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

[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?

Thanks for your help.

[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]

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

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.

[Nusa]

Don't forget that all those numbers are usually at 25C. Temperature changes the equation. The temperature inside the box the fuse is located is likely above ambient! And ambient isn't a fixed value either.

I've actually run into cases where the fuse was specced too close to the line, but it worked most of the time. But once a really hot day happened, it would blow after a couple hours.

[T_guttata]

Thanks for your help. Well, in my case I need a fuse, which will allow high current pulses in the range of ms (5-10A) but will have the lowest continuous rating possible. Thats why I thought I need a slow fuse. Is it the correct fuse type, or are there alternatives?

[SeanB]

Don't forget that all those numbers are usually at 25C. Temperature changes the equation. The temperature inside the box the fuse is located is likely above ambient! And ambient isn't a fixed value either.

I've actually run into cases where the fuse was specced too close to the line, but it worked most of the time. But once a really hot day happened, it would blow after a couple hours.

Had the same with a breaker, it was running at slightly above current rating, but if the load was applied for less than a certain time, it would not trip. Exceed this time by 5 seconds and it would reliably trip. I now have, forever as part of a installation book, a laminated piece of cardboard, that I grabbed from one of the boxes, that proposed a modification. Signed off by a PE at their local office as an approved modification to the site itself.  This is for a lift (elevator for those in the USA), where it would trip on overcurrent if you went from ground floor to the top, but not if you did a single stop anywhere short of that, just that 5 seconds of extra running would trip the breaker, with the car 1m short of the landing. Modification was to move 1 wire to another terminal on the 3 phase breaker, and add a single wire link, as they were using a 3 phase approved breaker with the one pole as part of the shaft safety circuit, instead of a dedicated and expensive overcurrent trip, that is notoriously more prone to failure, and is also not going to work without running the current through all 3 legs, to defeat the phase loss detection.

[golden_labels]

T_guttata: what’s the nature of those pulses? Is that a single event or are they repetitive?

A slow fuse is the right choice. But if it’s for example inrush current surge, you may also think about limiting the current in the first place by the means of putting an NTC in series with it.

[T_guttata]

It's quickly charging a cap. It will be repetitive, but with a very low duty cycle (<1%) I don't want to limit current too much, because I want to charge the cap fast. Currently it's not current controlled, therefore there will be a high peak, but it decreases rapidly.

[bdunham7]

It's quickly charging a cap. It will be repetitive, but with a very low duty cycle (<1%) I don't want to limit current too much, because I want to charge the cap fast. Currently it's not current controlled, therefore there will be a high peak, but it decreases rapidly.

What you propose would be outside the data on the datasheet.  You can try extrapolating at your own risk.  Just do the math and realize that if you have a current of 20X the rating, you are generating 400X the heat.  So at a 1% duty cycle, you are generating heat equivalent to 4X the rating, or about the same as a continuous 1 amp would generate. 

[T_guttata]

It's not that simple, because of the shape of the charge curve of a capacitor.

According to http://www.olino.org/blog/us/articles/2006/11/22/charge-efficiency-capacitor, charging a capacitor with a constant voltage source has an efficiency of 50% and is independant on the ESR.

If I take a 1000 uF cap and charge it to 30V, 1/2CV^2 = 0.45J is dumped into the series resistor.

According to the datasheet of the fuse, 0.375A is the rated current. With the fuse resistance of 0.6208 Ohm, heat dissipation inside the fuse will be 0.375*0.375*0.6208=0.087 W.

One charging cycle of the cap every 5.6s (0.18Hz) will generate the same amount of heat inside the fuse as the rated current. Is this correct?

[Alti]

Is this correct?

Not really because the resistance of the link varies significantly, especially when it is getting red hot.

[T_guttata]

If the fuse is used at rated current, it will certainly not get red hot?

[Alti]

If the fuse is used at rated current, it will certainly not get red hot?

100 % of Current Rating -> 4 hours, min

If it melts at rated current then what temperature can that be at?

[bdunham7]

One charging cycle of the cap every 5.6s (0.18Hz) will generate the same amount of heat inside the fuse as the rated current. Is this correct?

Your idea to do an more detailed modeling is the right way to go, but you don't have enough information.  If the resistance of the fuse is constant and is what you say it is, and the capacitor has negligible ESR and the voltage source has a very low impedance, then this is correct.  However, the peak current will be over 50 amps and I would guess that the fuse would blow on the first pulse.  The rule that charging a capacitor dissipates half the energy in series resistance is true, but it includes ALL of the series resistance.  If you really need to use such a small fuse, you should use a larger series resistance, whatever your intended use can tolerate.  10 to 100 ohms maybe?

[T_guttata]

Well, @ 10 Ohm charging of the cap takes a bit too long. But I could restrict the initial current to 10A. Actually a constant current source would be better for charging a cap anyway. Then you don't have huge peaks, and efficiency can bi >50%. But I could not find a boost converter yet which is current controlled. Designing my own is not simple as I'm not an electrical engineer.

