LLC Resonant Soft Switching for Plasma Ignition Pre-Charge Stages

LLC Resonant Soft Switching for Plasma Ignition Pre-Charge Stages

Abstract

A plasma igniter recharges its tank thousands of times a day, and a hard-switched pre-charge stage pays for that with loss, EMI and a tank voltage that moves between strikes. This article works the LLC tank values, the gain curve, the charge current, the magnetizing-current condition that holds zero-voltage switching, the two-mode charging profile and the ripple that reaches the firing instant.

1. Einleitung

Every ignition event starts with a recharge. In a machine firing hundreds of times a second that recharge is a continuous duty, and a hard-switched flyback or forward stage performs it badly: each edge contributes to the emission spectrum, each pulse stresses the switch with the full hard-switching loss, and the ripple left on the tank voltage moves the ignition pulse from strike to strike.

As repetition rates rise and emission limits tighten, the charging stage becomes the limit on the whole igniter. The losses land in a converter that has to run continuously, and the noise lands in a measurement band where the ignition stage is already the loudest source in the machine.

An LLC converter fits this duty better than a hard-switched stage because its gain depends on load. A discharged tank pulls the operating point down the gain curve, which raises the current; as the tank voltage climbs the point moves back toward resonance and the current tapers. The converter behaves as a current-limited charger without any current-loop control.

This article sizes the tank, checks the zero-voltage switching condition at both ends of the charge, sets the two-mode profile, and works the rectifier snubber that the secondary ringing needs.

2. Kernmechanismus

2.1 The two resonant frequencies

The resonant tank has a series branch and a magnetizing branch, and each sets a frequency.

f_r1 = 1 / (2π √(L_r × C_r))

where f_r1 is the series resonance of the tank, L_r is the series resonant inductance and C_r is the series resonant capacitance.

f_r2 = 1 / (2π √((L_r + L_m) × C_r))

where f_r2 is the lower resonance and L_m is the magnetizing inductance. With L_r at 31.8 µH, C_r at 79.6 nF and L_m at 159 µH, the two frequencies land at 100 kHz and 40.8 kHz. Zero-voltage switching holds for any switching frequency above f_r2, so the whole usable range sits between 40.8 kHz and the peak of the gain curve.

2.2 The gain curve

Load changes move the operating point, and the first-harmonic gain model predicts where.

M = 1 / √((1 + λ × (1 − 1/f_n²))² + Q² × (f_n − 1/f_n)²)

where M is the voltage gain from the bridge to the rectifier, λ is the ratio L_r / L_m, f_n is the switching frequency normalised to f_r1, and Q is the loaded quality factor. With λ at 0.2 the gain peaks at 1.39 near f_n = 0.5 for a light load and flattens to 1.0 at f_n = 1 for every load.

2.3 Charge current from the tank impedance

The rectifier current follows from the tank characteristic impedance.

I_Lr = (2 / π) × (V_in / 2) / Z_0

where I_Lr is the amplitude of the tank current, V_in is the DC input voltage and Z_0 is the tank characteristic impedance, √(L_r / C_r). A 400 V input through a 20 Ω tank gives 6.37 A. The rectifier averages that current and the turns ratio steps it down:

i_charge = (2 / π) × I_Lr / n

where i_charge is the charge current into the tank capacitor and n is the primary-to-secondary turns ratio, 50 for a 10 kV output. The two averages together give 81 mA, which is what the ignition capacitor sees at the resonant point of the sweep.

2.4 Charge time and ripple

The charge the tank needs and the ripple left on it both follow from the capacitance.

Q_charge = C_tank × V_C

where Q_charge is the charge delivered, C_tank is the ignition capacitance and V_C is the target voltage. A 4700 pF tank charged to 10 kV takes 47 µC, and at 81 mA that is 580 µs of charging inside a 2.5 ms ignition cycle.

ΔV_ripple = i_charge × (T_sw / 2) / C_tank

where ΔV_ripple is the switching ripple on the tank voltage, i_charge is the charge current, T_sw is the switching period and C_tank is the ignition capacitance. At 81 mA and 100 kHz the tank ripples 86 V, which is 0.86% of the target and inside the ±2% repeatability that the firing circuit needs, but with no margin.

2.5 The magnetizing current that holds ZVS

The switches commutate during the dead time, and the current available to do it comes from the magnetizing branch once the secondary stops conducting.

I_Lm(pk) = n × V_tank / (4 × L_m × f_sw)

where I_Lm(pk) is the peak magnetizing current, n is the turns ratio, V_tank is the tank voltage at that moment, L_m is the magnetizing inductance and f_sw is the switching frequency.

That current has to move the switch capacitance before the next device turns on:

½ × L_m × I_Lm(pk)² ≥ 2 × C_oss × (V_in / 2)²

where C_oss is the output capacitance of one switch and V_in is the DC input. With 120 pF at a 400 V input the requirement is 9.6 µJ, which needs 0.35 A of magnetizing current.

