Streuinduktivitätsverteilung und Lichtbogenzündstabilität in Plasmazündern

Streuinduktivitätsverteilung und Lichtbogenzündstabilität in Plasmazündern

Abstract

Two nominally identical plasma cutters can sit side by side, one striking instantly for years and the other needing two or three attempts from the first day. This article ties that difference to the ignition transformer: the loaded resonance, the secondaries that steal voltage, the detuning from leakage spread and core state, and the breakdown distribution that turns a 19% peak loss into a 38-point drop in first-attempt ignition.

1. Einleitung

First-attempt arc strike probability is the reliability number that a plasma cutting machine lives or dies by. A torch either starts on the first try or spends time, gas and consumable life on retries, and in an automated cell a failed start can scrap the work in process.

The part that governs that number is the high-voltage ignition transformer, and what governs the transformer is not its turns ratio. The governing quantities are the parasitics: leakage inductance, inter-winding capacitance, secondary self-capacitance and core hysteresis. Each one moves the resonant frequency, the peak voltage and the energy delivered to the gap.

The symptoms reach the field as the two-machine problem. Two cutters built to the same drawing, side by side, behave differently from the first day. Operators blame gas quality or electrode wear, and the real cause is a parasitic resonance sitting at the wrong place relative to the drive frequency.

This article quantifies the link: the loaded resonance of the ignition loop, the voltage divider that costs the gap its peak, the detuning from leakage spread and core state, and the breakdown distribution that decides whether the attempt succeeds.

2. Kernmechanismus

2.1 The loaded ignition resonance

The tank capacitor and the transformer leakage form the ignition resonance, and the secondary self-capacitance reflects back into it.

f_ign = 1 / (2π √((L_σ + L_reflected) × (C_tank + C_reflected)))

where f_ign is the loaded ignition resonance, L_σ is the primary-referred leakage inductance, L_reflected is any reflected inductance, C_tank is the tank capacitance and C_reflected is the secondary self-capacitance referred through the turns ratio as n² × C_s.

With 1.5 µH of loop inductance and 4700 pF the loop rings at 1.896 MHz. A leakage change of 10% moves that figure 5%, and the loop quality factor decides what a 5% move costs.

2.2 What a frequency offset costs

The tank voltage delivered at the gap falls away from resonance according to the loop Q.

η_Q = 1 / √(1 + (2Q × Δf / f)²)

where η_Q is the fraction of the tuned voltage that survives, Q is the loop quality factor and Δf / f is the fractional frequency offset from the loaded resonance.

A loop at Q 8 with a 5% offset returns 0.781. Raise the Q to 30, which is what a low-loss loop looks like, and the same offset returns 0.226. A high-Q ignition loop is sharp enough that production spread alone can destroy the peak.

2.3 Voltage lost before the arc sees it

The secondary self-capacitance divides against the gap capacitance, so the gap never receives the full transformer output.

V_gap = V_oc × C_s / (C_s + C_gap)

where V_gap is the voltage that reaches the gap, V_oc is the transformer open-circuit secondary voltage, C_s is the secondary self-capacitance and C_gap is the capacitance across the torch gap.

With 45 pF of secondary self-capacitance and 18 pF across the gap, the divider passes 0.714. A 1 to 1.5 transformer fed by a 10 kV tank gives 15 kV open circuit and 10.7 kV at the gap, so 4.3 kV never reaches the arc.

2.4 The peak voltage at the gap

Putting the transformer ratio, the divider and the detuning together gives the peak at the gap.

V_peak = n × V_C × η_Q × C_s / (C_s + C_gap)

where V_peak is the peak voltage at the gap, n is the turns ratio, V_C is the tank charge voltage and the remaining terms are the detuning factor and the divider ratio.

A nominal unit with a 10 kV tank, a ratio of 1.5 and a Q 8 loop at exact resonance delivers 10.7 kV. The same unit with 10% high leakage delivers 8.37 kV. Both are built to one drawing.