I will get some fuses see what happens :-)

[lovatt]

The full formula for the time to fuse is:

(k_i2t / k_i²) ln(i² / ((i - k_i)(i + k_i)))

Where k_i2t is the i²t rating and k_i current rating of the fuse.

The formula is derived for a constant current, if the fuse time of a repetitive waveform is required then using the RMS will be approximately correct provided that the period is a lot less, say factor of 4 less, than the time constant, k_i2t / k_i².

Note

• The graphs given in the fuse data are often more accurate than the above formula.
• The above formula tends to k_i2t / k_i² as i tends to infinity.

.

[Vovk_Z]

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

I^2 rating is a rating to blow, so it is not about rated current but about higher-than-rated current.

[Vovk_Z]

If the fuse is used at rated current, it will certainly not get red hot?

No, rated current is the current at which a protective device (all of them typically) has to conduct current and doesn't blow so it mustn't be red hot.

[Vovk_Z]

If it melts at rated current then what temperature can that be at?

It mustn't melt at rated current until ambient temperature is 20-25 C.

[Siwastaja]

If fast capacitor charge is a priority, then you just go for a switch mode constant current circuit. At the same time, you'll get the efficiency up from 50%.

Although, if the cap is rather small (such as 30V, 1000uF), then it's probably not worth the trouble. One middle ground solution is to provide two switched charge paths instead of one, with one having more series resistance than the other. Switch on the more resistive path first, wait until voltage is at maybe 50%, then switch on the second path. Efficiency is still just 50%, but now you have some control over the current without making the last drops take forever.

[golden_labels]

You folks do realize, you are answering an already answered 2021 thread?

[Siwastaja]

You folks do realize, you are answering an already answered 2021 thread?

No we don't. This happens all the time:
* Spambot bypasses poor registration security
* Spambot picks random old thread and posts something
* Only the spambot sees the "warning: you are replying to an old thread"
* Others miss this fact since the warning is only shown once

The root fix would be to increase security of forum registration (better captchas, etc.) Another improvement would be to make that "warning: you are replying to an old thread" message appear for 3-4, maybe 5 consecutive messages, after which the thread would be considered active again.

[Alti]

If the fuse is used at rated current, it will certainly not get red hot?

100 % of Current Rating -> 4 hours, min

If it melts at rated current then what temperature can that be at?

If it melts at rated current then what temperature can that be at?

It mustn't melt at rated current until ambient temperature is 20-25 C.

Hi. Did you bother opening the pdf from opening post?

First row in in "Clearing Time Characteristics" at ambient temperature and rated current, shows minimum clearing time as 4 hours, while maximum clearing time is not specified (it is not being tested).

Your response: this fuse must not melt at rated current.

Then contact Bourns and tell them they make lousy fuses as some burn in fifth hour at rated current.

I am curious what would have been their answer.

[Siwastaja]

First row in in "Clearing Time Characteristics" at ambient temperature and rated current, shows minimum clearing time as 4 hours, while maximum clearing time is not specified (it is not being tested).

That's kinda weird way to rate fuses, though. I think it's more usual to guarantee the fuse never blows at rated current.

The problem with this Bourns part is, the provided data does not allow the part to be designed in at all. There is no tabulated rating to tell the designer which current the fuse can be used at. Curves are only typical. Tabulated values show min/max, but the current rating where Min time is infinite (or years) is missing.

This is a good reminder to everyone: always read the datasheets instead of assuming. Conventions in electronics are weak. But this also teaches us: while you really can't assume, you have to assume anyway, because the data provided by manufacturer is not sufficient to use the product.

[Alti]

That's kinda weird way to rate fuses, though. I think it's more usual to guarantee the fuse never blows at rated current.

No, it is not more usual.

Traditionally Old World characterizes fuses that never trip at rated current while 'merican designs are not guaranteed to operate at rated current indefinitely. Those Bourns fuses from opening post are made to comply with UL 248-14 standard so it would have been surprising if these "guaranteed the fuse never blows at rated current". This "weirdness" is not a standard but just a tradition from some Edison era. That is one of the reasons you cannot replace 1A 'merican fuse with 1A IEC fuse - fuse standards do not overlap.

If you want more "weirdness" - Littelfuse Fuseology Selection Guide.

According to the IEC 60127 Standard, a one ampere-rated fuse can be operated at one ampere. A one ampere-rated fuse made to UL/CSA/ANCE 248-14 should not be operated at more than .75 ampere (25% derated — See RERATING section).

Anyway, weirdness or not weirdness - that is a separate subject.
Main problem is that if a datasheet does not state some property holds, then it simply does not.
This is a generic rule, nothing specific to fuses.

[Vovk_Z]

Hi. Did you bother opening the pdf from opening post?

First row in in "Clearing Time Characteristics" at ambient temperature and rated current, shows minimum clearing time as 4 hours, while maximum clearing time is not specified (it is not being tested).
Your response: this fuse must not melt at rated current.
Then contact Bourns and tell them they make lousy fuses as some burn in fifth hour at rated current.

Hi! I haven't seen this exact pdf. I just say typical glass fuse behavior (as I know it). Possibly something changed in different types of them. I don't want to dispute with Bourns.  I wish they were more specific about 100% behaviour but ok.

