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When datasheets lists(MAX9744) that the normal operating temp are b/w -40 c to 85 c
but the case temp should not be up above 165 c
what are they suggesting.

How come an IC work if its case temp gets to 100 c and work but if the ambient temp gets to 90 c, which the IC could also sense and then not work.

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The highest CASE temperature mentioned is in a diagram on page 9 - and max is about 110 C.

The highest device temperature quoted, apart from soldering temperaures is 150 C at the top of page 2 - and this is JUNCTION temperature.

Ambient temperatures are relevant but not under designer's control.

The JUNCTION is the actual IC core, inside the chip.
Junction temperature relative to case is determined by power input and Rjc = thermal resistance junction to case. BUT the datasheet seems to be bad in this respect and give only Rja (shown as Theta_ja) = resistance junction to air. You can see by using Rja whether you need a heatsink and whether that the datasheet should give Rjc. Looking at the figures:

Rja with 2 layer board = 27 C/W.
Device is said to be 93% efficient.
At 20W in 7% is dissipated at heat in IC = 1.4W.
At 27 C/w IC junction will rise above air by 27 C/W x 1.4 W ~+38 C rise.
Tj max = 150 C, so allowable ambient / air / board temperature is 150C - 38 = 112C.
If we use the 37 C/W Rja for single layer board we get differential rise junction to air of
37 x 1.4W =~ 52C rise over Tair, and max air/board temp of 150 - 52 = 98C.

Gven the various assumptions made, 98C is close to the specified 85C max - so we can see why they specify it. At 85C Tboard you can r un the IC at 20W power in and somewhat worse than 93% efficient and not (quite) exceed the 150C allowed max junction temperature.

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Devices that consume a non-negligible amount of power are subject to heating - aftr all, the power consumed very often just converts to heat. Therefore, the temperature of the die (and therefore the case) can be significantly higher than the ambient temperature. You can easily observe it with PCs, where CPU temperatures can go as high as 100°C also outside of the oven :)

The operation limit of 85°C refers instead to the ambient temperature, and can be due to the fact that over the temperature the heat dissipation may not be sufficient to guarantee operation.

Regarding the specific device, it can handle 20W and has an efficiency of around 90% - therefore it will dissipate about 2W. If this power is not properly dissipated, it will overheat the amplifier.

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165°C is the typical die temperature at which the amplifier enters thermal shutdown protection to prevent immediate destruction of the chip in the event of a fault. The chip will typically exit thermal shutdown at 150°C.

It is not a normal operating temperature. As they say "Most applications should never enter thermal shutdown".

Note that it is in excess of the absolute maximum junction temperature rating of 150°C. If you want the part to be reliable long-term, you should not allow the junction temperature to go anywhere near that high.

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