant inverter designs for DBD applications represents a valuable direction for future work . In summary, Table IV presents a generalized performance comparison of reported resonant inverters for DBD applications.

Vi. Pulsed Power Supplies

Certain DBD applications require PPSs which can offer distinct advantages over sinusoidal excitation methods. Their capability to generate HV, HF pulses with sharp rise times establishes them as viable solutions for a diverse range of DBD applications. This section elaborates on different pulsed power supplies developed for DBD excitation.

A Bridge-Based Converter

without a resonant tank is capable of generating pulsed waveforms, where the secondary voltage ideally assumes a bipolar square waveform, amplified by a high turn-ratio pulse

Transformer , –. The Same Topology In Fig. 16

can be used. Despite its simplicity, approaches using a pulse transformer present notable limitations, including the arbitrary nature of the output voltage waveform and significant current ripple due to leakage inductance and distributed capacitance, as shown in Fig. 21. These effects often require additional damping to suppress undershoot .

Bridge-based topologies are frequently combined with pulse forming lines (PFLs), such as the Blumlein configuration, to achieve high PRF with nanosecond-scale pulse widths and well-defined waveform shapes . PFLs utilize wave propagation in transmission lines to generate HV nanosec- ond pulses with rectangular flat-top characteristics. Owing to their stackable architecture, transformerless configurations are often feasible, enabling higher voltage gain . For example, reports voltage pulses with a rise time of 5.2 ns and pulse width of 10.6 ns. Although nanosecond-scale pulses are generally achievable, the required charging time limits the attainable PRF. However, by exploiting resonance, PRFs in the megahertz range can be realized .

Fig. 21. Waveforms of typical bridge-based PPSs with DBD load. 22.

Schematic of typical solid-state Marx generators. Fig. 23. Marx generator with a front-end boost converter.

Nonetheless, a major limitation of PFL-based systems is the fixed pulse width imposed by their physical configura- tion, making it difficult to implement adjustable pulse dura- tions. More critically, successful operation depends heavily on impedance matching between the generator and the load, an assumption that fails in the case of non-linear and time-varying DBD loads. Moreover, the ideal flat-top square waveforms produced by PFLs are often severely distorted when connected to DBD reactors . Also, physical limit of PFL often compromises power density.

2) Marx-Based Topologies: Marx generators are promising voltage-fed HF PPS for DBD applications due to their ability to produce unipolar or bipolar pulses while preventing HV stress on devices through a modular structure . Fig. 22 shows the basic configuration of solid-state Marx generators.

By applying complementary gate signals to the half-bridge structure of each stage, the charging and discharging phases are easily controlled, generating unipolar square-wave voltage across the capacitive load. For bipolar waveforms, a full-bridge configuration for each stage can be employed, enabling full- bridge voltage commutation across the load or the use of a dual power supply.

For unipolar pulse generation, Marx generators inherently eliminate the need for a transformer in their basic opera- tion, while isolated configurations utilizing pulse transformers may require a reset circuit to prevent core saturation. This distinction underscores the advantages of Marx generators, whose simple architecture and modular scalability make them an excellent solution for unipolar pulse generation in DBD applications, particularly when transformerless compact de- signs are preferred. This architecture enables nanosecond-scale

Deployment In Out-Of-Position Situations

D. Bendjaballah1, A. Bouchoucha1, M. L. Sahli1,2* and J-C. Gelin2

Abstract

Side-impact collisions represent the second greatest cause of fatality in motor vehicle accidents. Side-impact airbags have been installed in recent model year vehicle due to its effectiveness in reducing passengers’ injuries and fatality rates. In meeting these requirements, simulations of folding and deploying airbags are very useful and are widely used. The paper presents a simulation method for the deploying airbags using three materials in different working conditions. Finite element analysis is primarily used to evaluate this concept. In these simulations, the gas flow is described by the conservation laws of mass, momentum, and energy. The numerical results indicate that the FE method in this paper is capable of capturing airbag deploying process accurately.

Keywords: Airbag simulations, Out-of-position, Crash, Modeling, Out-of-position

Background

The passive safety of cars has become a very high prior- ity issue for the automotive industry. Today, there are not only one or two airbags in a car; certain models have ten times more than that. With the increasing usage of airbags, the number of accidents where the airbag itself can cause an injury to the occupant also increases

(Augenstein Et Al. 2003; Gabauer And Gabler 2010;

Audrey et al. 2011). As is well known, safety belts are also now devices designed to provide protection to the users of vehicles during crash events, minimizing the loads necessary to adapt their movement to the move- ment of the car (Freesmeier and Butler 1999; Schmitt et al. 1997). In general, the seat belt is designed to restrain the occupant in the vehicle and prevent the

Occupant From Having Harsh Contacts With Interior

surfaces of the vehicles. The airbag acts to cushion any impact with vehicle structure and has positive internal pressure, which can exert distributed restraining forces over the head and face. As a safety component of auto- mobile, an airbag decreases occupants’ injury likelihood effectively in case of an accident (Ruff et al. 2007). These safety elements can reduce the death rates on the roads, and its protection effects have been widely approved (Crandall et al. 2001; Teru and Ishikawa 2003). With computational tools such as finite element methods designed for dynamic contact problems, crashworthiness simulations can now be used with reliable accuracy to evaluate occupant protection in various collision condi- tions with safety metric/parameters such as acceleration, head injury criteria, intrusion distance, intrusion vel- ocity, and neck forces (neck injury risk or whiplash).

