You know the inrush on our switches is higher because the power supplies are beefy.
You also need an inverter with a true sin wave at the proper Hz that is rated for computer equipment.
A lot of the inverters you buy to plug into your cigarette lighters are too small and use a modified sin wave which is NOT guaranteed to work well with computer equipment.
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If you are powering a 250 watt switch you would need
at least a 500 watt pure sin wave or a very clean modified sin wave.
If you are powering a 400 watt switch you would need
at least a 1000 watt pure sin wave or a very clean modified sin wave.
Now that is not to say that a 250 watt power inverter that is well built with the ability to deliver Peak Power of 500+ watts for several seconds would not work but cheaper inverters tend to be built and rated at their limit. It is like rating a wireless link at the aggregated throughput, not a lie but is all hype!
The inverter rating is based on its ability to deliver constant power but the Peak Power depends on the cold start up or surge rating if the inverter which is just as importent.
Cheap inverters can not surge very far above their rating and if they do it is for a short duration.
Better inverters use a clean modified sin wave or pure sin wave and can usually surge to 200% or more for several seconds which is referred to as "Peak Power" but an import thing to look at is how long it can hold up at Peak Power. Inverters are rated ay Continuous Power but the Peak Power is important as most all electronics surge at start up usually well over double their ratted watts. Cheaper power supplies are incapable of dealing with spike or peak demands for long. Being able to handle spikes requires larger caps and coils which drive the proves up.