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سجل التغييرات الكاملالمحرّك 1.26.4

Fuse Sizing, Inrush & I²t

Protection & EMC

Will this fuse carry the load, survive every power-on, and open before the trace does?

هذه الصفحة غير مترجمة بالكامل بعد. الأجزاء غير المترجمة معروضة بالإنجليزية.

المدخلات

ملف اللوحة

Fills Copper weight وAmbient temperature from your board profile.

The highest continuous current through the fuse.
A
The highest value at switch-on.
V
All bulk and ceramic capacitance charged at switch-on.
F
470 µF
Source, fuse cold resistance, traces and capacitor ESR, added.
Ω
Blank: size only.
A
Fuse datasheet, temperature re-rating curve at your ambient (100 % at 25 °C). It does not follow the Ambient temperature field.
%
Nominal melting I²t. From the same fuse datasheet as the rating.
A²s
Clearing I²t at your voltage. From the same fuse datasheet as the rating. If only melting I²t is listed, the maker can give it.
A²s
The narrowest trace the fault current runs through.
NTC and power-ons
NTC datasheet, resistance at TA; 0 if none.
Ω
The pulse chart assumes at least 10 s between power-ons.
Temperature
The trace's temperature when the fault starts.
°C
The laminate's decomposition temperature Td, from its datasheet.
°C

النتائج

Minimum fuse rating Imin

Iop / (0.75 × kT), at 100 % re-rating
2A
ناجح

المعيار: Irated ≥ Imin (75 % load, Fuseology), failing below 0.75 × Imin: your 2.5 A fuse is 1.250 × Imin
أظهر خطوات الحساب
  1. Inrush peak currentI_pk = V_in / (R_path + R_NTC) = 12 / (0.5 + 0) = 24 A
  2. Inrush I²tI²t = V_in² × C / (2R) = 12² × 470 µF / (2 × 0.5) = 0.06768 A²s
  3. Melting I²t neededI²t_needed = I²t / k_pulse = 0.06768 A²s / 0.29 = 0.2334 A²s
  4. Minimum fuse ratingI_min = I_op / (0.75 × k_T) = 1.5 / (0.75 × 1) = 2 A
  5. Trace I²t to meltI²t_trace = A² × log10((1083 − T_A) / (234 + T_A) + 1) / 33 = 34.34² × log10(1058 / 259 + 1) / 33 = 25.24 A²s
Melting I²t needed I²tneed
0.2334A²s
Trace I²t margin I²ttrace/I²tclear
16.83:1
Inrush peak current Ipk

Vin / (Rpath + RNTC)
24A
كل النتائج (11)
Inrush I²t I²t

½ × Ipk² × τ, the whole charge
0.06768A²s
Time constant τ

(Rpath + RNTC) × C
235µs
Energy into the capacitor E

½ × C × Vin²; as much again is lost in R
33.84mJ
Pulse fraction used kpulse

the chart point at 10 000 pulses, for 10 000 power-ons
0.29
Fuse load at TA 

Iop / (kT × Irated)
60.0%
Current the trace must carry Icarry

2.1 × Irated: an IEC 60127-2 quick-acting fuse may take up to 30 min to open at this current
5.25A
Trace I²t to melt I²ttrace

Onderdonk, from 25 °C to 1083 °C
25.24A²s
Trace I²t to Tlim I²tlim

Onderdonk, from 25 °C to 300 °C, the laminate limit
11.23A²s
Fusing current, 10 ms If
Fusing current, 1 s If
Trace area A

w × tCu = 17400 µm²
34.34cmil
i(t)

إلى أي حد نعرف هذا الرقم

من أين تأتي الطريقة
  • Littelfuse
  • Brooks
  • Littelfuse

Littelfuse, Fuseology Design Guide المعادلة

Brooks, Fusing Current: When Traces Melt Without a Trace, giving Onderdonk's equation from the Standard Handbook for Electrical Engineers المعادلة

Littelfuse, Fuseology Design Guide: pulse I²t as a fraction of nominal melting I²t, against the number of pulses جدول منشور

يُقاس مقابل: IEC 60127-2, miniature fuses, the quick-acting F characteristic: 1.5 × I_N must not open within 60 min, 2.1 × I_N must open within 30 min, as stated in Schurter's 5 × 20 mm quick-acting fuse datasheet

صادقة ضمن
  • Power-on cycles in life at most 100 k

Power-on cycles in life The pulse chart stops at 100 000 power-ons (the count is in the NTC and power-ons group). Beyond it the fraction of melting I²t a fuse withstands is not known, so the I²t check is an extrapolation. Littelfuse, Fuseology Design Guide

مدى دقتها
Exact arithmetic on three models: an ideal RC charge from a voltage step, the fuse maker's pulse chart and Onderdonk's adiabatic copper equation.

