ece240: add mosfets

docs/2a/ece240.md

@@ -88,3 +88,48 @@ $$r_d=\left(\frac{\partial i_D}{\partial v_D}\right)^{-1} = \frac{V_T}{I_D}$$
 
 !!! warning
     Oftentimes, turning off a DC source to nowhere is actually a short to ground.
+
+## MOSFETs
+
+A MOSFET is a transistor. Current flows from the drain to the source, and only if voltage is applied to the gate.
+
+<img src="https://upload.wikimedia.org/wikipedia/commons/6/69/Mosfet_saturation.svg" width=500>(Source: Wikimedia Commons)</img>
+
+<img src="https://upload.wikimedia.org/wikipedia/commons/9/91/Transistor_Simple_Circuit_Diagram_with_NPN_Labels.svg" width=300>(Source: Wikimedia Commons)</img>
+
+In strictly DC, current passes the gate if the gate voltage is greater than the threshold voltage $V_G>V_t$. The difference between the two is known as the **overdrive voltage** $V_{ov}$:
+
+$$V_{ov}=V_G-V_t$$
+
+At a small $V_{DS}$, or in AC, the slope of $I_D$ to $V_{DS}$ is proportional to $V_G$. The **channel transconductance** $g_{DS}$ represents this slope, which is constant based on the **transconductance parameter** of the device.
+
+$$\frac{I_D}{V_{DS}}=g_{DS}=k_nV_{ov}$$
+
+Before the saturation region, the current grows exponentially:
+
+$$\boxed{I_s=k_n(V_{ov}-\tfrac 1 2V_{DS})V_{DS}}$$
+
+Afterward, it remains constant, based on the overdrive voltage:
+
+$$\boxed{I_s=\frac 1 2k_nV_{ov}^2}$$
+
+### Common-source amplifiers
+
+<img src="https://upload.wikimedia.org/wikipedia/commons/4/4f/N-channel_JFET_common_source.svg" width=200>(Source: Wikimedia Commons)</img>
+
+Where $V_{out}=$V_{DS}$:
+
+<img src="https://media.cheggcdn.com/media/b65/b65d59bd-ac35-4d28-b811-0ad1b5cf5bb6/phpCBbhn6" width=700 />
+
+$|V_{ds}|>|V_{gs}|$ indicates AC voltage gain.
+
+The gain can be modelled with Ohm's law:
+
+$$V_{DS}=V_{DD}-I_DR_D=V_{DD}-\frac 1 2k_n(V_{GS}-V_t)R_D$$
+
+At a certain gate voltage:
+
+\begin{align*}
+A_V&=\frac{\partial V_{DS}}{\partial V_{GS}} \\
+&=-g_{DS}R_D
+\end{align*}