2.5 The breakdown distribution and the acceptance rule

Breakdown is a statistical event, so the strike probability follows the breakdown distribution.

P_ign = Φ((V_peak − V_brk_mean) / σ_brk)

where P_ign is the first-attempt ignition probability, Φ is the standard normal cumulative distribution, V_peak is the peak voltage at the gap, V_brk_mean is the mean breakdown voltage and σ_brk is its standard deviation. The derivative of the ignition probability against peak voltage is the breakdown probability density at that peak, which is why the sensitivity is so high near the mean.

Shop air across a 0.9 mm gap breaks down at a mean of 8.20 kV with a standard deviation of 0.61 kV, which is 7.4% of the mean. That gives the design its numbers: 61% first-attempt ignition at 8.37 kV, 99.44% at 9.75 kV and 99.95% at 10.21 kV.

2.6 Energy, time constant and impedance

Three further quantities bound the design.

E = ½ × C × V²

where E is the stored pulse energy, C is the tank capacitance and V is the charge voltage. With C in nanofarads and V in kilovolts the result is in millijoules, so 4.7 nF at 10 kV returns 235 mJ and not 235 J.

τ = R × C

where τ is the discharge time constant, R is the loop resistance and C is the capacitance. Ohms times nanofarads return nanoseconds, so a Q 8 loop at 2.23 Ω with 4.7 nF returns 10.5 ns, which is 25 times shorter than the 264 ns half-cycle.

Z_0 = √(L / C)

where Z_0 is the loop characteristic impedance, L is the loop inductance and C is the tank capacitance. The same 1.5 µH and 4700 pF return 17.9 Ω, and that value sets the loop resistance for any target Q.

Fig. 1 — A 10% leakage spread leaves a unit at 61% first-attempt ignition, while a 3% spread holds 99.95% against the 99.5% requirement.

3. Schwachstellen im Engineering

Pain Point 1: Production spread in leakage inductance

Winding tension, layer count and bobbin geometry vary between batches, and a 10% leakage spread moves the loaded resonance 5%. On a loop at Q 8 that costs 19% of the peak; on a loop at Q 30 it costs 77%. A bench test that checks only turns ratio and insulation sees none of it.

Pain Point 2: Secondary self-capacitance taking voltage from the gap

High-ratio secondaries accumulate self-capacitance, and at the ignition frequency it divides against the gap capacitance. With 45 pF against 18 pF, 28.6% of the secondary voltage is lost before the arc sees it, which is 4.3 kV of a 15 kV open-circuit output.

Pain Point 3: Inter-winding coupling feeding the primary

Coupling capacitance returns secondary transients to the primary switch node, where they disturb the tank resonance and stress the switch. The parameter is hard to control once the assembly is potted, and the symptom appears on the switch instead of on the transformer.

Pain Point 4: Resonance that moves with the core state

The permeability of the ferrite depends on the remnant flux from the previous pulse, so the magnetizing inductance and therefore the resonance move 2 to 5% between consecutive attempts. On a fixed-frequency drive that costs 2% of the peak, which is enough to take a marginal unit from 99.95% to below the 99.5% line once every 127 attempts.

4. Entwurfsschritte

Strategy 1: Specify and measure the parasitics

Add leakage inductance, secondary self-capacitance and coupling capacitance limits to the transformer datasheet next to the turns ratio. Measure all three with a network analyser at the ignition frequency on every production unit, and reject anything outside the tolerance band that the peak target allows.

Strategy 2: Set the tolerance from the peak target

Work backwards from the 99.5% requirement. That needs 9.77 kV at the gap against a mean breakdown of 8.20 kV and a standard deviation of 0.61 kV. A 3% leakage tolerance holds the worst corner at 10.21 kV and 99.95%; 5% falls to 9.75 kV and 99.44%, which misses the line.

Strategy 3: Let the capacitor dominate the resonance

Passen Sie an N4700 Class I tank capacitor with tight tolerance and a ±30 ppm/°C coefficient so the loop resonance is set by the capacitor and not by the transformer spread. A capacitance window of 1% contributes a 0.5% frequency offset, against the 5% that a 10% leakage spread contributes, and the transformer spread then scales down by the same ratio.

