How does simscape calculate the MOSFET gain factor from the datasheet values?

Simscape calculates the MOSfet gain factor k with the value R_DS(on) and V_GS for R_DS(on). I don't get how it comes to the formula.

I tried some different equations and tested if it is true by using another MOSFET where I entered directly my calculated gain. But no matter what I do, I always get different results in my test circuit for those MOSFETs. The test circuit is just Vgs, Vds + Mosfet + resistor.

Does anybody know how they calculate the gain?

Apart from that I am also wondering why the current Id(R_DS(on)) is used for calculating the output resistance. What is this needed for, if the threshold-based model is based on the Schiman-Hodges equations?

Thanks!

Answer 1

[David John]

The gain is calculated by solving the Schichmann-Hodges equations for the gain given the Rds at a particular Vgs and Id. Specifying all of these points removes any ambiguity about where the Rds is defined (i.e., is it the slope at small Vds or is it the slope somewhere higher up the characteristic). In our case, it is the slope at a particular point (which is also why we need more data to specify exactly where the Rds is defined...it is not just a constant).

Note, too, that the intrinsic Rds for this calculation (i.e., for just the channel) must have the series source and drain resistances removed from the gain computation as well. This is all done internally to the block.