Correction des erreurs thermiques pour les résistances de shunt de courant des lampes UV

Correction des erreurs thermiques pour les résistances de shunt de courant des lampes UV

Abstract

Every UV light source depends on a constant-current loop, and the loop regulates to whatever its shunt reports. A shunt sits in a warm cabinet, carries tens of amperes and heats itself, so its resistance drifts with ambient and with load. This article gives the resistance, self-heating, error and correction arithmetic, four field failure modes, the NTC compensation method that reaches 0.003%, and the sense filter that must not add error of its own.

1. Introduction

Every UV light source, whether an LED array or a mercury arc lamp, depends on a constant-current loop to hold its optical output. The loop is no better than its current sensor, and the workhorse sensor is a low-value shunt resistor carrying the full load current.

In a curing line that shunt sits inside a warm cabinet, carries tens of amperes and dissipates watts in its own body. Its resistance then drifts for two reasons at once: the ambient temperature of the cabinet, and the self-heating on top of it.

A shunt with a temperature coefficient of 50 ppm/°C, running 34 K above its calibration temperature, reports a current that is 0.17% away from the calibrated value. That error flows straight into the delivered UV dose.

This article gives the error chain, the four field failure modes, the hardware and firmware corrections, and the sense-path filter that holds a fixed corner frequency over temperature.

2. Mécanisme de base

2.1 Resistance against temperature

The shunt converts current to voltage through a resistance that moves with its own temperature.

R(T) = R_0 · (1 + α · ΔT)

where R(T) is the resistance at the operating temperature, R_0 is the calibrated value at 25 °C, α is the temperature coefficient of resistance and ΔT is the rise above the calibration temperature. At 50 ppm/°C a 34 K rise adds 1700 ppm, or 0.17%, to the sensed value.

2.2 Self-heating at full load

The shunt heats itself in proportion to the square of the load current and to the thermal resistance of its mounting.

ΔT_self = I² · R_0 · R_th

where ΔT_self is the self-heating rise, I is the load current, R_0 is the shunt resistance and R_th is the thermal resistance from the element to ambient. A 0.25 mΩ shunt at 40 A dissipates 0.4 W; at 10 K/W that is a 4 K rise, and at 20 K/W it doubles to 8 K.

2.3 Total error and its correction

The two temperature terms add, and both scale the same resistance.

δI / I = α · (ΔT_amb + ΔT_self)

where δI/I is the relative current error, α is the temperature coefficient, ΔT_amb is the ambient rise at the shunt site and ΔT_self is the self-heating rise of §2.2. With 30 K of ambient rise, 4 K of self-heating and 50 ppm/°C the reading is 0.17% high. The same error term is correctable in firmware once the shunt temperature is known.

I_true = I_reported / (1 + α · (T_meas − T_cal))

where I_true is the corrected current, I_reported is the raw reading, T_meas is the measured shunt temperature and T_cal is the calibration temperature. The residual error then equals the NTC accuracy times α: at ±0.5 °C and 50 ppm/°C that is 0.003%.

2.4 The sense filter corner

The shunt voltage is only 50–100 mV at full current, so it needs a low-pass filter at the terminals before the amplifier.

f_c = 1 / (2 π · R_f · C_f)

where f_c is the filter corner frequency, R_f is the series filter resistance and C_f is the filter capacitance. A 1 kΩ resistor and a 100 nF capacitor put the corner at 1.6 kHz, which rejects the switching ripple. A Class II capacitor shifts that corner with bias and temperature; a Class I part holds it, so the filter adds no error term of its own.

Fig. 1 — Shunt error is linear in temperature rise, so a 34 K total rise costs 0.17% at 50 ppm/°C and 0.05% in manganin.

3. Points faibles en matière d'ingénierie

Pain Point 1: Self-heating error at high current

The shunt is bought for low loss, and at full UV power the self-heating term I² · R_0 · R_th dominates. A 40 A, 0.5 mΩ shunt with 20 K/W dissipates 0.8 W and runs 16 K hot; at 50 ppm/°C that is 0.08% of error, and it grows with the square of the load current.

