diff --git a/docs/2a/ece240.md b/docs/2a/ece240.md index 9b8c325..0787c76 100644 --- a/docs/2a/ece240.md +++ b/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. + +(Source: Wikimedia Commons) + +(Source: Wikimedia Commons) + +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 + +(Source: Wikimedia Commons) + +Where $V_{out}=$V_{DS}$: + + + +$|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*}