Your whole concept is wrong. Throw away those kinda thoughts, choosing amp is not based on the built-in amplification of your Headunit (HU).
Now, if your HU states 45w x 4, it means it has a built-in amplifier of 45w P.M.P.O (Max Power) per channel. P.M.P.O is the jargon of Peak Momentarily Power Output, which is the peak-to-peak measurement of a sine-wave such as alternating currents, or voltage.
In reality, there is no such thing as Perfect. Therefore, P.M.P.O is not really suitable to be used to measure the power output of an amplifier. RMS, or Root-Mean-Square is the "average" used to calculate a sine-wave.
Why not calculate the Mean/Average, instead Root-Mean-Square?
Example, in a sine-wave graph;
http://i6.photobucket.com/albums/y205/mxploit/Sine-Wave.jpg
The average (mean) of these 10 numbers;
[ 2+4+6+4+2+(-2)+(-4)+(-6)+(-4)+(-2) ] / 10 = 0 or spelled as Z-E-R-O.
The root-mean-square (RMS) value can be obtained by squaring each of the values and taking the average of these squared values, then get the square-root of it.
Sqrt { [ (2²)+(4²)+(6²)+(4²)+(2²)+(-2²)+(-4²)+(-6²)+(-4²)+(-2²) ] / 10 } = 3.899
But why sine-wave?
Our car current alternates....huh? why?..doesn't your car have something called an ALTERNATOR? Besides, the voltage reading is always fluctuating. It has a patent of a wave. Therefore..it's st*pid to be calculating the average.
So, what kinda power output should I expect from an amplifier?
It doesn't matter if your amp has a higher RMS Power output than your drivers/speaker's nominal power handling (RMS), what matters is the Gain control / Sensitivity setting. NOT Power!! Overpowering your drivers is acceptable but not to the extent of being excessive or extreme. This may cause your speaker's voice coil to burn due to excessive heat or mechanical stress. Besides, you will also get a higher-distortion level.
So, if my amp has a lower power output than my drivers, what will happen?
In other words, Underpowering your speakers doesn't cause any harm. It will not stress the drivers but will not extract its full potential. Unsatisfactory performance is the end result.
I hope this help solve your confusion on the 'POWER' issue.
