Teensy fuse values

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0.35A current limit device on LC and 0.5A on 3.x - based on I2T or what?

Thanks for your support of the Empire.
No idea what i2t is but the 0.5A limit is likely the result of the usual current limits for Usb unless the two devices handshake and decide to go higher (aside from the apple shortcut documented by Adafruit)
The USB can only be expected to provide up to 500mA, that is the primary limit.

The other underlying issue is the on chip power regulation and generation capabilities. The Processor chips take the incoming power as I understand it and generate the power for their use internally as well as their I/O & support circuitry. That is where the lower mA numbers come so allowing for more power would just make more smoke if you ever used that much - and the LC can utilize less power overall, so giving it a lower fuse threshold just allows it to safely shutdown when it starts routing more power than that, perhaps before the smoke starts.
Before talking about the design choices, I'd like to explain these "fuse" parts are actually just resistors that change value. They're not real fuses. They don't "blow" or somehow stop current flow.

Internally, the part uses a ceramic or polymer that has a high thermal expansion rate. Metal particles are suspended inside the ceramic. When it gets hot, due to high current flow, the material heats up and expands. As it expands, gaps form between the conductive particles, causing the resistance to increase.

The fault condition is still a continuous current flow. The "fuse" merely adds a resistor in series with the circuit. The current stabilizes at some value that depends on the resistance of the "fuse" at higher temperature (the current which will keep it hot), and whatever short or fault is allowing so much current.

The current rating is NOT the "trip" point. It's the maximum current, at room temperature, which will NOT get the part into its temperature range where the resistance increases very rapidly. These aren't highly precise devices. They're temperature dependent, so there's a substantial margin built in to the specs. It takes quite a bit more current to get into the limiting region.

On Teensy-LC, a slightly lower value was used for 2 reasons. First, there's no ground plane, and the power traces aren't wide due to limited routing space on the 2 layer PCB. I was concerned the 500 mA rating, plus margin, plus extra current at colder temperature would end up being too much. Second, this value in the larger 0805 size was less expensive... and LC tries to reduce the cost as much as possible but still give a good experience.

I know some people are very focused on numerical specs. For anyone thinking that way about PTC "fuses", I want to emphasize again the very imprecise nature of these devices. They're not a carefully calibrated, highly accurate, on-off current limiting device. They're really just a chunk of thermally expanding material with suspended conductive particles.
Just to add to Pauls comment. The PTC 'fuses' will only protect you from real short circuits. I do not know the type Paul used, but typically they will react very fast when drawing 10 times the nominal current, but at 3 times the nominal current it will typically take over a minute to trip. A real fuse will have much better tolerances and the trip point will be much closer to the nominal rating.
I notice on teensy3.2 that the fuse is connected between USB and VIN, but on teensy3.5 and > that VIN is connected directly to USB. Why does this difference exist?
No idea what i2t is but the 0.5A limit is likely the result of the usual current limits for Usb unless the two devices handshake and decide to go higher (aside from the apple shortcut documented by Adafruit)

I-squared-t is a fuse rating - I-squared is proportional to the power dissipated, so I-squared-t is a measure of the energy
needed to melt the fuse in terms that the rest of the circuit can understand (noone cares what the actual energy is, as
that depends on the resistance of the fuse which usually isn't something you care about).

So a 1A fuse with a 16A^2s rating would blow in one second at 4A, or perhaps 4 seconds at 2A. Its only really
meaningful if the current is much larger than the current rating. That 1A fuse won't blow in 16s at 1A, for instance!

The ratio of I2t rating to the current rating squared is what determines if a fuse is fast-blow, slow-blow or normal. Slow-blow
fuses have extra thermal mass (a blob in the middle of the wire, or a different alloy), fast-blow are often spring-loaded.

Much more detailed and correct information here: https://www.littelfuse.com/~/media/automotive/catalogs/littelfuse_fuseology.pdf
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