Through 159 µH at 100 kHz that current appears once the tank passes 1105 V, so 89% of the charge runs on magnetizing current alone. Only the first 1.1 kV depends on reflected load current. Note the direction of that dependence: magnetizing current grows with tank voltage, so the end of the charge has the largest ZVS margin and not the smallest.

2.6 Resonanzkondensatorverlust

The resonant capacitor carries the full tank current at the switching frequency.

ESR_diel = tanδ / (2π × f × C)

where ESR_diel is the dielectric part of the equivalent series resistance, tanδ is the loss factor, f is the switching frequency and C is the capacitance. A 79.6 nF part with a loss factor of 0.1% at 100 kHz returns 20 mΩ, and 4.5 A rms through it dissipates 0.41 W. A part with 1% loss factor returns 200 mΩ and dissipates 4.1 W in a component that sits inside the converter enclosure.

Fig. 1 — The LLC gain curve for Q 1.2 at the start of charge and Q 0.4 at 10 kV; the sweep stays inside the ZVS region.

3. Schwachstellen im Engineering

Pain Point 1: The light-load end of the charge

The usual light-load ZVS problem does not appear at the end of this charge. Magnetizing current grows with tank voltage, so the end of the charge carries the largest commutation margin. The risk sits at the start instead: at 0 V the magnetizing current is zero and commutation depends entirely on reflected load current.

Start the sweep below the peak-gain frequency to keep the tank current continuous and the switches soft. Start it above that frequency and every ignition cycle opens with a hard-switching edge.

Pain Point 2: Resonant capacitor selection

The resonant capacitor carries the full tank current at the switching frequency. A part with a loss factor of 1% instead of 0.1% returns 200 mΩ instead of 20 mΩ and burns 4.1 W instead of 0.41 W. Its self-resonance also has to sit far above the switching band, and a 79.6 nF part with 5 nH of loop inductance self-resonates at 8 MHz, which is 80 times the 100 kHz switching frequency and adequate.

Pain Point 3: Rectifier and winding parasitics

The LLC transformer absorbs its leakage into L_r, but the secondary leakage still rings against the rectifier junction capacitance. With 2 mH referred to the secondary and 30 pF of junction capacitance the ring sits at 650 kHz, and it shows up as spikes on the rectifier and as noise on the tank voltage.

Size the snubber from the ring excursion and not from the junction capacitance. A capacitor three times the junction value burns 37 W at that frequency, which is more than the loss the snubber removes.

Pain Point 4: Charge time against ripple at the fire instant

A fast charge leaves more ripple on the tank voltage at the moment of firing. At 81 mA the tank ripples 86 V, which is 0.86% of the target, and a repeatability requirement of ±2% leaves almost no room for anything else that moves the tank voltage. Charging the whole way at full current is the fastest option and the least predictable one.

4. Entwurfsschritte

Strategy 1: Pick the resonant capacitor for loss and self-resonance

Use a Class I part with a loss factor below 0.1% and a self-resonance far above the switching band. An N4700 part at 79.6 nF holds 20 mΩ of dielectric resistance at 100 kHz, which keeps the resonant branch cool without a heatsink and leaves the gain curve where the design put it.

Strategy 2: Hold ZVS across the whole charge envelope

Check the magnetizing-current condition at the lowest tank voltage the converter will run at, not at full charge. Above 1105 V the magnetizing branch alone meets the 9.6 µJ requirement; below that, rely on reflected load current and keep the operating point below the peak-gain frequency. Verify on the switch drain waveform at 0 V, at 1 kV and at 10 kV.

Strategy 3: Use a two-mode charging profile

Charge to 9 kV at 75 mA, which takes 565 µs, then trim the last 1 kV at 20 mA, which takes another 235 µs. The trim cuts the switching ripple on the tank from 80 V to 21 V at the moment the igniter fires, and the total 800 µs still fits inside a 2.5 ms cycle with 68% of the period spare.

Strategy 4: Damp the rectifier ring with a small snubber

Measure the ring frequency and its excursion, then fit a 10 pF capacitor in series with an 8.2 kΩ Dickschichtwiderstand across the rectifier. At 650 kHz and 800 V of excursion that branch dissipates 4.2 W. Sizing the capacitor from the junction value instead gives 90 pF and 37 W, which is a snubber that costs more than the loss it removes. Pair the rectifier with a schnelle Erholungsdiode so the ring itself stays small.

Strategy 5: Model the ignition capacitor as part of the converter

Put the measured capacitance and ESR of the 4700 pF tank into the gain model so the load the converter sees is the real one, and re-run it at the hot operating temperature. Capacitance drift moves both C_r and C_tank, and the gain curve moves with them.

