# MOSFET amplifier

I found the following problem in the Rashid book of microelectronic circuits. I am looking to solve it but I don't even know where to start. How can I solve everything? What results do you get so I can compare?

The MOSFET amplifier of Fig. P5.33 has:

• $R_S=500\Omega$
• $R_D=R_L=5k\Omega$
• $R_{G_1}=7M\Omega$
• $R_{G_2}=5M\Omega$
• $K_p=20\frac{mA}{V^2}$
• $V_t=3.5V$
• $\left\lvert{}V_M\right\rvert=200V$
• $V_{DD}=12V$

Calculate:

1. The input resistance $R_{in}=\dfrac{v_s}{i_s}$.
2. The no-load voltage gain $A_{v_O}=\dfrac{v_O}{v_g}$.
3. The output resistance $R_O$.
4. The overall voltage gain $A_v=\dfrac{v_L}{v_s}$.

## 2 Answers

1 .first find out DC biasing values using voltage division to find $r_o= \frac{|V_A|} {I_D}$ and $g_m=\frac{2I_D}{V_{ov}}$

2 . Draw this small signal equivalent circuit for MOSFET.

simulate this circuit – Schematic created using CircuitLab

3.Find the values of

• $A_{vo} =-g_m(r_o || R_D)$
• $R_{in} = R_G$ where $R_G = R_{G1} || R_{G2}$
• output resistance $R_o=r_o || R_D$
• overall voltage gain $A_v=\frac{R_{i}}{R_{in}+R_{sig}}.A_{vo}$

For any transistor amplifier, you can follow the steps below to analyze.

1. Draw the ac equivalent of the circuit by replacing capacitors with a short circuit and nullifying independent DC sources.

2. Replace the transistor with its equivalent model.

3. Use KCL and KVL to calculate what you want.