Why Boardband amplifier has high noise figure

maybe it's because the noise (thermal, white, gaussian) is directly proportional to the system's bandwidth

Because the Board is too wide?

Bullocks. The reason why most broadband amplifiers have high noise figure is because they consist a one or two-stage amplifier with resistive feedback applied around them. These resistors inject additional noise into the amplifier, which is substantially higher than that of a narrowband LNA, but pretty constant over frequency.

And then, what he must know is that resistors are noise sources. There are other topologies, as distributed amplifiers, balanced for example, that uses less resistors, and therefore, the noise figure is low.
Also, It is important the technology of the active device , for example, an amplifier using bipolar transistors ,generally, will have more NF than other using a PHEMT.
No bullocks.

If you see the equation
Pn=kt(delta)f
from this equation you can see that
the noise power increases with bandwidth thai is pn increases with delta F.
there fore noise figure increses.
Check book by Gonzalez on Amplifiers.

I hope this helps you & clear doubt

Abhishekabs

Because it is not easy to match, noise match and gain match.