Pain Point 2: Ambient drift across a shift

Cabinet temperature rises 10–25 °C between a cold start and steady state. An uncompensated shunt at 50 ppm/°C reports a current that drifts 0.05–0.125%, which is enough to move UV dose outside the process window for sensitive coatings and to produce gloss bands on a long run.

Pain Point 3: Sense-path noise corruption

A 50–100 mV sense signal sits in switching noise and ground bounce. Without a filter capacitor mounted at the shunt the amplifier sees 10 mV of ripple, an apparent error of 10–20%, and the loop modulates the lamp current at the switching frequency. The result is visible banding on the cured substrate.

Pain Point 4: Aging and tolerance spread

Shunts age under sustained power and drift 0.1–0.5% over service life, so a loop that was calibrated when the machine was new is no longer at the calibrated current after 10,000 hours. A replacement part from a different batch carries a different TCR, and the old calibration data no longer apply.

4. Étapes de conception

Strategy 1: Characterize the thermal environment first

Measure the shunt temperature at cold start and again after two hours at full power inside the production enclosure. That difference is the range the compensation has to cover, and it decides whether compensation is needed at all. The same test applies to every résistance d'échantillonnage in the supply, including the divider chain.

Strategy 2: Choose a low-TCR material and a low-R_th geometry

Specify manganin or an equivalent alloy at 15 ppm/°C or better with a thermal resistance below 10 K/W. Material choice is the highest-leverage fix because it shrinks the ambient term and the self-heating term at once.

Strategy 3: Compensate in firmware

Mount an NTC within 5 mm of the shunt, calibrate α and T_cal per unit at production test, and apply the correction in the controller. The residual error falls to the NTC accuracy, about 0.003% at ±0.5 °C. Where galvanic isolation is also required, a Rogowski coil replaces the shunt in the sense path.

Strategy 4: Filter the sense path with Class I capacitors

Place the low-pass filter with N4700 (T3M) Class I capacitors directly at the shunt terminals, with tanδ at or below 0.1% and ±30 ppm/°C. The corner frequency then stays at 1.6 kHz across the cabinet temperature range, and the filter contributes no temperature-dependent error.

Strategy 5: Add periodic auto-calibration

During lamp off-periods, short the shunt with a FET and measure the residual offset, then inject a known reference current and measure the gain. Store both corrections in non-volatile memory and re-validate the loop every shift.

Strategy 6: Verify the whole chain inside the loop

Close the loop and measure the delivered current ripple and the dose from −10 °C to +70 °C. Accept the design only when the current holds inside ±0.5% of target across the full range. The divider and bleeder sites in the same supply use a résistance à couche épaisse with its own thermal specification.

Paramètre de composant	Valeur typique	Condition de test
Puissance nominale (série HVR)	50 W à 70 °C	Boîtier en aluminium, air libre
Valeur de résistance	10 kΩ ±5%	Référence à 25 °C
Tension de travail	10 kV CA/CC	continu
Résistance aux impulsions	30 kV à 10 µs	10 impulsions
Coefficient de température (résistif)	±50 ppm/°C	−55 °C à +155 °C
La resistance d'isolement	supérieure à 1 GΩ à 1000 V CC	ligne de fuite minimale 25 mm
Capacité de courant de surtension	100 A à 1 ms	bobinage non inductif

5. HVC capacitors for the sense path

The sense path needs a filter whose corner does not move, and the high-voltage sites on the same board need a capacitor that does not erode. HVC builds N4700 parts for both.

Six paramètres importants ici

• N4700 (T3M) strontium titanate with ±30 ppm/°C holds the sense filter corner at 1.6 kHz across the cabinet temperature range, so the filter adds no error to the measurement.
• tanδ at or below 0.1% at 1 kHz adds no measurable loss or heating to a millivolt-level sense circuit.
• Ratings from 1 kV to 100 kV cover the low-voltage sense filter and the lamp ballast from one qualified family, including HVCT8G et des carrosseries de type 441.
• PD below 5 pC at 1.2× rated voltage keeps the high-voltage filter and coupling sites from eroding and corrupting the reference voltages that share the board.
• Class I production discipline holds the capacitance inside tight tolerance, so the filter corner repeats from board to board without per-unit tuning.
• Validation sur le terrain : un condensateur à vis HVC 40 kV / 441 a remplacé une pièce de marque de premier plan dans des programmes de service sur site haute tension, et la même construction correspond aux paramètres électriques de Vishay Gammes de câbles radiaux HVCC et KEMET.

