I don't understand how the resistor between GND and the source in a common-source amplifier stabilizes it
How does Rs stabilize the amplifier?


\$V_{GS} = V_G - V_S \$

\$V_S = I_D R_S \$

\$\Rightarrow V_{GS} = V_G - I_D R_S \$

Now, \$V_G\$ is constant so, if \$I_D\$ increases, \$V_{GS}\$ decreases.

But, if \$V_{GS}\$ decreases, \$I_D\$ decreases.\$^1\$

Thus, an increase in \$I_D\$ acts to decrease \$I_D\$.  This is the hallmark of negative feedback.

\$^1 I_D \approx K(V_{GS}-V_{TH})^2 \$