Electronic – how to determine the small signal parameters of nMOSFET from Datasheet

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as I want to calculate the transfer function of circuit that is meant to generate source current using an Op amp as control loop, I need the gm and r0 of the mosfet(to determine the transfer function of the Op amp current source with nMOSFET)
here is the picture of MOSFET with showed parameters
enter image description here
and here are the link for the datasheet

https://docs.rs-online.com/c5c9/0900766b80dcb3d2.pdf

Best Answer

Be aware that small-signal parameters assume linear operation, which usually means that the intended operating parameters vary over a small range. It is apparent that the intended application of this device is as a switch, operating over a very large range. Deriving small-signal parameters from this data sheet will likely result in gross approximations that vary with temperature, and vary from device-to-device.

Data sheet actually supplies \$g_m\$ of 370 Siemens, but that data point is far beyond any useful bias point (the device would very quickly go up in smoke).
data sheet gm
Data sheet also supplies ID/VDS curves from which small-signal parameters might be derived. Again, these plots are scaled to concentrate on large currents, scrunching the more useful region of lower ID current, where you most likely will be biased. Operating at high currents (many amps) and single-digit volts of \$V_{ds}\$ will overheat this device:
MOSfet device ID/VGS curve
Let's check that rogue forward transconductance of 370 S with a more reasonable bias point of 1V, 1A where the device only dissipates 1W:

I eyeball-estimate \$V_{gs}\$ of 2.4V at this bias point.
Use another point from this curve to calculate \$g_m\$: \$V_{gs}=2.5V, I_D=2A\$ @ Vds=1V
The difference in \$V_{gs}\$ of 0.1V yields a 1A change in \$I_D\$. Thus the transconductance \$g_m = 10 S\$. This is far different from 370 at that distant bias point of 10V & 220A.

The parameter \$r_o\$ would be derived from the slope of the bottom-most curve (Vgs=2.5V). Since it is not linear, you'd only get a very rough estimate of its value.

Be aware that most of the provided data covers a bias region where the device would dissipate-to-death from overheat. Do a dissipation calculation to ensure that at all bias points, this device won't overheat.

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