A supply that rises in a finite time gives less, so the inrush I²t is an upper bound for this R, and the charge path resistance, rarely known well, usually dominates it. Onderdonk assumes no heat leaves the copper and was not tested on board traces (Brooks), which is why the trace check asks for a margin.

عملياً يهيمن على عدم اليقين مدخل واحد: Charge path resistance. ضيّقه يضِق معه الجواب.

يُقاس مقابل

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Parts that track move together.القطع من النوع والتفاوت نفسه تتحرك معاً، كمصفوفة متوافقة أو بكرة واحدة، بدل أن تتحرك مستقلة.

Circuit

المبدأ

At switch-on the capacitance after the fuse charges through the path's resistance, and the fuse sees a pulse that peaks at Vin/R and decays with τ = R·C. A fuse that carries the load can still wear and open after thousands of these, so its melting I²t needs a margin over the pulse's I²t that grows with the number of power-ons. This page sizes the rating from the load and the temperature, checks the melting I²t against the inrush, and checks that the narrowest trace in the fault path takes the fuse's clearing I²t without melting.

Inrush peak and time constant
R=Rpath+RNTCIpk=VinRτ=R CR = R_{path} + R_{NTC} \qquad I_{pk} = \frac{V_{in}}{R} \qquad \tau = R\, C
An ideal RC charge from a voltage step, the fastest switch-on there is. A supply that rises more slowly gives less.
Inrush I²t and energy
I2tinrush=∫0∞i2 dt=12 Ipk2 τ=Vin2 C2RE=12 C Vin2I^{2}t_{inrush} = \int_{0}^{\infty} i^{2}\, dt = \frac{1}{2}\, I_{pk}^{2}\, \tau = \frac{V_{in}^{2}\, C}{2R} \qquad E = \frac{1}{2}\, C\, V_{in}^{2}
Littelfuse, Fuseology Design Guide, for an exponential pulse. As much energy is lost in R as C stores.
Current rating
Imin=Iop0.75 kTI_{min} = \frac{I_{op}}{0.75\, k_T}
Fuseology: run the fuse at no more than 75 % of its rating once the temperature re-rating kT at TA is applied. Littelfuse states the 75 % for fuses rated under UL 248-14. Read kT from your fuse's own datasheet: the curves differ by fuse type.
Pulse withstand
I2tmelt≥I2tinrushkpulse(N)I^{2}t_{melt} \geq \frac{I^{2}t_{inrush}}{k_{pulse}(N)}
kpulse is read from the Fuseology pulse chart at 100, 1 000, 10 000 or 100 000 pulses: the first point at or above N (below 100 pulses, that is the 100-pulse point). The chart assumes at least 10 s between pulses. The fraction is the margin, so nothing is added to it. The fractions are the guide's general chart. Where your fuse's datasheet gives its own pulse curve, use it: some sit below the chart.
Trace I²t, Onderdonk
I2ttrace=A233 log⁡10(Tm−TA234+TA+1)A=w tCuπ4 (25.4  μm)2I^{2}t_{trace} = \frac{A^{2}}{33}\, \log_{10}\left(\frac{T_m - T_A}{234 + T_A} + 1\right) \qquad A = \frac{w\, t_{Cu}}{\frac{\pi}{4}\, (25.4\; \mu\t{m})^{2}}
Onderdonk's equation, as given by Brooks, with A in circular mils, temperatures in °C and Tm = 1083 °C, the melting point of copper. It is adiabatic heating of copper whose resistance rises in line with temperature from −234 °C, so Tlim in place of Tm gives the I²t to the laminate limit. The 33 is copper's own: 3.45 MJ/(m³·K) and 1.724 × 10−8 Ω·m at 20 °C give about 33.3.
Fusing current and the trace margin
If(t)=I2ttracetM=I2ttraceI2tclear≥2I_f(t) = \sqrt{\frac{I^{2}t_{trace}}{t}} \qquad M = \frac{I^{2}t_{trace}}{I^{2}t_{clear}} \geq 2
The page shows If at 10 ms and 1 s. M ≥ 2 is a design margin: Onderdonk was not tested on board traces (Brooks). A clearing I²t above the I²t to Tlim reads Check: the copper holds, but passes the laminate limit.
