Question:

Please convert the below content to rendered equations without any errors.Perfect ? Here is the **complete, corrected, and final solution** for **all cases (a)–(h)**, with **(e) correctly treated as a PMOS**. I’ll keep it step-by-step but clean and exam-ready. --- # Given * **NMOS threshold voltage:** [ V_{THN} = +0.4\ \text{V} ] * **PMOS threshold voltage:** [ V_{THP} = -0.4\ \text{V} \Rightarrow |V_{THP}| = 0.4\ \text{V} ] --- # MOSFET Region Conditions (Use These) ### **NMOS** * **ON:** [ V_{GS} \ge V_{THN} ] * **Linear:** [ V_{DS} < V_{GS} - V_{THN} ] * **Saturation:** [ V_{DS} \ge V_{GS} - V_{THN} ] ### **PMOS** * **ON:** [ V_{SG} \ge |V_{THP}| ] * **Linear:** [ V_{SD} < V_{SG} - |V_{THP}| ] * **Saturation:** [ V_{SD} \ge V_{SG} - |V_{THP}| ] --- ## (a) * **NMOS** * Gate = 0 V, Source = 0 V [ V_{GS} = 0 ] [ V_{GS} < 0.4 ] ✅ **Cutoff** --- ## (b) * **NMOS** * Gate = 0 V, Source = 1 V [ V_{GS} = 0 - 1 = -1\ \text{V} ] [ V_{GS} < 0.4 ] ✅ **Cutoff** --- ## (c) * **NMOS** * Gate = 1 V, Source = 0.2 V [ V_{GS} = 1 - 0.2 = 0.8\ \text{V} > 0.4 \Rightarrow \text{ON} ] Drain = 0.2 V [ V_{DS} = 0 ] [ V_{GS} - V_{TH} = 0.4 ] [ V_{DS} < V_{GS} - V_{TH} ] ✅ **Linear (Triode)** --- ## (d) * **NMOS** * Gate = 1 V, Source = 0.2 V [ V_{GS} = 0.8\ \text{V} ] Drain = 0.7 V [ V_{DS} = 0.7 - 0.2 = 0.5\ \text{V} ] [ V_{GS} - V_{TH} = 0.4 ] [ V_{DS} > V_{GS} - V_{TH} ] ✅ **Saturation** --- ## (e) ✅ **Corrected** * **PMOS** * Source = 2 V * Gate = 2 V * Drain = 0 V [ V_{SG} = 2 - 2 = 0\ \text{V} ] [ V_{SG} < |V_{THP}| = 0.4 ] ✅ **Cutoff** --- ## (f) * **NMOS** * Gate = 0 V, Source = 0.3 V [ V_{GS} = -0.3\ \text{V} ] [ V_{GS} < 0.4 ] ✅ **Cutoff** --- ## (g) * **PMOS** * Source = 0.9 V, Gate = 0 V [ V_{SG} = 0.9\ \text{V} > 0.4 \Rightarrow \text{ON} ] Drain = 0.4 V [ V_{SD} = 0.9 - 0.4 = 0.5 ] [ V_{SG} - |V_{THP}| = 0.5 ] [ V_{SD} = V_{SG} - |V_{THP}| ] ✅ **Saturation (edge condition)** --- ## (h) * **PMOS** * Source = 1 V, Gate = 0.4 V [ V_{SG} = 1 - 0.4 = 0.6 ] Drain = 0.9 V [ V_{SD} = 1 - 0.9 = 0.1 ] [ V_{SG} - |V_{THP}| = 0.2 ] [ V_{SD} < V_{SG} - |V_{THP}| ] ✅ **Linear (Triode)** --- # ✅ Final Answer Summary | Circuit | MOS Type | Region of Operation | | ------- | -------- | ------------------- | | (a) | NMOS | Cutoff | | (b) | NMOS | Cutoff | | (c) | NMOS | Linear | | (d) | NMOS | Saturation | | (e) | PMOS | **Cutoff** | | (f) | NMOS | Cutoff | | (g) | PMOS | Saturation | | (h) | PMOS | Linear | --- If you want, I can also: * Convert this into a **1-page exam solution** * Provide **quick decision shortcuts** * Or draw a **source–drain identification guide** Just let me know ?