# Step-by-Step Solution: Small Signal Voltage Gain of MOSFET Amplifiers Let's analyze the voltage gain **polarity** (inverting or non-inverting) for both **common source (CS)** and **common gate (CG)** MOSFET amplifiers. --- ## 1. Common Source (CS) Amplifier - **Configuration:** Input at gate, output at drain, source grounded. - **Operation:** An increase in input voltage ($V_{in}$) at the gate increases $V_{gs}$, turning the MOSFET on harder. This increases drain current, causing a larger voltage drop across the drain resistor, so the drain voltage ($V_{out}$) decreases. - **Voltage Gain:** Negative (inverting amplifier) \[ A_v = -g_m R_D \] --- ## 2. Common Gate (CG) Amplifier - **Configuration:** Input at source, gate grounded, output at drain. - **Operation:** An increase in input voltage at the source reduces $V_{gs}$ (since gate is at AC ground), decreases drain current, so voltage at drain increases. - **Voltage Gain:** Positive (non-inverting amplifier) \[ A_v = g_m R_D \] --- ## 3. Evaluate Options ### Option A: **"Common source and common gate amplifiers are both inverting amplifiers"** - **Incorrect:** Only common source is inverting; common gate is non-inverting. ### Option B: **"Common source and common gate amplifiers are both non-inverting amplifiers"** - **Incorrect:** Only common gate is non-inverting; common source is inverting. ### Option C: **"Common source amplifier is inverting and common gate amplifier is non-inverting amplifier"** - **Correct:** Matches our analysis above. ### Option D: **"Common source amplifier is non-inverting and common gate amplifier is inverting amplifier"** - **Incorrect:** This is the opposite of the correct behavior. --- ## 4. **Final Answer** **Option C is correct:** > **Common source amplifier is inverting and common gate amplifier is non-inverting amplifier.** --- ## 5. **Summary Table** | Amplifier Type | Voltage Gain Sign | Inverting? | |----------------|------------------|----------------| | Common Source | Negative | Yes (Inverting)| | Common Gate | Positive | No (Non-inverting)| --- **Why others are incorrect:** - CS is always inverting, so any option labeling CS as non-inverting is wrong. - CG is always non-inverting, so any option labeling CG as inverting is wrong.