How to determine Vth, Kn and delta from NMOS datasheet

Given this two graphs below, how do I determine Vth, Kn and delta from this?

I used this formula's so far:

The graphs are taken from the datasheet of Supertex VN10K

Can someone please help me in the right direction?

(1) I used two Id(non-sat) equations to determine Vtn as 2.5V. When replacing this into one of the two equations I get 0*Kn = Id(non-sat)... That's impossible, right? Isn't Vtn a constant value for the mosfet?

(2) When replacing it into a new Id(non-sat) equation I get 115mA/V^2... When I substitue Kn and Vtn into a Id(sat) equation I get delta as a negative value...

Am I doing anything wrong? Is it possible for delta to have a negative value?

Thanks!

Answer

First observation: Vth is not accurately specified as you can see in the datasheet; this because the threshold voltage is depending heavily from temperature, and there is poor interest in making it precise. In that datasheet it's specified to be between 0.8 and 2.5V.

In your case, it's unlikely that it's 2.5V, as you can see that there is a plot for Vgs = 2V, that would be near to 0 if below threshold.

You could obtain approximate values of Vth and Kn taking some values of IDsat for different Vgs and trying to find the relationship (one is responsible for the linear increase while the other for the quadratic one); but since you don't have exact values, and for the considerations specified, you will hardly find reasonably accurate values.

Edit

You can find a first approximation of Kn if you fix Vth at an arbitrary value (possibly obtained from a measurement of your device). Then, if you take the value of \$R_{DSon} \$ in the datasheet (it gives only the maximum, 5 Ohm) and knowing that the values are for Vgs = 10 V and Ids = 500 mA, you can put it in the formula of IDS(lin) and obtain Kn. Note that Vds will be given by \$I_{DS} \$=0.5 A * \$R_{DSon} \$ = 5 Ohm.

An approximated threshold voltage can be argued from the figures at page 4, respectively figure 3 and 6 counting from left to right; it appears to be about 1.5 V in that curve. From figure 3 you can also have an idea of Kn, considering that in that case the MOS is saturated and taking one or two points and substituting Vgs and Ids in the formula.