Upgrading audio system.

it should work, but in a small car it seems like overkill. most quality aftermarket headunits will power some decent door speakers as loud as you need, if your not trying to annoy other drivers or cause the whole car to rattle and sound like garbage. by the time you add the sub and some sound dampening material, it should sound great and be loud enough to pleasantly vibrate the rear view mirror.

 

Without draining the battery, the Prius inverter can provide about 800W of 12V power continuously, after subtracting power for running all of the ECUs, etc. As power amps are about 50% efficient (class AB), this means you can deliver about 400W RMS to your speakers continuously without draining the battery. Assuming 820 Max translates to 410W RMS, which is typical for high end gear, it shouldn't be a problem. Only time you would run into problems is if you were maxing out your power draw (e.g. driving in the rain with lights and wipers on, stereo at max volume without distorting, A/C at max, etc.). In that situation you would just need to turn down your stereo a couple of notches (could still be playing really loud, just a few notches down from maximum).

I agree that getting separate amplifiers for speakers isn't needed for most people, as when you use a subwoofer, you can take the bass out of the speakers and therefore you can drive the midranges "harder" (On a typical car audio install with a sub, the bass requires ~90% of the power). Instead of using an active crossover, you may consider going passive instead. On my system, I wired some capacitors in series with my speakers to roll off the bass starting at 90Hz, and then my sub is crossed at 80Hz. IIRC I used 220uF capacitors (there are easy to use online calculators, I bought my capacitors at parts express). Or you can get a headunit with a digital high pass crossover for the speakers and a low pass output for your sub. I think it's worth getting a sub, headunit, and new speakers first and see if you're satisfied. If you aren't, you can add the additional amps and crossovers.

 

Not sure if this helps but I'm running a RockFord Fosgate 1000w mono amp as well as the factory JBL amp


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