In the square-law equations you use (VDS - VDS,sat) while other books use

only VDS. Would you comment on the difference?


Yes, in Eq. (6.42) we derived, for saturation operation,


ID = [(KP/2)(W/L)(VGS - VTHN)2](1 + λ(VDS - VDS,sat))


and for the triode region, Eq. (6.36)


ID = (KP)(W/L)[(VGS - VTHN)VDS - V 2DS/2]


It's important to note that at the border between the triode and saturation

regions, where VDS = VDS,sat = VGS - VTHN, these equations are equal and

given by


ID = ID,sat = [(KP/2)(W/L)(VGS - VTHN)2]



Okay, now as you have indicated others remove the VDS,sat  and use simply


ID = [(KP/2)(W/L)(VGS - VTHN)2](1 + λVDS)


which is the implementation also used in the Level 1 SPICE model.


So here's the rub, if you don't use VDS,sat then there is a discontinuity

at the border of the triode and saturation regions when VDS = VDS,sat. To

avoid this discontinuity you have to also multiply the equation for

operation in the triode region by (1 + λVDS) or


ID = (KPW/L)[(VGS - VTHN) VDS - V 2DS/2](1 + λVDS)


This is often not mentioned or indicated by other authors, but, again it is what

is used in the level 1 MOSFET SPICE model.


See, also, the bottom of page 146 in the third edition.