Livraison et support

Standard parts ship in 4–8 weeks and matched sets in 6–10 weeks. HVC applications engineering reviews the sense path, the shunt rating and the thermal environment of the cabinet.

Send the shunt specification, the load current, the cabinet thermal profile and the dose tolerance. HVC returns a sense-path review with Class I filter values, NTC placement guidance and measured filter stability data, plus samples in two weeks.

6. Questions fréquentes

Q1: How large is the shunt error in a real cabinet?

About 0.17% for a 0.25 mΩ shunt at 40 A with a 50 ppm/°C TCR, 30 K of ambient rise and 4 K of self-heating. The self-heating term is 4 K at 10 K/W and doubles if the mounting thermal resistance doubles.

Q2: Which is better, manganin or firmware compensation?

Both. Manganin at 15 ppm/°C shrinks every error term, and firmware compensation removes what remains and also corrects for aging between calibrations. The material sets the floor, and the firmware holds the loop to it.

Q3: How accurate is firmware compensation?

As accurate as the NTC and the stored coefficient. At ±0.5 °C and 50 ppm/°C the residual is about 0.003%, small compared with the 0.17% it removes. Calibrating α per unit at production test matters more than the sensor grade.

Q4: Why does the sense filter need a Class I capacitor?

Because the corner frequency depends on capacitance. A Class II part shifts with bias and temperature, so the corner moves and switching ripple reaches the amplifier. A Class I part at ±30 ppm/°C holds 1.6 kHz in place.

Q5: How much ripple can the sense path tolerate?

The sense level is 50–100 mV, so 10 mV of unfiltered ripple is a 10–20% apparent error. Filter at the shunt terminals, and keep the filter resistor and capacitor return on the same ground reference as the amplifier.

Q6: How is the corrected loop verified?

Close the loop and log the delivered current from −10 °C to +70 °C with the dose measured at the same time. Accept the design only when the current holds inside ±0.5% of target across the whole range.

7. Références

1. E. Kuffel, WS Zaengl, J. Kuffel, Principes fondamentaux de l'ingénierie haute tension, 2e éd., Newnes, 2000.
2. N. Mohan, TM Undeland, WP Robbins, Électronique de puissance : convertisseurs, applications et conception, 3e éd., Wiley, 2003.
3. Avis MIL-HDBK-217F 2, Prédiction de la fiabilité des équipements électroniques 1995.
4. CEI 60384-1:2018, Condensateurs fixes destinés aux équipements électroniques — Partie 1 : Spécifications générales.
5. A. Mariscotti et L. Vaccaro, Bobine de Rogowski pour applications haute tension, dans 2008 IEEE Instrumentation and Measurement Technology Conference, pp. 1069-1073, 2008. https://doi.org/10.1109/imtc.2008.4547197.
6. H. Nakao, Y. Yonezawa, T. Sugawara, Y. Nakashima et F. Kurokawa, Méthode d'évaluation en ligne de la dégradation des condensateurs électrolytiques pour la prédiction des défaillances des alimentations à découpage à commande numérique, IEEE Transactions on Power Electronics, vol. 33, no. 3, pp. 2552-2558, 2018. https://doi.org/10.1109/tpel.2017.2691048.
7. Manuel d'application Fuji IGBT, Chapitre 5 — Conception du circuit de protection (REH984), Fuji Electric, REH984, https://www.fujielectric.com/device/semi/technical/application/pdf/REH984/REH984_05.pdf .
8. GB/T 6346.1-2024, 电子设备用固定电容器 第1部分：总规范 (Condensateurs fixes destinés à être utilisés dans les équipements électroniques – Partie 1 : Spécification générique). Pékin : 国家市场监督管理总局, 2024.
9. MIL-PRF-49470D, Condensateur fixe à diélectrique céramique pour alimentation à découpage (usage général et stabilité en température), fiabilité standard et haute fiabilité, spécifications généralesWashington, DC : Département de la Défense des États-Unis, 2017.
10. Équipe d'ingénierie des applications HVC, Condensateur céramique haute tension Ressources techniques, https://www.hv-caps.com