gain vs noise figure.

is there any relation between gain and noise figure in lna's.
if lna gain is more then its noise figure will be less..
are there any relations .
could you please justify it.
thanks and regards
ram.

Yes, there is a relation between Noise Figure and Gain (actually gm of the transistor).
For CMOS here you can find a good explanation.
http://rfic.eecs.berkeley.edu/~nikne...pdf/lect14.pdf

Your confusion may stem from the fact that a low-noise amplifier is not used or tested alone. It is a front end (or a first stage) of a receiver.
If you have a LNA with say 3 dB noise figure and a low gain (say 10 dB), then in the RECEIVER (system) noise figure, the stages following the LNA will increase the RECEIVER noise figure abothe the 3 dB of LNA alone, by ~10% (due to 10 dB LNA gain). If LNA gain is 20 dB, then this contribution of the following stages will be reduced to 1% only.

The important equation for this was derived by Friis in ~1940, you can find it in any receiver textbook.

For the LNA, you can plot the gain and noise circles on the smith chart. Usually, the max gain point and the min noise point do not occur at the same spot on the smith chart. You can pick somewhere in between these two points to do your impedance match, so that you have tradeoff between noise and gain performances. Sometime to bring the max gain and min noise points closer together on the smith chart, you can try to scale the device size. But if that is not an option, you can change the bias or try tuning an inductor at the emitter/source, assuming it is a common-emitter/common-source amplifier.