Strategy 4: Reset the core before every attempt

Drive the transformer with a controlled reset pulse or a reset winding so the magnetizing flux starts from the same point each time. That removes the 2 to 5% inductance jitter and with it the 2% peak loss that pushes a marginal unit off the line.

Strategy 5: Verify the tolerance stack in simulation

Run a Monte-Carlo analysis with the distributions of leakage, secondary self-capacitance, coupling capacitance, tank capacitance and breakdown voltage. Freeze the design only when the predicted first-attempt ignition probability clears 99.5% at the worst-case corner, with the core at its worst remnant state.

Strategy 6: Instrument the ignition peak in the field

Log the peak secondary voltage per attempt through a calibrated divider, using a Abtastwiderstand and a matched thick-film part. A slow downward trend points at parasitic drift in the transformer or the capacitor, and it appears before the misfires do.

Komponentenparameter	Typischer Wert	Testbedingung
Nennspannung (HVCT8G Serie)	10 kV DC	Hi-Pot 1.5× für 60 s
Kapazität	4700 pF ±20% (472M)	1 MHz, 1 V<sub>eff</sub>
Capacitance tolerance window	inside 1% unit to unit	for resonance dominance
Temperaturkoeffizient	±30 ppm/°C	−40 °C bis +125 °C
ESR bei 1 MHz	unter 50 mΩ	-
Teilentladung	unter 5 pC	bei Nennspannung
Impuls-dv/dt-Fähigkeit	über 50 kV/µs	bei Nennspannung

5. HVC N4700 (T3M) capacitors for a stable ignition loop

A capacitor can absorb the spread that a wound transformer cannot. HVC builds the N4700 (T3M) Class I family for that role, with the Bemessung von Widerständen und der schnelle Erholungsdiode that complete the ignition loop, from a 6,000 m² owned factory in Dongguan across a 1 kV to 100 kV range.

Sechs Parameter, die hier von Bedeutung sind

• Tight tolerance from unit to unit. Ceramic capacitor tolerances are far tighter than wound-transformer spreads, so a capacitor-dominated loop narrows the production distribution that the ignition probability has to survive.
• Stable capacitance across temperature. A ±30 ppm/°C coefficient keeps the loaded resonance in place between a cold morning start and a hot afternoon, which is the condition the marginal unit fails on.
• Low loss that preserves the peak. A dissipation factor below 0.1% keeps the loop Q where the design put it, so the peak voltage at the gap stays the value the design was built on.
• Predictable impedance across the ignition band. The N4700 (T3M) platform holds its impedance from 20 kHz to 2 MHz, so the transformer parasitics stay computable across the frequency range that matters.
• High-voltage placement without discharge risk. Ratings from 1 kV to 100 kV and partial discharge below 5 pC let a damping or tuning capacitor sit directly on the high-voltage secondary without adding a discharge source.
• Proven in precision high-voltage systems. The 40 kV 441-series doorknob capacitors replaced first-tier brand parts in high-voltage field-service programs, and a Querverweis against those parts shows the tolerance and drift a loop would otherwise have to absorb.

Lieferung und Support

Standard parts ship in 4 to 8 weeks and matched ignition sets in 6 to 10 weeks. HVC applications engineering supports peak-voltage calculation, tolerance-stack analysis, resonance measurement and reset-pulse design. Send the turns ratio, leakage inductance, gap capacitance and the first-attempt target, and HVC returns a tank selection sheet with tolerance data and PD reports within five working days.

6. Häufig gestellte Fragen

Q1: What makes one machine strike and another need retries?

A spread in transformer leakage inductance and secondary self-capacitance. A unit 10% high on leakage moves the loaded resonance 5%, and on a loop at Q 8 that costs 19% of the peak voltage. The unit then sits at 8.37 kV against a mean breakdown of 8.20 kV, which strikes 61 times in 100.

