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How to read the fuse charts (I^2t)

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T_guttata:
Hi

Could anyone help me out on how to read the data sheet of fuses:

https://www.bourns.com/docs/product-datasheets/sf-2410hi-t.pdf?sfvrsn=4d8a79f6_6

A fuse with a rated current of 0.5A has an I^2t of 0.495. How can I determine the maximum peak currents (and time) the fuse will alow without triggering? What will the max current be for a pulse width of 10ms? 50ms?

cortex_m0:
The i2t rating is essentially defining a curve between current and time to blow.

i2t = 0.495

So you can pick i, or t, and solve. You proposed t = 50ms in your question.
i2(.05 s) = 0.495
i = 3.14A

If you want to validate that, go to the charts on page 2. Find the "Average Pre-Arcing Time vs Current" chart. Follow the curve for the 500mA part to its crossing of 3.14A. You'll find that the "pre-arcing time" is approx 50ms.

Note that fuses are far from ideal components. Dave did a video recently on what happens if you run a fuse slightly higher than its rated current continuously.

T_guttata:
But if I solve for the rated current of 0.5A, I get only t~2s?

bdunham7:

--- Quote from: T_guttata on August 04, 2021, 04:47:23 am ---But if I solve for the rated current of 0.5A, I get only t~2s?

--- End quote ---

You'll see that the **** note tells you that the I2T number is at 10X rated current, so 5 amps.  The I2T equation will roughly hold at currents higher than this, but since the fuse dissipates heat it obviously can't work for low currents.  If you used your method and solved for 50mA, you'd get t~200 seconds, and clearly that isn't right...

golden_labels:
10ms is outside of the specs for this fuse. Of course there may be some current which will cause it to blow in 10ms, but it’s not guaranteed by the datasheet. So I will skip that.

Fuses are not precision devices. Dave’s video shows that experimentally, but you can derive that yourself from the clearing time table on page 1. See the attachment for how you should visualize the table. Note that the time (vertical) axis is logarithmic. The green indicators are values from the table. The dark reddish nebulous blob is a ballpark estimate of where the fuse blows according to the datasheet. A bit over 100% the rated current is between a minute and a week, I would say. A bit over ampere for a 500mA fuse and you can’t tell if it blows in half a second or a minute.

50ms, you ask? Find the 50ms mark on the vertical axis, look to the right. My eye tells me it’s somewhere between 3.5× to 8× rated current (1.75–4A). Though above 8× there be dragons and those dragons seem to also sit comfortably around the 50ms line.

Now, you asked about I²t. Fuses are not reacting to current. Fuses are reacting to heat. The heat comes from energy dumped into them. As it happens, the power lost in a fuse is more or less proportional to the current it passes and the total energy dumped into it is proportional to the integral of power over time. The energy will be the same no matter if it’s low power over long time or much power over short time. And, since power is proportional to current through the fuse, instead of using joules, A²s are used for convenience, but expressing the very same concept.

At this point you may wish to calculate I²t for e.g. 50ms overcurrent of 2A. You get (2A)²·0.05s = 0.2A²s, which is within the allowed range. But then also (0.49A)²·1000s gives 240A²s, which is clearly above the rated I²t and that is a contradiction, as it’s 490mA — below fuse’s rated current. Here comes another factor. The fuse can cool down. If it cools down fast enough, it will not blow. Below the rated 500mA it simply dumps heat at a rate high enough that it can remove heat produced by the current, leading to inifnitely long operation. The precise physical models behind that are Complicated™. But fortunately you don’t need to calculate it. On page 2 you have a I2t vs time chart. Calculate I²t of the circuit, find it in the chart, follow the vertical line. You are allowed to dump the amount of energy proportional to that I²t as long as you do that over time expressed on the horizontal axis, if your vertical line is below the curve for a fuse. Our 240A²s for 490mA over 1000s is just a bit under the cuve for the 500mA model. Hence the fuse can handle that. It may feel weird to first multiply by time and then effectively divide by it, instead of simply having a chart for current, but remember that what I²t expresses is total energy dumped, not simply constant current over time. The shape of the current surge may vary and I²t must be calculated for that particular situation.

Then there come three more issues. First: the chart indicates the mean value. Fuses are not precise devices. Being just under the curve on that chart is not safe. Have some safety margin. Second: that chart tells you in which conditions the fuse is expected to survive surges. Not when it is expected to blow. It may as well survive way more than indicated in the chart. Third: the chart is for the time it takes for the fuse to start melting. Unlike the table on page 1, which gives total time the fuse need to completely break the circuit, this chart does not take into account potential arcing.

In othe words: the I²t charts and values indicate the safe operating area for the fuse in temporary, expected overcurrent event. They do not provide information on how fast fuse blows. Which is why you can’t derive answer for your question from them.