Thus, new types of airbag products are being developed to handle different collision scenarios.

Become Standard Equipment On Most New Passenger

vehicles (Braver and Kyrychenko 2004; Teng et al. 2007; Yoganandan et al. 2007). The airbag cushion is com- posed of a woven fabric which is rapidly inflated during a car crash. The airbag dissipates the passenger’s kinetic energy thereby reducing injury through biaxial stretching of the fabric bag and escaping gas through vents. There- fore, the performance of the airbag is greatly influenced by the mechanical properties of the fabric. Generally, air bags are designed to deploy in a crash that is equivalent to a vehicle crashing into a solid wall at 8 to 14 mph.

Air bags most often deploy when a vehicle collides with another vehicle or with a solid object like a tree. There are various types of airbags: frontal, side-impact, and curtain airbags. In general, the passenger side airbags are usually larger than the driver airbags (see Fig. 1).

Besançon, France

© The Author(s). 2017 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Bendjaballah et al. International Journal of Mechanical

Doi 10.1186/S40712-016-0070-2

Extensive studies have shown that the airbag deploy- ment in load cases consists of two occupant loading phases: a punch-out effect where the airbag bursts out of its container with the airbag and airbag module cover accelerating towards the occupant and a second loading phase during which the airbag is taking on its deployed shape and volume (membrane-loading effect). Bankdak et al. (2002) developed an experimental airbag test system to study airbag-occupant interactions during close proximity deployment. The results provided insight for simulating the effect of inflation energy and mass flow on target response. Bedard et al. (2002) found that while left-side (driver-side) impacts accounted for only 13.5% of all crashes, the fatality rate among these

Crashes Was 68.3% In Comparison To Front Impact

(48.3%), right-side impact (31.3%), and rear impact (38.4%). These studies underscore the importance of oc- cupant safety during side-impact collisions. In the last years, the current market requested to reduce the time and cost airbag development. In order to achieve this result, virtual simulations play an important role since they allow to minimize the number of experimental tests (Pei et al. 2013; Cao et al. 2014). Several simulation models of airbag were established (Wang et al. 2007). It is feasible to optimize the parameters of airbag deploy- ment using simulation technology. Experimental and numerical studies have quantified injury risks to close- proximity occupants from deploying side airbags. These studies have focused on the prevention of the most ad- verse effects of airbag deployment (Duma et al. 2003).

Other studies have proposed airbag characteristics to minimize particular biomechanical responses (Haland and Pipkorn 1996). In a more recent study, Marklund and Nilsson (2003) compared deformation patterns with experimental data as well as the computational costs associated with three different airbag deployment simu- lation methods; they concluded that the SPH method is relatively inexpensive and produces incremental deform- ation patterns that compare most closely to the experi- mental results. The process of inflation of an airbag is one of the determining factors in saving lives. The duration from the initial impact of the crash to the full inflation of an airbag is about 40 ms, and during this time, the airbag goes from being in a folded state to a fully inflated state, with a high internal pressure. After achieving this state, the airbag begins to deflate, thus providing a nice cushion for the body impacting it.

Ideally, the person in the crash should come into contact with the airbag at this time. In the present study, a large volume passenger side airbag model is developed to handle different collision scenarios. The main aim is evaluate the performance of deploying of passenger side airbag using finite element methods (FEM).

Materials

The tensile specimens were made in different airbags (P: Peugeot, R: Renault, and VW: Volkswagen) with a length of 200 mm long and a width of 40 mm. Table 1 shows the mechanical properties of the airbag.

Tensile Tests

To determine the mechanical properties of the material of airbag used in the test pieces, tensile tests were performed on Lloyd EZ20 universal testing machine in Constantine. These tests were conducted using rect- angular samples. The axial force and axial displacement acquired during a test are converted into stress and the strain in order to be used for the fabric material model.

The continuous recording of the stress-strain data was performed during both the load and unload phases. A minimum of five samples were made in order to check the repeatability of the measurements. All the data was collected by using a PC-based data acquisition system and analyzed by commercial software. The picture frame test device that is made for this study is shown in Fig. 2.