Q2: How much of the secondary voltage reaches the gap?

The secondary self-capacitance divides against the gap capacitance. With 45 pF against 18 pF the divider passes 0.714, so a 15 kV open-circuit secondary delivers 10.7 kV to the gap and 4.3 kV is lost. Reducing self-capacitance with split or interleaved winding geometry is the direct fix.

Q3: Why is a 5% leakage tolerance not enough?

Because the requirement is a probability, not a voltage. The 99.5% first-attempt line needs 9.77 kV at the gap, and a 5% leakage tolerance leaves the worst corner at 9.75 kV once the core-state jitter is added. That is 99.44%, which is short of the line.

Q4: What does the core do to the resonance?

Ferrite permeability depends on the remnant flux from the previous pulse, so magnetizing inductance and resonance move 2 to 5% between consecutive attempts. On a fixed-frequency drive that costs 2% of the peak, which is enough to push a marginal unit below the 99.5% line roughly once every 127 attempts.

Q5: How should I set the tank capacitor tolerance?

Tight enough that the capacitor, not the transformer, sets the loop resonance. A 1% capacitance window contributes a 0.5% frequency offset against the 5% that a 10% leakage spread contributes, so the transformer spread shrinks to a small term in the peak calculation.

Q6: How do I catch parasitic drift in the field?

Log the peak secondary voltage on every attempt through a calibrated divider built from a sampling resistor and a matched thick-film part. A slow downward trend in that number means the parasitics have moved, and it appears weeks before operators notice the misfires.

7. Referenzen

1. E. Kuffel, W. S. Zaengl, J. Kuffel, Grundlagen der Hochspannungstechnik, 2. Aufl., Newnes, 2000.
2. Mohan, N., Undeland, TM, und Robbins, WP, Leistungselektronik: Wandler, Anwendungen und Design, 3. Aufl. Hoboken, NJ: John Wiley & Sons, 2003.
3. MIL-HDBK-217F Mitteilung 2, Zuverlässigkeitsvorhersage elektronischer Geräte 1995.
4. IEC 60384-1:2021, Festkondensatoren für den Einsatz in elektronischen Geräten – Teil 1: Allgemeine Spezifikation, 6. Aufl. Genf: IEC, 2021.
5. IEC 61071:2017, Kondensatoren für Leistungselektronik, Ed. 2.0. Genf: Internationale Elektrotechnische Kommission, 2017.
6. H. Nakao, Y. Yonezawa, T. Sugawara, Y. Nakashima und F. Kurokawa, Online-Bewertungsmethode zur Bestimmung der Degradation von Elektrolytkondensatoren für die Ausfallvorhersage digital gesteuerter SchaltnetzteileIEEE Transactions on Power Electronics, Bd. 33, Nr. 3, S. 2552-2558, 2018. https://doi.org/10.1109/tpel.2017.2691048.
7. V. Belyaev, Modell des Oberflächenüberschlags eines Isolators im Vakuum, in: Proceedings ISDEIV. 18th International Symposium on Discharges and Electrical Insulation in Vacuum, S. 151-154, 1998. https://doi.org/10.1109/deiv.1998.740596.
8. AND9800/D — Auswahl von Dämpfungskondensatoren für Motorantriebsanwendungen (Testdaten in Tabelle 15), onsemi, AND9800-D, https://m.onsemi.jp/pub/Collateral/AND9800-D.PDF .
9. US 8,570,711, Mehrschichtige elektronische Keramikkomponente (Lichtbogenunterdrückung für 1–5 kV MLCCs), Samsung Electro-Mechanics Co., Ltd., erteilt 2013, https://www.freepatentsonline.com/8570711.html .
10. GB/T 17702-2021, 电力电子电容器 (Kondensatoren für die Leistungselektronik). Peking: 国家市场监督管理总局, 2021.
11. HVC-Anwendungsentwicklungsteam Hochspannungs-Keramikkondensator Technische Ressourcen, https://www.hv-caps.com