The transconductance of an NMOS is
$$ g_m = \frac{\partial i_d}{\partial V_{gs}} $$
Is the transconductance of a PMOS the same?
Electronic – What’s the transconductance of a PMOS
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Best Answer
No, replace Vgs with Vsg. The models for a PMOS and NMOS transistor are the same, except for PMOS you use Vsg instead of Vgs, Vsd instead of Vds, and the absolute value of \$\lambda\$ and \$V_a\$.
For instance, in a velocity-limited model (\$I_d=V_{sat} C_{ox} W_g (V_{sg}-|V_t|) (1+|\lambda| V_{sd})\$), the transconductance would be \$V_{sat}C_{ox}W_g(1+|\lambda| V_{sg})\$. In a mobility limited model it would be \$ \mu C_{ox} \frac{W_g}{L_g} (V_{sg}-|V_t|) (1+|\lambda| V_{sd})\$.
These results makes sense, because in a PMOS transistor the current is proportional to Vsg (or negative Vgs). As you can see, in both these expressions, the transconductance is positively proportional to Vsg, and thus the current changes with Vsg.