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Best of luck, rhd! I want to see this circuit finished
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The power or heat dissipated in a MOSFET is the drain current squared multiplied by the Resistance between the source and the drain in conduction, whether that is in the ohmic part of the conduction curve or the saturation part of the conduction curve.
The mosfet package is a SOT323 which is VERY small. it won't be able to dissipate any amount of heat.
Another thing is that there could be enough resistance in the wiring to the FET to cause a voltage drop and
bring it out of saturation. This could be fixed by adding a capacitor near the FET. Good luck, I hope you
get it working.
rhd, if you don't have access to an oscilloscope, you might be able to get a picture of the current at the time of actuation. I have 3 multimeters left, a Beckman Tech 310, a Triplett 9015, and a Mastech MS8268. The last of these meters has a hold function which you can use on any of the voltage or current settings. If you set it up to measure the current and push the hold function, it will measure and hold the current level at the moment you turn the unit on. That is the only other way I can think of to measure the current at the instant it begins to flow through your MOSFET. If you have a meter like this one, consider doing this.
rhd: I'm not really buying the thermal runaway problem either. The current path from drain to source is relatively robust. The gate is where damage usually occurs for assuming no short.
A more likely cause is some kind of effect on the gate: maybe some oscillations or discharge into the gate. Maybe it doesn't like your DC switch, or maybe some noise is causing oscillations. Can you take one of your modules and hack in a resistor between the gate and the switch? Maybe even a cap to smooth things out, and/or a protection diode? Protect that gate!