[Nusa]

But one must remember fuses are a safety devices, and the value picked should be higher than the expected normal draw of the device in question, but low enough that they'll blow before you get flames. Anyone who sizes the fuse to be exactly the same as the expected draw of the device has literally designed in a problem. Especially if they haven't tested in worst possible conditions (high ambient, sagging/over voltage, heavy duty use, etc).

[Siwastaja]

Anyone who sizes the fuse to be exactly the same as the expected draw of the device has literally designed in a problem.

As Alti explained, clearly in the US. of A, yes, which I was not aware of!

As per IEC standards, one can design a fuse to carry nominal rated current indefinitely - no problem.

This is just an arbitrary choice someone has made. Both ways of thinking are valid, but the USA way would require the fuse manufacturer to separately specify the current which can be used (equivalent to the European In, just under different name), and as the Bourns example shows, they don't always bother doing that (and then you need to assume some "derating" factor)! With our European fuses, this is simply the rated current, so one number less to specify.

Note this has nothing to do with fuse construction itself, curve shape or anything like that. Just a maybe ~25% discrepancy in nominal rating.

What to call "nominal" is always a tad problematic. For example, tantalum capacitor manufacturers define nominal voltage as something which will destroy the product in short time, so that significant derating is always needed, while aluminum electrolytic capacitor manufacturers chose nominal voltage as something that the part can be exposed to indefinitely.

[Nusa]

Being aware of the relevant standard is beside my point, although of course you should read the datasheet. My point is that you should always leave some overhead. If the question of how long it will last at the exact rating becomes important, you've failed at fuse selection and made product that may not be reliable. Which ends up costing money and reputation on the customer service side.

[Siwastaja]

Being aware of the relevant standard is beside my point, although of course you should read the datasheet. My point is that you should always leave some overhead. If the question of how long it will last at the exact rating becomes important, you've failed at fuse selection and made product that may not be reliable. Which ends up costing money and reputation on the customer service side.

I prefer the mindset of doing actual worst-case analysis, instead of leaving "some margin", but sure, the "some margin" way is used when there is not enough time, expertise or information to do proper worst-case analysis. It's important to note the "some margin" way is more risky, and failures happen when the assumed amount of derating was not sufficient.

In actual reality, combination of best effort worst case analysis and some additional derating is needed.

But IEC-style rated fuses do not need any extra derating. They are fine when used at In, but of course then you make sure you don't exceed In.

I think this is an important distinction. You need to understand why you are doing things. Some components require extra derating, some do not. This goes in addition to the derating you need to add due to the uncertainties of the rest of the circuit (e.g., tolerances of voltage supplies, load currents, etc.), and your generic "safety margin" which you apply as a last step. If you get too comfortable just adding a decent amount of generic margin and call it a day, components which require a lot of extra derating could catch you off guard.

[Nusa]

Certainly you should apply intelligence when selecting overhead. What I said is that not having any overhead is a problem. Because there's really no such thing as walking the line in real life...you're either under it or over it, not exactly on it.

[Alti]

But IEC-style rated fuses do not need any extra derating. They are fine when used at In, but of course then you make sure you don't exceed In.

If we talk about IEC 60127-4 (closest to UL 248-14 of Bourns from opening post) then test is specified at 1.25In for 1h min., in contrast to  1In for 4h min. for 'merican UL 248-14.

If you know that silver link melts at 960oC and it is more than certain a fuse is designed to barely survive that at 1.25In for 1h, keeping it at 600oC even for a day smells like asking for trouble. Does it guarantee "infinite" operation at 1In? I doubt it. It looks like it is further from the border line than 'merican but in practical application when you include elevated ambient temperature and thermal cycling, I wouldn't hang 1A on a IEC 60127-4 fuse with In=1A for "infinitely long". These are not optimized for dealing with 1In but for small size and decent reaction for short-circuits (i2t).


Then there are serious IEC 60269 fuses that are well known from industrial applications but are also quite common in residential. The most popular miniature are IEC 60127-2 that some call "glass fuses". Both of those standards are characterized at 1.5In for 1h minimum.

[Siwastaja]

Then there are serious IEC 60269 fuses that are well known from industrial applications but are also quite common in residential. The most popular miniature are IEC 60127-2 that some call "glass fuses". Both of those standards are characterized at 1.5In for 1h minimum.

I am thinking about these; they come in variety of form factors and are used extensively in households, industrial and also equipment. Google image searchs shows the typical form factors: https://www.google.com/search?q=IEC+60269&source=lnms&tbm=isch

These fuses are routinely used at In. Grey area is between In and 1.5*In.

[Vovk_Z]

Does it guarantee "infinite" operation at 1In? I doubt it. It looks like it is further from the border line than 'merican but in practical application when you include elevated ambient temperature and thermal cycling, I wouldn't hang 1A on a IEC 60127-4 fuse with In=1A for "infinitely long".

As for me, I haven't seen fuses used with In actual current. We usually choose them as 1.5-2.0x from the working current because we have to deal with inrush transients.