Ron is also equal to the ratio Vds/Ids

Reference: Microelectronics Circuit Design 4edition - page 154

Firstly, in the triode region, when Vgs increases, channel charge density also increases, and this will reduce the resistance of the channel for sure, and we get the on-resistance Vgs relationship above, but how about when the mos in saturation, the channel length depends on vds (channel length modulation), i think this will change the on resistance.

So the question is how about the on resistance if the NMOS operating in the saturation region? Can we use the above formula for saturation or what formula?

2. I am confusing on resistance of NMOS with small signal output resistance.

Based on the formula ro = 1/(lamda.id). the channel length modulation make the output resistance smaller rather than infinity.

what is the physics behind that causes small signal output resistance?

Thanks very much!