a) b) c) d) e) small signal parameters mo Draw the small signal circuit for the amplifier Input resistance Rin Output Resistance R out V Voltage gain Ay == V

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**Transcription for Educational Content**

**Amplifier Analysis Problems**

For each of the following problems, determine:

a) Small signal parameters \( g_m, r_o \)

b) Draw the small signal circuit for the amplifier

c) Input resistance \( R_{\text{in}} \)

d) Output resistance \( R_{\text{out}} \)

e) Voltage gain \( A_v = \frac{v_o}{v_i} \)

f) Overall voltage gain \( G_v = \frac{v_o}{v_s} \)

---

**Problem 1**

The nMOSFET has:

\[ V_t = 1V, \quad \frac{1}{2}k'\frac{W}{L} = 0.25, \quad V_A = 100V \]

Find \( R_1 \).

---

**Diagram Explanation:**

The provided circuit diagram includes:

- A voltage source \( V_s \) connected through a resistor \( R_s \) (5kΩ) to the gate of an nMOSFET.
- The MOSFET's gate is also connected to a 30kΩ resistor leading to the ground.
- The drain is connected to a resistor \( R_1 \) and a 2kΩ resistor leading to a 5V supply.
- The output voltage \( V_o \) is taken over a 5kΩ resistor, which is connected in series with the 2kΩ resistor.
- The source of the MOSFET is connected to a 1mA current source tied to the ground.
Transcribed Image Text:**Transcription for Educational Content** **Amplifier Analysis Problems** For each of the following problems, determine: a) Small signal parameters \( g_m, r_o \) b) Draw the small signal circuit for the amplifier c) Input resistance \( R_{\text{in}} \) d) Output resistance \( R_{\text{out}} \) e) Voltage gain \( A_v = \frac{v_o}{v_i} \) f) Overall voltage gain \( G_v = \frac{v_o}{v_s} \) --- **Problem 1** The nMOSFET has: \[ V_t = 1V, \quad \frac{1}{2}k'\frac{W}{L} = 0.25, \quad V_A = 100V \] Find \( R_1 \). --- **Diagram Explanation:** The provided circuit diagram includes: - A voltage source \( V_s \) connected through a resistor \( R_s \) (5kΩ) to the gate of an nMOSFET. - The MOSFET's gate is also connected to a 30kΩ resistor leading to the ground. - The drain is connected to a resistor \( R_1 \) and a 2kΩ resistor leading to a 5V supply. - The output voltage \( V_o \) is taken over a 5kΩ resistor, which is connected in series with the 2kΩ resistor. - The source of the MOSFET is connected to a 1mA current source tied to the ground.
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