Projeto de capacitores para cura UV: elevação de temperatura e ESR

Projeto de capacitores para cura UV: elevação de temperatura e ESR

Sumário

A 20 kW curing supply now fits in a cabinet that held 10 kW, so heat per cubic centimetre decides the layout. Capacitors are small heat sources and the most temperature-sensitive parts in the stage. This article gives the loss, thermal-resistance and Arrhenius life arithmetic, four field failure modes, the hot-spot target that returns 10 years of life, and the measurement that proves the design.

1. Introdução

Power density in UV curing equipment doubles every few years, driven by conveyor speed. A 20 kW mercury-lamp supply now fits into a cabinet that previously housed 10 kW, and heat per cubic centimetre has become the binding constraint on the layout.

Capacitors sit in an awkward position inside that constraint. They are not the largest heat sources, since the switching devices and the magnetics are. They are the parts most sensitive to temperature: a ceramic capacitor loses roughly half of its life for every 10 K of hot-spot rise.

A part rated for 105 °C operation delivers a fraction of its rated life when the local air is 75 °C and self-heating adds another 20 K. The failure arrives as a shift in capacitance or a rise in loss, months before anything opens.

This article gives the loss model, the thermal resistance chain, the life arithmetic and the four measurement rules that keep a capacitor hot spot inside the life-preserving band of a sealed cabinet.

2. Mecanismo Central

2.1 Loss in the capacitor

The heat a capacitor generates comes from the ripple current through its equivalent series resistance.

P_C = I_rms² · ESR

where P_C is the dissipated power, I_rms is the root-mean-square ripple current through the part and ESR is the equivalent series resistance at the operating frequency. In a 500 kHz resonant stage the ripple current often reaches 2–3× the DC current, so this term dominates the design.

2.2 Resistência Série Equivalente Dielétrica (ESR) na frequência de comutação

The dielectric contribution to ESR falls as frequency and capacitance rise, and it scales with the loss factor of the material.

ESR_diel = tanδ / (2 π f C)

where ESR_diel is the dielectric part of the series resistance, tanδ is the loss factor, f is the operating frequency and C is the capacitance. A 2.2 nF Class I tank capacitor with tanδ = 0.1% at 200 kHz works out at 362 mΩ. At 10 A rms that single part dissipates 36 W, which no sealed module can absorb. A Class II part with tanδ = 2.5% reaches 9.05 Ω and dissipates 905 W at the same current.

2.3 Cadeia de resistência térmica

Heat leaves the dielectric through the case and then into the air or the enclosure wall, and each step adds a thermal resistance.

ΔT = P_C · (R_th,jc + R_th,ca)

where ΔT is the hot-spot rise above ambient, P_C is the dissipated power, R_th,jc is the dielectric-to-case resistance and R_th,ca is the case-to-ambient resistance. A disc capacitor in free air shows 80–150 K/W for R_th,ca; a metal tab bonded to board copper pulls that down towards 20 K/W, and potting compound drives it back above 120 K/W.

2.4 Life against hot-spot temperature

Life follows an Arrhenius relation, so the hot spot enters the exponent.

t_life = A · exp(E_a / (k_B · T_hot))

where t_life is the service life, A is a constant for the construction, E_a is the activation energy, k_B is the Boltzmann constant and T_hot is the absolute hot-spot temperature. With E_a near 0.7 eV the life doubles for every 10 K of hot-spot reduction. A part rated 2000 h at 125 °C therefore reaches 16,000 h (1.8 years) at a 95 °C hot spot and 90,500 h (10 years) at 70 °C.

Fig. 1 — Each 10 K of hot-spot reduction doubles the life of a part rated 2000 h at 125 °C, and a 10 K reserve below the rating leaves only 1.8 years.

3. Pontos problemáticos de engenharia

Pain Point 1: Ripple current mis-rated from the datasheet

Designers select the capacitor by capacitance and voltage and ignore the ripple-current limit. In a 500 kHz resonant stage the ripple current reaches 2–3× the DC current, the part runs 40–60 K above ambient, and the over-specified 105 °C part fails in about 18 months.