Trace current under the fuse
Icarry=2.1 IratedI_{carry} = 2.1\, I_{rated}
IEC 60127-2, quick-acting F: at 2.1 × Irated the fuse must open within 30 min, and at 1.5 × Irated it must not open within 60 min. A slow overload just under 2.1 × Irated may flow for 30 min or more, so the trace should carry it steadily: size it with Trace Width. For a fuse rated to UL 248-14 instead (at 135 % it opens within 60 min, and at 200 % within 2 min for ratings up to 30 A), 2.1 × Irated is on the safe side. With no fuse entered the page uses Imin.
  • VinV_{in}supply voltage at switch-on, its highest
  • RpathR_{path}charge path resistance: source, fuse, traces and capacitor ESR
  • RNTCR_{NTC}NTC inrush limiter, cold, at TA; 0 if none
  • RRRpath + RNTC
  • CCcapacitance after the fuse
  • Ipk, τI_{pk},\,\tauinrush peak current and time constant
  • EEenergy stored in C, and lost again in R
  • FFthe fuse
  • IopI_{op}highest continuous current through the fuse
  • kTk_Tfuse re-rating at TA, from the fuse datasheet
  • Imin, IratedI_{min},\,I_{rated}the smallest rating to choose; your fuse's rating
  • kpulsek_{pulse}pulse I²t over nominal melting I²t, from the pulse chart at N pulses
  • NNpower-on cycles in the product's life
  • I2tmelt, I2tclearI^{2}t_{melt},\,I^{2}t_{clear}your fuse's nominal melting and clearing I²t
  • AAtrace cross-section, in circular mils
  • w, tCuw,\,t_{Cu}trace width and copper thickness
  • TmT_mmelting point of copper, 1083 °C
  • TAT_Aambient temperature, and the trace's temperature when the fault starts
  • TlimT_{lim}laminate limit, its decomposition temperature Td
  • If, tI_f,\,tfusing current, and the fault time it melts the trace in
  • MMtrace I²t margin
  • IcarryI_{carry}current the trace must carry through a slow overload
تفاصيل إضافية

Three checks on one fuse

The rating comes from the load: at most 75 % of the fuse's rating, after its temperature re-rating. The melting I²t comes from the inrush: every power-on is a pulse, and a fuse that survives one can wear and open after thousands, so the pulse chart allows less of its melting I²t the more pulses there are. The trace comes last: in a short circuit the fuse lets through its clearing I²t, and the narrowest trace in the path must take that without melting.

Limiting the inrush

A larger R lowers the peak and the I²t together. An NTC adds its resistance only while it is cold: hot, a quick off and on again sees far more inrush. A time-lag fuse has more melting I²t than a quick-acting one of the same rating.

Not modelled

The supply's rise time, current limit and cable inductance; the fuse's resistance rising as it heats; the NTC's own heating during the pulse; heat lost from the trace into the board; and power-ons closer together than 10 s.

Rate the fuse for the load, check its melting I²t against the inrush, and make the trace outlast its clearing I²t.
References: Littelfuse, Fuseology Design Guide: the load rule, the pulse I²t, the pulse chart and the temperature re-rating. IEC 60127-2, miniature fuses, the quick-acting F characteristic, as stated in Schurter's 5 × 20 mm quick-acting fuse datasheet. UL 248-14, as summarised in the Fuseology guide. Onderdonk's fusing equation, as given by D. Brooks, Fusing Current: When Traces Melt Without a Trace, from the Standard Handbook for Electrical Engineers. Consult the guide, the standard and your fuse's datasheet themselves for anything that matters. Related: Trace Width, for the current the trace must carry.

إصدار المحرك ⁨1.26.4⁩