# Definition![[Pasted image 20260803202943.png|right|300]] $V_{G}$ controls drain current $I_{D},$ flowing through $R_{D}$ producing $V_{D}$ $ V_{D}=V_{DD}-I_{D}R_{D} $ $ V_{G}\uparrow\implies I_{D}\uparrow\implies V_{D}\downarrow $ So common-source amplifier inverts the inputs: when input rises, output falls # Three Operating Regions - **Cutoff**: transistor off, no drain current flows $ V_{G}<V_{T}\ $ $ I_{D}=0,V_{D}=V_{DD} $ - **Saturation**: amplifier region -> $V_{G}$ strongly controls $I_{D}$ $ V_{G}>V_{T},\\~V_{D}>V_{G}-V_{T} $ $ I_{D}=\frac{k}{2}(V_{G}-V_{T})^2 $ - **Triode**: transistor acts like a low resistance -> drain is pulled closer to ground $\therefore$ increasing $V_{G}$ has left effect on $V_{D}$ $ V_{D}<V_{G}-V_{T} $ $ \text{Boundary: }V_{D}=V_{G}-V_{T} $ # Bias point $Q$ Gate signal contains a DC bias plus a changing AC signal $ v_{G}(t)=V_{G}+v_g(t) $ DC value $V_{G}$ establishes the $Q$-point. Ideally somewhere in the middle of saturation region so input can move in both directions w/o leaving saturation # Distortion - **Cutoff clipping**: input falls enough s.t $V_{G}<V_{T}.$ Transistor turns off so upper part of output becomes flat $ V_{D}=V_{DD} $ - **Triode flattening**: input rises too much and pushes transistor into triode. Transfer curve becomes flatter so output receives less amplification - **Quadratic distortion:** $I_{D}$ curved rather than perfectly linear. Large input changes shape slightly w/o entering cutoff or triode. Small input signals reduce the distortion $ I_{D}=\frac{k}{2}(V_{G}-V_{T})^2 $ $ \hat{v}_{g}\ll{2}(V_{T}-V_{T}) $ # Voltage Gain $ A_{V}=-R_{D}k(V_{G}-V_{T}) $ - $|A_{v}|>1$: signal amplified - Minus sign means output is inverted - Larger $R_{D},k,V_{G}-V_{T}$ gives greater gain magnitude