MOSFET - Width and Saturation

[yannik33]

Why does a wider MOSFET go into saturation earlyer than a Mosfet that is less wide (I_D vs U_DS)?

 

[dick_freebird]

If you insist that they have the same drain current this is
true. At the same drain current -density- they ought to
enter canonical saturation at the same Vds & Vgs. But
a wider FET needs less Vgs to make the drain current,
and saturation is about the relation of Vds>Vgs so less
Vds as well.

 

[yannik33]

And why is a wider FET early in saturation than a small FET (with the same Drain Current)?

BTW, why does a Wider FET need less VGS to make teh drain current?