This is the LTSpice model of the Fairchild 2N7002 NMOS transistor.
.model 2N7002 VDMOS(Rg=3 Vto=1.6 Rd=0 Rs=.75 Rb=.14 Kp=.17 mtriode=1.25 Cgdmax=80pCgdmin=12p Cgs=50p Cjo=50p Is=.04p ksubthres=.1 mfg=Fairchild Vds=60 Ron=2 Qg=1.5n)
The equation of a saturated N-MOSFET is
Reading the SPICE .model, I had thought that for this Fairchild 2N7002, the parameters were Vth = 1.6 V and k' = 170 mA/V².
Then, using LTSpice, I've obtained the ID vs. VDS characteristic of the Fairchild 2N7002:
Acording to the equation, for VGS = 3V, I should get a current of ID = 170 / 2 x (3 - 1.6)² = 166 mA, but in the plot I get 140 mA.
Acording to the equation, for VGS = 4V, I should get a current of ID = 170 / 2 x (4 - 1.6)² = 489 mA, but in the plot I get 378 mA
Moreover, if you treat Vth and k' as unknowns, you can compute them from the plot. For example, using the curves VGS = 4 V and VGS = 3 V, solving the system of equations 140 mA = k' / 2 × (3-Vth)² and 378 mA = k' / 2 × (4-Vth)². Then you get, k' = 0.1158 A/V² and Vth = 1.4452 V.
But if you use other curves, you get differente results. For example, using the curves VGS = 6 V and VGS = 5 V, solving the system of equations 700.36 mA = k' / 2 × (5-Vth)² and 1.088 A = k' / 2 × (6-Vth)². Then you get, k' = 0.08511 A/V² and Vth = 0.9431 V.
So, according to the plot, Vth and k' are not constants but variables.
So, why I get this difference? Which parameters are the true ones: those from the .model or those from the plot? Should I get this parameters from the datasheet instead?