how to manage psu for the car amplifier? with 5200 1943?

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Look at any commercial car power amp. - They all use switchmode power supplies if they deliver more than about 15W RMS. 'Sounds good but switchmode is not the sort of PSU you jump into designing and building without considerable experience. Audio is a piece of cake compared to efficient, reliable (and safe) switchmode supplies.

The better solution is to use appropriate prebuilt 12V supply SMPS units of either single or dual polarity to suit your amplifier design. There are thousands of products and suppliers of these all over the net and Ebay.
https://en.wikipedia.org/wiki/Switched-mode_power_supply
 
It's not that simple if you're thinking of designing an SMPS for a car amp by yourself - at least having no experience. Not only that a car is a desaster in terms of EMC - which means you have to do careful filtering - but also you have to consider a highly dynamic supply voltage. In normal operation (engine running, bat ok) you face ~14VDC, but it can easily go up to 16-17VDC or down to 7V (ISO start-cycle or in engine start-stopp-mode). You would need at least a boost+inverter design but you have to deal with enormous current.

I would double the recommendation to go for a SMPS that is readily available and designed, built and tested for automotive use. In fact, I would never consider to build a high power car amp on my own, though I'm into DIY audio and I know vehicle electrics very well ;)

BR,
Holgi

Edit: take a look at Rod Elliot's design, a nice introduction to car SMPS.
 
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