Strategy 6: Validate the whole cycle on a rig

Charge and fire at the maximum repetition rate while monitoring switch ZVS, tank ripple and ignition repeatability. Freeze the design only when the tank voltage lands within ±2% at the fire instant across a full thermal cycle. Test the tank capacitor with a partial-discharge check at rated voltage as well, because a charging capacitor sees every pulse the igniter fires.

Komponentenparameter	Typischer Wert	Testbedingung
Nennspannung (HVCT8G Serie)	10 kV DC	Hi-Pot 1.5× für 60 s
Ignition capacitance	4700 pF ±20% (472M)	1 MHz, 1 V<sub>eff</sub>
Resonant capacitance C_r	79.6 nF, loss factor below 0.1%	100 kHz
Resonant capacitor self-inductance	unter 5 nH	self-resonance above 8 MHz
Temperaturkoeffizient	±30 ppm/°C	−40 °C bis +125 °C
Teilentladung	unter 5 pC	bei Nennspannung
Tank voltage repeatability	inside ±2%	at the fire instant

5. HVC N4700 (T3M) capacitors for the resonant tank

An LLC holds its gain curve only if the capacitors hold their values. HVC builds the N4700 (T3M) Class I family for that duty, covering the resonant element at moderate voltage and the ignition capacitor at full voltage from one dielectric, from a 6,000 m² owned factory in Dongguan across a 1 kV to 100 kV range.

Sechs Parameter, die hier von Bedeutung sind

• Stable resonant capacitance. A ±30 ppm/°C coefficient keeps the gain curve fixed across a full thermal cycle, so the charging profile measured cold is the profile delivered after a shift of continuous firing.
• Low loss at the switching frequency. A dissipation factor below 0.1% at 100 kHz keeps the resonant branch at 0.41 W instead of 4.1 W, which removes a heat source from inside the converter enclosure.
• One dielectric for both elements. Ratings from 1 kV to 100 kV let the same qualified family serve the 600 V resonant capacitor and the 10 kV ignition capacitor, so the drift behaviour of both is known from the same data.
• Discharge below 5 pC. Neither element adds a discharge source to a stage whose whole purpose is a clean charge, and the ignition capacitor meets its own screening requirement from the same part number.
• Self-resonance headroom. A self-inductance below 5 nH keeps the component resonance far above the 100 kHz switching band, so the tank model the design was built on stays valid.
• Proven in resonant high-voltage supplies. The 40 kV 441-series doorknob capacitors replaced first-tier brand parts in high-voltage field-service programs, and a Querverweis gegen einen Folienkondensator shows the capacitance stability a resonant design would otherwise have to absorb.

Lieferung und Support

Standard parts ship in 4 to 8 weeks and matched resonant sets in 6 to 10 weeks. HVC applications engineering supports tank sizing, gain-curve modelling, ZVS verification and snubber design. Send the input voltage, the ignition capacitance, the repetition rate and the transformer data, and HVC returns a resonant selection sheet with impedance curves, loss figures and PD reports within five working days.

6. Häufig gestellte Fragen

Q1: Why use an LLC for ignition charging?

Because its gain depends on load. A discharged tank pulls the operating point down the gain curve and raises the current; as the tank voltage rises the current tapers with no current-loop control. The same converter also commutates softly, which removes the hard-switching edge that a flyback or forward stage puts into the emission spectrum.

Q2: How long does the charge take?

A 4700 pF tank to 10 kV needs 47 µC. At 81 mA the bulk phase reaches 9 kV in 565 µs and the trim adds 235 µs, so a full charge takes about 800 µs inside a 2.5 ms ignition cycle. That leaves 68% of the period for cooling and for waiting on the fire command.

Q3: Where is ZVS at risk during the charge?

At the start, where the tank voltage is near zero and the magnetizing current with it. Above 1105 V the magnetizing branch alone supplies the 0.35 A needed to move 120 pF of switch capacitance, so 89% of the charge is safe by construction. Below that, keep the sweep below the peak-gain frequency so the tank current stays continuous.

Q4: How do I size the rectifier snubber?

From the ring excursion, not from the junction capacitance. At 650 kHz with 800 V of excursion a 10 pF capacitor with an 8.2 kΩ resistor dissipates 4.2 W. The familiar three-times-junction rule gives 90 pF, which burns 37 W because dissipation scales with capacitance, voltage squared and frequency together.

Q5: How much ripple is left on the tank at the fire instant?

It depends on the charge current at that moment. At 81 mA the tank ripples 86 V, which is 0.86% of a 10 kV target. Trimming the last kilovolt at 20 mA drops the ripple to 21 V, or 0.21%, which leaves room inside a ±2% repeatability requirement.

Q6: What has to be true about the resonant capacitor?

Three things. Its loss factor has to sit near 0.1% so 4.5 A rms does not turn into 4 W of heat, its capacitance has to stay put over temperature so the gain curve does not move, and its self-resonance has to sit far above the 100 kHz band. A 79.6 nF part with 5 nH of loop inductance self-resonates at 8 MHz, which satisfies the third.

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