rogger123, with respect to your last post:
In the extreme case:
Let us leave any gate voltage off for a moment. We have a source depletion region and drain depletion region. If Vds is increased beyond Vds (sat), what we have done is increased the size of the drain depletion region through the repulsive effects of electric potential. Go further and apply enough voltage and the depletion regions overlap and allow current to "punch through" from source to drain -- inversion layer or not. Drain current becomes independent of gate voltage.
Back up to a scenario short of punch through but Vds>Vds(sat). The drain terminal location is still fixed, but the effective drain depletion region has grown. The threshold voltage lowers because source and drain distances have decreased. There is a small linear increase in local resistance between drain contact and the shorter inversion channel that is created once the gate voltage is applied -- due to the distance across the [now bigger] well depletion region travelled -- but, since drain current is a square function of the difference between Vgs and Vt, the drain current increases faster than the increased local drain resistance decreases current flow. Repeated, drain current increases faster than the local resistance impedes it.
Local resistance between drain and channel may increase linearly, but total output resistance lowers by a square relationship.
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