Pain Point 2: The cabinet thermometer reads the wrong place

The cabinet thermometer shows 45 °C while the capacitor next to the transformer sits at 75 °C. Without a measurement at the component site, every life calculation is wrong by 4× or more, because 30 K is three doublings.

Pain Point 3: Sealing defeats cooling

Manufacturers pot the high-voltage module to keep ozone and UV out. Potting compound conducts 0.2–0.3 W/m·K, so a part that shed 3 W into free air now sheds the same 3 W into a blanket. The hot spot climbs to a new equilibrium above 100 °C.

Pain Point 4: Micro-thermal cycling fatigue

Ripple at 200 kHz micro-cycles the dielectric at the ripple rate, whatever the average temperature. The strain at the electrode-dielectric interface accumulates, the insulation resistance falls over years, and no short-term test shows it.

4. Etapas de projeto

Strategy 1: Compute the loss at the operating frequency

Take ESR-versus-frequency data from the supplier and calculate P_C = I_rms² × ESR at the switching frequency and the worst-case current. Allow 2 W per part where a metal tab holds R_th,ca near 20 K/W, and 0.5 W inside a potted module.

Strategy 2: Break the runaway with a Class I dielectric

Selecionar N4700 (T3M) strontium titanate with tanδ at or below 0.1%. Class II loss factors climb with temperature, so ESR climbs, so P_C climbs. A flat loss factor removes that loop. A capacitor de filme with a higher loss factor carries the same feedback path.

Strategy 3: Measure the hot spot on the body

Thermal imaging on the first prototype is mandatory. Fit thermocouples to the capacitor body, log for one hour at full load, and accept the design only when the hot spot stays at least 10 K below the rating.

Strategy 4: Give the sealed module a thermal path

Use thermally conductive potting or a metal spreader plate bonded to the capacitor bank, so heat reaches the enclosure wall instead of accumulating in the compound. The temperature of the part then follows the wall, and the wall follows the ambient.

Strategy 5: Derate the ripple rating by 0.7

Datasheet ripple ratings assume free convection and an ideal mounting. In a UV cabinet apply a 0.7 derating factor, then confirm the number by measurement, so a batch-to-batch mounting variation cannot push the part past its limit.

Strategy 6: Trend the temperature in the controller

Fit NTC sensors to the two hottest capacitor sites and log the readings. A 10 K upward drift over a few months is an early warning of ESR growth or blocked airflow, and it arrives long before the capacitance moves.

Parâmetro do componente	Valor típico	Condição de teste
Tensão nominal (série HVCT8G)	10 kV CC	alta potência 1.5× por 60 s
Capacidade	4700 pF ±20% (472M)	1 MHz, 1 V rms
ESR a 1 MHz	abaixo de 50 mΩ	25 ° C
Indutância do laço (corda E40)	abaixo de 8 nH	Espaçamento entre terminais de 40 mm
resistência de isolamento	acima de 10 GΩ a 500 V CC	25 °C, 60% UR
Faixa de temperatura	-40°C a +125°C	Série IEC 60068-2
Capacidade de dv/dt de pulso	acima de 50 kV/µs	na tensão nominal

5. HVC Class I capacitors for hot cabinets

Three properties decide the hot spot of a capacitor in a sealed supply: the loss factor of the dielectric, the thermal resistance of the package, and the stability of both over temperature. HVC builds N4700 parts for all three.

Seis parâmetros que importam aqui.

• tanδ at or below 0.1% at 1 kHz holds the dielectric ESR at 362 mΩ for a 2.2 nF part at 200 kHz, which is the dominant heat term in the stage.
• ±30 ppm/°C keeps the loss factor and the capacitance flat from −40 °C to +125 °C, so self-heating cannot feed back into ESR.
• Disc, tubular and HVCT8G screw-type bodies offer low R_th,ca through large contact areas and metal-tab terminations that spread heat into board copper.
• PD below 5 pC at 1.2× rated voltage stops PD erosion from consuming the thermal margin inside the dielectric.
• Hot-spot temperature versus ripple-current curves ship with each lot, so the thermal margin is verifiable without a bench session.
• Field validation: an HVC 40 kV / 441 screw-type capacitor replaced a first-tier brand part in high-voltage field-service programs, and the same low-loss construction matches the electrical parameters of Vishay Gama de cabos radiais HVCC e KEMET.

