# 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

(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!

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 Vth is 2.5V: as you can see from the curve for Vgs = 2V, Id would be near 0 with Vgs 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.

• Thanks a lot for the answer! I would like to upvote it, but I don't have any reputation... So if they gave me a more accurate iD vs VDS graph with Vgs it might be possible? Did I follow the correct steps in obtaining the values?
– ISJ
Mar 20, 2012 at 17:11
• @ISJ honestly I didn't understand the passages you made (if you could try using the LaTeX engine...), but it's unlikely (even though possible) that you obtained 2.5V threshold. Mar 20, 2012 at 17:25
• On the datasheet they say Vgs(th) can be between 0.8 and 2.5 V... Isn't Vgs(th) the threshold voltage?
– ISJ
Mar 20, 2012 at 18:05
• Yes, but if you derived that value from the graph, probably it's wrong because the threshold seems to be lower, and the curve Ids-Vds for Vgs=2V saturates at about 50mA Mar 20, 2012 at 18:11