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what happens to the transconductance of a MOSFET in the saturation region if the gate-source voltage is less than the threshold voltage? Will the transconductance be negative since the equation is given by

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    \$\begingroup\$ if the gate-source voltage is less than the threshold voltage? Then the MOSFET is in weak inversion mode. Grab a textbook about MOSFETs and look up which formulas describe how the MOSFET works in that region of operation. \$\endgroup\$ Dec 7, 2020 at 13:52

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this equation is valid only in saturation mode which means:

  1. Vgs > Vth
  2. Vds > (Vgs-Vth) and it is the derivative of the saturation current equation. when Vgs < Vth you're no more in saturation mode. you can check on the web for (gm vs. Vgs) graph, where you can see that at Vgs<Vth the gm=0.
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