Entrega e suporte

Standard parts ship in 4–8 weeks and matched stacks in 6–10 weeks. Above 1 kV the site is available as a series stack with matching resistores de classificação.

Send the ripple-current profile, the operating frequency, the enclosure layout and the ambient temperature. HVC returns a selection with ESR-versus-frequency curves, hot-spot calculations and a thermal validation plan, plus samples for imaging within two weeks.

6. Perguntas frequentes

Q1: How do I compute self-heating at 200 kHz?

Take ESR at the switching frequency, not at 1 kHz. For a 2.2 nF Class I part with tanδ = 0.1% at 200 kHz the dielectric ESR is 362 mΩ, and P = I_rms² × ESR gives 36 W at 10 A rms and 2 W at 2.35 A rms.

Q2: How much ripple current can one 2.2 nF part carry?

For a 2 W target at 200 kHz the current limit is 2.35 A rms. A 10 A rms resonant current therefore needs five parallel parts, and a sealed module at 0.5 W per part needs ten.

Q3: What hot-spot temperature gives a 10-year life?

70 °C for a part rated 2000 h at 125 °C, which is 90,500 h. A 10 K reserve below a 105 °C rating, so 95 °C, reaches only 16,000 h or 1.8 years.

Q4: Does potting protect the capacitor?

It protects the surface from ozone and moisture and it also raises R_th,ca from 60 K/W to above 120 K/W. A part that ran 30 K above ambient in free air runs 60 K above ambient in compound at the same loss.

Q5: Why is the cabinet thermometer not enough?

Because the capacitor sits 15–25 K above the cabinet air, near the transformer and the heatsink. Reading 45 °C at the cabinet while the part runs at 75 °C understates the aging rate by 4× or more.

Q6: How is the thermal design verified?

Log the capacitor body temperature at full load for one hour against the computed thermal resistance, confirm the ripple-current derating by measurement, and check that the hot spot holds at least 10 K below the rating at the highest ambient in the specification.

7. Referências

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3. Aviso MIL-HDBK-217F 2, Previsão da confiabilidade de equipamentos eletrônicos 1995.
4. IEC 60384-1:2018, Capacitores fixos para uso em equipamentos eletrônicos — Parte 1: Especificação genérica.
5. H. Wang e F. Blaabjerg, Confiabilidade dos capacitores para aplicações de barramento CC em conversores eletrônicos de potência — Uma visão geral, IEEE Transactions on Industry Applications, vol. 50, no. 5, pp. 3569-3578, 2014. https://doi.org/10.1109/tia.2014.2308357.
6. D. Li, Y. Zhong, X. Zhou e G. Zhai, Método de análise da fratura de capacitores cerâmicos multicamadas pelo campo de fase, IEEE Transactions on Components, Packaging and Manufacturing Technology, vol. 14, no. 2, pp. 211-220, 2024. https://doi.org/10.1109/tcpmt.2024.3359598.
7. M. Marchesoni e outros, Minimização da ondulação da tensão do capacitor em conversores de fonte de tensão para aplicações HVDC, em 2019 AEIT HVDC International Conference (AEIT HVDC), pp. 1-6, 2019. https://doi.org/10.1109/aeit-hvdc.2019.8740647
8. Desenvolvimento de capacitores cerâmicos multicamadas BME X7R de alta capacitância e alta tensão, KEMET Electronics (CARTS USA 2011 Proceedings), https://www.mouser.jp/pdfdocs/2011-03CARTS-DevelopmentofHighCapacitance-HighVoltageBMEX7RMLCCapacitors.pdf .
9. MIL-PRF-49470D, Capacitor fixo, dielétrico cerâmico, fonte de alimentação comutada (uso geral e temperatura estável), confiabilidade padrão e alta confiabilidade, especificação geral paraWashington, DC: Departamento de Defesa dos EUA, 2017.
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11. Equipe de Engenharia de Aplicações HVC, Capacitor Cerâmico De Alta Tensão Recursos técnicos, https://www.hv-caps.com