To solve this problem, let's break down the information and apply the relevant formulas.

Given:

• $V_{DD} = 2 \, \text{V}$
• Maximum small-signal voltage gain: $|A_v|_{\text{max}} = 14 \, \text{V/V}$
• Required small-signal voltage gain: $A_v = -12 \, \text{V/V}$

To find:

• $V_{OV}$ (overdrive voltage)
• $V_{DS}$ (drain-source voltage)

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Solution

The small-signal voltage gain $A_v$ for a common-source MOS amplifier with a drain resistor $R_D$ is given by: $A_v = -g_m R_D$ where $g_m$ is the transconductance.

Since the maximum voltage gain is given as $|A_v|_{\text{max}} = 14 \, \text{V/V}$, we can write: $g_m R_D = 14$

Now, we need to determine the value of $g_m$ when $A_v = -12 \, \text{V/V}$: $g_m R_D = 12$

From the above equations, we have two conditions:

1. $g_{m, \text{max}} R_D = 14$
2. $g_{m, Q} R_D = 12$

Thus, the ratio of transconductances at the operating points is: $\frac{g_{m, Q}}{g_{m, \text{max}}} = \frac{12}{14} = \frac{6}{7}$

Step 2: Express $g_m$ in Terms of $V_{OV}$

The transconductance $g_m$ of a MOSFET in saturation is given by: $g_m = \frac{2I_D}{V_{OV}}$

Since $g_m \propto \frac{1}{V_{OV}}$, we have: $\frac{V_{OV, \text{max}}}{V_{OV, Q}} = \frac{g_{m, \text{max}}}{g_{m, Q}} = \frac{7}{6}$

So, $V_{OV, Q} = \frac{6}{7} V_{OV, \text{max}}$

To find $V_{OV, Q}$ and $V_{DS}$ specifically, additional details such as the value of $V_{OV, \text{max}}$ or specific information about the drain current $I_D$ would be required. If you have further details, please provide them, and I’ll continue the calculations.

Would you like to go deeper into any step?

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1. What is the significance of the overdrive voltage $V_{OV}$ in MOSFET operation?
2. How does the transconductance $g_m$ influence the gain of the MOS amplifier?
3. Why does $V_{OV}$ need to be adjusted for different gains?
4. How can $V_{DS}$ affect the MOSFET’s operation point?
5. What happens to gain if $V_{OV}$ is minimized?

Tip: Keep in mind that MOSFET small-signal parameters are tied to its operating region. Ensuring the MOSFET remains in saturation is key to maintaining a stable gain