Fig. 1 a Frontal and side airbags. b Oblique view of facet occupant model in sitting posture following airbag deployment (Lim et al. 2014)

0.150

Bendjaballah et al. International Journal of Mechanical and Materials Engineering (2017) 12:12

Page 2 Of 9

Figure 3 shows the stress-strain relationship of the airbag sample under axial tensile loads. The results are showing a linear increase in extension with the increas- ing stresses. This is an expected output and it confirms with the theoretical behavior of a sample subjected to tensile stress. The rupture strain values for different airbags (R/P/VW) were 0.322, 0.441, and 0.472, respect- ively. The measured elastic parameters (i.e., Young’s modulus E and initial yield strength) and Poisson’s ratio are summarized in Table 2. The tensile tests of the woven fabrics can show differences on mechanical prop- erties because woven fabrics can resist in-plane shear loads once the yarn lock-up angle has been reached. The differences of material property on material direction can affect the shape of fully deployed bag (see Fig. 3b).

Theoretical Background

Numerical simulations of airbags use very complex and techniques such as an orthotropic model to identify the mechanical behaviors during the airbag inflation and the fluid mechanics (gas flow) to describe the inflator gas flow (pressure gradient) and improve the representation of the pressures within the airbag. To model the airbag as an orthotropic model, three material constants have to be provided. Assuming a plane stress condition, the

Ð1Þ

where σ is the normal stress and τ is the shear stress, the subscript refers to the principal material directions, i.e., the fill and warp directions. Also, ε and γ are the strain components. The material elastic constants Qij are

Ð2Þ

where E1 and E2 are the Young’s modulus in the fill and wrap directions and G12 is the shear modulus of the fabric material. νij is the Poisson ratio of the material.

The gas exerts a pressure load on the airbag causing it to expand. This expansion puts the airbag under tensile stress lowering the expansion rate. In this study, heat conduction and heat transfer is not taken into account.

Fig. 2 A photograph of Lloyd EZ20 universal testing Fig. 3 Stress versus strain using Lloyd EZ20 machine for a three different airbags at 0° and 90° and b VW airbag test specimens at

Different Angles

Table 2 Physical and mechanical properties of the airbag

Page 3 Of 9

In the deployment of an airbag, an inflator supplies high velocity gas into an airbag causing it to expand rapidly. The gas inside the airbag is assumed to be ideal, to be of constant entropy, and to satisfy the equation of state:

Ð3Þ

Here p, ρ, and e are respectively the pressure, density, and specific internal energy, and γ is the ratio of the heat capacities of the gas. The gas flow is described by the conservation laws for mass, momentum, and energy that

Ð4Þ

here, V is a volume, A is the boundary of this volume,

N Is The Normal Vector Along The Surface A, And U

denotes the velocity vector in the volume. Applying Bernoulli’s equation in the case of an ideal gas with

Ð5Þ

Here, the subscript ex denotes quantities at the throat of the tube. Furthermore u, p, and ρ denote the quan- tities inside that part of the tube that is supplying mass.

Materials And Boundary Conditions

The airbag system mainly consists of three parts: the airbag itself, the inflator unit, and the crash sensor or diagnostic unit. Thus, to study the behavior of the airbag using FE simulations, we need to have an FE model of the airbag in the folded position. A FE model of the airbag was used to simulate the test condition as shown in Fig. 5. LS-DYNA® material model FABRIC (MAT_34) is used to simulate the airbag material. It is a variation of the layered orthotropic material model. Additionally, in the LS-DYNA® material model, fabric leakage can be accounted for. However, for this CAB material, the leak- age is almost negligible and therefore no leakage is specified. The mechanical properties can be determined from the physical test. Typical material properties for airbag fabrics are taken as given in Chawla et al. (2004a) (Table 3). These properties are used to simulate inflation process of airbag (see Table 1). The car dashboard is modeled as the rectangular thin plate using a MAT_RI-

Gid Material, And The Degrees Of Freedom Are Con-

strained in all the directions. The similar properties of thermoplastic polymer are assigned for contact purposes. The porosity of the fabric is assumed zero. The nitro- gen gas is taken for inflating the airbag. Properties of nitrogen gas and initial bag conditions are shown in Table 4. The example on which we perform the study is a typical passenger side airbag. The geometric de- tails have been measured from a commercially avail- able airbag. The initial state of the airbag is a closed rectangular whose sides are to be finished to 482 × 635 mm2 and is shown in Fig. 4.

Table 3 Material properties of airbag and rigid plate used in FE

–

Table 4 Initial values used for FE simulation of the swelling of

3.33 × 10−4

Fig. 4 The initial airbag geometry in the form of a rectangular Bendjaballah et al. International Journal of Mechanical and Materials Engineering (2017) 12:12

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